Merge pull request #18356 from ivashmak:update_ransac

* update new RANSAC

* fix warning

* change gamma values table

* resolve conflict

* resolve conflict

* GammaValues as singleton

diff --git a/modules/calib3d/include/opencv2/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d.hpp
index d14a810..f0b8beb 100644 (file)
--- a/modules/calib3d/include/opencv2/calib3d.hpp
+++ b/modules/calib3d/include/opencv2/calib3d.hpp
@@ -450,7 +450,7 @@ enum { LMEDS  = 4,  //!< least-median of squares algorithm
        USAC_FAST = 35,     //!< USAC, fast settings
        USAC_ACCURATE = 36, //!< USAC, accurate settings
        USAC_PROSAC = 37,   //!< USAC, sorted points, runs PROSAC
-       USAC_MAGSAC = 38    //!< USAC, sorted points, runs PROSAC
+       USAC_MAGSAC = 38    //!< USAC, runs MAGSAC++
      };
 
 enum SolvePnPMethod {

diff --git a/modules/calib3d/src/usac.hpp b/modules/calib3d/src/usac.hpp
index f658e87..c18de92 100644 (file)
--- a/modules/calib3d/src/usac.hpp
+++ b/modules/calib3d/src/usac.hpp
@@ -193,6 +193,26 @@ public:
     }
 };
 
+class GammaValues
+{
+    const double max_range_complete /*= 4.62*/, max_range_gamma /*= 1.52*/;
+    const int max_size_table /* = 3000 */;
+
+    std::vector<double> gamma_complete, gamma_incomplete, gamma;
+
+    GammaValues();  // use getSingleton()
+
+public:
+    static const GammaValues& getSingleton();
+
+    const std::vector<double>& getCompleteGammaValues() const;
+    const std::vector<double>& getIncompleteGammaValues() const;
+    const std::vector<double>& getGammaValues() const;
+    double getScaleOfGammaCompleteValues () const;
+    double getScaleOfGammaValues () const;
+    int getTableSize () const;
+};
+
 ////////////////////////////////////////// QUALITY ///////////////////////////////////////////
 class Quality : public Algorithm {
 public:
@@ -269,10 +289,6 @@ public:
     virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/) const {
         return true;
     }
-    virtual bool isModelValid (const Mat &/*model*/, const std::vector<int> &/*sample*/,
-            int /*sample_size*/) const {
-        return true;
-    }
     /*
      * Fix degenerate model.
      * Return true if model is degenerate, false - otherwise
@@ -286,7 +302,7 @@ public:
 
 class EpipolarGeometryDegeneracy : public Degeneracy {
 public:
-    static void recoverRank (Mat &model);
+    static void recoverRank (Mat &model, bool is_fundamental_mat);
     static Ptr<EpipolarGeometryDegeneracy> create (const Mat &points_, int sample_size_);
 };
 
@@ -405,9 +421,7 @@ struct SPRT_history {
     double epsilon, delta, A;
     // number of samples processed by test
     int tested_samples; // k
-    SPRT_history ()
-        : epsilon(0), delta(0), A(0)
-    {
+    SPRT_history () {
         tested_samples = 0;
     }
 };
@@ -465,7 +479,7 @@ class GridNeighborhoodGraph : public NeighborhoodGraph {
 public:
     static Ptr<GridNeighborhoodGraph> create(const Mat &points, int points_size,
             int cell_size_x_img1_, int cell_size_y_img1_,
-            int cell_size_x_img2_, int cell_size_y_img2_);
+            int cell_size_x_img2_, int cell_size_y_img2_, int max_neighbors);
 };
 
 ////////////////////////////////////// UNIFORM SAMPLER ////////////////////////////////////////////
@@ -568,7 +582,7 @@ namespace Math {
     // return skew symmetric matrix
     Matx33d getSkewSymmetric(const Vec3d &v_);
     // eliminate matrix with m rows and n columns to be upper triangular.
-    void eliminateUpperTriangular (std::vector<double> &a, int m, int n);
+    bool eliminateUpperTriangular (std::vector<double> &a, int m, int n);
     Matx33d rotVec2RotMat (const Vec3d &v);
     Vec3d rotMat2RotVec (const Matx33d &R);
 }
@@ -746,6 +760,7 @@ public:
     virtual int getLOInnerMaxIters() const = 0;
     virtual const std::vector<int> &getGridCellNumber () const = 0;
     virtual int getRandomGeneratorState () const = 0;
+    virtual int getMaxItersBeforeLO () const = 0;
 
     // setters
     virtual void setLocalOptimization (LocalOptimMethod lo_) = 0;
@@ -759,6 +774,7 @@ public:
     virtual void setLOIterations (int iters) = 0;
     virtual void setLOIterativeIters (int iters) = 0;
     virtual void setLOSampleSize (int lo_sample_size) = 0;
+    virtual void setThresholdMultiplierLO (double thr_mult) = 0;
     virtual void setRandomGeneratorState (int state) = 0;
 
     virtual void maskRequired (bool required) = 0;

diff --git a/modules/calib3d/src/usac/degeneracy.cpp b/modules/calib3d/src/usac/degeneracy.cpp
index 75711e8..7963ef3 100644 (file)
--- a/modules/calib3d/src/usac/degeneracy.cpp
+++ b/modules/calib3d/src/usac/degeneracy.cpp
@@ -18,17 +18,11 @@ public:
      * Do oriented constraint to verify if epipolar geometry is in front or behind the camera.
      * Return: true if all points are in front of the camers w.r.t. tested epipolar geometry - satisfies constraint.
      *         false - otherwise.
-     */
-    inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
-        return isModelValid(F, sample, min_sample_size);
-    }
-
-    /* Oriented constraint:
      * x'^T F x = 0
      * e' × x' ~+ Fx   <=>  λe' × x' = Fx, λ > 0
      * e  × x ~+ x'^T F
      */
-    inline bool isModelValid(const Mat &F_, const std::vector<int> &sample, int sample_size_) const override {
+    inline bool isModelValid(const Mat &F_, const std::vector<int> &sample) const override {
         // F is of rank 2, taking cross product of two rows we obtain null vector of F
         Vec3d ec_mat = F_.row(0).cross(F_.row(2));
         auto * ec = ec_mat.val; // of size 3x1
@@ -40,7 +34,6 @@ public:
             ec_mat = F_.row(1).cross(F_.row(2));
             ec = ec_mat.val;
         }
-        // F is 9x1 row-major ordered F matrix. ec is 3x1
         const auto * const F = (double *) F_.data;
 
         // without loss of generality, let the first point in sample be in front of the camera.
@@ -50,17 +43,12 @@ public:
         // sign1 = s1 * s2
         const double sign1 = (F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1]);
 
-        int num_pts_behind = 0;
-        for (int i = 1; i < sample_size_; i++) {
+        for (int i = 1; i < min_sample_size; i++) {
             pt = 4 * sample[i];
             // if signum of the first point and tested point differs
             // then two points are on different sides of the camera.
             if (sign1*(F[0]*points[pt+2]+F[3]*points[pt+3]+F[6])*(ec[1]-ec[2]*points[pt+1])<0)
-                // if 3 points are behind the camera for non-minimal sample then model is
-                // not valid. Testing by one point as in case for minimal sample is not very
-                // precise. The number 3 was chosen experimentally.
-                if (min_sample_size == sample_size_ || ++num_pts_behind >= 3)
-                    return false;
+                return false;
         }
         return true;
     }
@@ -69,15 +57,20 @@ public:
         return makePtr<EpipolarGeometryDegeneracyImpl>(*points_mat, min_sample_size);
     }
 };
-void EpipolarGeometryDegeneracy::recoverRank (Mat &model) {
+void EpipolarGeometryDegeneracy::recoverRank (Mat &model, bool is_fundamental_mat) {
     /*
      * Do singular value decomposition.
      * Make last eigen value zero of diagonal matrix of singular values.
      */
     Matx33d U, Vt;
     Vec3d w;
-    SVD::compute(model, w, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
-    model = Mat(U * Matx33d(w(0), 0, 0, 0, w(1), 0, 0, 0, 0) * Vt);
+    SVD::compute(model, w, U, Vt, SVD::MODIFY_A);
+    if (is_fundamental_mat)
+        model = Mat(U * Matx33d(w(0), 0, 0, 0, w(1), 0, 0, 0, 0) * Vt);
+    else {
+        const double mean_singular_val = (w[0] + w[1]) * 0.5;
+        model = Mat(U * Matx33d(mean_singular_val, 0, 0, 0, mean_singular_val, 0, 0, 0, 0) * Vt);
+    }
 }
 Ptr<EpipolarGeometryDegeneracy> EpipolarGeometryDegeneracy::create (const Mat &points_,
         int sample_size_) {
@@ -157,11 +150,15 @@ private:
     const float * const points;
     const Mat * points_mat;
     const Ptr<ReprojectionErrorForward> h_reproj_error;
+    Ptr<HomographyNonMinimalSolver> h_non_min_solver;
     const EpipolarGeometryDegeneracyImpl ep_deg;
     // threshold to find inliers for homography model
     const double homography_threshold, log_conf = log(0.05);
     // points (1-7) to verify in sample
     std::vector<std::vector<int>> h_sample {{0,1,2},{3,4,5},{0,1,6},{3,4,6},{2,5,6}};
+    std::vector<int> h_inliers;
+    std::vector<double> weights;
+    std::vector<Mat> h_models;
     const int points_size, sample_size;
 public:
 
@@ -179,14 +176,12 @@ public:
             h_sample.emplace_back(std::vector<int>{3, 6, 7});
             h_sample.emplace_back(std::vector<int>{2, 4, 7});
         }
+        h_inliers = std::vector<int>(points_size);
+        h_non_min_solver = HomographyNonMinimalSolver::create(points_);
     }
     inline bool isModelValid(const Mat &F, const std::vector<int> &sample) const override {
         return ep_deg.isModelValid(F, sample);
     }
-    inline bool isModelValid(const Mat &F, const std::vector<int> &sample, int sample_size_) const override {
-        return ep_deg.isModelValid(F, sample, sample_size_);
-    }
-
     bool recoverIfDegenerate (const std::vector<int> &sample, const Mat &F_best,
                  Mat &non_degenerate_model, Score &non_degenerate_model_score) override {
         non_degenerate_model_score = Score(); // set worst case
@@ -239,23 +234,32 @@ public:
             }
 
             // compute H
-            const Matx33d H = A - e_prime * (M.inv() * b).t();
+            Matx33d H = A - e_prime * (M.inv() * b).t();
 
-            int inliers_on_plane = 0;
+            int inliers_out_plane = 0;
             h_reproj_error->setModelParameters(Mat(H));
 
             // find inliers from sample, points related to H, x' ~ Hx
             for (int s = 0; s < sample_size; s++)
-                if (h_reproj_error->getError(sample[s]) < homography_threshold)
-                    if (++inliers_on_plane >= 5)
+                if (h_reproj_error->getError(sample[s]) > homography_threshold)
+                    if (++inliers_out_plane > 2)
                         break;
 
             // if there are at least 5 points lying on plane then F is degenerate
-            if (inliers_on_plane >= 5) {
+            if (inliers_out_plane <= 2) {
                 is_model_degenerate = true;
 
+                // update homography by polishing on all inliers
+                int h_inls_cnt = 0;
+                const auto &h_errors = h_reproj_error->getErrors(Mat(H));
+                for (int pt = 0; pt < points_size; pt++)
+                    if (h_errors[pt] < homography_threshold)
+                        h_inliers[h_inls_cnt++] = pt;
+                if (h_non_min_solver->estimate(h_inliers, h_inls_cnt, h_models, weights) != 0)
+                    H = Matx33d(h_models[0]);
+
                 Mat newF;
-                const Score newF_score = planeAndParallaxRANSAC(H, newF);
+                const Score newF_score = planeAndParallaxRANSAC(H, newF, h_errors);
                 if (newF_score.isBetter(non_degenerate_model_score)) {
                     // store non degenerate model
                     non_degenerate_model_score = newF_score;
@@ -271,7 +275,7 @@ public:
     }
 private:
     // RANSAC with plane-and-parallax to find new Fundamental matrix
-    Score planeAndParallaxRANSAC (const Matx33d &H, Mat &best_F) {
+    Score planeAndParallaxRANSAC (const Matx33d &H, Mat &best_F, const std::vector<float> &h_errors) {
         int max_iters = 100; // with 95% confidence assume at least 17% of inliers
         Score best_score;
         for (int iters = 0; iters < max_iters; iters++) {
@@ -282,18 +286,17 @@ private:
                 h_outlier2 = rng.uniform(0, points_size);
 
             // find outliers of homography H
-            if (h_reproj_error->getError(h_outlier1) > homography_threshold &&
-                h_reproj_error->getError(h_outlier2) > homography_threshold) {
+            if (h_errors[h_outlier1] > homography_threshold &&
+                h_errors[h_outlier2] > homography_threshold) {
 
                 // do plane and parallax with outliers of H
-                const Vec3d pt1 (points[4*h_outlier1], points[4*h_outlier1+1], 1);
-                const Vec3d pt2 (points[4*h_outlier2], points[4*h_outlier2+1], 1);
-                const Vec3d pt1_prime (points[4*h_outlier1+2],points[4*h_outlier1+3],1);
-                const Vec3d pt2_prime (points[4*h_outlier2+2],points[4*h_outlier2+3],1);
-
                 // F = [(p1' x Hp1) x (p2' x Hp2)]_x H
-                const Matx33d F = Math::getSkewSymmetric((pt1_prime.cross(H * pt1)).cross
-                                                         (pt2_prime.cross(H * pt2))) * H;
+                const Matx33d F = Math::getSkewSymmetric(
+                       (Vec3d(points[4*h_outlier1+2], points[4*h_outlier1+3], 1).cross   // p1'
+                   (H * Vec3d(points[4*h_outlier1  ], points[4*h_outlier1+1], 1))).cross // Hp1
+                       (Vec3d(points[4*h_outlier2+2], points[4*h_outlier2+3], 1).cross   // p2'
+                   (H * Vec3d(points[4*h_outlier2  ], points[4*h_outlier2+1], 1)))       // Hp2
+                 ) * H;
 
                 const Score score = quality->getScore(Mat(F));
                 if (score.isBetter(best_score)) {

diff --git a/modules/calib3d/src/usac/dls_solver.cpp b/modules/calib3d/src/usac/dls_solver.cpp
index 0bffc6c..0898734 100644 (file)
--- a/modules/calib3d/src/usac/dls_solver.cpp
+++ b/modules/calib3d/src/usac/dls_solver.cpp
@@ -214,7 +214,6 @@ public:
 
             if (all_points_in_front_of_camera) {
                 Mat model;
-//                hconcat(rot_mat, soln_translation, model);
                 hconcat(Math::rotVec2RotMat(Math::rotMat2RotVec(rot_mat)), soln_translation, model);
                 models_.emplace_back(K * model);
             }

diff --git a/modules/calib3d/src/usac/essential_solver.cpp b/modules/calib3d/src/usac/essential_solver.cpp
index a2e2467..0adca09 100644 (file)
--- a/modules/calib3d/src/usac/essential_solver.cpp
+++ b/modules/calib3d/src/usac/essential_solver.cpp
@@ -54,7 +54,8 @@ public:
         const int num_cols = 9, num_e_mat = 4;
         double ee[36]; // 9*4
         // eliminate linear equations
-        Math::eliminateUpperTriangular(coefficients, 5, num_cols);
+        if (!Math::eliminateUpperTriangular(coefficients, 5, num_cols))
+            return 0;
         for (int i = 0; i < num_e_mat; i++)
             for (int j = 5; j < num_cols; j++)
                 ee[num_cols * i + j] = (i + 5 == j) ? 1 : 0;
@@ -244,25 +245,91 @@ Ptr<EssentialMinimalSolverStewenius5pts> EssentialMinimalSolverStewenius5pts::cr
 class EssentialNonMinimalSolverImpl : public EssentialNonMinimalSolver {
 private:
     const Mat * points_mat;
-    const Ptr<FundamentalNonMinimalSolver> non_min_fundamental;
+    const float * const points;
 public:
     /*
      * Input calibrated points K^-1 x.
      * Linear 8 points algorithm is used for estimation.
      */
     explicit EssentialNonMinimalSolverImpl (const Mat &points_) :
-        points_mat(&points_), non_min_fundamental(FundamentalNonMinimalSolver::create(points_)) {}
+        points_mat(&points_), points ((float *) points_.data) {}
 
     int estimate (const std::vector<int> &sample, int sample_size, std::vector<Mat>
-        &models, const std::vector<double> &weights) const override {
-        return non_min_fundamental->estimate(sample, sample_size, models, weights);
-    }
-    int getMinimumRequiredSampleSize() const override {
-        return non_min_fundamental->getMinimumRequiredSampleSize();
-    }
-    int getMaxNumberOfSolutions () const override {
-        return non_min_fundamental->getMaxNumberOfSolutions();
+            &models, const std::vector<double> &weights) const override {
+        if (sample_size < getMinimumRequiredSampleSize())
+            return 0;
+
+        // ------- 8 points algorithm with Eigen and covariance matrix --------------
+        double a[9] = {0, 0, 0, 0, 0, 0, 0, 0, 1};
+        double AtA[81] = {0}; // 9x9
+
+        if (weights.empty()) {
+            for (int i = 0; i < sample_size; i++) {
+                const int pidx = 4*sample[i];
+                const double x1 = points[pidx  ], y1 = points[pidx+1],
+                             x2 = points[pidx+2], y2 = points[pidx+3];
+                a[0] = x2*x1;
+                a[1] = x2*y1;
+                a[2] = x2;
+                a[3] = y2*x1;
+                a[4] = y2*y1;
+                a[5] = y2;
+                a[6] = x1;
+                a[7] = y1;
+
+                // calculate covariance for eigen
+                for (int row = 0; row < 9; row++)
+                    for (int col = row; col < 9; col++)
+                        AtA[row*9+col] += a[row]*a[col];
+            }
+        } else {
+            for (int i = 0; i < sample_size; i++) {
+                const int smpl = 4*sample[i];
+                const double weight = weights[i];
+                const double x1 = points[smpl  ], y1 = points[smpl+1],
+                             x2 = points[smpl+2], y2 = points[smpl+3];
+                const double weight_times_x2 = weight * x2,
+                             weight_times_y2 = weight * y2;
+
+                a[0] = weight_times_x2 * x1;
+                a[1] = weight_times_x2 * y1;
+                a[2] = weight_times_x2;
+                a[3] = weight_times_y2 * x1;
+                a[4] = weight_times_y2 * y1;
+                a[5] = weight_times_y2;
+                a[6] = weight * x1;
+                a[7] = weight * y1;
+                a[8] = weight;
+
+                // calculate covariance for eigen
+                for (int row = 0; row < 9; row++)
+                    for (int col = row; col < 9; col++)
+                        AtA[row*9+col] += a[row]*a[col];
+            }
+        }
+
+        // copy symmetric part of covariance matrix
+        for (int j = 1; j < 9; j++)
+            for (int z = 0; z < j; z++)
+                AtA[j*9+z] = AtA[z*9+j];
+
+#ifdef HAVE_EIGEN
+        models = std::vector<Mat>{ Mat_<double>(3,3) };
+        const Eigen::JacobiSVD<Eigen::Matrix<double, 9, 9>> svd((Eigen::Matrix<double, 9, 9>(AtA)),
+                Eigen::ComputeFullV);
+        // extract the last nullspace
+        Eigen::Map<Eigen::Matrix<double, 9, 1>>((double *)models[0].data) = svd.matrixV().col(8);
+#else
+        Matx<double, 9, 9> AtA_(AtA), U, Vt;
+        Vec<double, 9> W;
+        SVD::compute(AtA_, W, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
+        models = std::vector<Mat> { Mat_<double>(3, 3, Vt.val + 72 /*=8*9*/) };
+#endif
+        FundamentalDegeneracy::recoverRank(models[0], false /*E*/);
+        return 1;
     }
+    int getMinimumRequiredSampleSize() const override { return 8; }
+    int getMaxNumberOfSolutions () const override { return 1; }
     Ptr<NonMinimalSolver> clone () const override {
         return makePtr<EssentialNonMinimalSolverImpl>(*points_mat);
     }

diff --git a/modules/calib3d/src/usac/estimator.cpp b/modules/calib3d/src/usac/estimator.cpp
index 46c9d4c..91abe30 100644 (file)
--- a/modules/calib3d/src/usac/estimator.cpp
+++ b/modules/calib3d/src/usac/estimator.cpp
@@ -69,13 +69,7 @@ public:
     }
     int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
             std::vector<Mat> &models, const std::vector<double> &weights) const override {
-        std::vector<Mat> Fs;
-        const int num_est_models = non_min_solver->estimate(sample, sample_size, Fs, weights);
-        int valid_models_count = 0;
-        for (int i = 0; i < num_est_models; i++)
-            if (degeneracy->isModelValid (Fs[i], sample, sample_size))
-                models[valid_models_count++] = Fs[i];
-        return valid_models_count;
+        return non_min_solver->estimate(sample, sample_size, models, weights);
     }
     int getMaxNumSolutions () const override {
         return min_solver->getMaxNumberOfSolutions();
@@ -123,13 +117,7 @@ public:
 
     int estimateModelNonMinimalSample(const std::vector<int> &sample, int sample_size,
             std::vector<Mat> &models, const std::vector<double> &weights) const override {
-        std::vector<Mat> Es;
-        const int num_est_models = non_min_solver->estimate(sample, sample_size, Es, weights);
-        int valid_models_count = 0;
-        for (int i = 0; i < num_est_models; i++)
-            if (degeneracy->isModelValid (Es[i], sample, sample_size))
-                models[valid_models_count++] = Es[i];
-        return valid_models_count;
+        return non_min_solver->estimate(sample, sample_size, models, weights);
     };
     int getMaxNumSolutions () const override {
         return min_solver->getMaxNumberOfSolutions();
@@ -231,7 +219,7 @@ Ptr<PnPEstimator> PnPEstimator::create (const Ptr<MinimalSolver> &min_solver_,
 
 ///////////////////////////////////////////// ERROR /////////////////////////////////////////
 // Symmetric Reprojection Error
-class ReprojectedErrorSymmetricImpl : public ReprojectionErrorSymmetric {
+class ReprojectionErrorSymmetricImpl : public ReprojectionErrorSymmetric {
 private:
     const Mat * points_mat;
     const float * const points;
@@ -239,7 +227,7 @@ private:
     float minv11, minv12, minv13, minv21, minv22, minv23, minv31, minv32, minv33;
     std::vector<float> errors;
 public:
-    explicit ReprojectedErrorSymmetricImpl (const Mat &points_)
+    explicit ReprojectionErrorSymmetricImpl (const Mat &points_)
         : points_mat(&points_), points ((float *) points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0), m31(0), m32(0), m33(0)
         , minv11(0), minv12(0), minv13(0), minv21(0), minv22(0), minv23(0), minv31(0), minv32(0), minv33(0)
@@ -287,23 +275,23 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedErrorSymmetricImpl>(*points_mat);
+        return makePtr<ReprojectionErrorSymmetricImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorSymmetric>
 ReprojectionErrorSymmetric::create(const Mat &points) {
-    return makePtr<ReprojectedErrorSymmetricImpl>(points);
+    return makePtr<ReprojectionErrorSymmetricImpl>(points);
 }
 
 // Forward Reprojection Error
-class ReprojectedErrorForwardImpl : public ReprojectionErrorForward {
+class ReprojectionErrorForwardImpl : public ReprojectionErrorForward {
 private:
     const Mat * points_mat;
     const float * const points;
     float m11, m12, m13, m21, m22, m23, m31, m32, m33;
     std::vector<float> errors;
 public:
-    explicit ReprojectedErrorForwardImpl (const Mat &points_)
+    explicit ReprojectionErrorForwardImpl (const Mat &points_)
         : points_mat(&points_), points ((float *)points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0), m31(0), m32(0), m33(0)
         , errors(points_.rows)
@@ -338,12 +326,12 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedErrorForwardImpl>(*points_mat);
+        return makePtr<ReprojectionErrorForwardImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorForward>
 ReprojectionErrorForward::create(const Mat &points) {
-    return makePtr<ReprojectedErrorForwardImpl>(points);
+    return makePtr<ReprojectionErrorForwardImpl>(points);
 }
 
 class SampsonErrorImpl : public SampsonError {
@@ -527,7 +515,7 @@ Ptr<ReprojectionErrorPmatrix> ReprojectionErrorPmatrix::create(const Mat &points
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 // Computes forward reprojection error for affine transformation.
-class ReprojectedDistanceAffineImpl : public ReprojectionErrorAffine {
+class ReprojectionDistanceAffineImpl : public ReprojectionErrorAffine {
 private:
     /*
      * m11 m12 m13
@@ -539,7 +527,7 @@ private:
     float m11, m12, m13, m21, m22, m23;
     std::vector<float> errors;
 public:
-    explicit ReprojectedDistanceAffineImpl (const Mat &points_)
+    explicit ReprojectionDistanceAffineImpl (const Mat &points_)
         : points_mat(&points_), points ((float *) points_.data)
         , m11(0), m12(0), m13(0), m21(0), m22(0), m23(0)
         , errors(points_.rows)
@@ -569,12 +557,12 @@ public:
         return errors;
     }
     Ptr<Error> clone () const override {
-        return makePtr<ReprojectedDistanceAffineImpl>(*points_mat);
+        return makePtr<ReprojectionDistanceAffineImpl>(*points_mat);
     }
 };
 Ptr<ReprojectionErrorAffine>
 ReprojectionErrorAffine::create(const Mat &points) {
-    return makePtr<ReprojectedDistanceAffineImpl>(points);
+    return makePtr<ReprojectionDistanceAffineImpl>(points);
 }
 
 ////////////////////////////////////// NORMALIZING TRANSFORMATION /////////////////////////

diff --git a/modules/calib3d/src/usac/fundamental_solver.cpp b/modules/calib3d/src/usac/fundamental_solver.cpp
index 5048aa0..00d4feb 100644 (file)
--- a/modules/calib3d/src/usac/fundamental_solver.cpp
+++ b/modules/calib3d/src/usac/fundamental_solver.cpp
@@ -20,7 +20,7 @@ public:
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
         const int m = 7, n = 9; // rows, cols
-        std::vector<double> a(m*n);
+        std::vector<double> a(63); // m*n
         auto * a_ = &a[0];
 
         for (int i = 0; i < m; i++ ) {
@@ -39,7 +39,8 @@ public:
             (*a_++) = 1;
         }
 
-        Math::eliminateUpperTriangular(a, m, n);
+        if (!Math::eliminateUpperTriangular(a, m, n))
+            return 0;
 
         /*
          [a11 a12 a13 a14 a15 a16 a17 a18 a19]
@@ -165,7 +166,7 @@ public:
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
         const int m = 8, n = 9; // rows, cols
-        std::vector<double> a(m*n);
+        std::vector<double> a(72); // m*n
         auto * a_ = &a[0];
 
         for (int i = 0; i < m; i++ ) {
@@ -184,7 +185,8 @@ public:
             (*a_++) = 1;
         }
 
-        Math::eliminateUpperTriangular(a, m, n);
+        if (!Math::eliminateUpperTriangular(a, m, n))
+            return 0;
 
         /*
          [a11 a12 a13 a14 a15 a16 a17 a18 a19]
@@ -313,16 +315,15 @@ public:
         Matx<double, 9, 9> AtA_(AtA), U, Vt;
         Vec<double, 9> W;
         SVD::compute(AtA_, W, U, Vt, SVD::FULL_UV + SVD::MODIFY_A);
-        models = std::vector<Mat> { Mat(Vt.row(8).reshape<3,3>()) };
+        models = std::vector<Mat> { Mat_<double>(3, 3, Vt.val + 72 /*=8*9*/) };
 #endif
+        FundamentalDegeneracy::recoverRank(models[0], true/*F*/);
 
         // Transpose T2 (in T2 the lower diagonal is zero)
         T2(2, 0) = T2(0, 2); T2(2, 1) = T2(1, 2);
         T2(0, 2) = 0; T2(1, 2) = 0;
 
         models[0] = T2 * models[0] * T1;
-
-        FundamentalDegeneracy::recoverRank(models[0]);
         return 1;
     }
 

diff --git a/modules/calib3d/src/usac/gamma_values.cpp b/modules/calib3d/src/usac/gamma_values.cpp
new file mode 100644 (file)
index 0000000..1e82d8e
--- /dev/null
+++ b/modules/calib3d/src/usac/gamma_values.cpp
@@ -0,0 +1,107 @@
+// This file is part of OpenCV project.
+// It is subject to the license terms in the LICENSE file found in the top-level directory
+// of this distribution and at http://opencv.org/license.html.
+
+#include "../precomp.hpp"
+#include "../usac.hpp"
+
+namespace cv { namespace usac {
+
+GammaValues::GammaValues()
+    : max_range_complete(4.62)
+    , max_range_gamma(1.52)
+    , max_size_table(3000)
+{
+    /*
+     * Gamma values for degrees of freedom n = 2 and sigma quantile 99% of chi distribution
+     * (squared root of chi-squared distribution), in the range <0; 4.62> for complete values
+     * and <0, 1.52> for gamma values.
+     * Number of anchor points is 50. Other values are approximated using linear interpolation
+     */
+    const int number_of_anchor_points = 50;
+    std::vector<double> gamma_complete_anchor = std::vector<double>
+       {1.7724538509055159, 1.182606138403832, 0.962685372890749, 0.8090013493715409,
+        0.6909325812483967, 0.5961199186942078, 0.5179833984918483, 0.45248091153099873,
+        0.39690029823142897, 0.34930995878395804, 0.3082742109224103, 0.2726914551904204,
+        0.2416954924567404, 0.21459196516027726, 0.190815580770884, 0.16990026519723456,
+        0.15145770273372564, 0.13516150988807635, 0.12073530906427948, 0.10794357255251595,
+        0.0965844793065712, 0.08648426334883624, 0.07749268706639856, 0.06947937608738222,
+        0.062330823249820304, 0.05594791865006951, 0.05024389794830681, 0.045142626552664405,
+        0.040577155977706246, 0.03648850256745103, 0.03282460924226794, 0.029539458909083157,
+        0.02659231432268328, 0.023947063970062663, 0.021571657306774475, 0.01943761564987864,
+        0.017519607407598645, 0.015795078236273064, 0.014243928262247118, 0.012848229767187478,
+        0.011591979769030827, 0.010460882783057988, 0.009442159753944173, 0.008524379737926344,
+        0.007697311406424555, 0.006951791856026042, 0.006279610558635573, 0.005673406581042374,
+        0.005126577454218803, 0.004633198286725555};
+
+    std::vector<double> gamma_incomplete_anchor = std::vector<double>
+        {0.0, 0.01773096912803939, 0.047486924846289004, 0.08265437835139826, 0.120639343491371,
+         0.15993024714868515, 0.19954558593754865, 0.23881753504915218, 0.2772830648361923,
+         0.3146208784488923, 0.3506114446939783, 0.385110056889967, 0.41802785670077697,
+         0.44931803198258047, 0.47896553567848993, 0.5069792897777948, 0.5333861945970247,
+         0.5582264802664578, 0.581550074874317, 0.6034137543595729, 0.6238789008764282,
+         0.6430097394182639, 0.6608719532994989, 0.6775316015953519, 0.6930542783709592,
+         0.7075044661695132, 0.7209450459078338, 0.733436932830201, 0.7450388140484766,
+         0.7558069678435577, 0.7657951486073097, 0.7750545242776943, 0.7836336555215403,
+         0.7915785078697124, 0.798932489600361, 0.8057365094688473, 0.8120290494534339,
+         0.8178462485678104, 0.8232219945197348, 0.8281880205973585, 0.8327740056635289,
+         0.8370076755516281, 0.8409149044990385, 0.8445198155381767, 0.8478448790000731,
+         0.8509110084798414, 0.8537376537738418, 0.8563428904304485, 0.8587435056647642,
+         0.8609550804762539};
+
+    std::vector<double> gamma_anchor = std::vector<double>
+        {1.7724538509055159, 1.427187162582056, 1.2890382454046982, 1.186244737282388,
+         1.1021938955410173, 1.0303674512016956, 0.9673796229113404, 0.9111932804012203,
+         0.8604640514722175, 0.814246149432561, 0.7718421763436497, 0.7327190195355812,
+         0.6964573670982434, 0.6627197089339725, 0.6312291454822467, 0.6017548373556638,
+         0.5741017071093776, 0.5481029597580317, 0.523614528104858, 0.5005108666212138,
+         0.478681711577816, 0.4580295473431646, 0.43846759792922513, 0.41991821541471996,
+         0.40231157253054745, 0.38558459136185, 0.3696800574963841, 0.3545458813847714,
+         0.340134477710645, 0.32640224021796493, 0.3133090943985706, 0.3008181141790485,
+         0.28889519159238314, 0.2775087506098113, 0.2666294980086962, 0.2562302054837794,
+         0.24628551826026082, 0.2367717863030556, 0.22766691488600885, 0.21895023182476064,
+         0.2106023691144937, 0.2026051570714723, 0.19494152937027823, 0.18759543761063277,
+         0.1805517742482484, 0.17379630289125447, 0.16731559510356395, 0.1610969729740903,
+         0.1551284568099053, 0.14939871739550692};
+
+    // allocate tables
+    gamma_complete = std::vector<double>(max_size_table);
+    gamma_incomplete = std::vector<double>(max_size_table);
+    gamma = std::vector<double>(max_size_table);
+
+    const int step = (int)((double)max_size_table / (number_of_anchor_points-1));
+    int arr_cnt = 0;
+    for (int i = 0; i < number_of_anchor_points-1; i++) {
+         const double complete_x0 = gamma_complete_anchor[i], step_complete = (gamma_complete_anchor[i+1] - complete_x0) / step;
+         const double incomplete_x0 = gamma_incomplete_anchor[i], step_incomplete = (gamma_incomplete_anchor[i+1] - incomplete_x0) / step;
+         const double gamma_x0 = gamma_anchor[i], step_gamma = (gamma_anchor[i+1] - gamma_x0) / step;
+
+         for (int j = 0; j < step; j++) {
+             gamma_complete[arr_cnt] = complete_x0 + j * step_complete;
+             gamma_incomplete[arr_cnt] = incomplete_x0 + j * step_incomplete;
+             gamma[arr_cnt++] = gamma_x0 + j * step_gamma;
+         }
+    }
+    if (arr_cnt < max_size_table) {
+        // if array was not totally filled (in some cases can happen) then copy last values
+        std::fill(gamma_complete.begin()+arr_cnt, gamma_complete.end(), gamma_complete[arr_cnt-1]);
+        std::fill(gamma_incomplete.begin()+arr_cnt, gamma_incomplete.end(), gamma_incomplete[arr_cnt-1]);
+        std::fill(gamma.begin()+arr_cnt, gamma.end(), gamma[arr_cnt-1]);
+    }
+}
+
+const std::vector<double>& GammaValues::getCompleteGammaValues() const { return gamma_complete; }
+const std::vector<double>& GammaValues::getIncompleteGammaValues() const { return gamma_incomplete; }
+const std::vector<double>& GammaValues::getGammaValues() const { return gamma; }
+double GammaValues::getScaleOfGammaCompleteValues () const { return gamma_complete.size() / max_range_complete; }
+double GammaValues::getScaleOfGammaValues () const { return gamma.size() / max_range_gamma; }
+int GammaValues::getTableSize () const { return max_size_table; }
+
+/* static */
+const GammaValues& GammaValues::getSingleton()
+{
+    static GammaValues g_gammaValues;
+    return g_gammaValues;
+}
+
+}}  // namespace

diff --git a/modules/calib3d/src/usac/gamma_values.hpp b/modules/calib3d/src/usac/gamma_values.hpp
deleted file mode 100644 (file)
index 5a30289..0000000
--- a/modules/calib3d/src/usac/gamma_values.hpp
+++ /dev/null
@@ -1,237 +0,0 @@
-// This file is part of OpenCV project.
-// It is subject to the license terms in the LICENSE file found in the top-level directory
-// of this distribution and at http://opencv.org/license.html.
-
-constexpr int stored_gamma_number = 2999;
-constexpr int stored_incomplete_gamma_number = 3999;
-constexpr double scale_of_stored_gammas_n4 = 1647.8;
-constexpr double scale_of_stored_incomplete_gammas_n4 = 603.64;
-
-constexpr double stored_complete_gamma_values_n4[] = {0.88623,0.88618,0.8861,0.88599,0.88587,0.88573,0.88557,0.8854,0.88522,0.88502,0.88482,0.8846,0.88438,0.88415,0.8839,0.88365,0.8834,0.88313,0.88285,0.88257,0.88229,0.88199,0.88169,0.88138,0.88107,0.88075,0.88042,0.88009,0.87975,0.87941,0.87906,0.8787,0.87834,0.87798,0.87761,0.87724,0.87686,0.87647,0.87609,0.87569,0.8753,0.8749,0.87449,0.87408,0.87367,0.87325,0.87283,0.8724,0.87197,0.87154,0.8711,0.87066,0.87022,0.86977,0.86932,0.86886,0.8684,0.86794,0.86748,0.86701,0.86654,0.86606,0.86559,0.86511,0.86462,0.86414,0.86365,0.86315,0.86266,0.86216,0.86166,0.86116,0.86065,0.86014,0.85963,0.85911,0.8586,0.85808,0.85755,0.85703,0.8565,0.85597,0.85544,0.85491,0.85437,0.85383,0.85329,0.85275,0.8522,0.85165,0.8511,0.85055,0.85,0.84944,0.84888,0.84832,0.84776,0.8472,0.84663,0.84606,
-0.84549,0.84492,0.84434,0.84377,0.84319,0.84261,0.84203,0.84145,0.84086,0.84027,0.83969,0.83909,0.8385,0.83791,0.83731,0.83672,0.83612,0.83552,0.83492,0.83431,0.83371,0.8331,0.8325,0.83189,0.83128,0.83066,0.83005,0.82943,0.82882,0.8282,0.82758,0.82696,0.82634,0.82572,0.82509,0.82447,0.82384,0.82321,0.82258,0.82195,0.82132,0.82068,0.82005,0.81941,0.81878,0.81814,0.8175,0.81686,0.81622,0.81558,0.81493,0.81429,0.81364,0.813,0.81235,0.8117,0.81105,0.8104,0.80975,0.80909,0.80844,0.80779,0.80713,0.80647,0.80582,0.80516,0.8045,0.80384,0.80318,0.80251,0.80185,0.80119,0.80052,0.79986,0.79919,0.79852,0.79786,0.79719,0.79652,0.79585,0.79518,0.7945,0.79383,0.79316,0.79248,0.79181,0.79113,0.79046,0.78978,0.7891,0.78843,0.78775,0.78707,0.78639,0.78571,0.78503,0.78434,0.78366,0.78298,0.78229,
-0.78161,0.78093,0.78024,0.77955,0.77887,0.77818,0.77749,0.7768,0.77612,0.77543,0.77474,0.77405,0.77336,0.77266,0.77197,0.77128,0.77059,0.76989,0.7692,0.76851,0.76781,0.76712,0.76642,0.76573,0.76503,0.76433,0.76364,0.76294,0.76224,0.76154,0.76085,0.76015,0.75945,0.75875,0.75805,0.75735,0.75665,0.75595,0.75525,0.75454,0.75384,0.75314,0.75244,0.75174,0.75103,0.75033,0.74963,0.74892,0.74822,0.74751,0.74681,0.74611,0.7454,0.7447,0.74399,0.74328,0.74258,0.74187,0.74117,0.74046,0.73975,0.73905,0.73834,0.73763,0.73692,0.73622,0.73551,0.7348,0.73409,0.73339,0.73268,0.73197,0.73126,0.73055,0.72984,0.72913,0.72842,0.72772,0.72701,0.7263,0.72559,0.72488,0.72417,0.72346,0.72275,0.72204,0.72133,0.72062,0.71991,0.7192,0.71849,0.71778,0.71707,0.71636,0.71565,0.71494,0.71423,0.71352,0.71281,0.71209,
-0.71138,0.71067,0.70996,0.70925,0.70854,0.70783,0.70712,0.70641,0.7057,0.70499,0.70428,0.70357,0.70286,0.70215,0.70144,0.70073,0.70002,0.69931,0.6986,0.69789,0.69718,0.69647,0.69576,0.69505,0.69434,0.69363,0.69292,0.69221,0.6915,0.69079,0.69008,0.68937,0.68867,0.68796,0.68725,0.68654,0.68583,0.68512,0.68441,0.68371,0.683,0.68229,0.68158,0.68088,0.68017,0.67946,0.67875,0.67805,0.67734,0.67663,0.67593,0.67522,0.67451,0.67381,0.6731,0.6724,0.67169,0.67099,0.67028,0.66958,0.66887,0.66817,0.66746,0.66676,0.66605,0.66535,0.66465,0.66394,0.66324,0.66254,0.66183,0.66113,0.66043,0.65973,0.65903,0.65832,0.65762,0.65692,0.65622,0.65552,0.65482,0.65412,0.65342,0.65272,0.65202,0.65132,0.65062,0.64992,0.64922,0.64853,0.64783,0.64713,0.64643,0.64574,0.64504,0.64434,0.64365,0.64295,0.64225,0.64156,
-0.64086,0.64017,0.63947,0.63878,0.63808,0.63739,0.6367,0.636,0.63531,0.63462,0.63393,0.63323,0.63254,0.63185,0.63116,0.63047,0.62978,0.62909,0.6284,0.62771,0.62702,0.62633,0.62564,0.62495,0.62427,0.62358,0.62289,0.6222,0.62152,0.62083,0.62014,0.61946,0.61877,0.61809,0.6174,0.61672,0.61604,0.61535,0.61467,0.61399,0.6133,0.61262,0.61194,0.61126,0.61058,0.6099,0.60922,0.60854,0.60786,0.60718,0.6065,0.60582,0.60514,0.60446,0.60379,0.60311,0.60243,0.60176,0.60108,0.60041,0.59973,0.59906,0.59838,0.59771,0.59703,0.59636,0.59569,0.59501,0.59434,0.59367,0.593,0.59233,0.59166,0.59099,0.59032,0.58965,0.58898,0.58831,0.58764,0.58698,0.58631,0.58564,0.58498,0.58431,0.58365,0.58298,0.58232,0.58165,0.58099,0.58032,0.57966,0.579,0.57834,0.57767,0.57701,0.57635,0.57569,0.57503,0.57437,0.57371,
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-0.00497,0.00497,0.00496,0.00495,0.00494,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00487,0.00486,0.00485,0.00484,0.00484,0.00483,0.00482,0.00481,0.00481,0.0048,0.00479,0.00479,0.00478,0.00477,0.00476,0.00476,0.00475,0.00474,0.00473,0.00473,0.00472,0.00471,0.0047,0.0047,0.00469,0.00468,0.00468,0.00467,0.00466,0.00465,0.00465,0.00464,0.00463,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459,0.00458,0.00458,0.00457,0.00456,0.00455,0.00455,0.00454,0.00453,0.00453,0.00452,0.00451,0.00451,0.0045,0.00449,0.00448,0.00448,0.00447,0.00446,0.00446,0.00445,0.00444,0.00444,0.00443,0.00442,0.00442,0.00441,0.0044,0.0044,0.00439,0.00438,0.00438,0.00437,0.00436,0.00436,0.00435,0.00434,0.00434,0.00433,0.00432,0.00432,0.00431,0.0043,0.0043,0.00429,0.00428,0.00428,0.00427,
-0.00426,0.00426,0.00425,0.00424,0.00424,0.00423,0.00422,0.00422,0.00421,0.0042,0.0042,0.00419,0.00418,0.00418,0.00417,0.00416,0.00416,0.00415,0.00415,0.00414,0.00413,0.00413,0.00412,0.00411,0.00411,0.0041,0.00409,0.00409,0.00408,0.00408,0.00407,0.00406,0.00406,0.00405,0.00404,0.00404,0.00403,0.00403,0.00402,0.00401,0.00401,0.004,0.00399,0.00399,0.00398,0.00398,0.00397,0.00396,0.00396,0.00395,0.00395,0.00394,0.00393,0.00393,0.00392,0.00391,0.00391,0.0039,0.0039,0.00389,0.00388,0.00388,0.00387,0.00387,0.00386,0.00385,0.00385,0.00384,0.00384,0.00383,0.00383,0.00382,0.00381,0.00381,0.0038,0.0038,0.00379,0.00378,0.00378,0.00377,0.00377,0.00376,0.00375,0.00375,0.00374,0.00374,0.00373,0.00373,0.00372,0.00371,0.00371,0.0037,0.0037,0.00369,0.00369,0.00368,0.00367,0.00367,0.00366,0.00366};
-
-constexpr double stored_lower_incomplete_gamma_values_n4[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,3e-05,3e-05,4e-05,4e-05,5e-05,6e-05,7e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00014,0.00015,0.00016,0.00018,0.0002,0.00021,0.00023,0.00025,0.00027,0.00029,0.00031,0.00033,0.00036,0.00038,0.00041,0.00043,0.00046,0.00049,0.00051,0.00054,0.00058,0.00061,0.00064,0.00067,0.00071,0.00074,0.00078,0.00082,0.00086,0.0009,0.00094,0.00098,0.00102,0.00107,0.00111,0.00116,0.00121,0.00126,0.00131,0.00136,0.00141,0.00146,0.00152,0.00157,0.00163,0.00169,0.00175,0.00181,0.00187,0.00193,0.00199,0.00206,0.00212,0.00219,0.00226,0.00233,0.0024,0.00247,0.00254,0.00262,0.00269,0.00277,0.00285,0.00293,0.00301,0.00309,0.00317,0.00325,0.00334,0.00343,0.00351,0.0036,0.00369,0.00379,0.00388,
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-0.02,0.02023,0.02046,0.02069,0.02092,0.02115,0.02138,0.02162,0.02186,0.02209,0.02233,0.02257,0.02282,0.02306,0.0233,0.02355,0.0238,0.02405,0.0243,0.02455,0.0248,0.02505,0.02531,0.02556,0.02582,0.02608,0.02634,0.0266,0.02687,0.02713,0.0274,0.02766,0.02793,0.0282,0.02847,0.02874,0.02902,0.02929,0.02957,0.02984,0.03012,0.0304,0.03068,0.03097,0.03125,0.03153,0.03182,0.03211,0.0324,0.03269,0.03298,0.03327,0.03356,0.03386,0.03415,0.03445,0.03475,0.03505,0.03535,0.03565,0.03596,0.03626,0.03657,0.03688,0.03719,0.0375,0.03781,0.03812,0.03843,0.03875,0.03906,0.03938,0.0397,0.04002,0.04034,0.04066,0.04099,0.04131,0.04164,0.04197,0.04229,0.04262,0.04296,0.04329,0.04362,0.04396,0.04429,0.04463,0.04497,0.04531,0.04565,0.04599,0.04633,0.04668,0.04702,0.04737,0.04772,0.04806,0.04841,0.04877,
-0.04912,0.04947,0.04983,0.05018,0.05054,0.0509,0.05126,0.05162,0.05198,0.05234,0.05271,0.05307,0.05344,0.05381,0.05418,0.05455,0.05492,0.05529,0.05566,0.05604,0.05641,0.05679,0.05717,0.05755,0.05793,0.05831,0.05869,0.05908,0.05946,0.05985,0.06023,0.06062,0.06101,0.0614,0.06179,0.06219,0.06258,0.06297,0.06337,0.06377,0.06417,0.06456,0.06496,0.06537,0.06577,0.06617,0.06658,0.06698,0.06739,0.0678,0.06821,0.06862,0.06903,0.06944,0.06985,0.07027,0.07068,0.0711,0.07152,0.07194,0.07236,0.07278,0.0732,0.07362,0.07405,0.07447,0.0749,0.07532,0.07575,0.07618,0.07661,0.07704,0.07747,0.07791,0.07834,0.07878,0.07921,0.07965,0.08009,0.08053,0.08097,0.08141,0.08185,0.0823,0.08274,0.08319,0.08363,0.08408,0.08453,0.08498,0.08543,0.08588,0.08633,0.08679,0.08724,0.08769,0.08815,0.08861,0.08907,0.08953,
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-0.14049,0.14103,0.14158,0.14212,0.14267,0.14322,0.14377,0.14432,0.14487,0.14542,0.14598,0.14653,0.14708,0.14764,0.14819,0.14875,0.14931,0.14986,0.15042,0.15098,0.15154,0.1521,0.15266,0.15322,0.15378,0.15435,0.15491,0.15547,0.15604,0.1566,0.15717,0.15774,0.1583,0.15887,0.15944,0.16001,0.16058,0.16115,0.16172,0.16229,0.16287,0.16344,0.16401,0.16459,0.16516,0.16574,0.16632,0.16689,0.16747,0.16805,0.16863,0.16921,0.16979,0.17037,0.17095,0.17153,0.17211,0.1727,0.17328,0.17387,0.17445,0.17504,0.17562,0.17621,0.1768,0.17739,0.17797,0.17856,0.17915,0.17974,0.18033,0.18093,0.18152,0.18211,0.1827,0.1833,0.18389,0.18449,0.18508,0.18568,0.18628,0.18687,0.18747,0.18807,0.18867,0.18927,0.18987,0.19047,0.19107,0.19167,0.19227,0.19287,0.19348,0.19408,0.19469,0.19529,0.1959,0.1965,0.19711,0.19771,
-0.19832,0.19893,0.19954,0.20015,0.20076,0.20137,0.20198,0.20259,0.2032,0.20381,0.20442,0.20504,0.20565,0.20626,0.20688,0.20749,0.20811,0.20872,0.20934,0.20996,0.21057,0.21119,0.21181,0.21243,0.21305,0.21367,0.21429,0.21491,0.21553,0.21615,0.21677,0.21739,0.21802,0.21864,0.21926,0.21989,0.22051,0.22114,0.22176,0.22239,0.22301,0.22364,0.22427,0.22489,0.22552,0.22615,0.22678,0.22741,0.22804,0.22867,0.2293,0.22993,0.23056,0.23119,0.23182,0.23246,0.23309,0.23372,0.23436,0.23499,0.23563,0.23626,0.2369,0.23753,0.23817,0.2388,0.23944,0.24008,0.24071,0.24135,0.24199,0.24263,0.24327,0.24391,0.24455,0.24519,0.24583,0.24647,0.24711,0.24775,0.24839,0.24904,0.24968,0.25032,0.25096,0.25161,0.25225,0.2529,0.25354,0.25419,0.25483,0.25548,0.25612,0.25677,0.25742,0.25806,0.25871,0.25936,0.26001,0.26065,
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-1.28759,1.28764,1.2877,1.28775,1.28781,1.28786,1.28792,1.28797,1.28803,1.28808,1.28813,1.28819,1.28824,1.2883,1.28835,1.2884,1.28846,1.28851,1.28856,1.28862,1.28867,1.28872,1.28878,1.28883,1.28888,1.28894,1.28899,1.28904,1.2891,1.28915,1.2892,1.28925,1.28931,1.28936,1.28941,1.28946,1.28952,1.28957,1.28962,1.28967,1.28973,1.28978,1.28983,1.28988,1.28993,1.28999,1.29004,1.29009,1.29014,1.29019,1.29024,1.29029,1.29035,1.2904,1.29045,1.2905,1.29055,1.2906,1.29065,1.2907,1.29075,1.29081,1.29086,1.29091,1.29096,1.29101,1.29106,1.29111,1.29116,1.29121,1.29126,1.29131,1.29136,1.29141,1.29146,1.29151,1.29156,1.29161,1.29166,1.29171,1.29176,1.29181,1.29186,1.29191,1.29195,1.292,1.29205,1.2921,1.29215,1.2922,1.29225,1.2923,1.29235,1.2924,1.29244,1.29249,1.29254,1.29259,1.29264,1.29269,
-1.29274,1.29278,1.29283,1.29288,1.29293,1.29298,1.29302,1.29307,1.29312,1.29317,1.29321,1.29326,1.29331,1.29336,1.29341,1.29345,1.2935,1.29355,1.29359,1.29364,1.29369,1.29374,1.29378,1.29383,1.29388,1.29392,1.29397,1.29402,1.29406,1.29411,1.29416,1.2942,1.29425,1.2943,1.29434,1.29439,1.29443,1.29448,1.29453,1.29457,1.29462,1.29466,1.29471,1.29476,1.2948,1.29485,1.29489,1.29494,1.29498,1.29503,1.29507,1.29512,1.29517,1.29521,1.29526,1.2953,1.29535,1.29539,1.29544,1.29548,1.29552,1.29557,1.29561,1.29566,1.2957,1.29575,1.29579,1.29584,1.29588,1.29593,1.29597,1.29601,1.29606,1.2961,1.29615,1.29619,1.29623,1.29628,1.29632,1.29637,1.29641,1.29645,1.2965,1.29654,1.29658,1.29663,1.29667,1.29671,1.29676,1.2968,1.29684,1.29689,1.29693,1.29697,1.29701,1.29706,1.2971,1.29714,1.29719,1.29723,
-1.29727,1.29731,1.29736,1.2974,1.29744,1.29748,1.29752,1.29757,1.29761,1.29765,1.29769,1.29774,1.29778,1.29782,1.29786,1.2979,1.29794,1.29799,1.29803,1.29807,1.29811,1.29815,1.29819,1.29823,1.29828,1.29832,1.29836,1.2984,1.29844,1.29848,1.29852,1.29856,1.2986,1.29865,1.29869,1.29873,1.29877,1.29881,1.29885,1.29889,1.29893,1.29897,1.29901,1.29905,1.29909,1.29913,1.29917,1.29921,1.29925,1.29929,1.29933,1.29937,1.29941,1.29945,1.29949,1.29953,1.29957,1.29961,1.29965,1.29969,1.29973,1.29977,1.29981,1.29985,1.29988,1.29992,1.29996,1.3,1.30004,1.30008,1.30012,1.30016,1.3002,1.30024,1.30027,1.30031,1.30035,1.30039,1.30043,1.30047,1.30051,1.30054,1.30058,1.30062,1.30066,1.3007,1.30074,1.30077,1.30081,1.30085,1.30089,1.30093,1.30096,1.301,1.30104,1.30108,1.30111,1.30115,1.30119,1.30123};
-
-constexpr double stored_gamma_values_n4[] = {0.88623,0.88622,0.8862,0.88618,0.88615,0.88612,0.88608,0.88604,0.886,0.88596,0.88591,0.88586,0.88581,0.88576,0.88571,0.88565,0.88559,0.88553,0.88547,0.88541,0.88534,0.88528,0.88521,0.88514,0.88507,0.88499,0.88492,0.88484,0.88477,0.88469,0.88461,0.88453,0.88444,0.88436,0.88428,0.88419,0.8841,0.88401,0.88392,0.88383,0.88374,0.88365,0.88356,0.88346,0.88336,0.88327,0.88317,0.88307,0.88297,0.88287,0.88277,0.88266,0.88256,0.88245,0.88235,0.88224,0.88213,0.88203,0.88192,0.88181,0.88169,0.88158,0.88147,0.88136,0.88124,0.88113,0.88101,0.88089,0.88077,0.88066,0.88054,0.88042,0.8803,0.88017,0.88005,0.87993,0.8798,0.87968,0.87955,0.87943,0.8793,0.87917,0.87904,0.87891,0.87878,0.87865,0.87852,0.87839,0.87826,0.87812,0.87799,0.87786,0.87772,0.87758,0.87745,0.87731,0.87717,0.87703,0.8769,0.87676,
-0.87662,0.87647,0.87633,0.87619,0.87605,0.8759,0.87576,0.87562,0.87547,0.87532,0.87518,0.87503,0.87488,0.87474,0.87459,0.87444,0.87429,0.87414,0.87399,0.87384,0.87368,0.87353,0.87338,0.87322,0.87307,0.87292,0.87276,0.8726,0.87245,0.87229,0.87213,0.87198,0.87182,0.87166,0.8715,0.87134,0.87118,0.87102,0.87086,0.8707,0.87053,0.87037,0.87021,0.87004,0.86988,0.86972,0.86955,0.86938,0.86922,0.86905,0.86889,0.86872,0.86855,0.86838,0.86821,0.86804,0.86787,0.8677,0.86753,0.86736,0.86719,0.86702,0.86685,0.86667,0.8665,0.86633,0.86615,0.86598,0.8658,0.86563,0.86545,0.86528,0.8651,0.86492,0.86475,0.86457,0.86439,0.86421,0.86403,0.86386,0.86368,0.8635,0.86332,0.86313,0.86295,0.86277,0.86259,0.86241,0.86222,0.86204,0.86186,0.86167,0.86149,0.86131,0.86112,0.86094,0.86075,0.86056,0.86038,0.86019,
-0.86,0.85982,0.85963,0.85944,0.85925,0.85906,0.85887,0.85868,0.85849,0.8583,0.85811,0.85792,0.85773,0.85754,0.85735,0.85716,0.85696,0.85677,0.85658,0.85638,0.85619,0.856,0.8558,0.85561,0.85541,0.85522,0.85502,0.85482,0.85463,0.85443,0.85423,0.85404,0.85384,0.85364,0.85344,0.85324,0.85304,0.85285,0.85265,0.85245,0.85225,0.85205,0.85185,0.85164,0.85144,0.85124,0.85104,0.85084,0.85064,0.85043,0.85023,0.85003,0.84982,0.84962,0.84941,0.84921,0.84901,0.8488,0.8486,0.84839,0.84818,0.84798,0.84777,0.84757,0.84736,0.84715,0.84694,0.84674,0.84653,0.84632,0.84611,0.8459,0.84569,0.84549,0.84528,0.84507,0.84486,0.84465,0.84444,0.84423,0.84401,0.8438,0.84359,0.84338,0.84317,0.84296,0.84274,0.84253,0.84232,0.8421,0.84189,0.84168,0.84146,0.84125,0.84104,0.84082,0.84061,0.84039,0.84018,0.83996,
-0.83974,0.83953,0.83931,0.8391,0.83888,0.83866,0.83845,0.83823,0.83801,0.83779,0.83757,0.83736,0.83714,0.83692,0.8367,0.83648,0.83626,0.83604,0.83582,0.8356,0.83538,0.83516,0.83494,0.83472,0.8345,0.83428,0.83406,0.83384,0.83361,0.83339,0.83317,0.83295,0.83273,0.8325,0.83228,0.83206,0.83183,0.83161,0.83139,0.83116,0.83094,0.83071,0.83049,0.83026,0.83004,0.82981,0.82959,0.82936,0.82914,0.82891,0.82869,0.82846,0.82823,0.82801,0.82778,0.82755,0.82733,0.8271,0.82687,0.82664,0.82641,0.82619,0.82596,0.82573,0.8255,0.82527,0.82504,0.82481,0.82458,0.82436,0.82413,0.8239,0.82367,0.82344,0.82321,0.82298,0.82274,0.82251,0.82228,0.82205,0.82182,0.82159,0.82136,0.82113,0.82089,0.82066,0.82043,0.8202,0.81996,0.81973,0.8195,0.81926,0.81903,0.8188,0.81856,0.81833,0.8181,0.81786,0.81763,0.81739,
-0.81716,0.81693,0.81669,0.81646,0.81622,0.81599,0.81575,0.81551,0.81528,0.81504,0.81481,0.81457,0.81433,0.8141,0.81386,0.81363,0.81339,0.81315,0.81291,0.81268,0.81244,0.8122,0.81196,0.81173,0.81149,0.81125,0.81101,0.81077,0.81054,0.8103,0.81006,0.80982,0.80958,0.80934,0.8091,0.80886,0.80862,0.80838,0.80814,0.8079,0.80766,0.80742,0.80718,0.80694,0.8067,0.80646,0.80622,0.80598,0.80574,0.8055,0.80526,0.80501,0.80477,0.80453,0.80429,0.80405,0.80381,0.80356,0.80332,0.80308,0.80284,0.80259,0.80235,0.80211,0.80187,0.80162,0.80138,0.80114,0.80089,0.80065,0.80041,0.80016,0.79992,0.79967,0.79943,0.79919,0.79894,0.7987,0.79845,0.79821,0.79796,0.79772,0.79747,0.79723,0.79698,0.79674,0.79649,0.79625,0.796,0.79576,0.79551,0.79526,0.79502,0.79477,0.79453,0.79428,0.79403,0.79379,0.79354,0.79329,
-0.79305,0.7928,0.79255,0.79231,0.79206,0.79181,0.79156,0.79132,0.79107,0.79082,0.79057,0.79033,0.79008,0.78983,0.78958,0.78933,0.78909,0.78884,0.78859,0.78834,0.78809,0.78784,0.7876,0.78735,0.7871,0.78685,0.7866,0.78635,0.7861,0.78585,0.7856,0.78535,0.7851,0.78485,0.7846,0.78435,0.7841,0.78385,0.7836,0.78335,0.7831,0.78285,0.7826,0.78235,0.7821,0.78185,0.7816,0.78135,0.7811,0.78085,0.7806,0.78034,0.78009,0.77984,0.77959,0.77934,0.77909,0.77884,0.77858,0.77833,0.77808,0.77783,0.77758,0.77732,0.77707,0.77682,0.77657,0.77632,0.77606,0.77581,0.77556,0.77531,0.77505,0.7748,0.77455,0.77429,0.77404,0.77379,0.77354,0.77328,0.77303,0.77278,0.77252,0.77227,0.77202,0.77176,0.77151,0.77126,0.771,0.77075,0.77049,0.77024,0.76999,0.76973,0.76948,0.76922,0.76897,0.76872,0.76846,0.76821,
-0.76795,0.7677,0.76744,0.76719,0.76693,0.76668,0.76642,0.76617,0.76592,0.76566,0.76541,0.76515,0.7649,0.76464,0.76438,0.76413,0.76387,0.76362,0.76336,0.76311,0.76285,0.7626,0.76234,0.76209,0.76183,0.76157,0.76132,0.76106,0.76081,0.76055,0.7603,0.76004,0.75978,0.75953,0.75927,0.75901,0.75876,0.7585,0.75825,0.75799,0.75773,0.75748,0.75722,0.75696,0.75671,0.75645,0.75619,0.75594,0.75568,0.75542,0.75517,0.75491,0.75465,0.75439,0.75414,0.75388,0.75362,0.75337,0.75311,0.75285,0.75259,0.75234,0.75208,0.75182,0.75156,0.75131,0.75105,0.75079,0.75053,0.75028,0.75002,0.74976,0.7495,0.74925,0.74899,0.74873,0.74847,0.74821,0.74796,0.7477,0.74744,0.74718,0.74692,0.74667,0.74641,0.74615,0.74589,0.74563,0.74538,0.74512,0.74486,0.7446,0.74434,0.74408,0.74383,0.74357,0.74331,0.74305,0.74279,0.74253,
-0.74227,0.74202,0.74176,0.7415,0.74124,0.74098,0.74072,0.74046,0.7402,0.73994,0.73969,0.73943,0.73917,0.73891,0.73865,0.73839,0.73813,0.73787,0.73761,0.73735,0.7371,0.73684,0.73658,0.73632,0.73606,0.7358,0.73554,0.73528,0.73502,0.73476,0.7345,0.73424,0.73398,0.73372,0.73347,0.73321,0.73295,0.73269,0.73243,0.73217,0.73191,0.73165,0.73139,0.73113,0.73087,0.73061,0.73035,0.73009,0.72983,0.72957,0.72931,0.72905,0.72879,0.72853,0.72827,0.72801,0.72775,0.72749,0.72723,0.72697,0.72671,0.72645,0.72619,0.72593,0.72567,0.72541,0.72515,0.72489,0.72463,0.72437,0.72412,0.72386,0.7236,0.72334,0.72307,0.72281,0.72255,0.72229,0.72203,0.72177,0.72151,0.72125,0.72099,0.72073,0.72047,0.72021,0.71995,0.71969,0.71943,0.71917,0.71891,0.71865,0.71839,0.71813,0.71787,0.71761,0.71735,0.71709,0.71683,0.71657,
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-0.35913,0.35896,0.35879,0.35862,0.35845,0.35828,0.35811,0.35794,0.35777,0.3576,0.35743,0.35726,0.35709,0.35692,0.35675,0.35658,0.35641,0.35624,0.35607,0.3559,0.35573,0.35556,0.35539,0.35523,0.35506,0.35489,0.35472,0.35455,0.35438,0.35421,0.35404,0.35387,0.35371,0.35354,0.35337,0.3532,0.35303,0.35286,0.3527,0.35253,0.35236,0.35219,0.35202,0.35186,0.35169,0.35152,0.35135,0.35119,0.35102,0.35085,0.35068,0.35052,0.35035,0.35018,0.35002,0.34985,0.34968,0.34951,0.34935,0.34918,0.34901,0.34885,0.34868,0.34851,0.34835,0.34818,0.34802,0.34785,0.34768,0.34752,0.34735,0.34719,0.34702,0.34685,0.34669,0.34652,0.34636,0.34619,0.34603,0.34586,0.3457,0.34553,0.34536,0.3452,0.34503,0.34487,0.3447,0.34454,0.34437,0.34421,0.34405,0.34388,0.34372,0.34355,0.34339,0.34322,0.34306,0.34289,0.34273,0.34257,
-0.3424,0.34224,0.34207,0.34191,0.34175,0.34158,0.34142,0.34126,0.34109,0.34093,0.34077,0.3406,0.34044,0.34028,0.34011,0.33995,0.33979,0.33963,0.33946,0.3393,0.33914,0.33897,0.33881,0.33865,0.33849,0.33832,0.33816,0.338,0.33784,0.33768,0.33751,0.33735,0.33719,0.33703,0.33687,0.33671,0.33654,0.33638,0.33622,0.33606,0.3359,0.33574,0.33558,0.33541,0.33525,0.33509,0.33493,0.33477,0.33461,0.33445,0.33429,0.33413,0.33397,0.33381,0.33365,0.33349,0.33333,0.33317,0.33301,0.33285,0.33269,0.33253,0.33237,0.33221,0.33205,0.33189,0.33173,0.33157,0.33141,0.33125,0.33109,0.33093,0.33077,0.33061,0.33045,0.33029,0.33013,0.32998,0.32982,0.32966,0.3295,0.32934,0.32918,0.32902,0.32886,0.32871,0.32855,0.32839,0.32823,0.32807,0.32792,0.32776,0.3276,0.32744,0.32728,0.32713,0.32697,0.32681,0.32665,0.3265,
-0.32634,0.32618,0.32602,0.32587,0.32571,0.32555,0.3254,0.32524,0.32508,0.32493,0.32477,0.32461,0.32446,0.3243,0.32414,0.32399,0.32383,0.32367,0.32352,0.32336,0.3232,0.32305,0.32289,0.32274,0.32258,0.32243,0.32227,0.32211,0.32196,0.3218,0.32165,0.32149,0.32134,0.32118,0.32103,0.32087,0.32072,0.32056,0.32041,0.32025,0.3201,0.31994,0.31979,0.31963,0.31948,0.31932,0.31917,0.31902,0.31886,0.31871,0.31855,0.3184,0.31824,0.31809,0.31794,0.31778,0.31763,0.31748,0.31732,0.31717,0.31701,0.31686,0.31671,0.31655,0.3164,0.31625,0.31609,0.31594,0.31579,0.31564,0.31548,0.31533,0.31518,0.31502,0.31487,0.31472,0.31457,0.31441,0.31426,0.31411,0.31396,0.31381,0.31365,0.3135,0.31335,0.3132,0.31305,0.31289,0.31274,0.31259,0.31244,0.31229,0.31214,0.31199,0.31183,0.31168,0.31153,0.31138,0.31123,0.31108,
-0.31093,0.31078,0.31063,0.31047,0.31032,0.31017,0.31002,0.30987,0.30972,0.30957,0.30942,0.30927,0.30912,0.30897,0.30882,0.30867,0.30852,0.30837,0.30822,0.30807,0.30792,0.30777,0.30762,0.30747,0.30732,0.30717,0.30702,0.30688,0.30673,0.30658,0.30643,0.30628,0.30613,0.30598,0.30583,0.30568,0.30554,0.30539,0.30524,0.30509,0.30494,0.30479,0.30464,0.3045,0.30435,0.3042,0.30405,0.3039,0.30376,0.30361,0.30346,0.30331,0.30317,0.30302,0.30287,0.30272,0.30258,0.30243,0.30228,0.30213,0.30199,0.30184,0.30169,0.30155,0.3014,0.30125,0.30111,0.30096,0.30081,0.30067,0.30052,0.30037,0.30023,0.30008,0.29993,0.29979,0.29964,0.29949,0.29935,0.2992,0.29906,0.29891,0.29877,0.29862,0.29847,0.29833,0.29818,0.29804,0.29789,0.29775,0.2976,0.29746,0.29731,0.29717,0.29702,0.29688,0.29673,0.29659,0.29644,0.2963,
-0.29615,0.29601,0.29586,0.29572,0.29557,0.29543,0.29529,0.29514,0.295,0.29485,0.29471,0.29456,0.29442,0.29428,0.29413,0.29399,0.29385,0.2937,0.29356,0.29341,0.29327,0.29313,0.29298,0.29284,0.2927,0.29256,0.29241,0.29227,0.29213,0.29198,0.29184,0.2917,0.29156,0.29141,0.29127,0.29113,0.29099,0.29084,0.2907,0.29056,0.29042,0.29027,0.29013,0.28999,0.28985,0.28971,0.28956,0.28942,0.28928,0.28914,0.289,0.28886,0.28871,0.28857,0.28843,0.28829,0.28815,0.28801,0.28787,0.28773,0.28758,0.28744,0.2873,0.28716,0.28702,0.28688,0.28674,0.2866,0.28646,0.28632,0.28618,0.28604,0.2859,0.28576,0.28562,0.28548,0.28534,0.2852,0.28506,0.28492,0.28478,0.28464,0.2845,0.28436,0.28422,0.28408,0.28394,0.2838,0.28366,0.28352,0.28338,0.28324,0.28311,0.28297,0.28283,0.28269,0.28255,0.28241,0.28227,0.28213,
-0.282,0.28186,0.28172,0.28158,0.28144,0.2813,0.28117,0.28103,0.28089,0.28075,0.28061,0.28048,0.28034,0.2802,0.28006,0.27992,0.27979,0.27965,0.27951,0.27937,0.27924,0.2791,0.27896,0.27883,0.27869,0.27855,0.27841,0.27828,0.27814,0.278,0.27787,0.27773,0.27759,0.27746,0.27732,0.27718,0.27705,0.27691,0.27678,0.27664,0.2765,0.27637,0.27623,0.27609,0.27596,0.27582,0.27569,0.27555,0.27542,0.27528,0.27514,0.27501,0.27487,0.27474,0.2746,0.27447,0.27433,0.2742,0.27406,0.27393,0.27379,0.27366,0.27352,0.27339,0.27325,0.27312,0.27298,0.27285,0.27271,0.27258,0.27245,0.27231,0.27218,0.27204,0.27191,0.27177,0.27164,0.27151,0.27137,0.27124,0.2711,0.27097,0.27084,0.2707,0.27057,0.27044,0.2703,0.27017,0.27004,0.2699,0.26977,0.26964,0.2695,0.26937,0.26924,0.26911,0.26897,0.26884,0.26871,0.26857};
-
-constexpr double scale_of_stored_gammas_n5 = 1545.88;
-constexpr double scale_of_stored_incomplete_gammas_n5 = 531.27;
-
-constexpr double stored_complete_gamma_values_n5[] = {1.0,1.0,0.99999,0.99998,0.99997,0.99996,0.99994,0.99991,0.99989,0.99986,0.99983,0.99979,0.99975,0.99971,0.99966,0.99961,0.99956,0.9995,0.99944,0.99938,0.99931,0.99924,0.99917,0.99909,0.99901,0.99893,0.99884,0.99875,0.99866,0.99856,0.99846,0.99836,0.99826,0.99815,0.99804,0.99792,0.99781,0.99768,0.99756,0.99743,0.9973,0.99717,0.99704,0.9969,0.99675,0.99661,0.99646,0.99631,0.99616,0.996,0.99584,0.99568,0.99551,0.99534,0.99517,0.995,0.99482,0.99464,0.99446,0.99427,0.99408,0.99389,0.9937,0.9935,0.9933,0.9931,0.99289,0.99269,0.99248,0.99226,0.99205,0.99183,0.99161,0.99138,0.99115,0.99093,0.99069,0.99046,0.99022,0.98998,0.98974,0.98949,0.98925,0.989,0.98874,0.98849,0.98823,0.98797,0.98771,0.98744,0.98717,0.9869,0.98663,0.98635,0.98608,0.9858,0.98551,0.98523,0.98494,0.98465,
-0.98436,0.98406,0.98377,0.98347,0.98317,0.98286,0.98256,0.98225,0.98194,0.98162,0.98131,0.98099,0.98067,0.98035,0.98002,0.97969,0.97936,0.97903,0.9787,0.97836,0.97803,0.97769,0.97734,0.977,0.97665,0.9763,0.97595,0.9756,0.97524,0.97489,0.97453,0.97416,0.9738,0.97343,0.97307,0.9727,0.97232,0.97195,0.97157,0.9712,0.97082,0.97043,0.97005,0.96966,0.96928,0.96889,0.96849,0.9681,0.9677,0.96731,0.96691,0.9665,0.9661,0.9657,0.96529,0.96488,0.96447,0.96405,0.96364,0.96322,0.9628,0.96238,0.96196,0.96154,0.96111,0.96068,0.96026,0.95982,0.95939,0.95896,0.95852,0.95808,0.95764,0.9572,0.95676,0.95631,0.95586,0.95542,0.95497,0.95451,0.95406,0.9536,0.95315,0.95269,0.95223,0.95177,0.9513,0.95084,0.95037,0.9499,0.94943,0.94896,0.94849,0.94801,0.94754,0.94706,0.94658,0.9461,0.94562,0.94513,
-0.94465,0.94416,0.94367,0.94318,0.94269,0.9422,0.9417,0.94121,0.94071,0.94021,0.93971,0.93921,0.9387,0.9382,0.93769,0.93719,0.93668,0.93617,0.93566,0.93514,0.93463,0.93411,0.9336,0.93308,0.93256,0.93204,0.93151,0.93099,0.93046,0.92994,0.92941,0.92888,0.92835,0.92782,0.92728,0.92675,0.92621,0.92568,0.92514,0.9246,0.92406,0.92352,0.92297,0.92243,0.92188,0.92134,0.92079,0.92024,0.91969,0.91914,0.91859,0.91803,0.91748,0.91692,0.91636,0.91581,0.91525,0.91469,0.91412,0.91356,0.913,0.91243,0.91186,0.9113,0.91073,0.91016,0.90959,0.90902,0.90844,0.90787,0.9073,0.90672,0.90614,0.90556,0.90498,0.9044,0.90382,0.90324,0.90266,0.90207,0.90149,0.9009,0.90032,0.89973,0.89914,0.89855,0.89796,0.89737,0.89677,0.89618,0.89558,0.89499,0.89439,0.89379,0.8932,0.8926,0.892,0.89139,0.89079,0.89019,
-0.88959,0.88898,0.88838,0.88777,0.88716,0.88655,0.88594,0.88533,0.88472,0.88411,0.8835,0.88289,0.88227,0.88166,0.88104,0.88043,0.87981,0.87919,0.87857,0.87795,0.87733,0.87671,0.87609,0.87547,0.87484,0.87422,0.87359,0.87297,0.87234,0.87171,0.87109,0.87046,0.86983,0.8692,0.86857,0.86794,0.8673,0.86667,0.86604,0.8654,0.86477,0.86413,0.8635,0.86286,0.86222,0.86158,0.86095,0.86031,0.85967,0.85903,0.85838,0.85774,0.8571,0.85646,0.85581,0.85517,0.85452,0.85388,0.85323,0.85258,0.85194,0.85129,0.85064,0.84999,0.84934,0.84869,0.84804,0.84739,0.84674,0.84608,0.84543,0.84478,0.84412,0.84347,0.84281,0.84216,0.8415,0.84085,0.84019,0.83953,0.83887,0.83821,0.83755,0.8369,0.83623,0.83557,0.83491,0.83425,0.83359,0.83293,0.83226,0.8316,0.83094,0.83027,0.82961,0.82894,0.82828,0.82761,0.82694,0.82628,
-0.82561,0.82494,0.82427,0.82361,0.82294,0.82227,0.8216,0.82093,0.82026,0.81959,0.81892,0.81824,0.81757,0.8169,0.81623,0.81555,0.81488,0.81421,0.81353,0.81286,0.81218,0.81151,0.81083,0.81016,0.80948,0.8088,0.80813,0.80745,0.80677,0.8061,0.80542,0.80474,0.80406,0.80338,0.8027,0.80202,0.80134,0.80066,0.79998,0.7993,0.79862,0.79794,0.79726,0.79658,0.7959,0.79521,0.79453,0.79385,0.79317,0.79248,0.7918,0.79112,0.79043,0.78975,0.78906,0.78838,0.78769,0.78701,0.78632,0.78564,0.78495,0.78427,0.78358,0.7829,0.78221,0.78152,0.78084,0.78015,0.77946,0.77878,0.77809,0.7774,0.77671,0.77602,0.77534,0.77465,0.77396,0.77327,0.77258,0.77189,0.77121,0.77052,0.76983,0.76914,0.76845,0.76776,0.76707,0.76638,0.76569,0.765,0.76431,0.76362,0.76293,0.76224,0.76155,0.76086,0.76017,0.75947,0.75878,0.75809,
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-0.01045,0.01043,0.01041,0.0104,0.01038,0.01036,0.01035,0.01033,0.01031,0.0103,0.01028,0.01026,0.01024,0.01023,0.01021,0.01019,0.01018,0.01016,0.01014,0.01013,0.01011,0.01009,0.01008,0.01006,0.01005,0.01003,0.01001,0.01,0.00998,0.00996,0.00995,0.00993,0.00991,0.0099,0.00988,0.00987,0.00985,0.00983,0.00982,0.0098,0.00979,0.00977,0.00975,0.00974,0.00972,0.00971,0.00969,0.00967,0.00966,0.00964,0.00963,0.00961,0.0096,0.00958,0.00956,0.00955,0.00953,0.00952,0.0095,0.00949,0.00947,0.00946,0.00944,0.00942,0.00941,0.00939,0.00938,0.00936,0.00935,0.00933,0.00932,0.0093,0.00929,0.00927,0.00926,0.00924,0.00923,0.00921,0.0092,0.00918,0.00917,0.00915,0.00914,0.00912,0.00911,0.00909,0.00908,0.00906,0.00905,0.00903,0.00902,0.009,0.00899,0.00897,0.00896,0.00894,0.00893,0.00891,0.0089,0.00888,
-0.00887,0.00886,0.00884,0.00883,0.00881,0.0088,0.00878,0.00877,0.00875,0.00874,0.00873,0.00871,0.0087,0.00868,0.00867,0.00865,0.00864,0.00863,0.00861,0.0086,0.00858,0.00857,0.00856,0.00854,0.00853,0.00851,0.0085,0.00849,0.00847,0.00846,0.00844,0.00843,0.00842,0.0084,0.00839,0.00837,0.00836,0.00835,0.00833,0.00832,0.00831,0.00829,0.00828,0.00827,0.00825,0.00824,0.00822,0.00821,0.0082,0.00818,0.00817,0.00816,0.00814,0.00813,0.00812,0.0081,0.00809,0.00808,0.00806,0.00805,0.00804,0.00802,0.00801,0.008,0.00798,0.00797,0.00796,0.00795,0.00793,0.00792,0.00791,0.00789,0.00788,0.00787,0.00785,0.00784,0.00783,0.00782,0.0078,0.00779,0.00778,0.00776,0.00775,0.00774,0.00773,0.00771,0.0077,0.00769,0.00768,0.00766,0.00765,0.00764,0.00763,0.00761,0.0076,0.00759,0.00758,0.00756,0.00755,0.00754,
-0.00753,0.00751,0.0075,0.00749,0.00748,0.00746,0.00745,0.00744,0.00743,0.00742,0.0074,0.00739,0.00738,0.00737,0.00735,0.00734,0.00733,0.00732,0.00731,0.00729,0.00728,0.00727,0.00726,0.00725,0.00723,0.00722,0.00721,0.0072,0.00719,0.00717,0.00716,0.00715,0.00714,0.00713,0.00712,0.0071,0.00709,0.00708,0.00707,0.00706,0.00705,0.00703,0.00702,0.00701,0.007,0.00699,0.00698,0.00697,0.00695,0.00694,0.00693,0.00692,0.00691,0.0069,0.00689,0.00687,0.00686,0.00685,0.00684,0.00683,0.00682,0.00681,0.00679,0.00678,0.00677,0.00676,0.00675,0.00674,0.00673,0.00672,0.00671,0.00669,0.00668,0.00667,0.00666,0.00665,0.00664,0.00663,0.00662,0.00661,0.0066,0.00659,0.00657,0.00656,0.00655,0.00654,0.00653,0.00652,0.00651,0.0065,0.00649,0.00648,0.00647,0.00646,0.00645,0.00643,0.00642,0.00641,0.0064,0.00639,
-0.00638,0.00637,0.00636,0.00635,0.00634,0.00633,0.00632,0.00631,0.0063,0.00629,0.00628,0.00627,0.00626,0.00625,0.00624,0.00623,0.00622,0.00621,0.00619,0.00618,0.00617,0.00616,0.00615,0.00614,0.00613,0.00612,0.00611,0.0061,0.00609,0.00608,0.00607,0.00606,0.00605,0.00604,0.00603,0.00602,0.00601,0.006,0.00599,0.00598,0.00597,0.00596,0.00595,0.00594,0.00593,0.00592,0.00591,0.0059,0.0059,0.00589,0.00588,0.00587,0.00586,0.00585,0.00584,0.00583,0.00582,0.00581,0.0058,0.00579,0.00578,0.00577,0.00576,0.00575,0.00574,0.00573,0.00572,0.00571,0.0057,0.00569,0.00568,0.00568,0.00567,0.00566,0.00565,0.00564,0.00563,0.00562,0.00561,0.0056,0.00559,0.00558,0.00557,0.00556,0.00555,0.00555,0.00554,0.00553,0.00552,0.00551,0.0055,0.00549,0.00548,0.00547,0.00546,0.00545,0.00544,0.00544,0.00543,0.00542,
-0.00541,0.0054,0.00539,0.00538,0.00537,0.00536,0.00536,0.00535,0.00534,0.00533,0.00532,0.00531,0.0053,0.00529,0.00528,0.00528,0.00527,0.00526,0.00525,0.00524,0.00523,0.00522,0.00522,0.00521,0.0052,0.00519,0.00518,0.00517,0.00516,0.00516,0.00515,0.00514,0.00513,0.00512,0.00511,0.0051,0.0051,0.00509,0.00508,0.00507,0.00506,0.00505,0.00505,0.00504,0.00503,0.00502,0.00501,0.005,0.005,0.00499,0.00498,0.00497,0.00496,0.00495,0.00495,0.00494,0.00493,0.00492,0.00491,0.0049,0.0049,0.00489,0.00488,0.00487,0.00486,0.00486,0.00485,0.00484,0.00483,0.00482,0.00482,0.00481,0.0048,0.00479,0.00478,0.00478,0.00477,0.00476,0.00475,0.00474,0.00474,0.00473,0.00472,0.00471,0.00471,0.0047,0.00469,0.00468,0.00467,0.00467,0.00466,0.00465,0.00464,0.00464,0.00463,0.00462,0.00461,0.0046,0.0046,0.00459};
-
-constexpr double stored_lower_incomplete_gamma_values_n5[] = {0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1e-05,1e-05,1e-05,1e-05,1e-05,1e-05,2e-05,2e-05,2e-05,3e-05,3e-05,3e-05,4e-05,4e-05,5e-05,5e-05,6e-05,6e-05,7e-05,8e-05,8e-05,9e-05,0.0001,0.00011,0.00012,0.00012,0.00013,0.00014,0.00016,0.00017,0.00018,0.00019,0.0002,0.00022,0.00023,0.00024,0.00026,0.00027,0.00029,0.00031,0.00032,0.00034,0.00036,0.00038,0.0004,0.00042,0.00044,0.00046,0.00049,0.00051,0.00053,0.00056,0.00058,0.00061,0.00064,0.00066,0.00069,0.00072,0.00075,0.00078,0.00081,0.00084,0.00088,0.00091,0.00095,0.00098,0.00102,0.00105,0.00109,0.00113,0.00117,0.00121,0.00125,0.0013,0.00134,0.00138,0.00143,0.00147,0.00152,0.00157,0.00162,0.00167,0.00172,0.00177,0.00182,0.00188,
-0.00193,0.00199,0.00204,0.0021,0.00216,0.00222,0.00228,0.00234,0.00241,0.00247,0.00254,0.0026,0.00267,0.00274,0.00281,0.00288,0.00295,0.00302,0.00309,0.00317,0.00325,0.00332,0.0034,0.00348,0.00356,0.00364,0.00373,0.00381,0.0039,0.00398,0.00407,0.00416,0.00425,0.00434,0.00443,0.00453,0.00462,0.00472,0.00481,0.00491,0.00501,0.00511,0.00522,0.00532,0.00542,0.00553,0.00564,0.00575,0.00586,0.00597,0.00608,0.00619,0.00631,0.00643,0.00654,0.00666,0.00678,0.0069,0.00703,0.00715,0.00728,0.0074,0.00753,0.00766,0.00779,0.00793,0.00806,0.00819,0.00833,0.00847,0.00861,0.00875,0.00889,0.00903,0.00918,0.00932,0.00947,0.00962,0.00977,0.00992,0.01008,0.01023,0.01039,0.01055,0.0107,0.01086,0.01103,0.01119,0.01135,0.01152,0.01169,0.01186,0.01203,0.0122,0.01237,0.01255,0.01272,0.0129,0.01308,0.01326,
-0.01345,0.01363,0.01381,0.014,0.01419,0.01438,0.01457,0.01476,0.01496,0.01515,0.01535,0.01555,0.01575,0.01595,0.01616,0.01636,0.01657,0.01677,0.01698,0.0172,0.01741,0.01762,0.01784,0.01805,0.01827,0.01849,0.01872,0.01894,0.01916,0.01939,0.01962,0.01985,0.02008,0.02031,0.02055,0.02078,0.02102,0.02126,0.0215,0.02174,0.02198,0.02223,0.02248,0.02273,0.02298,0.02323,0.02348,0.02373,0.02399,0.02425,0.02451,0.02477,0.02503,0.0253,0.02556,0.02583,0.0261,0.02637,0.02664,0.02692,0.02719,0.02747,0.02775,0.02803,0.02831,0.02859,0.02888,0.02917,0.02945,0.02974,0.03004,0.03033,0.03062,0.03092,0.03122,0.03152,0.03182,0.03212,0.03243,0.03273,0.03304,0.03335,0.03366,0.03397,0.03429,0.03461,0.03492,0.03524,0.03556,0.03589,0.03621,0.03654,0.03686,0.03719,0.03752,0.03785,0.03819,0.03852,0.03886,0.0392,
-0.03954,0.03988,0.04023,0.04057,0.04092,0.04127,0.04162,0.04197,0.04232,0.04268,0.04303,0.04339,0.04375,0.04411,0.04448,0.04484,0.04521,0.04558,0.04595,0.04632,0.04669,0.04707,0.04744,0.04782,0.0482,0.04858,0.04896,0.04935,0.04973,0.05012,0.05051,0.0509,0.0513,0.05169,0.05209,0.05248,0.05288,0.05328,0.05369,0.05409,0.0545,0.0549,0.05531,0.05572,0.05613,0.05655,0.05696,0.05738,0.0578,0.05822,0.05864,0.05907,0.05949,0.05992,0.06035,0.06078,0.06121,0.06164,0.06208,0.06251,0.06295,0.06339,0.06383,0.06427,0.06472,0.06516,0.06561,0.06606,0.06651,0.06697,0.06742,0.06788,0.06833,0.06879,0.06925,0.06971,0.07018,0.07064,0.07111,0.07158,0.07205,0.07252,0.07299,0.07347,0.07395,0.07442,0.0749,0.07539,0.07587,0.07635,0.07684,0.07733,0.07782,0.07831,0.0788,0.07929,0.07979,0.08028,0.08078,0.08128,
-0.08179,0.08229,0.08279,0.0833,0.08381,0.08432,0.08483,0.08534,0.08586,0.08637,0.08689,0.08741,0.08793,0.08845,0.08897,0.0895,0.09003,0.09055,0.09108,0.09162,0.09215,0.09268,0.09322,0.09376,0.09429,0.09484,0.09538,0.09592,0.09647,0.09701,0.09756,0.09811,0.09866,0.09921,0.09977,0.10032,0.10088,0.10144,0.102,0.10256,0.10312,0.10369,0.10426,0.10482,0.10539,0.10596,0.10654,0.10711,0.10768,0.10826,0.10884,0.10942,0.11,0.11058,0.11117,0.11175,0.11234,0.11293,0.11352,0.11411,0.1147,0.1153,0.11589,0.11649,0.11709,0.11769,0.11829,0.11889,0.1195,0.1201,0.12071,0.12132,0.12193,0.12254,0.12316,0.12377,0.12439,0.125,0.12562,0.12624,0.12687,0.12749,0.12811,0.12874,0.12937,0.13,0.13063,0.13126,0.13189,0.13253,0.13316,0.1338,0.13444,0.13508,0.13572,0.13636,0.13701,0.13765,0.1383,0.13895,
-0.1396,0.14025,0.1409,0.14156,0.14221,0.14287,0.14353,0.14418,0.14485,0.14551,0.14617,0.14684,0.1475,0.14817,0.14884,0.14951,0.15018,0.15085,0.15153,0.1522,0.15288,0.15356,0.15424,0.15492,0.1556,0.15628,0.15697,0.15766,0.15834,0.15903,0.15972,0.16041,0.16111,0.1618,0.1625,0.16319,0.16389,0.16459,0.16529,0.16599,0.16669,0.1674,0.1681,0.16881,0.16952,0.17023,0.17094,0.17165,0.17237,0.17308,0.1738,0.17451,0.17523,0.17595,0.17667,0.17739,0.17812,0.17884,0.17957,0.18029,0.18102,0.18175,0.18248,0.18321,0.18395,0.18468,0.18542,0.18615,0.18689,0.18763,0.18837,0.18911,0.18986,0.1906,0.19135,0.19209,0.19284,0.19359,0.19434,0.19509,0.19584,0.1966,0.19735,0.19811,0.19886,0.19962,0.20038,0.20114,0.2019,0.20267,0.20343,0.2042,0.20496,0.20573,0.2065,0.20727,0.20804,0.20881,0.20958,0.21036,
-0.21113,0.21191,0.21269,0.21347,0.21425,0.21503,0.21581,0.21659,0.21738,0.21816,0.21895,0.21974,0.22053,0.22132,0.22211,0.2229,0.22369,0.22449,0.22528,0.22608,0.22688,0.22767,0.22847,0.22928,0.23008,0.23088,0.23168,0.23249,0.23329,0.2341,0.23491,0.23572,0.23653,0.23734,0.23815,0.23897,0.23978,0.24059,0.24141,0.24223,0.24305,0.24387,0.24469,0.24551,0.24633,0.24715,0.24798,0.2488,0.24963,0.25046,0.25129,0.25212,0.25295,0.25378,0.25461,0.25544,0.25628,0.25711,0.25795,0.25879,0.25963,0.26046,0.2613,0.26215,0.26299,0.26383,0.26467,0.26552,0.26637,0.26721,0.26806,0.26891,0.26976,0.27061,0.27146,0.27231,0.27317,0.27402,0.27488,0.27573,0.27659,0.27745,0.2783,0.27916,0.28002,0.28089,0.28175,0.28261,0.28348,0.28434,0.28521,0.28607,0.28694,0.28781,0.28868,0.28955,0.29042,0.29129,0.29217,0.29304,
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-1.92989,1.92999,1.93008,1.93018,1.93028,1.93038,1.93048,1.93057,1.93067,1.93077,1.93087,1.93096,1.93106,1.93116,1.93125,1.93135,1.93145,1.93154,1.93164,1.93174,1.93183,1.93193,1.93202,1.93212,1.93222,1.93231,1.93241,1.9325,1.9326,1.93269,1.93279,1.93288,1.93298,1.93307,1.93316,1.93326,1.93335,1.93345,1.93354,1.93363,1.93373,1.93382,1.93391,1.93401,1.9341,1.93419,1.93429,1.93438,1.93447,1.93456,1.93466,1.93475,1.93484,1.93493,1.93502,1.93512,1.93521,1.9353,1.93539,1.93548,1.93557,1.93566,1.93575,1.93584,1.93593,1.93603,1.93612,1.93621,1.9363,1.93639,1.93648,1.93657,1.93666,1.93674,1.93683,1.93692,1.93701,1.9371,1.93719,1.93728,1.93737,1.93746,1.93754,1.93763,1.93772,1.93781,1.9379,1.93799,1.93807,1.93816,1.93825,1.93834,1.93842,1.93851,1.9386,1.93868,1.93877,1.93886,1.93894,1.93903,
-1.93912,1.9392,1.93929,1.93937,1.93946,1.93955,1.93963,1.93972,1.9398,1.93989,1.93997,1.94006,1.94014,1.94023,1.94031,1.9404,1.94048,1.94057,1.94065,1.94074,1.94082,1.9409,1.94099,1.94107,1.94115,1.94124,1.94132,1.9414,1.94149,1.94157,1.94165,1.94174,1.94182,1.9419,1.94198,1.94207,1.94215,1.94223,1.94231,1.94239,1.94248,1.94256,1.94264,1.94272,1.9428,1.94288,1.94296,1.94305,1.94313,1.94321,1.94329,1.94337,1.94345,1.94353,1.94361,1.94369,1.94377,1.94385,1.94393,1.94401,1.94409,1.94417,1.94425,1.94433,1.94441,1.94449,1.94456,1.94464,1.94472,1.9448,1.94488,1.94496,1.94504,1.94511,1.94519,1.94527,1.94535,1.94543,1.9455,1.94558,1.94566,1.94574,1.94581,1.94589,1.94597,1.94605,1.94612,1.9462,1.94628,1.94635,1.94643,1.94651,1.94658,1.94666,1.94673,1.94681,1.94689,1.94696,1.94704,1.94711,
-1.94719,1.94726,1.94734,1.94741,1.94749,1.94756,1.94764,1.94771,1.94779,1.94786,1.94794,1.94801,1.94809,1.94816,1.94823,1.94831,1.94838,1.94845,1.94853,1.9486,1.94868,1.94875,1.94882,1.94889,1.94897,1.94904,1.94911,1.94919,1.94926,1.94933,1.9494,1.94948,1.94955,1.94962,1.94969,1.94976,1.94984,1.94991,1.94998,1.95005,1.95012,1.95019,1.95027,1.95034,1.95041,1.95048,1.95055,1.95062,1.95069,1.95076,1.95083,1.9509,1.95097,1.95104,1.95111,1.95118,1.95125,1.95132,1.95139,1.95146,1.95153,1.9516,1.95167,1.95174,1.95181,1.95188,1.95195,1.95202,1.95208,1.95215,1.95222,1.95229,1.95236,1.95243,1.95249,1.95256,1.95263,1.9527,1.95277,1.95283,1.9529,1.95297,1.95304,1.9531,1.95317,1.95324,1.95331,1.95337,1.95344,1.95351,1.95357,1.95364,1.95371,1.95377,1.95384,1.95391,1.95397,1.95404,1.9541,1.95417,
-1.95424,1.9543,1.95437,1.95443,1.9545,1.95456,1.95463,1.95469,1.95476,1.95482,1.95489,1.95495,1.95502,1.95508,1.95515,1.95521,1.95528,1.95534,1.95541,1.95547,1.95553,1.9556,1.95566,1.95573,1.95579,1.95585,1.95592,1.95598,1.95604,1.95611,1.95617,1.95623,1.9563,1.95636,1.95642,1.95648,1.95655,1.95661,1.95667,1.95673,1.9568,1.95686,1.95692,1.95698,1.95704,1.95711,1.95717,1.95723,1.95729,1.95735,1.95741,1.95748,1.95754,1.9576,1.95766,1.95772,1.95778,1.95784,1.9579,1.95796,1.95802,1.95808,1.95815,1.95821,1.95827,1.95833,1.95839,1.95845,1.95851,1.95857,1.95863,1.95869,1.95875,1.9588,1.95886,1.95892,1.95898,1.95904,1.9591,1.95916,1.95922,1.95928,1.95934,1.9594,1.95945,1.95951,1.95957,1.95963,1.95969,1.95975,1.9598,1.95986,1.95992,1.95998,1.96004,1.96009,1.96015,1.96021,1.96027,1.96032};
-
-constexpr double stored_gamma_values_n5[] = {1.0,1.0,1.0,1.0,1.0,0.99999,0.99999,0.99999,0.99999,0.99998,0.99998,0.99997,0.99997,0.99996,0.99996,0.99995,0.99995,0.99994,0.99993,0.99993,0.99992,0.99991,0.9999,0.99989,0.99988,0.99987,0.99986,0.99985,0.99984,0.99983,0.99981,0.9998,0.99979,0.99978,0.99976,0.99975,0.99973,0.99972,0.9997,0.99969,0.99967,0.99965,0.99964,0.99962,0.9996,0.99958,0.99957,0.99955,0.99953,0.99951,0.99949,0.99947,0.99945,0.99943,0.9994,0.99938,0.99936,0.99934,0.99931,0.99929,0.99927,0.99924,0.99922,0.99919,0.99917,0.99914,0.99911,0.99909,0.99906,0.99903,0.99901,0.99898,0.99895,0.99892,0.99889,0.99886,0.99883,0.9988,0.99877,0.99874,0.99871,0.99867,0.99864,0.99861,0.99858,0.99854,0.99851,0.99847,0.99844,0.9984,0.99837,0.99833,0.9983,0.99826,0.99822,0.99819,0.99815,0.99811,0.99807,0.99803,
-0.998,0.99796,0.99792,0.99788,0.99784,0.9978,0.99775,0.99771,0.99767,0.99763,0.99759,0.99754,0.9975,0.99746,0.99741,0.99737,0.99732,0.99728,0.99723,0.99718,0.99714,0.99709,0.99704,0.997,0.99695,0.9969,0.99685,0.9968,0.99676,0.99671,0.99666,0.99661,0.99656,0.9965,0.99645,0.9964,0.99635,0.9963,0.99624,0.99619,0.99614,0.99608,0.99603,0.99598,0.99592,0.99587,0.99581,0.99576,0.9957,0.99564,0.99559,0.99553,0.99547,0.99541,0.99536,0.9953,0.99524,0.99518,0.99512,0.99506,0.995,0.99494,0.99488,0.99482,0.99476,0.99469,0.99463,0.99457,0.99451,0.99444,0.99438,0.99431,0.99425,0.99419,0.99412,0.99406,0.99399,0.99392,0.99386,0.99379,0.99372,0.99366,0.99359,0.99352,0.99345,0.99339,0.99332,0.99325,0.99318,0.99311,0.99304,0.99297,0.9929,0.99283,0.99275,0.99268,0.99261,0.99254,0.99247,0.99239,
-0.99232,0.99225,0.99217,0.9921,0.99202,0.99195,0.99187,0.9918,0.99172,0.99164,0.99157,0.99149,0.99141,0.99134,0.99126,0.99118,0.9911,0.99102,0.99094,0.99086,0.99078,0.9907,0.99062,0.99054,0.99046,0.99038,0.9903,0.99022,0.99014,0.99005,0.98997,0.98989,0.9898,0.98972,0.98964,0.98955,0.98947,0.98938,0.9893,0.98921,0.98913,0.98904,0.98895,0.98887,0.98878,0.98869,0.9886,0.98852,0.98843,0.98834,0.98825,0.98816,0.98807,0.98798,0.98789,0.9878,0.98771,0.98762,0.98753,0.98744,0.98735,0.98725,0.98716,0.98707,0.98698,0.98688,0.98679,0.9867,0.9866,0.98651,0.98641,0.98632,0.98622,0.98613,0.98603,0.98593,0.98584,0.98574,0.98564,0.98555,0.98545,0.98535,0.98525,0.98515,0.98506,0.98496,0.98486,0.98476,0.98466,0.98456,0.98446,0.98436,0.98426,0.98415,0.98405,0.98395,0.98385,0.98375,0.98364,0.98354,
-0.98344,0.98333,0.98323,0.98313,0.98302,0.98292,0.98281,0.98271,0.9826,0.9825,0.98239,0.98228,0.98218,0.98207,0.98196,0.98186,0.98175,0.98164,0.98153,0.98142,0.98131,0.98121,0.9811,0.98099,0.98088,0.98077,0.98066,0.98055,0.98043,0.98032,0.98021,0.9801,0.97999,0.97988,0.97976,0.97965,0.97954,0.97942,0.97931,0.9792,0.97908,0.97897,0.97885,0.97874,0.97862,0.97851,0.97839,0.97828,0.97816,0.97805,0.97793,0.97781,0.97769,0.97758,0.97746,0.97734,0.97722,0.9771,0.97699,0.97687,0.97675,0.97663,0.97651,0.97639,0.97627,0.97615,0.97603,0.97591,0.97579,0.97566,0.97554,0.97542,0.9753,0.97518,0.97505,0.97493,0.97481,0.97468,0.97456,0.97443,0.97431,0.97419,0.97406,0.97394,0.97381,0.97369,0.97356,0.97343,0.97331,0.97318,0.97305,0.97293,0.9728,0.97267,0.97255,0.97242,0.97229,0.97216,0.97203,0.9719,
-0.97177,0.97165,0.97152,0.97139,0.97126,0.97113,0.97099,0.97086,0.97073,0.9706,0.97047,0.97034,0.97021,0.97007,0.96994,0.96981,0.96968,0.96954,0.96941,0.96928,0.96914,0.96901,0.96887,0.96874,0.96861,0.96847,0.96833,0.9682,0.96806,0.96793,0.96779,0.96766,0.96752,0.96738,0.96724,0.96711,0.96697,0.96683,0.96669,0.96656,0.96642,0.96628,0.96614,0.966,0.96586,0.96572,0.96558,0.96544,0.9653,0.96516,0.96502,0.96488,0.96474,0.9646,0.96446,0.96432,0.96417,0.96403,0.96389,0.96375,0.9636,0.96346,0.96332,0.96317,0.96303,0.96289,0.96274,0.9626,0.96245,0.96231,0.96216,0.96202,0.96187,0.96173,0.96158,0.96143,0.96129,0.96114,0.961,0.96085,0.9607,0.96055,0.96041,0.96026,0.96011,0.95996,0.95981,0.95967,0.95952,0.95937,0.95922,0.95907,0.95892,0.95877,0.95862,0.95847,0.95832,0.95817,0.95802,0.95787,
-0.95771,0.95756,0.95741,0.95726,0.95711,0.95695,0.9568,0.95665,0.9565,0.95634,0.95619,0.95604,0.95588,0.95573,0.95557,0.95542,0.95527,0.95511,0.95496,0.9548,0.95465,0.95449,0.95433,0.95418,0.95402,0.95387,0.95371,0.95355,0.9534,0.95324,0.95308,0.95292,0.95277,0.95261,0.95245,0.95229,0.95213,0.95197,0.95182,0.95166,0.9515,0.95134,0.95118,0.95102,0.95086,0.9507,0.95054,0.95038,0.95022,0.95006,0.94989,0.94973,0.94957,0.94941,0.94925,0.94909,0.94892,0.94876,0.9486,0.94844,0.94827,0.94811,0.94795,0.94778,0.94762,0.94745,0.94729,0.94713,0.94696,0.9468,0.94663,0.94647,0.9463,0.94614,0.94597,0.9458,0.94564,0.94547,0.94531,0.94514,0.94497,0.94481,0.94464,0.94447,0.9443,0.94414,0.94397,0.9438,0.94363,0.94347,0.9433,0.94313,0.94296,0.94279,0.94262,0.94245,0.94228,0.94211,0.94194,0.94177,
-0.9416,0.94143,0.94126,0.94109,0.94092,0.94075,0.94058,0.94041,0.94023,0.94006,0.93989,0.93972,0.93955,0.93937,0.9392,0.93903,0.93886,0.93868,0.93851,0.93834,0.93816,0.93799,0.93781,0.93764,0.93747,0.93729,0.93712,0.93694,0.93677,0.93659,0.93642,0.93624,0.93607,0.93589,0.93571,0.93554,0.93536,0.93518,0.93501,0.93483,0.93465,0.93448,0.9343,0.93412,0.93394,0.93377,0.93359,0.93341,0.93323,0.93305,0.93288,0.9327,0.93252,0.93234,0.93216,0.93198,0.9318,0.93162,0.93144,0.93126,0.93108,0.9309,0.93072,0.93054,0.93036,0.93018,0.93,0.92982,0.92963,0.92945,0.92927,0.92909,0.92891,0.92873,0.92854,0.92836,0.92818,0.928,0.92781,0.92763,0.92745,0.92726,0.92708,0.9269,0.92671,0.92653,0.92634,0.92616,0.92598,0.92579,0.92561,0.92542,0.92524,0.92505,0.92487,0.92468,0.92449,0.92431,0.92412,0.92394,
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-0.58387,0.58365,0.58343,0.58321,0.58298,0.58276,0.58254,0.58232,0.5821,0.58188,0.58165,0.58143,0.58121,0.58099,0.58077,0.58055,0.58033,0.58011,0.57988,0.57966,0.57944,0.57922,0.579,0.57878,0.57856,0.57834,0.57812,0.5779,0.57768,0.57746,0.57723,0.57701,0.57679,0.57657,0.57635,0.57613,0.57591,0.57569,0.57547,0.57525,0.57503,0.57481,0.57459,0.57437,0.57415,0.57393,0.57371,0.57349,0.57327,0.57305,0.57283,0.57261,0.57239,0.57217,0.57195,0.57174,0.57152,0.5713,0.57108,0.57086,0.57064,0.57042,0.5702,0.56998,0.56976,0.56954,0.56932,0.56911,0.56889,0.56867,0.56845,0.56823,0.56801,0.56779,0.56757,0.56736,0.56714,0.56692,0.5667,0.56648,0.56626,0.56605,0.56583,0.56561,0.56539,0.56517,0.56495,0.56474,0.56452,0.5643,0.56408,0.56387,0.56365,0.56343,0.56321,0.56299,0.56278,0.56256,0.56234,0.56212,
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-0.49889,0.49869,0.49848,0.49828,0.49808,0.49788,0.49768,0.49747,0.49727,0.49707,0.49687,0.49667,0.49646,0.49626,0.49606,0.49586,0.49566,0.49546,0.49526,0.49505,0.49485,0.49465,0.49445,0.49425,0.49405,0.49385,0.49365,0.49344,0.49324,0.49304,0.49284,0.49264,0.49244,0.49224,0.49204,0.49184,0.49164,0.49144,0.49124,0.49104,0.49084,0.49064,0.49044,0.49024,0.49004,0.48984,0.48964,0.48944,0.48924,0.48904,0.48884,0.48864,0.48844,0.48824,0.48804,0.48784,0.48764,0.48744,0.48724,0.48704,0.48684,0.48664,0.48644,0.48624,0.48605,0.48585,0.48565,0.48545,0.48525,0.48505,0.48485,0.48465,0.48446,0.48426,0.48406,0.48386,0.48366,0.48346,0.48327,0.48307,0.48287,0.48267,0.48247,0.48228,0.48208,0.48188,0.48168,0.48148,0.48129,0.48109,0.48089,0.48069,0.4805,0.4803,0.4801,0.4799,0.47971,0.47951,0.47931,0.47912,
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\ No newline at end of file

diff --git a/modules/calib3d/src/usac/homography_solver.cpp b/modules/calib3d/src/usac/homography_solver.cpp
index 3579618..b60e397 100644 (file)
--- a/modules/calib3d/src/usac/homography_solver.cpp
+++ b/modules/calib3d/src/usac/homography_solver.cpp
@@ -18,155 +18,48 @@ public:
         points_mat(&points_), points ((float*) points_.data) {}
 
     int estimate (const std::vector<int>& sample, std::vector<Mat> &models) const override {
-        // OpenCV RHO:
-        const int smpl0 = 4*sample[0], smpl1 = 4*sample[1], smpl2 = 4*sample[2], smpl3 = 4*sample[3];
-        const auto x0 = points[smpl0], y0 = points[smpl0+1], X0 = points[smpl0+2], Y0 = points[smpl0+3];
-        const auto x1 = points[smpl1], y1 = points[smpl1+1], X1 = points[smpl1+2], Y1 = points[smpl1+3];
-        const auto x2 = points[smpl2], y2 = points[smpl2+1], X2 = points[smpl2+2], Y2 = points[smpl2+3];
-        const auto x3 = points[smpl3], y3 = points[smpl3+1], X3 = points[smpl3+2], Y3 = points[smpl3+3];
-        const double x0X0 = x0*X0, x1X1 = x1*X1, x2X2 = x2*X2, x3X3 = x3*X3;
-        const double x0Y0 = x0*Y0, x1Y1 = x1*Y1, x2Y2 = x2*Y2, x3Y3 = x3*Y3;
-        const double y0X0 = y0*X0, y1X1 = y1*X1, y2X2 = y2*X2, y3X3 = y3*X3;
-        const double y0Y0 = y0*Y0, y1Y1 = y1*Y1, y2Y2 = y2*Y2, y3Y3 = y3*Y3;
-
-        double minor[2][4] = {{x0-x2, x1-x2, x2, x3-x2},
-                              {y0-y2, y1-y2, y2, y3-y2}};
-
-        double major[3][8] = {{x2X2-x0X0, x2X2-x1X1, -x2X2, x2X2-x3X3, x2Y2-x0Y0, x2Y2-x1Y1, -x2Y2, x2Y2-x3Y3},
-                              {y2X2-y0X0, y2X2-y1X1, -y2X2, y2X2-y3X3, y2Y2-y0Y0, y2Y2-y1Y1, -y2Y2, y2Y2-y3Y3},
-                              {X0-X2    , X1-X2    , X2   , X3-X2    , Y0-Y2    , Y1-Y2    , Y2   , Y3-Y2    }};
-        /**
-         * int i;
-         * for(i=0;i<8;i++) major[2][i]=-major[2][i];
-         * Eliminate column 0 of rows 1 and 3
-         * R(1)=(x0-x2)*R(1)-(x1-x2)*R(0),     y1'=(y1-y2)(x0-x2)-(x1-x2)(y0-y2)
-         * R(3)=(x0-x2)*R(3)-(x3-x2)*R(0),     y3'=(y3-y2)(x0-x2)-(x3-x2)(y0-y2)
-         */
-
-        double scalar1=minor[0][0], scalar2=minor[0][1];
-        minor[1][1]=minor[1][1]*scalar1-minor[1][0]*scalar2;
-
-        major[0][1]=major[0][1]*scalar1-major[0][0]*scalar2;
-        major[1][1]=major[1][1]*scalar1-major[1][0]*scalar2;
-        major[2][1]=major[2][1]*scalar1-major[2][0]*scalar2;
-
-        major[0][5]=major[0][5]*scalar1-major[0][4]*scalar2;
-        major[1][5]=major[1][5]*scalar1-major[1][4]*scalar2;
-        major[2][5]=major[2][5]*scalar1-major[2][4]*scalar2;
-
-        scalar2=minor[0][3];
-        minor[1][3]=minor[1][3]*scalar1-minor[1][0]*scalar2;
-
-        major[0][3]=major[0][3]*scalar1-major[0][0]*scalar2;
-        major[1][3]=major[1][3]*scalar1-major[1][0]*scalar2;
-        major[2][3]=major[2][3]*scalar1-major[2][0]*scalar2;
-
-        major[0][7]=major[0][7]*scalar1-major[0][4]*scalar2;
-        major[1][7]=major[1][7]*scalar1-major[1][4]*scalar2;
-        major[2][7]=major[2][7]*scalar1-major[2][4]*scalar2;
-
-        /**
-         * Eliminate column 1 of rows 0 and 3
-         * R(3)=y1'*R(3)-y3'*R(1)
-         * R(0)=y1'*R(0)-(y0-y2)*R(1)
-         */
-
-        scalar1=minor[1][1];scalar2=minor[1][3];
-        major[0][3]=major[0][3]*scalar1-major[0][1]*scalar2;
-        major[1][3]=major[1][3]*scalar1-major[1][1]*scalar2;
-        major[2][3]=major[2][3]*scalar1-major[2][1]*scalar2;
-
-        major[0][7]=major[0][7]*scalar1-major[0][5]*scalar2;
-        major[1][7]=major[1][7]*scalar1-major[1][5]*scalar2;
-        major[2][7]=major[2][7]*scalar1-major[2][5]*scalar2;
-
-        scalar2=minor[1][0];
-        minor[0][0]=minor[0][0]*scalar1-minor[0][1]*scalar2;
-
-        major[0][0]=major[0][0]*scalar1-major[0][1]*scalar2;
-        major[1][0]=major[1][0]*scalar1-major[1][1]*scalar2;
-        major[2][0]=major[2][0]*scalar1-major[2][1]*scalar2;
+        int m = 8, n = 9;
+        std::vector<double> A(72, 0);
+        int cnt = 0;
+        for (int i = 0; i < 4; i++) {
+            const int smpl = 4*sample[i];
+            const double x1 = points[smpl], y1 = points[smpl+1], x2 = points[smpl+2], y2 = points[smpl+3];
+
+            A[cnt++] = -x1;
+            A[cnt++] = -y1;
+            A[cnt++] = -1;
+            cnt += 3; // skip zeros
+            A[cnt++] = x2*x1;
+            A[cnt++] = x2*y1;
+            A[cnt++] = x2;
+
+            cnt += 3;
+            A[cnt++] = -x1;
+            A[cnt++] = -y1;
+            A[cnt++] = -1;
+            A[cnt++] = y2*x1;
+            A[cnt++] = y2*y1;
+            A[cnt++] = y2;
+        }
 
-        major[0][4]=major[0][4]*scalar1-major[0][5]*scalar2;
-        major[1][4]=major[1][4]*scalar1-major[1][5]*scalar2;
-        major[2][4]=major[2][4]*scalar1-major[2][5]*scalar2;
+        if (!Math::eliminateUpperTriangular(A, m, n))
+            return 0;
 
-        /**
-         * Eliminate columns 0 and 1 of row 2
-         * R(0)/=x0'
-         * R(1)/=y1'
-         * R(2)-= (x2*R(0) + y2*R(1))
-         */
+        models = std::vector<Mat>{ Mat_<double>(3,3) };
+        auto * h = (double *) models[0].data;
+        h[8] = 1.;
 
-        scalar1=1.0f/minor[0][0];
-        major[0][0]*=scalar1;
-        major[1][0]*=scalar1;
-        major[2][0]*=scalar1;
-        major[0][4]*=scalar1;
-        major[1][4]*=scalar1;
-        major[2][4]*=scalar1;
-
-        scalar1=1.0f/minor[1][1];
-        major[0][1]*=scalar1;
-        major[1][1]*=scalar1;
-        major[2][1]*=scalar1;
-        major[0][5]*=scalar1;
-        major[1][5]*=scalar1;
-        major[2][5]*=scalar1;
-
-        scalar1=minor[0][2];scalar2=minor[1][2];
-        major[0][2]-=major[0][0]*scalar1+major[0][1]*scalar2;
-        major[1][2]-=major[1][0]*scalar1+major[1][1]*scalar2;
-        major[2][2]-=major[2][0]*scalar1+major[2][1]*scalar2;
-
-        major[0][6]-=major[0][4]*scalar1+major[0][5]*scalar2;
-        major[1][6]-=major[1][4]*scalar1+major[1][5]*scalar2;
-        major[2][6]-=major[2][4]*scalar1+major[2][5]*scalar2;
-
-        /* Only major matters now. R(3) and R(7) correspond to the hollowed-out rows. */
-        scalar1=major[0][7];
-        major[1][7]/=scalar1;
-        major[2][7]/=scalar1;
-        const double m17 = major[1][7], m27 = major[2][7];
-        scalar1=major[0][0];major[1][0]-=scalar1*m17;major[2][0]-=scalar1*m27;
-        scalar1=major[0][1];major[1][1]-=scalar1*m17;major[2][1]-=scalar1*m27;
-        scalar1=major[0][2];major[1][2]-=scalar1*m17;major[2][2]-=scalar1*m27;
-        scalar1=major[0][3];major[1][3]-=scalar1*m17;major[2][3]-=scalar1*m27;
-        scalar1=major[0][4];major[1][4]-=scalar1*m17;major[2][4]-=scalar1*m27;
-        scalar1=major[0][5];major[1][5]-=scalar1*m17;major[2][5]-=scalar1*m27;
-        scalar1=major[0][6];major[1][6]-=scalar1*m17;major[2][6]-=scalar1*m27;
-
-        /* One column left (Two in fact, but the last one is the homography) */
-        major[2][3]/=major[1][3];
-        const double m23 = major[2][3];
-
-        major[2][0]-=major[1][0]*m23;
-        major[2][1]-=major[1][1]*m23;
-        major[2][2]-=major[1][2]*m23;
-        major[2][4]-=major[1][4]*m23;
-        major[2][5]-=major[1][5]*m23;
-        major[2][6]-=major[1][6]*m23;
-        major[2][7]-=major[1][7]*m23;
-
-        // check if homography does not contain NaN values
-        for (int i = 0; i < 8; i++)
-            if (std::isnan(major[2][i])) return 0;
-
-        /* Homography is done. */
-        models = std::vector<Mat>(1, Mat_<double>(3,3));
-        auto * H_ = (double *) models[0].data;
-        H_[0]=major[2][0];
-        H_[1]=major[2][1];
-        H_[2]=major[2][2];
-
-        H_[3]=major[2][4];
-        H_[4]=major[2][5];
-        H_[5]=major[2][6];
-
-        H_[6]=major[2][7];
-        H_[7]=major[2][3];
-        H_[8]=1.0;
+        // start from the last row
+        for (int i = m-1; i >= 0; i--) {
+            double acc = 0;
+            for (int j = i+1; j < n; j++)
+                acc -= A[i*n+j]*h[j];
 
+            h[i] = acc / A[i*n+i];
+            // due to numerical errors return 0 solutions
+            if (std::isnan(h[i]))
+                return 0;
+        }
         return 1;
     }
 
@@ -280,7 +173,7 @@ public:
         Matx<double, 9, 9> Vt;
         Vec<double, 9> D;
         if (! eigen(Matx<double, 9, 9>(AtA), D, Vt)) return 0;
-        Mat H = Mat(Vt.row(8).reshape<3,3>());
+        Mat H = Mat_<double>(3, 3, Vt.val + 72/*=8*9*/);
 #endif
 
         models = std::vector<Mat>{ T2.inv() * H * T1 };

diff --git a/modules/calib3d/src/usac/local_optimization.cpp b/modules/calib3d/src/usac/local_optimization.cpp
index fa0cc8f..ff8089b 100644 (file)
--- a/modules/calib3d/src/usac/local_optimization.cpp
+++ b/modules/calib3d/src/usac/local_optimization.cpp
@@ -5,7 +5,6 @@
 #include "../precomp.hpp"
 #include "../usac.hpp"
 #include "opencv2/imgproc/detail/gcgraph.hpp"
-#include "gamma_values.hpp"
 
 namespace cv { namespace usac {
 class GraphCutImpl : public GraphCut {
@@ -47,7 +46,7 @@ public:
 
     bool refineModel (const Mat &best_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
-        if (best_model_score.inlier_number < gc_sample_size)
+        if (best_model_score.inlier_number < estimator->getNonMinimalSampleSize())
             return false;
 
         // improve best model by non minimal estimation
@@ -69,24 +68,12 @@ public:
                             (lo_sampler->generateUniqueRandomSubset(labeling_inliers,
                                    labeling_inliers_size), gc_sample_size, gc_models, weights);
                 } else {
-                    if (iter > 0)
-                        break; // break inliers are not updated
+                    if (iter > 0) break; // break inliers are not updated
                     num_of_estimated_models = estimator->estimateModelNonMinimalSample
                             (labeling_inliers, labeling_inliers_size, gc_models, weights);
                 }
-                if (num_of_estimated_models == 0)
-                    break;
-
-                bool zero_inliers = false;
                 for (int model_idx = 0; model_idx < num_of_estimated_models; model_idx++) {
-                    Score gc_temp_score = quality->getScore(gc_models[model_idx]);
-                    if (gc_temp_score.inlier_number == 0){
-                        zero_inliers = true; break;
-                    }
-
-                    if (best_model_score.isBetter(gc_temp_score))
-                        continue;
-
+                    const Score gc_temp_score = quality->getScore(gc_models[model_idx]);
                     // store the best model from estimated models
                     if (gc_temp_score.isBetter(new_model_score)) {
                         is_best_model_updated = true;
@@ -94,9 +81,6 @@ public:
                         gc_models[model_idx].copyTo(new_model);
                     }
                 }
-
-                if (zero_inliers)
-                    break;
             } // end of inner GC local optimization
         } // end of while loop
 
@@ -119,10 +103,8 @@ private:
         // Estimate the vertex capacities
         for (int pt = 0; pt < points_size; pt++) {
             tmp_squared_distance = errors[pt];
-            if (std::isnan(tmp_squared_distance)) {
-                energies[pt] = std::numeric_limits<float>::max();
-                continue;
-            }
+            if (std::isnan(tmp_squared_distance))
+                tmp_squared_distance = std::numeric_limits<float>::max();
             energy = tmp_squared_distance / sqr_trunc_thr; // Truncated quadratic cost
 
             if (tmp_squared_distance <= sqr_trunc_thr)
@@ -130,8 +112,7 @@ private:
             else
                 graph.addTermWeights(pt, one_minus_lambda * energy, 0);
 
-            if (energy > 1) energy = 1;
-            energies[pt] = energy;
+            energies[pt] = energy > 1 ? 1 : energy;
         }
 
         std::fill(used_edges.begin(), used_edges.end(), false);
@@ -184,7 +165,7 @@ private:
     }
     Ptr<LocalOptimization> clone(int state) const override {
         return makePtr<GraphCutImpl>(estimator->clone(), error->clone(), quality->clone(),
-                neighborhood_graph,lo_sampler->clone(state), sqrt(sqr_trunc_thr / 2),
+                neighborhood_graph,lo_sampler->clone(state), sqr_trunc_thr / 2.25,
                 spatial_coherence, lo_inner_iterations);
     }
 };
@@ -257,12 +238,11 @@ public:
      */
     bool refineModel (const Mat &so_far_the_best_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
-        if (best_model_score.inlier_number < lo_sample_size)
+        if (best_model_score.inlier_number < estimator->getNonMinimalSampleSize())
             return false;
 
         so_far_the_best_model.copyTo(new_model);
         new_model_score = best_model_score;
-
         // get inliers from so far the best model.
         int num_inliers_of_best_model = quality->getInliers(so_far_the_best_model,
                                                            inliers_of_best_model);
@@ -276,7 +256,6 @@ public:
                 num_estimated_models = estimator->estimateModelNonMinimalSample
                         (lo_sampler->generateUniqueRandomSubset(inliers_of_best_model,
                                 num_inliers_of_best_model), lo_sample_size, lo_models, weights);
-                if (num_estimated_models == 0) continue;
             } else {
                 // if model was not updated in first iteration, so break.
                 if (iters > 0) break;
@@ -284,12 +263,11 @@ public:
                 // if it fails -> end Lo.
                 num_estimated_models = estimator->estimateModelNonMinimalSample
                     (inliers_of_best_model, num_inliers_of_best_model, lo_models, weights);
-                if (num_estimated_models == 0) return false;
             }
 
             //////// Choose the best lo_model from estimated lo_models.
             for (int model_idx = 0; model_idx < num_estimated_models; model_idx++) {
-                Score temp_score = quality->getScore(lo_models[model_idx]);
+                const Score temp_score = quality->getScore(lo_models[model_idx]);
                 if (temp_score.isBetter(new_model_score)) {
                     new_model_score = temp_score;
                     lo_models[model_idx].copyTo(new_model);
@@ -323,26 +301,24 @@ public:
                     if (num_estimated_models == 0) break;
 
                     // Get score and update virtual inliers with current threshold
-                    //////// Choose the best lo_iter_model from estimated lo_iter_models.
+                    ////// Choose the best lo_iter_model from estimated lo_iter_models.
                     lo_iter_models[0].copyTo(lo_iter_model);
                     lo_iter_score = quality->getScore(lo_iter_model);
                     for (int model_idx = 1; model_idx < num_estimated_models; model_idx++) {
-                        Score temp_score = quality->getScore(lo_iter_models[model_idx]);
+                        const Score temp_score = quality->getScore(lo_iter_models[model_idx]);
                         if (temp_score.isBetter(lo_iter_score)) {
                             lo_iter_score = temp_score;
                             lo_iter_models[model_idx].copyTo(lo_iter_model);
                         }
                     }
 
-                    virtual_inliers_size = quality->getInliers(lo_iter_model, virtual_inliers, lo_threshold);
+                    if (iterations != lo_iter_max_iterations-1)
+                        virtual_inliers_size = quality->getInliers(lo_iter_model, virtual_inliers, lo_threshold);
                 }
-                if (fabs (lo_threshold - threshold) < FLT_EPSILON) {
-                    // Success, threshold does not differ
-                    // last score correspond to user-defined threshold. Inliers are real.
-                    if (lo_iter_score.isBetter(new_model_score)) {
-                        new_model_score = lo_iter_score;
-                        lo_iter_model.copyTo(new_model);
-                    }
+
+                if (lo_iter_score.isBetter(new_model_score)) {
+                    new_model_score = lo_iter_score;
+                    lo_iter_model.copyTo(new_model);
                 }
             }
 
@@ -375,6 +351,7 @@ private:
     const Ptr<Quality> quality;
     const Ptr<Error> error;
     const Ptr<ModelVerifier> verifier;
+    const GammaValues& gamma_generator;
     // The degrees of freedom of the data from which the model is estimated.
     // E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
     const int degrees_of_freedom;
@@ -394,25 +371,26 @@ private:
     double C_times_two_ad_dof;
     // Calculating the gamma value of (DoF - 1) / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
-    double gamma_value, squared_sigma_max_2, one_over_sigma;
+    double squared_sigma_max_2, one_over_sigma;
     // Calculating the upper incomplete gamma value of (DoF - 1) / 2 with k^2 / 2.
     const double gamma_k;
     // Calculating the lower incomplete gamma value of (DoF - 1) / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
-    double gamma_difference;
+    double max_sigma_sqr;
     const int points_size, number_of_irwls_iters;
     const double maximum_threshold, max_sigma;
 
-    std::vector<double> residuals, sigma_weights, stored_gamma_values;
-    std::vector<int> residuals_idxs;
+    std::vector<double> sqr_residuals, sigma_weights;
+    std::vector<int> sqr_residuals_idxs;
     // Models fit by weighted least-squares fitting
     std::vector<Mat> sigma_models;
     // Points used in the weighted least-squares fitting
     std::vector<int> sigma_inliers;
     // Weights used in the the weighted least-squares fitting
-    int max_lo_sample_size;
+    int max_lo_sample_size, stored_gamma_number_min1;
     double scale_of_stored_gammas;
     RNG rng;
+    const std::vector<double> &stored_gamma_values;
 public:
 
     SigmaConsensusImpl (const Ptr<Estimator> &estimator_, const Ptr<Error> &error_,
@@ -420,103 +398,93 @@ public:
         int max_lo_sample_size_, int number_of_irwls_iters_, int DoF,
         double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
         double maximum_thr) : estimator (estimator_), quality(quality_),
-          error (error_), verifier(verifier_), degrees_of_freedom(DoF),
-          k (sigma_quantile), C(C_), sample_size(estimator_->getMinimalSampleSize()),
+          error (error_), verifier(verifier_),
+          gamma_generator(GammaValues::getSingleton()),
+          degrees_of_freedom(DoF), k (sigma_quantile), C(C_),
+          sample_size(estimator_->getMinimalSampleSize()),
           gamma_k (upper_incomplete_of_sigma_quantile), points_size (quality_->getPointsSize()),
           number_of_irwls_iters (number_of_irwls_iters_),
-          maximum_threshold(maximum_thr), max_sigma (maximum_thr) {
-
+          maximum_threshold(maximum_thr), max_sigma (maximum_thr),
+          stored_gamma_values(gamma_generator.getGammaValues())
+    {
         dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
         two_ad_dof = std::pow(2.0, dof_minus_one_per_two);
         C_times_two_ad_dof = C * two_ad_dof;
-        gamma_value = tgamma(dof_minus_one_per_two);
-        gamma_difference = gamma_value - gamma_k;
         // Calculate 2 * \sigma_{max}^2 a priori
         squared_sigma_max_2 = max_sigma * max_sigma * 2.0;
         // Divide C * 2^(DoF - 1) by \sigma_{max} a priori
         one_over_sigma = C_times_two_ad_dof / max_sigma;
-
-        residuals = std::vector<double>(points_size);
-        residuals_idxs = std::vector<int>(points_size);
+        max_sigma_sqr = squared_sigma_max_2 * 0.5;
+        sqr_residuals = std::vector<double>(points_size);
+        sqr_residuals_idxs = std::vector<int>(points_size);
         sigma_inliers = std::vector<int>(points_size);
         max_lo_sample_size = max_lo_sample_size_;
         sigma_weights = std::vector<double>(points_size);
         sigma_models = std::vector<Mat>(estimator->getMaxNumSolutionsNonMinimal());
-
-        if (DoF == 4) {
-            scale_of_stored_gammas = scale_of_stored_gammas_n4;
-            stored_gamma_values = std::vector<double>(stored_gamma_values_n4,
-                    stored_gamma_values_n4+stored_gamma_number+1);
-        } else if (DoF == 5) {
-            scale_of_stored_gammas = scale_of_stored_gammas_n5;
-            stored_gamma_values = std::vector<double>(stored_gamma_values_n5,
-                    stored_gamma_values_n5+stored_gamma_number+1);
-        } else
-            CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
+        stored_gamma_number_min1 = gamma_generator.getTableSize()-1;
+        scale_of_stored_gammas = gamma_generator.getScaleOfGammaValues();
     }
 
     // https://github.com/danini/magsac
-    bool refineModel (const Mat &in_model, const Score &in_model_score,
+    bool refineModel (const Mat &in_model, const Score &best_model_score,
                       Mat &new_model, Score &new_model_score) override {
         int residual_cnt = 0;
 
-         if (verifier->isModelGood(in_model)) {
-             if (verifier->hasErrors()) {
-                 const std::vector<float> &errors = verifier->getErrors();
-                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
-                     // Calculate the residual of the current point
-                     const auto residual = sqrtf(errors[point_idx]);
-                     if (max_sigma > residual) {
-                         // Store the residual of the current point and its index
-                         residuals[residual_cnt] = residual;
-                         residuals_idxs[residual_cnt++] = point_idx;
-                     }
-
-                     // Interrupt if there is no chance of being better
-                     if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
-                         return false;
-                 }
-             } else {
+        if (verifier->isModelGood(in_model)) {
+            if (verifier->hasErrors()) {
+                const std::vector<float> &errors = verifier->getErrors();
+                for (int point_idx = 0; point_idx < points_size; ++point_idx) {
+                    // Calculate the residual of the current point
+                    const auto residual = sqrtf(errors[point_idx]);
+                    if (max_sigma > residual) {
+                        // Store the residual of the current point and its index
+                        sqr_residuals[residual_cnt] = residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
+                    }
+
+                    // Interrupt if there is no chance of being better
+                    if (residual_cnt + points_size - point_idx < best_model_score.inlier_number)
+                        return false;
+                }
+            } else {
                 error->setModelParameters(in_model);
 
                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
-                    const double residual = sqrtf(error->getError(point_idx));
-                    if (max_sigma > residual) {
+                    const double sqr_residual = error->getError(point_idx);
+                    if (sqr_residual < max_sigma_sqr) {
                         // Store the residual of the current point and its index
-                        residuals[residual_cnt] = residual;
-                        residuals_idxs[residual_cnt++] = point_idx;
+                        sqr_residuals[residual_cnt] = sqr_residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
                     }
 
-                    if (residual_cnt + points_size - point_idx < in_model_score.inlier_number)
+                    if (residual_cnt + points_size - point_idx < best_model_score.inlier_number)
                         return false;
                 }
-             }
-         } else return false;
+            }
+        } else return false;
 
-        // Initialize the polished model with the initial one
-        Mat polished_model;
-        in_model.copyTo(polished_model);
-        // A flag to determine if the initial model has been updated
-        bool updated = false;
+        in_model.copyTo(new_model);
+        new_model_score = Score();
 
         // Do the iteratively re-weighted least squares fitting
-        for (int iterations = 0; iterations < number_of_irwls_iters; ++iterations) {
+        for (int iterations = 0; iterations < number_of_irwls_iters; iterations++) {
             int sigma_inliers_cnt = 0;
             // If the current iteration is not the first, the set of possibly inliers
             // (i.e., points closer than the maximum threshold) have to be recalculated.
             if (iterations > 0) {
-                error->setModelParameters(polished_model);
+                // error->setModelParameters(polished_model);
+                error->setModelParameters(new_model);
                 // Remove everything from the residual vector
                 residual_cnt = 0;
 
                 // Collect the points which are closer than the maximum threshold
                 for (int point_idx = 0; point_idx < points_size; ++point_idx) {
                     // Calculate the residual of the current point
-                    const double residual = error->getError(point_idx);
-                    if (residual < max_sigma) {
+                    const double sqr_residual = error->getError(point_idx);
+                    if (sqr_residual < max_sigma_sqr) {
                         // Store the residual of the current point and its index
-                        residuals[residual_cnt] = residual;
-                        residuals_idxs[residual_cnt++] = point_idx;
+                        sqr_residuals[residual_cnt] = sqr_residual;
+                        sqr_residuals_idxs[residual_cnt++] = point_idx;
                     }
                 }
                 sigma_inliers_cnt = 0;
@@ -524,54 +492,39 @@ public:
 
             // Calculate the weight of each point
             for (int i = 0; i < residual_cnt; i++) {
-                const double residual = residuals[i];
-                const int idx = residuals_idxs[i];
-                // If the residual is ~0, the point fits perfectly and it is handled differently
-                if (residual > std::numeric_limits<double>::epsilon()) {
-                    // Calculate the squared residual
-                    const double squared_residual = residual * residual;
-                    // Get the position of the gamma value in the lookup table
-                    int x = (int)round(scale_of_stored_gammas * squared_residual
-                            / squared_sigma_max_2);
-
-                    // If the sought gamma value is not stored in the lookup, return the closest element
-                    if (x >= stored_gamma_number || x < 0 /*overflow*/) // actual number of gamma values is 1 more, so >=
-                        x  = stored_gamma_number;
-
-                    sigma_inliers[sigma_inliers_cnt] = idx; // store index of point for LSQ
-                    sigma_weights[sigma_inliers_cnt++] = one_over_sigma * (stored_gamma_values[x] - gamma_k);
-                }
+                // Get the position of the gamma value in the lookup table
+                int x = (int)round(scale_of_stored_gammas * sqr_residuals[i]
+                        / squared_sigma_max_2);
+
+                // If the sought gamma value is not stored in the lookup, return the closest element
+                if (x >= stored_gamma_number_min1 || x < 0 /*overflow*/) // actual number of gamma values is 1 more, so >=
+                    x  = stored_gamma_number_min1;
+
+                sigma_inliers[sigma_inliers_cnt] = sqr_residuals_idxs[i]; // store index of point for LSQ
+                sigma_weights[sigma_inliers_cnt++] = one_over_sigma * (stored_gamma_values[x] - gamma_k);
             }
 
+            // random shuffle sigma inliers
             if (sigma_inliers_cnt > max_lo_sample_size)
                 for (int i = sigma_inliers_cnt-1; i > 0; i--) {
                     const int idx = rng.uniform(0, i+1);
                     std::swap(sigma_inliers[i], sigma_inliers[idx]);
                     std::swap(sigma_weights[i], sigma_weights[idx]);
                 }
-            int num_est_models = estimator->estimateModelNonMinimalSample
+            const int num_est_models = estimator->estimateModelNonMinimalSample
                   (sigma_inliers, std::min(max_lo_sample_size, sigma_inliers_cnt),
                           sigma_models, sigma_weights);
 
-            // If there are fewer than the minimum point close to the model, terminate.
-            // Estimate the model parameters using weighted least-squares fitting
-            if (num_est_models == 0) {
-                // If the estimation failed and the iteration was never successfull,
-                // terminate with failure.
-                if (iterations == 0)
-                    return false;
-                // Otherwise, if the iteration was successfull at least one,
-                // simply break it.
-                break;
-            }
+            if (num_est_models == 0)
+                break; // break iterations
 
             // Update the model parameters
-            polished_model = sigma_models[0];
+            Mat polished_model = sigma_models[0];
             if (num_est_models > 1) {
                 // find best over other models
                 Score sigma_best_score = quality->getScore(polished_model);
                 for (int m = 1; m < num_est_models; m++) {
-                    Score sc = quality->getScore(sigma_models[m]);
+                    const Score sc = quality->getScore(sigma_models[m]);
                     if (sc.isBetter(sigma_best_score)) {
                         polished_model = sigma_models[m];
                         sigma_best_score = sc;
@@ -579,21 +532,25 @@ public:
                 }
             }
 
-            // The model has been updated
-            updated = true;
+            const Score polished_model_score = quality->getScore(polished_model);
+            if (polished_model_score.isBetter(new_model_score)){
+                new_model_score = polished_model_score;
+                polished_model.copyTo(new_model);
+            }
         }
 
-        if (updated) {
-            new_model_score = quality->getScore(polished_model);
-            new_model = polished_model;
-            return true;
+        const Score in_model_score = quality->getScore(in_model);
+        if (in_model_score.isBetter(new_model_score)) {
+            new_model_score = in_model_score;
+            in_model.copyTo(new_model);
         }
-        return false;
+
+        return true;
     }
     Ptr<LocalOptimization> clone(int state) const override {
         return makePtr<SigmaConsensusImpl>(estimator->clone(), error->clone(), quality->clone(),
-                verifier->clone(state), max_lo_sample_size, number_of_irwls_iters,
-                degrees_of_freedom, k, gamma_k, C, maximum_threshold);
+                verifier->clone(state), max_lo_sample_size,
+                number_of_irwls_iters, degrees_of_freedom, k, gamma_k, C, maximum_threshold);
     }
 };
 Ptr<SigmaConsensus>
@@ -602,9 +559,9 @@ SigmaConsensus::create(const Ptr<Estimator> &estimator_, const Ptr<Error> &error
         int max_lo_sample_size, int number_of_irwls_iters_, int DoF,
         double sigma_quantile, double upper_incomplete_of_sigma_quantile, double C_,
         double maximum_thr) {
-    return makePtr<SigmaConsensusImpl>(estimator_, error_, quality, verifier_, max_lo_sample_size,
-            number_of_irwls_iters_, DoF, sigma_quantile, upper_incomplete_of_sigma_quantile,
-            C_, maximum_thr);
+    return makePtr<SigmaConsensusImpl>(estimator_, error_, quality, verifier_,
+            max_lo_sample_size, number_of_irwls_iters_, DoF, sigma_quantile,
+            upper_incomplete_of_sigma_quantile, C_, maximum_thr);
 }
 
 /////////////////////////////////////////// FINAL MODEL POLISHER ////////////////////////
@@ -612,7 +569,6 @@ class LeastSquaresPolishingImpl : public LeastSquaresPolishing {
 private:
     const Ptr<Estimator> estimator;
     const Ptr<Quality> quality;
-    Score score;
     int lsq_iterations;
     std::vector<int> inliers;
     std::vector<Mat> models;
@@ -646,8 +602,7 @@ public:
             const int num_models = estimator->estimateModelNonMinimalSample(inliers,
                                                       inlier_number, models, weights);
             for (int model_idx = 0; model_idx < num_models; model_idx++) {
-                score = quality->getScore(models[model_idx]);
-
+                const Score score = quality->getScore(models[model_idx]);
                 if (best_model_score.isBetter(score))
                     continue;
                 if (score.isBetter(out_score)) {

diff --git a/modules/calib3d/src/usac/pnp_solver.cpp b/modules/calib3d/src/usac/pnp_solver.cpp
index 99f344c..e095eef 100644 (file)
--- a/modules/calib3d/src/usac/pnp_solver.cpp
+++ b/modules/calib3d/src/usac/pnp_solver.cpp
@@ -71,7 +71,7 @@ public:
     */
 
     int estimate (const std::vector<int> &sample, std::vector<Mat> &models) const override {
-        std::vector<double> A1 (5*12, 0), A2(7*8, 0);
+        std::vector<double> A1 (60, 0), A2(56, 0); // 5x12, 7x8
 
         int cnt1 = 0, cnt2 = 0;
         for (int i = 0; i < 6; i++) {
@@ -100,6 +100,7 @@ public:
             A2[cnt2++] = -v * Z;
             A2[cnt2++] = -v;
         }
+        // matrix is sparse -> do not test for singularity
         Math::eliminateUpperTriangular(A1, 5, 12);
 
         int offset = 4*12;
@@ -107,7 +108,9 @@ public:
         for (int i = 0; i < 8; i++)
             A2[cnt2++] = A1[offset + i + 4/* skip 4 first cols*/];
 
-        Math::eliminateUpperTriangular(A2, 7, 8);
+        // must be full-rank
+        if (!Math::eliminateUpperTriangular(A2, 7, 8))
+            return 0;
         // fixed scale to 1. In general the projection matrix is up-to-scale.
         // P = alpha * P^, alpha = 1 / P^_[3,4]
 

diff --git a/modules/calib3d/src/usac/quality.cpp b/modules/calib3d/src/usac/quality.cpp
index 8e438e7..856dbb5 100644 (file)
--- a/modules/calib3d/src/usac/quality.cpp
+++ b/modules/calib3d/src/usac/quality.cpp
@@ -4,7 +4,6 @@
 
 #include "../precomp.hpp"
 #include "../usac.hpp"
-#include "gamma_values.hpp"
 
 namespace cv { namespace usac {
 int Quality::getInliers(const Ptr<Error> &error, const Mat &model, std::vector<int> &inliers, double threshold) {
@@ -79,11 +78,13 @@ protected:
     const Ptr<Error> error;
     const int points_size;
     const double threshold;
-    double best_score;
+    double best_score, norm_thr, one_over_thr;
 public:
     MsacQualityImpl (int points_size_, double threshold_, const Ptr<Error> &error_)
             : error (error_), points_size (points_size_), threshold (threshold_) {
         best_score = std::numeric_limits<double>::max();
+        norm_thr = threshold*9/4;
+        one_over_thr = 1 / norm_thr;
     }
 
     inline Score getScore (const Mat &model) const override {
@@ -92,12 +93,12 @@ public:
         int inlier_number = 0;
         for (int point = 0; point < points_size; point++) {
             err = error->getError(point);
-            if (err < threshold) {
-                sum_errors += err;
-                inlier_number++;
-            } else
-                sum_errors += threshold;
-            if (sum_errors > best_score)
+            if (err < norm_thr) {
+                sum_errors -= (1 - err * one_over_thr);
+                if (err < threshold)
+                    inlier_number++;
+            }
+            if (sum_errors - points_size + point > best_score)
                 break;
         }
         return Score(inlier_number, sum_errors);
@@ -127,17 +128,16 @@ Ptr<MsacQuality> MsacQuality::create(int points_size_, double threshold_,
 class MagsacQualityImpl : public MagsacQuality {
 private:
     const Ptr<Error> error;
+    const GammaValues& gamma_generator;
     const int points_size;
 
     // for example, maximum standard deviation of noise.
-    const double maximum_threshold, tentative_inlier_threshold;
+    const double maximum_threshold_sqr, tentative_inlier_threshold;
     // The degrees of freedom of the data from which the model is estimated.
     // E.g., for models coming from point correspondences (x1,y1,x2,y2), it is 4.
     const int degrees_of_freedom;
     // A 0.99 quantile of the Chi^2-distribution to convert sigma values to residuals
     const double k;
-    // A multiplier to convert residual values to sigmas
-    float threshold_to_sigma_multiplier;
     // Calculating k^2 / 2 which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
     double squared_k_per_2;
@@ -167,54 +167,57 @@ private:
     float maximum_sigma_2_per_2;
     // Calculate 2 * \sigma_{max}^2
     float maximum_sigma_2_times_2;
-    // Calculate the loss implied by an outlier
-    double outlier_loss;
     // Calculating 2^(DoF + 1) / \sigma_{max} which will be used for the estimation and,
     // due to being constant, it is better to calculate it a priori.
     double two_ad_dof_plus_one_per_maximum_sigma;
     double scale_of_stored_incomplete_gammas;
-    std::vector<double> stored_complete_gamma_values, stored_lower_incomplete_gamma_values;
+    double max_loss;
+    const std::vector<double> &stored_complete_gamma_values, &stored_lower_incomplete_gamma_values;
+    int stored_incomplete_gamma_number_min1;
 public:
 
     MagsacQualityImpl (double maximum_thr, int points_size_, const Ptr<Error> &error_,
                        double tentative_inlier_threshold_, int DoF, double sigma_quantile,
                        double upper_incomplete_of_sigma_quantile,
                        double lower_incomplete_of_sigma_quantile, double C_)
-            : error (error_), points_size(points_size_), maximum_threshold(maximum_thr),
+            : error (error_), gamma_generator(GammaValues::getSingleton()), points_size(points_size_),
+            maximum_threshold_sqr(maximum_thr*maximum_thr),
             tentative_inlier_threshold(tentative_inlier_threshold_), degrees_of_freedom(DoF),
             k(sigma_quantile), C(C_), gamma_value_of_k (upper_incomplete_of_sigma_quantile),
-            lower_gamma_value_of_k (lower_incomplete_of_sigma_quantile) {
+            lower_gamma_value_of_k (lower_incomplete_of_sigma_quantile),
+            stored_complete_gamma_values(gamma_generator.getCompleteGammaValues()),
+            stored_lower_incomplete_gamma_values(gamma_generator.getIncompleteGammaValues())
+    {
         previous_best_loss = std::numeric_limits<double>::max();
-        threshold_to_sigma_multiplier = 1.f / (float)k;
         squared_k_per_2 = k * k / 2.0;
         dof_minus_one_per_two = (degrees_of_freedom - 1.0) / 2.0;
         dof_plus_one_per_two = (degrees_of_freedom + 1.0) / 2.0;
         two_ad_dof_minus_one = std::pow(2.0, dof_minus_one_per_two);
         two_ad_dof_plus_one = std::pow(2.0, dof_plus_one_per_two);
-        maximum_sigma = threshold_to_sigma_multiplier * (float)maximum_threshold;
+        maximum_sigma = (float)sqrt(maximum_threshold_sqr) / (float) k;
         maximum_sigma_2 = maximum_sigma * maximum_sigma;
         maximum_sigma_2_per_2 = maximum_sigma_2 / 2.f;
         maximum_sigma_2_times_2 = maximum_sigma_2 * 2.f;
-        // penalization for outlier
-        outlier_loss = 10 * maximum_sigma * two_ad_dof_minus_one  * lower_gamma_value_of_k;
         two_ad_dof_plus_one_per_maximum_sigma = two_ad_dof_plus_one / maximum_sigma;
-
-        if (DoF == 4) {
-            scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n4;
-            stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n4,
-                      stored_complete_gamma_values_n4+stored_incomplete_gamma_number+1);
-            stored_lower_incomplete_gamma_values = std::vector<double>
-                    (stored_lower_incomplete_gamma_values_n4,
-                     stored_lower_incomplete_gamma_values_n4+stored_incomplete_gamma_number+1);
-        } else if (DoF == 5) {
-            scale_of_stored_incomplete_gammas = scale_of_stored_incomplete_gammas_n5;
-            stored_complete_gamma_values = std::vector<double>(stored_complete_gamma_values_n5,
-                 stored_complete_gamma_values_n5+stored_incomplete_gamma_number+1);
-            stored_lower_incomplete_gamma_values = std::vector<double>
-                    (stored_lower_incomplete_gamma_values_n5,
-                     stored_lower_incomplete_gamma_values_n5+stored_incomplete_gamma_number+1);
-        } else
-            CV_Error(cv::Error::StsNotImplemented, "Sigma values are not generated");
+        scale_of_stored_incomplete_gammas = gamma_generator.getScaleOfGammaCompleteValues();
+        stored_incomplete_gamma_number_min1 = gamma_generator.getTableSize()-1;
+        max_loss = 1e-10;
+        // MAGSAC maximum / minimum loss does not have to be in extrumum residuals
+        // make 50 iterations to find maximum loss
+        const double step = maximum_threshold_sqr / 30;
+        double sqr_res = 0;
+        while (sqr_res < maximum_threshold_sqr) {
+            int x=(int)round(scale_of_stored_incomplete_gammas * sqr_res
+                        / maximum_sigma_2_times_2);
+            if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                x  = stored_incomplete_gamma_number_min1;
+            const double loss = two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                    stored_lower_incomplete_gamma_values[x] + sqr_res * 0.25 *
+                    (stored_complete_gamma_values[x] - gamma_value_of_k));
+            if (max_loss < loss)
+                max_loss = loss;
+            sqr_res += step;
+        }
     }
 
     // https://github.com/danini/magsac
@@ -226,20 +229,20 @@ public:
             const float squared_residual = error->getError(point_idx);
             if (squared_residual < tentative_inlier_threshold)
                 num_tentative_inliers++;
-            if (squared_residual < maximum_threshold) { // consider point as inlier
+            if (squared_residual < maximum_threshold_sqr) { // consider point as inlier
                 // Get the position of the gamma value in the lookup table
                 int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
                         / maximum_sigma_2_times_2);
                 // If the sought gamma value is not stored in the lookup, return the closest element
-                if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
-                    x  = stored_incomplete_gamma_number;
+                if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                    x  = stored_incomplete_gamma_number_min1;
                 // Calculate the loss implied by the current point
-                total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                total_loss -= (1 - two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
                     stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
-                    (stored_complete_gamma_values[x] - gamma_value_of_k));
-            } else total_loss += outlier_loss; // outlier
-            if (total_loss > previous_best_loss)
-                break; // break if total loss is alreay higher than the best one
+                    (stored_complete_gamma_values[x] - gamma_value_of_k)) / max_loss);
+            }
+            if (total_loss - (points_size - point_idx) > previous_best_loss)
+                break;
         }
         return Score(num_tentative_inliers, total_loss);
     }
@@ -251,16 +254,16 @@ public:
             const float squared_residual = errors[point_idx];
             if (squared_residual < tentative_inlier_threshold)
                 num_tentative_inliers++;
-            if (squared_residual < maximum_threshold) {
+            if (squared_residual < maximum_threshold_sqr) {
                 int x=(int)round(scale_of_stored_incomplete_gammas * squared_residual
                                  / maximum_sigma_2_times_2);
-                if (x >= stored_incomplete_gamma_number || x < 0 /*overflow*/)
-                    x  = stored_incomplete_gamma_number;
-                total_loss += two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
+                if (x >= stored_incomplete_gamma_number_min1 || x < 0 /*overflow*/)
+                    x  = stored_incomplete_gamma_number_min1;
+                total_loss -= (1 - two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 *
                         stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 *
-                        (stored_complete_gamma_values[x] - gamma_value_of_k));
-            } else total_loss += outlier_loss;
-            if (total_loss > previous_best_loss)
+                        (stored_complete_gamma_values[x] - gamma_value_of_k)) / max_loss);
+            }
+            if (total_loss - (points_size - point_idx) > previous_best_loss)
                 break;
         }
         return Score(num_tentative_inliers, total_loss);
@@ -279,8 +282,8 @@ public:
     int getPointsSize () const override { return points_size; }
     Ptr<Quality> clone () const override {
         return makePtr<MagsacQualityImpl>(maximum_sigma, points_size, error->clone(),
-                tentative_inlier_threshold, degrees_of_freedom, k, gamma_value_of_k,
-                lower_gamma_value_of_k, C);
+                tentative_inlier_threshold, degrees_of_freedom,
+                k, gamma_value_of_k, lower_gamma_value_of_k, C);
     }
 };
 Ptr<MagsacQuality> MagsacQuality::create(double maximum_thr, int points_size_, const Ptr<Error> &error_,
@@ -354,7 +357,7 @@ private:
     int highest_inlier_number, current_sprt_idx; // i
     // time t_M needed to instantiate a model hypothesis given a sample
     // Let m_S be the number of models that are verified per sample
-    const double inlier_threshold, t_M, m_S;
+    const double inlier_threshold, norm_thr, one_over_thr, t_M, m_S;
 
     double lowest_sum_errors, current_epsilon, current_delta, current_A,
             delta_to_epsilon, complement_delta_to_complement_epsilon;
@@ -371,7 +374,8 @@ public:
           double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model,
           double time_sample, double avg_num_models, ScoreMethod score_type_) : rng(state), err(err_),
           points_size(points_size_), inlier_threshold (inlier_threshold_),
-          t_M (time_sample), m_S (avg_num_models), score_type (score_type_) {
+          norm_thr(inlier_threshold_*9/4), one_over_thr (1/norm_thr), t_M (time_sample),
+          m_S (avg_num_models), score_type (score_type_) {
 
         // Generate array of random points for randomized evaluation
         points_random_pool = std::vector<int> (points_size_);
@@ -439,8 +443,9 @@ public:
                     break;
             }
             if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
-                sum_errors += error < inlier_threshold ? error : inlier_threshold;
-                if (sum_errors > lowest_sum_errors)
+                if (error < norm_thr)
+                    sum_errors -= (1 - error * one_over_thr);
+                if (sum_errors - points_size + tested_point > lowest_sum_errors)
                     break;
             } else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC) {
                 if (tested_inliers + points_size - tested_point < highest_inlier_number)
@@ -455,7 +460,8 @@ public:
             score.inlier_number = tested_inliers;
             if (score_type == ScoreMethod::SCORE_METHOD_MSAC) {
                 score.score = sum_errors;
-                lowest_sum_errors = sum_errors;
+                if (lowest_sum_errors > sum_errors)
+                    lowest_sum_errors = sum_errors;
             } else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC)
                 score.score = -static_cast<double>(tested_inliers);
             else if (score_type == ScoreMethod::SCORE_METHOD_LMEDS)

diff --git a/modules/calib3d/src/usac/ransac_solvers.cpp b/modules/calib3d/src/usac/ransac_solvers.cpp
index 5372dbc..65fa2d3 100644 (file)
--- a/modules/calib3d/src/usac/ransac_solvers.cpp
+++ b/modules/calib3d/src/usac/ransac_solvers.cpp
@@ -119,12 +119,25 @@ public:
         // check if LO
         const bool LO = params->getLO() != LocalOptimMethod::LOCAL_OPTIM_NULL;
         const bool is_magsac = params->getLO() == LocalOptimMethod::LOCAL_OPTIM_SIGMA;
-        const int repeat_magsac = 10;
+        const int max_hyp_test_before_ver = params->getMaxNumHypothesisToTestBeforeRejection();
+        const int repeat_magsac = 10, max_iters_before_LO = params->getMaxItersBeforeLO();
         Score best_score;
         Mat best_model;
         int final_iters;
 
         if (! parallel) {
+            auto update_best = [&] (const Mat &new_model, const Score &new_score) {
+                best_score = new_score;
+                // remember best model
+                new_model.copyTo(best_model);
+                // update quality and verifier to save evaluation time of a model
+                _quality->setBestScore(best_score.score);
+                // update verifier
+                _model_verifier->update(best_score.inlier_number);
+                // update upper bound of iterations
+                return _termination_criteria->update(best_model, best_score.inlier_number);
+            };
+            bool was_LO_run = false;
             Mat non_degenerate_model, lo_model;
             Score current_score, lo_score, non_denegenerate_model_score;
 
@@ -139,65 +152,54 @@ public:
                 const int number_of_models = _estimator->estimateModels(sample, models);
 
                 for (int i = 0; i < number_of_models; i++) {
-                    if (is_magsac && iters % repeat_magsac == 0) {
-                        if (!_local_optimization->refineModel
-                                (models[i], best_score, models[i], current_score))
-                            continue;
-                    } else if (_model_verifier->isModelGood(models[i])) {
-                        if (!_model_verifier->getScore(current_score)) {
-                            if (_model_verifier->hasErrors())
-                                current_score = _quality->getScore(_model_verifier->getErrors());
-                            else current_score = _quality->getScore(models[i]);
-                        }
-                    } else continue;
+                    if (iters < max_hyp_test_before_ver) {
+                        current_score = _quality->getScore(models[i]);
+                    } else {
+                        if (is_magsac && iters % repeat_magsac == 0) {
+                            if (!_local_optimization->refineModel
+                                    (models[i], best_score, models[i], current_score))
+                                continue;
+                        } else if (_model_verifier->isModelGood(models[i])) {
+                            if (!_model_verifier->getScore(current_score)) {
+                                if (_model_verifier->hasErrors())
+                                    current_score = _quality->getScore(_model_verifier->getErrors());
+                                else current_score = _quality->getScore(models[i]);
+                            }
+                        } else continue;
+                    }
 
                     if (current_score.isBetter(best_score)) {
                         if (_degeneracy->recoverIfDegenerate(sample, models[i],
                                 non_degenerate_model, non_denegenerate_model_score)) {
                             // check if best non degenerate model is better than so far the best model
-                            if (non_denegenerate_model_score.isBetter(best_score)) {
-                                best_score = non_denegenerate_model_score;
-                                non_degenerate_model.copyTo(best_model);
-                            } else
-                                // non degenerate models are worse then so far the best model.
-                                continue;
-                        } else {
-                            // copy current score to best score
-                            best_score = current_score;
-                            // remember best model
-                            models[i].copyTo(best_model);
-                        }
-
-                        // update quality to save evaluation time of a model
-                        // with no chance of being better than so-far-the-best
-                        _quality->setBestScore(best_score.score);
-
-                        // update upper bound of iterations
-                        max_iters = _termination_criteria->update
-                                (best_model, best_score.inlier_number);
-                        if (iters > max_iters)
-                            break;
+                            if (non_denegenerate_model_score.isBetter(best_score))
+                                max_iters = update_best(non_degenerate_model, non_denegenerate_model_score);
+                            else continue;
+                        } else max_iters = update_best(models[i], current_score);
 
-                        if (LO) {//} && iters >= max_iters_before_LO) {
+                        if (LO && iters >= max_iters_before_LO) {
                             // do magsac if it wasn't already run
-                            if (is_magsac && iters % repeat_magsac == 0) continue; // magsac has already run
+                            if (is_magsac && iters % repeat_magsac == 0 && iters >= max_hyp_test_before_ver) continue; // magsac has already run
+                            was_LO_run = true;
                             // update model by Local optimization
                             if (_local_optimization->refineModel
-                                    (best_model, best_score, lo_model, lo_score))
-                                if (lo_score.isBetter(best_score)) {
-                                    best_score = lo_score;
-                                    lo_model.copyTo(best_model);
-                                    // update quality and verifier and termination again
-                                    _quality->setBestScore(best_score.score);
-                                    _model_verifier->update(best_score.inlier_number);
-                                    max_iters = _termination_criteria->update
-                                            (best_model, best_score.inlier_number);
-                                    if (iters > max_iters)
-                                        break;
+                                    (best_model, best_score, lo_model, lo_score)) {
+                                if (lo_score.isBetter(best_score)){
+                                    max_iters = update_best(lo_model, lo_score);
                                 }
+                            }
                         }
+                        if (iters > max_iters)
+                            break;
                     } // end of if so far the best score
                 } // end loop of number of models
+                if (LO && !was_LO_run && iters >= max_iters_before_LO) {
+                    was_LO_run = true;
+                    if (_local_optimization->refineModel(best_model, best_score, lo_model, lo_score))
+                        if (lo_score.isBetter(best_score)){
+                            max_iters = update_best(lo_model, lo_score);
+                        }
+                }
             } // end main while loop
 
             final_iters = iters;
@@ -223,7 +225,9 @@ public:
                 Ptr<Degeneracy> degeneracy = _degeneracy->clone(thread_state++);
                 Ptr<Quality> quality = _quality->clone();
                 Ptr<ModelVerifier> model_verifier = _model_verifier->clone(thread_state++); // update verifier
-                Ptr<LocalOptimization> local_optimization = _local_optimization->clone(thread_state++);
+                Ptr<LocalOptimization> local_optimization;
+                if (LO)
+                    local_optimization = _local_optimization->clone(thread_state++);
                 Ptr<TerminationCriteria> termination_criteria = _termination_criteria->clone();
                 Ptr<Sampler> sampler;
                 if (!is_prosac)
@@ -243,8 +247,12 @@ public:
                     new_model.copyTo(best_model_thread);
                     best_model_thread.copyTo(best_models[thread_rng_id]);
                     best_score_all_threads = best_score_thread;
+                    // update upper bound of iterations
+                    return termination_criteria->update
+                            (best_model_thread, best_score_thread.inlier_number);
                 };
 
+                bool was_LO_run = false;
                 for (iters = 0; iters < max_iters && !success; iters++) {
                     success = num_hypothesis_tested++ > max_iters;
 
@@ -274,56 +282,55 @@ public:
 
                     const int number_of_models = estimator->estimateModels(sample, models);
                     for (int i = 0; i < number_of_models; i++) {
-                        if (is_magsac && iters % repeat_magsac == 0) {
-                            if (!local_optimization->refineModel
-                                    (models[i], best_score_thread, models[i], current_score))
-                                continue;
-                        } else if (model_verifier->isModelGood(models[i])) {
-                            if (!model_verifier->getScore(current_score)) {
-                                if (model_verifier->hasErrors())
-                                    current_score = quality->getScore(model_verifier->getErrors());
-                                else current_score = quality->getScore(models[i]);
-                            }
-                        } else continue;
+                        if (iters < max_hyp_test_before_ver) {
+                            current_score = quality->getScore(models[i]);
+                        } else {
+                            if (is_magsac && iters % repeat_magsac == 0) {
+                                if (!local_optimization->refineModel
+                                        (models[i], best_score_thread, models[i], current_score))
+                                    continue;
+                            } else if (model_verifier->isModelGood(models[i])) {
+                                if (!model_verifier->getScore(current_score)) {
+                                    if (model_verifier->hasErrors())
+                                        current_score = quality->getScore(model_verifier->getErrors());
+                                    else current_score = quality->getScore(models[i]);
+                                }
+                            } else continue;
+                        }
 
                         if (current_score.isBetter(best_score_all_threads)) {
                             if (degeneracy->recoverIfDegenerate(sample, models[i],
                                         non_degenerate_model, non_denegenerate_model_score)) {
                                 // check if best non degenerate model is better than so far the best model
                                 if (non_denegenerate_model_score.isBetter(best_score_thread))
-                                    update_best(non_denegenerate_model_score, non_degenerate_model);
-                                else
-                                    // non degenerate models are worse then so far the best model.
-                                    continue;
+                                    max_iters = update_best(non_denegenerate_model_score, non_degenerate_model);
+                                else continue;
                             } else
-                                update_best(current_score, models[i]);
+                                max_iters = update_best(current_score, models[i]);
 
-                            // update upper bound of iterations
-                            max_iters = termination_criteria->update
-                                    (best_model_thread, best_score_thread.inlier_number);
-                            if (num_hypothesis_tested > max_iters) {
-                                success = true; break;
-                            }
-
-                            if (LO) {
+                            if (LO && iters >= max_iters_before_LO) {
                                 // do magsac if it wasn't already run
-                                if (is_magsac && iters % repeat_magsac == 0) continue;
+                                if (is_magsac && iters % repeat_magsac == 0 && iters >= max_hyp_test_before_ver) continue;
+                                was_LO_run = true;
                                 // update model by Local optimizaion
                                 if (local_optimization->refineModel
                                        (best_model_thread, best_score_thread, lo_model, lo_score))
                                     if (lo_score.isBetter(best_score_thread)) {
-                                        update_best(lo_score, lo_model);
-                                        // update termination again
-                                        max_iters = termination_criteria->update
-                                                (best_model_thread, best_score_thread.inlier_number);
-                                        if (num_hypothesis_tested > max_iters) {
-                                            success = true;
-                                            break;
-                                        }
+                                        max_iters = update_best(lo_score, lo_model);
                                     }
                             }
+                            if (num_hypothesis_tested > max_iters) {
+                                success = true; break;
+                            }
                         } // end of if so far the best score
                     } // end loop of number of models
+                    if (LO && !was_LO_run && iters >= max_iters_before_LO) {
+                        was_LO_run = true;
+                        if (_local_optimization->refineModel(best_model, best_score, lo_model, lo_score))
+                            if (lo_score.isBetter(best_score)){
+                                max_iters = update_best(lo_score, lo_model);
+                            }
+                    }
                 } // end of loop over iters
             }}); // end parallel
             ///////////////////////////////////////////////////////////////////////////////////////////////////////
@@ -354,7 +361,6 @@ public:
                     polished_model.copyTo(best_model);
                 }
         }
-
         // ================= here is ending ransac main implementation ===========================
         std::vector<bool> inliers_mask;
         if (params->isMaskRequired()) {
@@ -402,7 +408,7 @@ int mergePoints (InputArray pts1_, InputArray pts2_, Mat &pts, bool ispnp) {
 void saveMask (OutputArray mask, const std::vector<bool> &inliers_mask) {
     if (mask.needed()) {
         const int points_size = (int) inliers_mask.size();
-        mask.create(1, points_size, CV_8U);
+        mask.create(points_size, 1, CV_8U);
         auto * maskptr = mask.getMat().ptr<uchar>();
         for (int i = 0; i < points_size; i++)
             maskptr[i] = (uchar) inliers_mask[i];
@@ -433,7 +439,8 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
                                    ScoreMethod::SCORE_METHOD_MAGSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_SIGMA);
-            params->setLOSampleSize(100);
+            params->setLOSampleSize(params->isHomography() ? 75 : 50);
+            params->setLOIterations(params->isHomography() ? 15 : 10);
             break;
         case USAC_PARALLEL:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
@@ -445,13 +452,15 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
                                    ScoreMethod::SCORE_METHOD_MSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_GC);
+            params->setLOSampleSize(20);
+            params->setLOIterations(25);
             break;
         case USAC_FAST:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_UNIFORM, conf, max_iters,
-                                   ScoreMethod::SCORE_METHOD_RANSAC);
+                                   ScoreMethod::SCORE_METHOD_MSAC);
             params->setLocalOptimization(LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO);
-            params->setLOIterations(7);
-            params->setLOIterativeIters(4);
+            params->setLOIterations(5);
+            params->setLOIterativeIters(3);
             break;
         case USAC_PROSAC:
             params = Model::create(thr, estimator, SamplingMethod::SAMPLING_PROSAC, conf, max_iters,
@@ -465,6 +474,13 @@ void setParameters (int flag, Ptr<Model> &params, EstimationMethod estimator, do
             break;
         default: CV_Error(cv::Error::StsBadFlag, "Incorrect flag for USAC!");
     }
+    // do not do too many iterations for PnP
+    if (estimator == EstimationMethod::P3P) {
+        if (params->getLOInnerMaxIters() > 15)
+            params->setLOIterations(15);
+        params->setLOIterativeIters(0);
+    }
+
     params->maskRequired(mask_needed);
 }
 
@@ -477,7 +493,12 @@ Mat findHomography (InputArray srcPoints, InputArray dstPoints, int method, doub
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel() / ransac_output->getModel().at<double>(2,2);
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(srcPoints.getMat().rows, srcPoints.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 Mat findFundamentalMat( InputArray points1, InputArray points2, int method, double thr,
@@ -489,7 +510,12 @@ Mat findFundamentalMat( InputArray points1, InputArray points2, int method, doub
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel();
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(points1.getMat().rows, points1.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 Mat findEssentialMat (InputArray points1, InputArray points2, InputArray cameraMatrix1,
@@ -501,7 +527,12 @@ Mat findEssentialMat (InputArray points1, InputArray points2, InputArray cameraM
             ransac_output, cameraMatrix1, cameraMatrix1, noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel();
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(points1.getMat().rows, points1.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
@@ -519,7 +550,12 @@ bool solvePnPRansac( InputArray objectPoints, InputArray imagePoints,
         model.col(0).copyTo(rvec);
         model.col(1).copyTo(tvec);
         return true;
-    } else return false;
+    }
+    if (mask.needed()){
+        mask.create(std::max(objectPoints.getMat().rows, objectPoints.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return false;
 }
 
 Mat estimateAffine2D(InputArray from, InputArray to, OutputArray mask, int method,
@@ -531,7 +567,12 @@ Mat estimateAffine2D(InputArray from, InputArray to, OutputArray mask, int metho
             ransac_output, noArray(), noArray(), noArray(), noArray())) {
         saveMask(mask, ransac_output->getInliersMask());
         return ransac_output->getModel().rowRange(0,2);
-    } else return Mat();
+    }
+    if (mask.needed()){
+        mask.create(std::max(from.getMat().rows, from.getMat().cols), 1, CV_8U);
+        mask.setTo(Scalar::all(0));
+    }
+    return Mat();
 }
 
 class ModelImpl : public Model {
@@ -546,14 +587,14 @@ private:
 
     // for neighborhood graph
     int k_nearest_neighbors = 8;//, flann_search_params = 5, num_kd_trees = 1; // for FLANN
-    int cell_size = 25; // pixels, for grid neighbors searching
-    int radius = 20; // pixels, for radius-search neighborhood graph
+    int cell_size = 50; // pixels, for grid neighbors searching
+    int radius = 30; // pixels, for radius-search neighborhood graph
     NeighborSearchMethod neighborsType = NeighborSearchMethod::NEIGH_GRID;
 
     // Local Optimization parameters
     LocalOptimMethod lo = LocalOptimMethod ::LOCAL_OPTIM_INNER_AND_ITER_LO;
-    int lo_sample_size=14, lo_inner_iterations=15, lo_iterative_iterations=5,
-            lo_thr_multiplier=3, lo_iter_sample_size = 30;
+    int lo_sample_size=16, lo_inner_iterations=15, lo_iterative_iterations=8,
+            lo_thr_multiplier=15, lo_iter_sample_size = 30;
 
     // Graph cut parameters
     const double spatial_coherence_term = 0.975;
@@ -563,11 +604,11 @@ private:
 
     // preemptive verification test
     VerificationMethod verifier = VerificationMethod ::SprtVerifier;
-    const int max_hypothesis_test_before_verification = 10;
+    const int max_hypothesis_test_before_verification = 15;
 
     // sprt parameters
-    // lower bound estimate is 1.1% of inliers
-    double sprt_eps = 0.011, sprt_delta = 0.01, avg_num_models, time_for_model_est;
+    // lower bound estimate is 1% of inliers
+    double sprt_eps = 0.01, sprt_delta = 0.008, avg_num_models, time_for_model_est;
 
     // estimator error
     ErrorMetric est_error;
@@ -578,15 +619,16 @@ private:
     const std::vector<int> grid_cell_number = {16, 8, 4, 2};
 
     //for final least squares polisher
-    int final_lsq_iters = 2;
+    int final_lsq_iters = 3;
 
     bool need_mask = true, is_parallel = false;
     int random_generator_state = 0;
+    const int max_iters_before_LO = 100;
 
     // magsac parameters:
-    int DoF = 4;
-    double sigma_quantile = 3.64, upper_incomplete_of_sigma_quantile = 0.00365,
-        lower_incomplete_of_sigma_quantile = 1.30122, C = 0.25, maximum_thr = 10.;
+    int DoF = 2;
+    double sigma_quantile = 3.04, upper_incomplete_of_sigma_quantile = 0.00419,
+        lower_incomplete_of_sigma_quantile = 0.8629, C = 0.5, maximum_thr = 7.5;
 public:
     ModelImpl (double threshold_, EstimationMethod estimator_, SamplingMethod sampler_, double confidence_=0.95,
                int max_iterations_=5000, ScoreMethod score_ =ScoreMethod::SCORE_METHOD_MSAC) {
@@ -603,16 +645,16 @@ public:
                 avg_num_models = 1; time_for_model_est = 50;
                 sample_size = 3; est_error = ErrorMetric ::FORW_REPR_ERR; break;
             case (EstimationMethod::Homography):
-                avg_num_models = 1; time_for_model_est = 90;
+                avg_num_models = 1; time_for_model_est = 150;
                 sample_size = 4; est_error = ErrorMetric ::FORW_REPR_ERR; break;
             case (EstimationMethod::Fundamental):
-                avg_num_models = 2.38; time_for_model_est = 150; maximum_thr = 3;
+                avg_num_models = 2.38; time_for_model_est = 180; maximum_thr = 2.5;
                 sample_size = 7; est_error = ErrorMetric ::SAMPSON_ERR; break;
             case (EstimationMethod::Fundamental8):
-                avg_num_models = 1; time_for_model_est = 100; maximum_thr = 3;
+                avg_num_models = 1; time_for_model_est = 100; maximum_thr = 2.5;
                 sample_size = 8; est_error = ErrorMetric ::SAMPSON_ERR; break;
             case (EstimationMethod::Essential):
-                avg_num_models = 3.93; time_for_model_est = 2000; maximum_thr = 3;
+                avg_num_models = 3.93; time_for_model_est = 1000; maximum_thr = 2.5;
                 sample_size = 5; est_error = ErrorMetric ::SGD_ERR; break;
             case (EstimationMethod::P3P):
                 avg_num_models = 1.38; time_for_model_est = 800;
@@ -620,18 +662,19 @@ public:
             case (EstimationMethod::P6P):
                 avg_num_models = 1; time_for_model_est = 300;
                 sample_size = 6; est_error = ErrorMetric ::RERPOJ; break;
-            default: CV_Assert(0 && "Estimator has not implemented yet!");
+            default: CV_Error(cv::Error::StsNotImplemented, "Estimator has not implemented yet!");
         }
 
         if (estimator_ == EstimationMethod::P3P || estimator_ == EstimationMethod::P6P) {
             neighborsType = NeighborSearchMethod::NEIGH_FLANN_KNN;
             k_nearest_neighbors = 2;
-            DoF = 5;
-            sigma_quantile = 3.88;
-            upper_incomplete_of_sigma_quantile = 0.00458;
-            lower_incomplete_of_sigma_quantile = 1.96032;
-            C = 0.13298;
         }
+        if (estimator == EstimationMethod::Fundamental || estimator == EstimationMethod::Essential) {
+            lo_sample_size = 21;
+            lo_thr_multiplier = 10;
+        }
+        if (estimator == EstimationMethod::Homography)
+            maximum_thr = 8.;
         threshold = threshold_;
     }
     void setVerifier (VerificationMethod verifier_) override { verifier = verifier_; }
@@ -645,6 +688,7 @@ public:
     void setLOIterations (int iters) override { lo_inner_iterations = iters; }
     void setLOIterativeIters (int iters) override {lo_iterative_iterations = iters; }
     void setLOSampleSize (int lo_sample_size_) override { lo_sample_size = lo_sample_size_; }
+    void setThresholdMultiplierLO (double thr_mult) override { lo_thr_multiplier = (int) round(thr_mult); }
     void maskRequired (bool need_mask_) override { need_mask = need_mask_; }
     void setRandomGeneratorState (int state) override { random_generator_state = state; }
     bool isMaskRequired () const override { return need_mask; }
@@ -682,6 +726,7 @@ public:
     VerificationMethod getVerifier () const override { return verifier; }
     SamplingMethod getSampler () const override { return sampler; }
     int getRandomGeneratorState () const override { return random_generator_state; }
+    int getMaxItersBeforeLO () const override { return max_iters_before_LO; }
     double getSPRTdelta () const override { return sprt_delta; }
     double getSPRTepsilon () const override { return sprt_eps; }
     double getSPRTavgNumModels () const override { return avg_num_models; }
@@ -734,7 +779,9 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
             K1 = K1_.getMat(); K1.convertTo(K1, CV_64F);
             if (! dist_coeff1.empty()) {
                 // undistortPoints also calibrate points using K
-                undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                if (points1.isContinuous())
+                     undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                else undistortPoints(points1.getMat().clone(), undist_points1, K1_, dist_coeff1);
                 points_size = mergePoints(undist_points1, points2, points, true);
                 Utils::normalizeAndDecalibPointsPnP (K1, points, calib_points);
             } else {
@@ -750,8 +797,12 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
             K2 = K2_.getMat(); K2.convertTo(K2, CV_64F);
             if (! dist_coeff1.empty() || ! dist_coeff2.empty()) {
                 // undistortPoints also calibrate points using K
-                cv::undistortPoints(points1, undist_points1, K1_, dist_coeff1);
-                cv::undistortPoints(points2, undist_points2, K2_, dist_coeff2);
+                if (points1.isContinuous())
+                     undistortPoints(points1, undist_points1, K1_, dist_coeff1);
+                else undistortPoints(points1.getMat().clone(), undist_points1, K1_, dist_coeff1);
+                if (points2.isContinuous())
+                     undistortPoints(points2, undist_points2, K2_, dist_coeff2);
+                else undistortPoints(points2.getMat().clone(), undist_points2, K2_, dist_coeff2);
                 points_size = mergePoints(undist_points1, undist_points2, calib_points, false);
             } else {
                 points_size = mergePoints(points1, points2, points, false);
@@ -771,7 +822,7 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
         if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_GRID) {
             graph = GridNeighborhoodGraph::create(points, points_size,
                 params->getCellSize(), params->getCellSize(),
-                params->getCellSize(), params->getCellSize());
+                params->getCellSize(), params->getCellSize(), 10);
         } else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_KNN) {
             graph = FlannNeighborhoodGraph::create(points, points_size,params->getKNN(), false, 5, 1);
         } else if (params->getNeighborsSearch() == NeighborSearchMethod::NEIGH_FLANN_RADIUS) {
@@ -802,7 +853,7 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
                         "Cell number in layers must be in decreasing order!");
             layers.emplace_back(GridNeighborhoodGraph::create(points, points_size,
           (int)(img1_width / (float)cell_number), (int)(img1_height / (float)cell_number),
-          (int)(img2_width / (float)cell_number), (int)(img2_height / (float)cell_number)));
+          (int)(img2_width / (float)cell_number), (int)(img2_height / (float)cell_number), 10));
         }
     }
 
@@ -811,8 +862,10 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
         points = calib_points;
         // if maximum calibrated threshold significanlty differs threshold then set upper bound
         if (max_thr > 10*threshold)
-            max_thr = 10*threshold;
+            max_thr = sqrt(10*threshold); // max thr will be squared after
     }
+    if (max_thr < threshold)
+        max_thr = threshold;
 
     switch (params->getError()) {
         case ErrorMetric::SYMM_REPR_ERR:
@@ -936,7 +989,8 @@ bool run (const Ptr<const Model> &params, InputArray points1, InputArray points2
                 lo = GraphCut::create(estimator, error, quality, graph, lo_sampler, threshold,
                    params->getGraphCutSpatialCoherenceTerm(), params->getLOInnerMaxIters()); break;
             case LocalOptimMethod::LOCAL_OPTIM_SIGMA:
-                lo = SigmaConsensus::create(estimator, error, quality, verifier, params->getLOSampleSize(), 1,
+                lo = SigmaConsensus::create(estimator, error, quality, verifier,
+                     params->getLOSampleSize(), params->getLOInnerMaxIters(),
                      params->getDegreesOfFreedom(), params->getSigmaQuantile(),
                      params->getUpperIncompleteOfSigmaQuantile(), params->getC(), max_thr); break;
             default: CV_Error(cv::Error::StsNotImplemented , "Local Optimization is not implemented!");

diff --git a/modules/calib3d/src/usac/sampler.cpp b/modules/calib3d/src/usac/sampler.cpp
index d045e1f..c443728 100644 (file)
--- a/modules/calib3d/src/usac/sampler.cpp
+++ b/modules/calib3d/src/usac/sampler.cpp
@@ -256,8 +256,6 @@ public:
     }
 
     void generateSample (std::vector<int> &sample) override {
-        // std::cout << "PROSAC sampler, termination length " << termination_length << "\n";
-
         if (kth_sample_number > growth_max_samples) {
             // if PROSAC has not converged to solution then do uniform sampling.
             random_gen->generateUniqueRandomSet(sample, sample_size, points_size);

diff --git a/modules/calib3d/src/usac/utils.cpp b/modules/calib3d/src/usac/utils.cpp
index 9a371a4..1c781a7 100644 (file)
--- a/modules/calib3d/src/usac/utils.cpp
+++ b/modules/calib3d/src/usac/utils.cpp
@@ -168,7 +168,7 @@ Vec3d Math::rotMat2RotVec (const Matx33d &R) {
 /*
  * Eliminate matrix of m rows and n columns to be upper triangular.
  */
-void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
+bool Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
     for (int r = 0; r < m; r++){
         double pivot = a[r*n+r];
         int row_with_pivot = r;
@@ -182,7 +182,7 @@ void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
 
         // if pivot value is 0 continue
         if (fabs(pivot) < DBL_EPSILON)
-            continue;
+            return false; // matrix is not full rank -> terminate
 
         // swap row with maximum pivot value with current row
         for (int c = r; c < n; c++)
@@ -190,11 +190,14 @@ void Math::eliminateUpperTriangular (std::vector<double> &a, int m, int n) {
 
         // eliminate other rows
         for (int j = r+1; j < m; j++){
-            const auto fac = a[j*n+r] / pivot;
-            for (int c = r; c < n; c++)
-                a[j*n+c] -= fac * a[r*n+c];
+            const int row_idx1 = j*n, row_idx2 = r*n;
+            const auto fac = a[row_idx1+r] / pivot;
+            a[row_idx1+r] = 0; // zero eliminated element
+            for (int c = r+1; c < n; c++)
+                a[row_idx1+c] -= fac * a[row_idx2+c];
         }
     }
+    return true;
 }
 
 //////////////////////////////////////// RANDOM GENERATOR /////////////////////////////
@@ -467,7 +470,8 @@ private:
     std::vector<std::vector<int>> graph;
 public:
     GridNeighborhoodGraphImpl (const Mat &container_, int points_size,
-          int cell_size_x_img1, int cell_size_y_img1, int cell_size_x_img2, int cell_size_y_img2) {
+          int cell_size_x_img1, int cell_size_y_img1, int cell_size_x_img2, int cell_size_y_img2,
+          int max_neighbors) {
 
         const auto * const container = (float *) container_.data;
         // <int, int, int, int> -> {neighbors set}
@@ -501,11 +505,14 @@ public:
             for (int v_in_cell : neighbors) {
                 // there is always at least one neighbor
                 auto &graph_row = graph[v_in_cell];
-                graph_row = std::vector<int>(neighbors_in_cell-1);
+                graph_row = std::vector<int>(std::min(max_neighbors, neighbors_in_cell-1));
                 int j = 0;
                 for (int n : neighbors)
-                    if (n != v_in_cell)
+                    if (n != v_in_cell){
                         graph_row[j++] = n;
+                        if (j >= max_neighbors)
+                            break;
+                    }
             }
         }
     }
@@ -519,8 +526,8 @@ public:
 
 Ptr<GridNeighborhoodGraph> GridNeighborhoodGraph::create(const Mat &points,
      int points_size, int cell_size_x_img1_, int cell_size_y_img1_,
-     int cell_size_x_img2_, int cell_size_y_img2_) {
+     int cell_size_x_img2_, int cell_size_y_img2_, int max_neighbors) {
     return makePtr<GridNeighborhoodGraphImpl>(points, points_size,
-      cell_size_x_img1_, cell_size_y_img1_, cell_size_x_img2_, cell_size_y_img2_);
+      cell_size_x_img1_, cell_size_y_img1_, cell_size_x_img2_, cell_size_y_img2_, max_neighbors);
 }
 }}
\ No newline at end of file