examples/robust_curve_fitting.cc

// Ceres Solver - A fast non-linear least squares minimizer
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// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// This example fits the curve f(x;m,c) = e^(m * x + c) to data. However unlike
// the data in curve_fitting.cc, the data here has outliers in it, so minimizing
// the sum squared loss will result in a bad fit. So this example illustrates
// the use of a robust loss function (CauchyLoss) to reduce the influence of the
// outliers on the fit.

#include "absl/log/check.h"
#include "absl/log/initialize.h"
#include "ceres/ceres.h"

// Data generated using the following octave code.
//   randn('seed', 23497);
//   m = 0.3;
//   c = 0.1;
//   x=[0:0.075:5];
//   y = exp(m * x + c);
//   noise = randn(size(x)) * 0.2;
//   outlier_noise = rand(size(x)) < 0.05;
//   y_observed = y + noise + outlier_noise;
//   data = [x', y_observed'];

const int kNumObservations = 67;
// clang-format off
const double data[] = {
0.000000e+00, 1.133898e+00,
7.500000e-02, 1.334902e+00,
1.500000e-01, 1.213546e+00,
2.250000e-01, 1.252016e+00,
3.000000e-01, 1.392265e+00,
3.750000e-01, 1.314458e+00,
4.500000e-01, 1.472541e+00,
5.250000e-01, 1.536218e+00,
6.000000e-01, 1.355679e+00,
6.750000e-01, 1.463566e+00,
7.500000e-01, 1.490201e+00,
8.250000e-01, 1.658699e+00,
9.000000e-01, 1.067574e+00,
9.750000e-01, 1.464629e+00,
1.050000e+00, 1.402653e+00,
1.125000e+00, 1.713141e+00,
1.200000e+00, 1.527021e+00,
1.275000e+00, 1.702632e+00,
1.350000e+00, 1.423899e+00,
1.425000e+00, 5.543078e+00, // Outlier point
1.500000e+00, 5.664015e+00, // Outlier point
1.575000e+00, 1.732484e+00,
1.650000e+00, 1.543296e+00,
1.725000e+00, 1.959523e+00,
1.800000e+00, 1.685132e+00,
1.875000e+00, 1.951791e+00,
1.950000e+00, 2.095346e+00,
2.025000e+00, 2.361460e+00,
2.100000e+00, 2.169119e+00,
2.175000e+00, 2.061745e+00,
2.250000e+00, 2.178641e+00,
2.325000e+00, 2.104346e+00,
2.400000e+00, 2.584470e+00,
2.475000e+00, 1.914158e+00,
2.550000e+00, 2.368375e+00,
2.625000e+00, 2.686125e+00,
2.700000e+00, 2.712395e+00,
2.775000e+00, 2.499511e+00,
2.850000e+00, 2.558897e+00,
2.925000e+00, 2.309154e+00,
3.000000e+00, 2.869503e+00,
3.075000e+00, 3.116645e+00,
3.150000e+00, 3.094907e+00,
3.225000e+00, 2.471759e+00,
3.300000e+00, 3.017131e+00,
3.375000e+00, 3.232381e+00,
3.450000e+00, 2.944596e+00,
3.525000e+00, 3.385343e+00,
3.600000e+00, 3.199826e+00,
3.675000e+00, 3.423039e+00,
3.750000e+00, 3.621552e+00,
3.825000e+00, 3.559255e+00,
3.900000e+00, 3.530713e+00,
3.975000e+00, 3.561766e+00,
4.050000e+00, 3.544574e+00,
4.125000e+00, 3.867945e+00,
4.200000e+00, 4.049776e+00,
4.275000e+00, 3.885601e+00,
4.350000e+00, 4.110505e+00,
4.425000e+00, 4.345320e+00,
4.500000e+00, 4.161241e+00,
4.575000e+00, 4.363407e+00,
4.650000e+00, 4.161576e+00,
4.725000e+00, 4.619728e+00,
4.800000e+00, 4.737410e+00,
4.875000e+00, 4.727863e+00,
4.950000e+00, 4.669206e+00
};
// clang-format on

struct ExponentialResidual {
  ExponentialResidual(double x, double y) : x_(x), y_(y) {}

  template <typename T>
  bool operator()(const T* const m, const T* const c, T* residual) const {
    residual[0] = y_ - exp(m[0] * x_ + c[0]);
    return true;
  }

 private:
  const double x_;
  const double y_;
};

int main(int argc, char** argv) {
  absl::InitializeLog();

  const double initial_m = 0.0;
  const double initial_c = 0.0;
  double m = initial_m;
  double c = initial_c;

  ceres::Problem problem;
  for (int i = 0; i < kNumObservations; ++i) {
    ceres::CostFunction* cost_function =
        new ceres::AutoDiffCostFunction<ExponentialResidual, 1, 1, 1>(
            data[2 * i], data[2 * i + 1]);
    problem.AddResidualBlock(cost_function, new ceres::CauchyLoss(0.5), &m, &c);
  }

  ceres::Solver::Options options;
  options.max_num_iterations = 25;
  options.linear_solver_type = ceres::DENSE_QR;
  options.minimizer_progress_to_stdout = true;

  ceres::Solver::Summary summary;
  ceres::Solve(options, &problem, &summary);
  std::cout << summary.BriefReport() << "\n";
  std::cout << "Initial m: " << initial_m << " c: " << initial_c << "\n";
  std::cout << "Final   m: " << m << " c: " << c << "\n";
  return 0;
}