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diff --git a/examples/ellipse_approximation.cc b/examples/ellipse_approximation.cc new file mode 100644 index 0000000..a5bbe02 --- /dev/null +++ b/examples/ellipse_approximation.cc @@ -0,0 +1,451 @@ +// Ceres Solver - A fast non-linear least squares minimizer +// Copyright 2014 Google Inc. All rights reserved. +// http://code.google.com/p/ceres-solver/ +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are met: +// +// * Redistributions of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// * Neither the name of Google Inc. nor the names of its contributors may be +// used to endorse or promote products derived from this software without +// specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE +// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +// POSSIBILITY OF SUCH DAMAGE. +// +// Author: richie.stebbing@gmail.com (Richard Stebbing) +// +// This fits points randomly distributed on an ellipse with an approximate +// line segment contour. This is done by jointly optimizing the control points +// of the line segment contour along with the preimage positions for the data +// points. The purpose of this example is to show an example use case for +// dynamic_sparsity, and how it can benefit problems which are numerically +// dense but dynamically sparse. + +#include <cmath> +#include <vector> +#include "ceres/ceres.h" +#include "glog/logging.h" + +// Data generated with the following Python code. +// import numpy as np +// np.random.seed(1337) +// t = np.linspace(0.0, 2.0 * np.pi, 212, endpoint=False) +// t += 2.0 * np.pi * 0.01 * np.random.randn(t.size) +// theta = np.deg2rad(15) +// a, b = np.cos(theta), np.sin(theta) +// R = np.array([[a, -b], +// [b, a]]) +// Y = np.dot(np.c_[4.0 * np.cos(t), np.sin(t)], R.T) + +const int kYRows = 212; +const int kYCols = 2; +const double kYData[kYRows * kYCols] = { + +3.871364e+00, +9.916027e-01, + +3.864003e+00, +1.034148e+00, + +3.850651e+00, +1.072202e+00, + +3.868350e+00, +1.014408e+00, + +3.796381e+00, +1.153021e+00, + +3.857138e+00, +1.056102e+00, + +3.787532e+00, +1.162215e+00, + +3.704477e+00, +1.227272e+00, + 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the line segment contour. + for (int i = 0; i < num_segments_; ++i) { + mutable_parameter_block_sizes()->push_back(2); + } + set_num_residuals(2); + } + + virtual bool Evaluate(const double* const* x, + double* residuals, + double** jacobians) const { + // Convert the preimage position `t` into a segment index `i0` and the + // line segment interpolation parameter `u`. `i1` is the index of the next + // control point. + const double t = ModuloNumSegments(*x[0]); + CHECK_GE(t, 0.0); + CHECK_LT(t, num_segments_); + const int i0 = floor(t), i1 = (i0 + 1) % num_segments_; + const double u = t - i0; + + // Linearly interpolate between control points `i0` and `i1`. + residuals[0] = y_[0] - ((1.0 - u) * x[1 + i0][0] + u * x[1 + i1][0]); + residuals[1] = y_[1] - ((1.0 - u) * x[1 + i0][1] + u * x[1 + i1][1]); + + if (jacobians == NULL) { + return true; + } + + if (jacobians[0] != NULL) { + jacobians[0][0] = x[1 + i0][0] - x[1 + i1][0]; + jacobians[0][1] = x[1 + i0][1] - x[1 + i1][1]; + } + for (int i = 0; i < num_segments_; ++i) { + if (jacobians[i + 1] != NULL) { + ceres::MatrixRef(jacobians[i + 1], 2, 2).setZero(); + if (i == i0) { + jacobians[i + 1][0] = -(1.0 - u); + jacobians[i + 1][3] = -(1.0 - u); + } else if (i == i1) { + jacobians[i + 1][0] = -u; + jacobians[i + 1][3] = -u; + } + } + } + return true; + } + + static ceres::CostFunction* Create(const int num_segments, + const Eigen::Vector2d y) { + return new PointToLineSegmentContourCostFunction(num_segments, y); + } + + private: + inline double ModuloNumSegments(const double& t) const { + return t - num_segments_ * floor(t / num_segments_); + } + + const int num_segments_; + const Eigen::Vector2d y_; +}; + +struct EuclideanDistanceFunctor { + EuclideanDistanceFunctor(const double& sqrt_weight) + : sqrt_weight_(sqrt_weight) {} + + template <typename T> + bool operator()(const T* x0, const T* x1, T* residuals) const { + residuals[0] = T(sqrt_weight_) * (x0[0] - x1[0]); + residuals[1] = T(sqrt_weight_) * (x0[1] - x1[1]); + return true; + } + + static ceres::CostFunction* Create(const double& sqrt_weight) { + return new ceres::AutoDiffCostFunction<EuclideanDistanceFunctor, 2, 2, 2>( + new EuclideanDistanceFunctor(sqrt_weight)); + } + + private: + const double sqrt_weight_; +}; + +bool SolveWithFullReport(ceres::Solver::Options options, + ceres::Problem* problem, + bool dynamic_sparsity) { + options.dynamic_sparsity = dynamic_sparsity; + + ceres::Solver::Summary summary; + ceres::Solve(options, problem, &summary); + + std::cout << "####################" << std::endl; + std::cout << "dynamic_sparsity = " << dynamic_sparsity << std::endl; + std::cout << "####################" << std::endl; + std::cout << summary.FullReport() << std::endl; + + return summary.termination_type == ceres::CONVERGENCE; +} + +int main(int argc, char** argv) { + google::InitGoogleLogging(argv[0]); + + // Problem configuration. + const int num_segments = 151; + const double regularization_weight = 1e-2; + + // Eigen::MatrixXd is column major so we define our own MatrixXd which is + // row major. Eigen::VectorXd can be used directly. + typedef Eigen::Matrix<double, + Eigen::Dynamic, Eigen::Dynamic, + Eigen::RowMajor> MatrixXd; + using Eigen::VectorXd; + + // `X` is the matrix of control points which make up the contour of line + // segments. The number of control points is equal to the number of line + // segments because the contour is closed. + // + // Initialize `X` to points on the unit circle. + VectorXd w(num_segments + 1); + w.setLinSpaced(num_segments + 1, 0.0, 2.0 * M_PI); + w.conservativeResize(num_segments); + MatrixXd X(num_segments, 2); + X.col(0) = w.array().cos(); + X.col(1) = w.array().sin(); + + // Each data point has an associated preimage position on the line segment + // contour. For each data point we initialize the preimage positions to + // the index of the closest control point. + const int num_observations = kY.rows(); + VectorXd t(num_observations); + for (int i = 0; i < num_observations; ++i) { + (X.rowwise() - kY.row(i)).rowwise().squaredNorm().minCoeff(&t[i]); + } + + ceres::Problem problem; + + // For each data point add a residual which measures its distance to its + // corresponding position on the line segment contour. + std::vector<double*> parameter_blocks(1 + num_segments); + parameter_blocks[0] = NULL; + for (int i = 0; i < num_segments; ++i) { + parameter_blocks[i + 1] = X.data() + 2 * i; + } + for (int i = 0; i < num_observations; ++i) { + parameter_blocks[0] = &t[i]; + problem.AddResidualBlock( + PointToLineSegmentContourCostFunction::Create(num_segments, kY.row(i)), + NULL, + parameter_blocks); + } + + // Add regularization to minimize the length of the line segment contour. + for (int i = 0; i < num_segments; ++i) { + problem.AddResidualBlock( + EuclideanDistanceFunctor::Create(sqrt(regularization_weight)), + NULL, + X.data() + 2 * i, + X.data() + 2 * ((i + 1) % num_segments)); + } + + ceres::Solver::Options options; + options.max_num_iterations = 100; + options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY; + + // First, solve `X` and `t` jointly with dynamic_sparsity = true. + MatrixXd X0 = X; + VectorXd t0 = t; + CHECK(SolveWithFullReport(options, &problem, true)); + + // Second, solve with dynamic_sparsity = false. + X = X0; + t = t0; + CHECK(SolveWithFullReport(options, &problem, false)); + + return 0; +} |