--- /dev/null
+.. _realTimePoseEstimation:
+
+Real Time pose estimation of a textured object
+**********************************************
+
+Nowadays, augmented reality is one of the top research topic in computer vision and robotics fields. The most elemental problem in augmented reality is the estimation of the camera pose respect of an object in the case of computer vision area to do later some 3D rendering or in the case of robotics obtain an object pose in order to grasp it and do some manipulation. However, this is not a trivial problem to solve due to the fact that the most common issue in image processing is the computational cost of applying a lot of algorithms or mathematical operations for solving a problem which is basic and immediateley for humans.
+
+
+Goal
+====
+
+In this tutorial is explained how to build a real time application to estimate the camera pose in order to track a textured object with six degrees of freedom given a 2D image and its 3D textured model.
+
+The application will have the followings parts:
+
+.. container:: enumeratevisibleitemswithsquare
+
+ + Read 3D textured object model and object mesh.
+ + Take input from Camera or Video.
+ + Extract ORB features and descriptors from the scene.
+ + Match scene descriptors with model descriptors using Flann matcher.
+ + Estimate pose using PnP + Ransac.
+ + Use Linear Kalman Filter to reject bad poses.
+
+
+Theory
+======
+
+In computer vision estimate the camera pose from *n* 3D-to-2D point correspondences is a fundamental and well understood problem. The most general version of the problem requires estimating the six degrees of freedom of the pose and five calibration parameters: focal length,
+principal point, aspect ratio and skew. It could be established with a minimum of 6 correspondences, using the well known Direct Linear Transform (DLT) algorithm. There are, though, several simplifications to the problem which turn into an extensive list of
+different algorithms that improve the accuracy of the DLT.
+
+The most common simplification is to assume known calibration parameters which is the so-called Perspective-*n*-Point problem:
+
+.. image:: images/pnp.jpg
+ :alt: Perspective-n-Point problem scheme
+ :align: center
+
+**Problem Formulation:** Given a set of correspondences between 3D points :math:`p_i` expressed in a world reference frame, and their 2D projections :math:`u_i` onto the image, we seek to retrieve the pose (:math:`R` and :math:`t`) of the camera w.r.t. the world and the focal length :math:`f`.
+
+OpenCV provides three different approaches to solve the Perspective-*n*-Point problem which return :math:`R` and :math:`t`. Then, using the following formula it's possible to project 3D points into the image plane:
+
+.. math::
+
+ s\ \left [ \begin{matrix} u \\ v \\ 1 \end{matrix} \right ] = \left [ \begin{matrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{matrix} \right ] \left [ \begin{matrix} r_{11} & r_{12} & r_{13} & t_1 \\ r_{21} & r_{22} & r_{23} & t_2 \\ r_{31} & r_{32} & r_{33} & t_3 \end{matrix} \right ] \left [ \begin{matrix} X \\ Y \\ Z\\ 1 \end{matrix} \right ]
+
+The complete documentation of how to manage with this equations is in :calib3d:`Camera Calibration and 3D Reconstruction <>`.
+
+Source code
+===========
+
+You can find the source code of this tutorial in the :file:`samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/` folder of the OpenCV source library.
+
+The tutorial consists of two main programs:
+
+**1. Model registration**
+
+This applicaton is exclusive to whom don't have a 3D textured model of the object to be detected. You can use this program to create your own textured 3D model. This program only works for planar objects, then if you want to model an object with complex shape you should use a sophisticated software to create it.
+
+The application needs an input image of the object to be registered and its 3D mesh. We have also to provide the intrinsic parameters of the camera with which the input image was taken. All the files need to be specified using the absolute path or the relative one from your application’s working directory. If none files are specified the program will try to open the provided default parameters.
+
+The application starts up extracting the ORB features and descriptors from the input image and then uses the mesh along with the `Möller–Trumbore intersection algorithm <http://http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm/>`_ to compute the 3D coordinates of the found features. Finally, the 3D points and the descriptors are stored in different lists in a file with YAML format which each row is a different point. The technical background on how to store the files can be found in the :ref:`fileInputOutputXMLYAML` tutorial.
+
+.. image:: images/registration.png
+ :alt: Model registration
+ :align: center
+
+
+**2. Model detection**
+
+The aim of this application is estimate in real time the object pose given its 3D textured model.
+
+The application starts up loading the 3D textured model in YAML file format with the same structure explained in the model registration program. From the scene the ORB features and descriptors are detected and extracted. Then, is used :features2d:`FlannBasedMatcher <flannbasedmatcher>` with :flann:`LshIndexParams <flann-index-t-index>` to do the matching between the scene descriptors and the model descriptors. Using the found matches along with :calib3d:`solvePnPRansac() <solvepnpransac>` function the :math:`R` and :math:`t` of the camera are computed. Finally, a :video:`Linear Kalman Filter <kalmanfilter>` is applied in order to reject bad poses.
+
+
+Explanation
+===========
+
+Here is explained in detail the code for the real time application:
+
+**1. Read 3D textured object model and object mesh.**
+
+In order to load the textured model I implemented the *class* **Model** which has the function *load()* that opens a YAML file and take the stored 3D points with its corresponding descriptors. You can find an example of a 3D textured model in :file:`samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/Data/cookies_ORB.yml` or :download:`download from here <./../../../samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/Data/cookies_ORB.yml>`.
+
+ .. code-block:: cpp
+
+ /** Load a YAML file using OpenCV **/
+ void Model::load(const std::string path)
+ {
+ cv::Mat points3d_mat;
+
+ cv::FileStorage storage(path, cv::FileStorage::READ);
+ storage["points_3d"] >> points3d_mat;
+ storage["descriptors"] >> descriptors_;
+
+ points3d_mat.copyTo(list_points3d_in_);
+
+ storage.release();
+
+ }
+
+In the main program the model is loaded as follows:
+
+ .. code-block:: cpp
+
+ Model model; // instantiate Model object
+ model.load(yml_read_path); // load a 3D textured object model
+
+
+
+In order to read the model mesh I implemented a *class* **Mesh** which has a function *load()* that opens a *.ply file and store the 3D points of the object and also the composed triangles. You can find an example of a model mesh in :file:`samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/Data/box.ply` or :download:`download from here <./../../../samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/Data/box.ply>`.
+
+ .. code-block:: cpp
+
+ /** Load a CSV with *.ply format **/
+ void Mesh::load(const std::string path)
+ {
+
+ // Create the reader
+ CsvReader csvReader(path);
+
+ // Clear previous data
+ list_vertex_.clear();
+ list_triangles_.clear();
+
+ // Read from .ply file
+ csvReader.readPLY(list_vertex_, list_triangles_);
+
+ // Update mesh attributes
+ num_vertexs_ = list_vertex_.size();
+ num_triangles_ = list_triangles_.size();
+
+ }
+
+In the main program the mesh is loaded as follows:
+
+ .. code-block:: cpp
+
+ Mesh mesh; // instantiate Mesh object
+ mesh.load(ply_read_path); // load an object mesh
+
+
+**2. Take input from Camera or Video**
+
+To detect is necessary capture video. It's done loading a recorded video by passing the absolute path where it is located in your machine or using the default camera device:
+
+ .. code-block:: cpp
+
+ cv::VideoCapture cap; // instantiate VideoCapture
+ (argc < 2) ? cap.open(0) : cap.open(argv[1]); // open the default camera device
+ // or a recorder video
+
+ if(!cap.isOpened()) // check if we succeeded
+ {
+ std::cout << "Could not open the camera device" << std::endl;
+ return -1;
+ }
+
+Then the algorithm is computed frame per frame:
+
+ .. code-block:: cpp
+
+ cv::Mat frame, frame_vis;
+
+ while(cap.read(frame) && cv::waitKey(30) != 27) // capture frame until ESC is pressed
+ {
+
+ frame_vis = frame.clone(); // refresh visualisation frame
+
+ // MAIN ALGORITHM
+
+ }
+
+
+**3. Extract ORB features and descriptors from the scene**
+
+The next step is to detect the scene features and extract it descriptors. For this task I implemented a *class* **RobustMatcher** which has a function for keypoints detection and features extraction. You can find it in :file:`samples/cpp/tutorial_code/calib3d/real_time_pose_estimation/src/RobusMatcher.cpp`. In your *RobusMatch* object you can use any of the 2D features detectors of OpenCV. In this case I used ORB features because is based on FAST to detect the keypoints and BRIEF to extract the descriptors which means that is fast and robust to rotations. You can find more detailed information about ORB :features2d:`here <orb>` in the documentation.
+
+The following code is how to instantiate and set the features detector and the descriptors extractor:
+
+ .. code-block:: cpp
+
+ RobustMatcher rmatcher; // instantiate RobustMatcher
+
+ cv::FeatureDetector * detector = new cv::OrbFeatureDetector(numKeyPoints); // instatiate ORB feature detector
+ cv::DescriptorExtractor * extractor = new cv::OrbDescriptorExtractor(); // instatiate ORB descriptor extractor
+
+ rmatcher.setFeatureDetector(detector); // set feature detector
+ rmatcher.setDescriptorExtractor(extractor); // set descriptor extractor
+
+The features and descriptors will be computed by the *RobustMatcher* inside the matching function.
+
+
+**4. Match scene descriptors with model descriptors using Flann matcher**
+
+It is the first step in our detection algorithm. The main idea is to match the scene descriptors with our model descriptors in order to know the 3D coordinates of the found features into the current scene.
+
+First, we have to set which matcher we want to use. In this case is used *FlannBased* matcher which in terms of computational cost is faster than the *BruteForce* matcher as we increase the trained collectction of features. Then, for FlannBased matcher the index created is *Multi-Probe LSH: Efficient Indexing for High-Dimensional Similarity Search* due to *ORB* descriptors are binary.
+
+You can tune the *LSH* and search parameters to improve the matching efficiency:
+
+ .. code-block:: cpp
+
+ cv::Ptr<cv::flann::IndexParams> indexParams = cv::makePtr<cv::flann::LshIndexParams>(6, 12, 1); // instantiate LSH index parameters
+ cv::Ptr<cv::flann::SearchParams> searchParams = cv::makePtr<cv::flann::SearchParams>(50); // instantiate flann search parameters
+
+ cv::DescriptorMatcher * matcher = new cv::FlannBasedMatcher(indexParams, searchParams); // instantiate FlannBased matcher
+ rmatcher.setDescriptorMatcher(matcher); // set matcher
+
+
+Secondly, we have to call the matcher by using *robustMatch()* or *fastRobustMatch()* function. The difference of using this two functions is its computational cost. The first method is slower but more robust at filtering good matches due to that uses two ratio test and a symmetry test. In contrast, the second method is faster but less robust due to that only applies a single ratio test to the matches.
+
+The following code is to get the model 3D points and its descriptors and then call the matcher in the main program:
+
+ .. code-block:: cpp
+
+ // Get the MODEL INFO
+
+ std::vector<cv::Point3f> list_points3d_model = model.get_points3d(); // list with model 3D coordinates
+ cv::Mat descriptors_model = model.get_descriptors(); // list with descriptors of each 3D coordinate
+
+ .. code-block:: cpp
+
+ // -- Step 1: Robust matching between model descriptors and scene descriptors
+
+ std::vector<cv::DMatch> good_matches; // to obtain the model 3D points in the scene
+ std::vector<cv::KeyPoint> keypoints_scene; // to obtain the 2D points of the scene
+
+ if(fast_match)
+ {
+ rmatcher.robustMatch(frame, good_matches, keypoints_scene, descriptors_model);
+ }
+ else
+ {
+ rmatcher.fastRobustMatch(frame, good_matches, keypoints_scene, descriptors_model);
+ }
+
+The following code corresponds to the *robustMatch()* function which belongs to the *RobustMatcher* class. This function uses the given image to detect the keypoints and extract the descriptors, match using *2 Nearest Neighbour* the extracted descriptors with the given model descriptors and vice versa. Then, is applied a ratio test to the two direction matches in order to remove these matches which its distance ratio between the first and second best match is larger than a given threshold. Finally, a symmetry test is applied in order the remove non symmetrical matches.
+
+ .. code-block:: cpp
+
+ void RobustMatcher::robustMatch( const cv::Mat& frame, std::vector<cv::DMatch>& good_matches,
+ std::vector<cv::KeyPoint>& keypoints_frame,
+ const std::vector<cv::KeyPoint>& keypoints_model, const cv::Mat& descriptors_model )
+ {
+
+ // 1a. Detection of the ORB features
+ this->computeKeyPoints(frame, keypoints_frame);
+
+ // 1b. Extraction of the ORB descriptors
+ cv::Mat descriptors_frame;
+ this->computeDescriptors(frame, keypoints_frame, descriptors_frame);
+
+ // 2. Match the two image descriptors
+ std::vector<std::vector<cv::DMatch> > matches12, matches21;
+
+ // 2a. From image 1 to image 2
+ matcher_->knnMatch(descriptors_frame, descriptors_model, matches12, 2); // return 2 nearest neighbours
+
+ // 2b. From image 2 to image 1
+ matcher_->knnMatch(descriptors_model, descriptors_frame, matches21, 2); // return 2 nearest neighbours
+
+ // 3. Remove matches for which NN ratio is > than threshold
+ // clean image 1 -> image 2 matches
+ int removed1 = ratioTest(matches12);
+ // clean image 2 -> image 1 matches
+ int removed2 = ratioTest(matches21);
+
+ // 4. Remove non-symmetrical matches
+ symmetryTest(matches12, matches21, good_matches);
+
+ }
+
+After the matches filtering we have to get the 2D an 3D correspondences using the obtained *DMatches* vector. For more information about :core:`DMatch <dmatch>` check the documentation.
+
+ .. code-block:: cpp
+
+ // -- Step 2: Find out the 2D/3D correspondences
+
+ std::vector<cv::Point3f> list_points3d_model_match; // container for the model 3D coordinates found in the scene
+ std::vector<cv::Point2f> list_points2d_scene_match; // container for the model 2D coordinates found in the scene
+
+ for(unsigned int match_index = 0; match_index < good_matches.size(); ++match_index)
+ {
+ cv::Point3f point3d_model = list_points3d_model[ good_matches[match_index].trainIdx ]; // 3D point from model
+ cv::Point2f point2d_scene = keypoints_scene[ good_matches[match_index].queryIdx ].pt; // 2D point from the scene
+ list_points3d_model_match.push_back(point3d_model); // add 3D point
+ list_points2d_scene_match.push_back(point2d_scene); // add 2D point
+ }
+
+
+**5. Estimate pose using PnP + Ransac**
+
+With the 2D and 3D correspondences we have to apply the PnP algorithm using :calib3d:`solvePnPRansac() <solvepnpransac>` function in order to estimate the camera pose. The reason why we have to use :calib3d:`solvePnPRansac() <solvepnpransac>` instead of :calib3d:`solvePnP() <solvepnp>` is due to the fact that after the matching not all the found correspondences are correct and may be there are bad correspondences or also called *outliers*. The `Random Sample Consensus <http://en.wikipedia.org/wiki/RANSAC>`_ or *Ransac* is a non-deterministic iterative method which estimate parameters of a mathematical model from observed data producing an aproximate result as the number of iterations increase. After appyling *Ransac* all these *outliers* will be eliminated to then estimate the camera pose with a certain probability.
+
+For the camera pose estimation I have implemented a *class* **PnPProblem**. This *class* has 4 atributes: a given calibration matrix, the rotation matrix, the translation matrix and the rotation-translation matrix. To declare it we need the intrinsic calibration parameters of the camera which you will use to estimate the pose. To obtain these parameters you can check :ref:`CameraCalibrationSquareChessBoardTutorial` and :ref:`cameraCalibrationOpenCV` tutorials.
+
+The following code is how to declare the *PnPProblem class* in the main program:
+
+ .. code-block:: cpp
+
+ /*
+ * Set up the intrinsic camera parameters: UVC WEBCAM
+ */
+
+ double f = 55; // focal length in mm
+ double sx = 22.3, sy = 14.9; // sensor size
+ double width = 640, height = 480; // image size
+
+ double params_WEBCAM[] = { width*f/sx, // fx
+ height*f/sy, // fy
+ width/2, // cx
+ height/2}; // cy
+
+ PnPProblem pnp_detection(params_WEBCAM); // instantiate PnPProblem class
+
+The following code is how the *PnPProblem class* initialises its atributes:
+
+ .. code-block:: cpp
+
+ // Custom constructor given the intrinsic camera parameters
+
+ PnPProblem::PnPProblem(const double params[])
+ {
+ _A_matrix = cv::Mat::zeros(3, 3, CV_64FC1); // intrinsic camera parameters
+ _A_matrix.at<double>(0, 0) = params[0]; // [ fx 0 cx ]
+ _A_matrix.at<double>(1, 1) = params[1]; // [ 0 fy cy ]
+ _A_matrix.at<double>(0, 2) = params[2]; // [ 0 0 1 ]
+ _A_matrix.at<double>(1, 2) = params[3];
+ _A_matrix.at<double>(2, 2) = 1;
+ _R_matrix = cv::Mat::zeros(3, 3, CV_64FC1); // rotation matrix
+ _t_matrix = cv::Mat::zeros(3, 1, CV_64FC1); // translation matrix
+ _P_matrix = cv::Mat::zeros(3, 4, CV_64FC1); // rotation-translation matrix
+
+ }
+
+OpenCV provides four PnP methods: ITERATIVE, EPNP, P3P and ? . If we want a real time time application the more suitable methods are EPNP and P3P due to are faster than ITERATIVE finding a solution. Otherwise, EPNP and P3P are not robust especially in front of planar surfaces and sometimes the pose estimation seems to have like a mirror effect. Therefore, in this this tutorial is used ITERATIVE method due to the object to be detected has planar surfaces.
+
+The OpenCV Ransac implementation wants you to provide three parameters: the maximum number of iterations until stop the algorithm, the maximum allowed distance between the observed and computed point projections to consider it an inlier and a threshold of minimum number of inliers found. You can tune these paramaters in order to improve your algorithm performance. Increasing the number of iterations you will have a more accurate solution, but will take more time to find a solution. Increasing the reprojection error will reduce the computation time, but your solution will be unaccurate. Decreasing the minimum number of inliers will reduce the computation time with high probability to obtain a bad solution.
+
+The following parameters works for this application:
+
+ .. code-block:: cpp
+
+ // RANSAC parameters
+
+ int iterationsCount = 500; // number of Ransac iterations.
+ int reprojectionError = 2.0; // maximum allowed distance to consider it an inlier.
+ int minInliersCount = 70; // thresold of found inliers.
+
+
+The following code corresponds to the *estimatePoseRANSAC()* function which belongs to the *PnPProblem class*. This function estimates the rotation and translation matrix given a set of 2D/3D correspondences, the desired PnP method to use, the output inliers container and the Ransac parameters:
+
+ .. code-block:: cpp
+
+ // Estimate the pose given a list of 2D/3D correspondences with RANSAC and the method to use
+
+ void PnPProblem::estimatePoseRANSAC( const std::vector<cv::Point3f> &list_points3d, // list with model 3D coordinates
+ const std::vector<cv::Point2f> &list_points2d, // list with scene 2D coordinates
+ int flags, cv::Mat &inliers, int iterationsCount, // PnP method; inliers container
+ double reprojectionError, int minInliersCount ) // Ransac parameters
+ {
+ cv::Mat distCoeffs = cv::Mat::zeros(4, 1, CV_64FC1); // vector of distortion coefficients
+ cv::Mat rvec = cv::Mat::zeros(3, 1, CV_64FC1); // output rotation vector
+ cv::Mat tvec = cv::Mat::zeros(3, 1, CV_64FC1); // output translation vector
+
+ bool useExtrinsicGuess = false; // if true the function uses the provided rvec and tvec values as
+ // initial approximations of the rotation and translation vectors
+
+ cv::solvePnPRansac( list_points3d, list_points2d, _A_matrix, distCoeffs, rvec, tvec,
+ useExtrinsicGuess, iterationsCount, reprojectionError, minInliersCount,
+ inliers, flags );
+
+ Rodrigues(rvec,_R_matrix); // converts Rotation Vector to Matrix
+ _t_matrix = tvec; // set translation matrix
+
+ this->set_P_matrix(_R_matrix, _t_matrix); // set rotation-translation matrix
+
+ }
+
+In the following code are the 3th and 4th steps of the main algorithm. The first, calling the above function and the second taking the output inliers vector from Ransac to get the 2D scene points for drawing purpose. As seen in the code we must be sure to apply Ransac if we have matches, in the other case, the function :calib3d:`solvePnPRansac() <solvepnpransac>` crashes due to some OpenCV *bug*.
+
+ .. code-block:: cpp
+
+ if(good_matches.size() > 0) // None matches, then RANSAC crashes
+ {
+
+ // -- Step 3: Estimate the pose using RANSAC approach
+ pnp_detection.estimatePoseRANSAC( list_points3d_model_match, list_points2d_scene_match,
+ cv::ITERATIVE, inliers_idx,
+ iterationsCount, reprojectionError, minInliersCount );
+
+
+ // -- Step 4: Catch the inliers keypoints to draw
+ for(int inliers_index = 0; inliers_index < inliers_idx.rows; ++inliers_index)
+ {
+ int n = inliers_idx.at<int>(inliers_index); // i-inlier
+ cv::Point2f point2d = list_points2d_scene_match[n]; // i-inlier point 2D
+ list_points2d_inliers.push_back(point2d); // add i-inlier to list
+ }
+
+
+Finally, once the camera pose has been estimated we can use the :math:`R` and :math:`t` in order to compute the 2D projection onto the image of a given 3D point expressed in a world reference frame using the showed formula on *Theory*.
+
+The following code corresponds to the *backproject3DPoint()* function which belongs to the *PnPProblem class*. This function backproject a given 3D point expressed in a world reference frame onto a 2D image:
+
+ .. code-block:: cpp
+
+ // Backproject a 3D point to 2D using the estimated pose parameters
+
+ cv::Point2f PnPProblem::backproject3DPoint(const cv::Point3f &point3d)
+ {
+ // 3D point vector [x y z 1]'
+ cv::Mat point3d_vec = cv::Mat(4, 1, CV_64FC1);
+ point3d_vec.at<double>(0) = point3d.x;
+ point3d_vec.at<double>(1) = point3d.y;
+ point3d_vec.at<double>(2) = point3d.z;
+ point3d_vec.at<double>(3) = 1;
+
+ // 2D point vector [u v 1]'
+ cv::Mat point2d_vec = cv::Mat(4, 1, CV_64FC1);
+ point2d_vec = _A_matrix * _P_matrix * point3d_vec;
+
+ // Normalization of [u v]'
+ cv::Point2f point2d;
+ point2d.x = point2d_vec.at<double>(0) / point2d_vec.at<double>(2);
+ point2d.y = point2d_vec.at<double>(1) / point2d_vec.at<double>(2);
+
+ return point2d;
+ }
+
+The above function then is used to compute all the 3D points of the object *Mesh* to show the pose of the object.
+
+
+**6. Use Linear Kalman Filter to reject bad poses**
+
+Is it common in computer vision or robotics fields that after applying detection or tracking techniques bad results are obtained due to some sensor errors. In order to avoid these bad detections in this tutorialis explained how to implement a Linear Kalman Filter after getting a good pose estimation. The definition of a good pose is arbitrary, so here we will define good pose as a detection with high number of inliers.
+
+You can find more information about what `Kalman Filter <http://en.wikipedia.org/wiki/Kalman_filter>`_ is. In this tutorial it's used the OpenCV implementation of the :video:`Kalman Filter <kalmanfilter>` based on `Linear Kalman Filter for position and orientation tracking <http://campar.in.tum.de/Chair/KalmanFilter>`_ to set the dynamics and measurement models.
+
+First, we have to define our state vector which will have 18 states: the positional data (x,y,z) with its first and second derivatives (velocity and acceleration), then rotation is added in form of three euler angles (roll, pitch, jaw) together with their first and second derivatives (angular velocity and acceleration)
+
+ .. math::
+
+ X = (x,y,z,\dot x,\dot y,\dot z,\ddot x,\ddot y,\ddot z,\psi,\theta,\phi,\dot \psi,\dot \theta,\dot \phi,\ddot \psi,\ddot \theta,\ddot \phi)^T
+
+Secondly, we have to define the number of measuremnts which will be 6: from :math:`R` and :math:`t` we can extract :math:`(x,y,z)` and :math:`(\psi,\theta,\phi)`. Thirdly, we have t define the number of control actions to apply to the system which in this case will be *zero*. Finally, we have to define the differential time between the measurements which in this case is :math:`1/T`, where *T* is the frame rate of the video.
+
+ .. code-block:: cpp
+
+ cv::KalmanFilter KF; // instantiate Kalman Filter
+
+ int nStates = 18; // the number of states
+ int nMeasurements = 6; // the number of measured states
+ int nInputs = 0; // the number of action control
+
+ double dt = 0.125; // time between measurements (1/FPS)
+
+ initKalmanFilter(KF, nStates, nMeasurements, nInputs, dt); // init function
+
+
+The following code corresponds to the Kalman Filter initialisation. First, is set the process noise, the measurement noise and the error covariance matrix. Secondly, are set the transition matrix which is the dynamic model and then the measurement matrix which is the measurement model.
+
+You can tune the process and measurement noise to improve the Kalman Filter performance. As you reduce the measurement noise the faster will converge but will be more sensible in front of bad measurements.
+
+ .. code-block:: cpp
+
+ void initKalmanFilter(cv::KalmanFilter &KF, int nStates, int nMeasurements, int nInputs, double dt)
+ {
+
+ KF.init(nStates, nMeasurements, nInputs, CV_64F); // init Kalman Filter
+
+ cv::setIdentity(KF.processNoiseCov, cv::Scalar::all(1e-5)); // set process noise
+ cv::setIdentity(KF.measurementNoiseCov, cv::Scalar::all(1e-4)); // set measurement noise
+ cv::setIdentity(KF.errorCovPost, cv::Scalar::all(1)); // error covariance
+
+
+ /** DYNAMIC MODEL **/
+
+ // [1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2 0 0]
+ // [0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
+
+ // position
+ KF.transitionMatrix.at<double>(0,3) = dt;
+ KF.transitionMatrix.at<double>(1,4) = dt;
+ KF.transitionMatrix.at<double>(2,5) = dt;
+ KF.transitionMatrix.at<double>(3,6) = dt;
+ KF.transitionMatrix.at<double>(4,7) = dt;
+ KF.transitionMatrix.at<double>(5,8) = dt;
+ KF.transitionMatrix.at<double>(0,6) = 0.5*pow(dt,2);
+ KF.transitionMatrix.at<double>(1,7) = 0.5*pow(dt,2);
+ KF.transitionMatrix.at<double>(2,8) = 0.5*pow(dt,2);
+
+ // orientation
+ KF.transitionMatrix.at<double>(9,12) = dt;
+ KF.transitionMatrix.at<double>(10,13) = dt;
+ KF.transitionMatrix.at<double>(11,14) = dt;
+ KF.transitionMatrix.at<double>(12,15) = dt;
+ KF.transitionMatrix.at<double>(13,16) = dt;
+ KF.transitionMatrix.at<double>(14,17) = dt;
+ KF.transitionMatrix.at<double>(9,15) = 0.5*pow(dt,2);
+ KF.transitionMatrix.at<double>(10,16) = 0.5*pow(dt,2);
+ KF.transitionMatrix.at<double>(11,17) = 0.5*pow(dt,2);
+
+
+ /** MEASUREMENT MODEL **/
+
+ // [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
+ // [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
+
+ KF.measurementMatrix.at<double>(0,0) = 1; // x
+ KF.measurementMatrix.at<double>(1,1) = 1; // y
+ KF.measurementMatrix.at<double>(2,2) = 1; // z
+ KF.measurementMatrix.at<double>(3,9) = 1; // roll
+ KF.measurementMatrix.at<double>(4,10) = 1; // pitch
+ KF.measurementMatrix.at<double>(5,11) = 1; // yaw
+
+ std::cout << "A " << std::endl << KF.transitionMatrix << std::endl;
+ std::cout << "C " << std::endl << KF.measurementMatrix << std::endl;
+
+ }
+
+In the following code is 5th step of the main algorithm. When the obtained number of inliers after *Ransac* is over the threshold, the measurements matrix is filled and then the Kalman Filter is updated:
+
+ .. code-block:: cpp
+
+ // -- Step 5: Kalman Filter
+
+ // GOOD MEASUREMENT
+ if( inliers_idx.rows >= minInliersKalman )
+ {
+
+ // Get the measured translation
+ cv::Mat translation_measured(3, 1, CV_64F);
+ translation_measured = pnp_detection.get_t_matrix();
+
+ // Get the measured rotation
+ cv::Mat rotation_measured(3, 3, CV_64F);
+ rotation_measured = pnp_detection.get_R_matrix();
+
+ // fill the measurements vector
+ fillMeasurements(measurements, translation_measured, rotation_measured);
+
+ }
+
+ // Instantiate estimated translation and rotation
+ cv::Mat translation_estimated(3, 1, CV_64F);
+ cv::Mat rotation_estimated(3, 3, CV_64F);
+
+ // update the Kalman filter with good measurements
+ updateKalmanFilter( KF, measurements,
+ translation_estimated, rotation_estimated);
+
+The following code corresponds to the *fillMeasurements()* function which converts the measured `Rotation Matrix to Eulers angles <http://euclideanspace.com/maths/geometry/rotations/conversions/matrixToEuler/index.htm>`_ and fill the measurements matrix along with the measured translation vector:
+
+ .. code-block:: cpp
+
+ void fillMeasurements( cv::Mat &measurements,
+ const cv::Mat &translation_measured, const cv::Mat &rotation_measured)
+ {
+ // Convert rotation matrix to euler angles
+ cv::Mat measured_eulers(3, 1, CV_64F);
+ measured_eulers = rot2euler(rotation_measured);
+
+ // Set measurement to predict
+ measurements.at<double>(0) = translation_measured.at<double>(0); // x
+ measurements.at<double>(1) = translation_measured.at<double>(1); // y
+ measurements.at<double>(2) = translation_measured.at<double>(2); // z
+ measurements.at<double>(3) = measured_eulers.at<double>(0); // roll
+ measurements.at<double>(4) = measured_eulers.at<double>(1); // pitch
+ measurements.at<double>(5) = measured_eulers.at<double>(2); // yaw
+ }
+
+
+The following code corresponds to the *updateKalmanFilter()* function which update the Kalman Filter and set the estimated Rotation Matrix and translation vector. The estimated Rotation Matrix comes from the estimated `Euler angles to Rotation Matrix <http://euclideanspace.com/maths/geometry/rotations/conversions/eulerToMatrix/index.htm>`_.
+
+ .. code-block:: cpp
+
+ void updateKalmanFilter( cv::KalmanFilter &KF, cv::Mat &measurement,
+ cv::Mat &translation_estimated, cv::Mat &rotation_estimated )
+ {
+
+ // First predict, to update the internal statePre variable
+ cv::Mat prediction = KF.predict();
+
+ // The "correct" phase that is going to use the predicted value and our measurement
+ cv::Mat estimated = KF.correct(measurement);
+
+ // Estimated translation
+ translation_estimated.at<double>(0) = estimated.at<double>(0);
+ translation_estimated.at<double>(1) = estimated.at<double>(1);
+ translation_estimated.at<double>(2) = estimated.at<double>(2);
+
+ // Estimated euler angles
+ cv::Mat eulers_estimated(3, 1, CV_64F);
+ eulers_estimated.at<double>(0) = estimated.at<double>(9);
+ eulers_estimated.at<double>(1) = estimated.at<double>(10);
+ eulers_estimated.at<double>(2) = estimated.at<double>(11);
+
+ // Convert estimated quaternion to rotation matrix
+ rotation_estimated = euler2rot(eulers_estimated);
+
+ }
+
+The 6th step is set the estimated rotation-translation matrix:
+
+ .. code-block:: cpp
+
+ // -- Step 6: Set estimated projection matrix
+ pnp_detection_est.set_P_matrix(rotation_estimated, translation_estimated);
+
+
+The last and optional step is draw the found pose. To do it I implemented a function to draw all the mesh 3D points and an extra reference axis:
+
+ .. code-block:: cpp
+
+ // -- Step X: Draw pose
+
+ drawObjectMesh(frame_vis, &mesh, &pnp_detection, green); // draw current pose
+ drawObjectMesh(frame_vis, &mesh, &pnp_detection_est, yellow); // draw estimated pose
+
+ double l = 5;
+ std::vector<cv::Point2f> pose_points2d;
+ pose_points2d.push_back(pnp_detection_est.backproject3DPoint(cv::Point3f(0,0,0))); // axis center
+ pose_points2d.push_back(pnp_detection_est.backproject3DPoint(cv::Point3f(l,0,0))); // axis x
+ pose_points2d.push_back(pnp_detection_est.backproject3DPoint(cv::Point3f(0,l,0))); // axis y
+ pose_points2d.push_back(pnp_detection_est.backproject3DPoint(cv::Point3f(0,0,l))); // axis z
+ draw3DCoordinateAxes(frame_vis, pose_points2d); // draw axes
+
+
+Results
+=======
+
+The following videos are the results of pose estimation in real time using the explained detection algorithm with the following parameters:
+
+ .. code-block:: cpp
+
+ // Robust Matcher parameters
+
+ int numKeyPoints = 2000; // number of detected keypoints
+ float ratio = 0.70f; // ratio test
+ bool fast_match = true; // fastRobustMatch() or robustMatch()
+
+
+ // RANSAC parameters
+
+ int iterationsCount = 500; // number of Ransac iterations.
+ int reprojectionError = 2.0; // maximum allowed distance to consider it an inlier.
+ int minInliersCount = 70; // thresold of found inliers.
+
+
+ // Kalman Filter parameters
+
+ int minInliersKalman = 30; // Kalman threshold updating
+
+
+.. raw:: html
+
+ <div align="center">
+ <iframe width="560" height="315" src="//www.youtube.com/embed/msFFuHsiUns?rel=0" frameborder="0" allowfullscreen></iframe>
+ </div>
+
+
projects / platform / upstream / opencv.git / commitdiff
