examples/robust_curve_fitting.cc

   1 // Ceres Solver - A fast non-linear least squares minimizer
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  28 //
  29 // Author: sameeragarwal@google.com (Sameer Agarwal)
  30
  31 #include "ceres/ceres.h"
  32 #include "glog/logging.h"
  33
  34 // Data generated using the following octave code.
  35 //   randn('seed', 23497);
  36 //   m = 0.3;
  37 //   c = 0.1;
  38 //   x=[0:0.075:5];
  39 //   y = exp(m * x + c);
  40 //   noise = randn(size(x)) * 0.2;
  41 //   outlier_noise = rand(size(x)) < 0.05;
  42 //   y_observed = y + noise + outlier_noise;
  43 //   data = [x', y_observed'];
  44
  45 const int kNumObservations = 67;
  46 const double data[] = {
  47 0.000000e+00, 1.133898e+00,
  48 7.500000e-02, 1.334902e+00,
  49 1.500000e-01, 1.213546e+00,
  50 2.250000e-01, 1.252016e+00,
  51 3.000000e-01, 1.392265e+00,
  52 3.750000e-01, 1.314458e+00,
  53 4.500000e-01, 1.472541e+00,
  54 5.250000e-01, 1.536218e+00,
  55 6.000000e-01, 1.355679e+00,
  56 6.750000e-01, 1.463566e+00,
  57 7.500000e-01, 1.490201e+00,
  58 8.250000e-01, 1.658699e+00,
  59 9.000000e-01, 1.067574e+00,
  60 9.750000e-01, 1.464629e+00,
  61 1.050000e+00, 1.402653e+00,
  62 1.125000e+00, 1.713141e+00,
  63 1.200000e+00, 1.527021e+00,
  64 1.275000e+00, 1.702632e+00,
  65 1.350000e+00, 1.423899e+00,
  66 1.425000e+00, 5.543078e+00, // Outlier point
  67 1.500000e+00, 5.664015e+00, // Outlier point
  68 1.575000e+00, 1.732484e+00,
  69 1.650000e+00, 1.543296e+00,
  70 1.725000e+00, 1.959523e+00,
  71 1.800000e+00, 1.685132e+00,
  72 1.875000e+00, 1.951791e+00,
  73 1.950000e+00, 2.095346e+00,
  74 2.025000e+00, 2.361460e+00,
  75 2.100000e+00, 2.169119e+00,
  76 2.175000e+00, 2.061745e+00,
  77 2.250000e+00, 2.178641e+00,
  78 2.325000e+00, 2.104346e+00,
  79 2.400000e+00, 2.584470e+00,
  80 2.475000e+00, 1.914158e+00,
  81 2.550000e+00, 2.368375e+00,
  82 2.625000e+00, 2.686125e+00,
  83 2.700000e+00, 2.712395e+00,
  84 2.775000e+00, 2.499511e+00,
  85 2.850000e+00, 2.558897e+00,
  86 2.925000e+00, 2.309154e+00,
  87 3.000000e+00, 2.869503e+00,
  88 3.075000e+00, 3.116645e+00,
  89 3.150000e+00, 3.094907e+00,
  90 3.225000e+00, 2.471759e+00,
  91 3.300000e+00, 3.017131e+00,
  92 3.375000e+00, 3.232381e+00,
  93 3.450000e+00, 2.944596e+00,
  94 3.525000e+00, 3.385343e+00,
  95 3.600000e+00, 3.199826e+00,
  96 3.675000e+00, 3.423039e+00,
  97 3.750000e+00, 3.621552e+00,
  98 3.825000e+00, 3.559255e+00,
  99 3.900000e+00, 3.530713e+00,
 100 3.975000e+00, 3.561766e+00,
 101 4.050000e+00, 3.544574e+00,
 102 4.125000e+00, 3.867945e+00,
 103 4.200000e+00, 4.049776e+00,
 104 4.275000e+00, 3.885601e+00,
 105 4.350000e+00, 4.110505e+00,
 106 4.425000e+00, 4.345320e+00,
 107 4.500000e+00, 4.161241e+00,
 108 4.575000e+00, 4.363407e+00,
 109 4.650000e+00, 4.161576e+00,
 110 4.725000e+00, 4.619728e+00,
 111 4.800000e+00, 4.737410e+00,
 112 4.875000e+00, 4.727863e+00,
 113 4.950000e+00, 4.669206e+00
 114 };
 115
 116 using ceres::AutoDiffCostFunction;
 117 using ceres::CostFunction;
 118 using ceres::CauchyLoss;
 119 using ceres::Problem;
 120 using ceres::Solve;
 121 using ceres::Solver;
 122
 123 struct ExponentialResidual {
 124   ExponentialResidual(double x, double y)
 125       : x_(x), y_(y) {}
 126
 127   template <typename T> bool operator()(const T* const m,
 128                                         const T* const c,
 129                                         T* residual) const {
 130     residual[0] = y_ - exp(m[0] * x_ + c[0]);
 131     return true;
 132   }
 133
 134  private:
 135   const double x_;
 136   const double y_;
 137 };
 138
 139 int main(int argc, char** argv) {
 140   google::InitGoogleLogging(argv[0]);
 141
 142   double m = 0.0;
 143   double c = 0.0;
 144
 145   Problem problem;
 146   for (int i = 0; i < kNumObservations; ++i) {
 147     CostFunction* cost_function =
 148         new AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>(
 149             new ExponentialResidual(data[2 * i], data[2 * i + 1]));
 150     problem.AddResidualBlock(cost_function,
 151                              new CauchyLoss(0.5),
 152                              &m, &c);
 153   }
 154
 155   Solver::Options options;
 156   options.linear_solver_type = ceres::DENSE_QR;
 157   options.minimizer_progress_to_stdout = true;
 158
 159   Solver::Summary summary;
 160   Solve(options, &problem, &summary);
 161   std::cout << summary.BriefReport() << "\n";
 162   std::cout << "Initial m: " << 0.0 << " c: " << 0.0 << "\n";
 163   std::cout << "Final   m: " << m << " c: " << c << "\n";
 164   return 0;
 165 }