examples/denoising.cc - ceres-solver - Git at Google

 // Ceres Solver - A fast non-linear least squares minimizer
 // Copyright 2012 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: strandmark@google.com (Petter Strandmark)
 //
 // Denoising using Fields of Experts and the Ceres minimizer.
 //
 // Note that for good denoising results the weighting between the data term
 // and the Fields of Experts term needs to be adjusted. This is discussed
 // in [1]. This program assumes Gaussian noise. The noise model can be changed
 // by substituing another function for QuadraticCostFunction.
 //
 // [1] S. Roth and M.J. Black. "Fields of Experts." International Journal of
 //     Computer Vision, 82(2):205--229, 2009.

 #include <algorithm>
 #include <cmath>
 #include <iostream>
 #include <vector>
 #include <sstream>
 #include <string>

 #include "ceres/ceres.h"
 #include "gflags/gflags.h"
 #include "glog/logging.h"

 #include "fields_of_experts.h"
 #include "pgm_image.h"

 DEFINE_string(input, "", "File to which the output image should be written");
 DEFINE_string(foe_file, "", "FoE file to use");
 DEFINE_string(output, "", "File to which the output image should be written");
 DEFINE_double(sigma, 20.0, "Standard deviation of noise");
 DEFINE_bool(verbose, false, "Prints information about the solver progress.");
 DEFINE_bool(line_search, false, "Use a line search instead of trust region "
             "algorithm.");

 namespace ceres {
 namespace examples {

 // This cost function is used to build the data term.
 //
 //   f_i(x) = a * (x_i - b)^2
 //
 class QuadraticCostFunction : public ceres::SizedCostFunction<1, 1> {
  public:
   QuadraticCostFunction(double a, double b)
     : sqrta_(std::sqrt(a)), b_(b) {}
   virtual bool Evaluate(double const* const* parameters,
                         double* residuals,
                         double** jacobians) const {
     const double x = parameters[0][0];
     residuals[0] = sqrta_ * (x - b_);
     if (jacobians != NULL && jacobians[0] != NULL) {
       jacobians[0][0] = sqrta_;
     }
     return true;
   }
  private:
   double sqrta_, b_;
 };

 // Creates a Fields of Experts MAP inference problem.
 void CreateProblem(const FieldsOfExperts& foe,
                    const PGMImage<double>& image,
                    Problem* problem,
                    PGMImage<double>* solution) {
   // Create the data term
   CHECK_GT(FLAGS_sigma, 0.0);
   const double coefficient = 1 / (2.0 * FLAGS_sigma * FLAGS_sigma);
   for (unsigned index = 0; index < image.NumPixels(); ++index) {
     ceres::CostFunction* cost_function =
         new QuadraticCostFunction(coefficient,
                                   image.PixelFromLinearIndex(index));
     problem->AddResidualBlock(cost_function,
                               NULL,
                               solution->MutablePixelFromLinearIndex(index));
   }

   // Create Ceres cost and loss functions for regularization. One is needed for
   // each filter.
   std::vector<ceres::LossFunction*> loss_function(foe.NumFilters());
   std::vector<ceres::CostFunction*> cost_function(foe.NumFilters());
   for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
     loss_function[alpha_index] = foe.NewLossFunction(alpha_index);
     cost_function[alpha_index] = foe.NewCostFunction(alpha_index);
   }

   // Add FoE regularization for each patch in the image.
   for (int x = 0; x < image.width() - (foe.Size() - 1); ++x) {
     for (int y = 0; y < image.height() - (foe.Size() - 1); ++y) {
       // Build a vector with the pixel indices of this patch.
       std::vector<double*> pixels;
       const std::vector<int>& x_delta_indices = foe.GetXDeltaIndices();
       const std::vector<int>& y_delta_indices = foe.GetYDeltaIndices();
       for (int i = 0; i < foe.NumVariables(); ++i) {
         double* pixel = solution->MutablePixel(x + x_delta_indices[i],
                                                y + y_delta_indices[i]);
         pixels.push_back(pixel);
       }
       // For this patch with coordinates (x, y), we will add foe.NumFilters()
       // terms to the objective function.
       for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
         problem->AddResidualBlock(cost_function[alpha_index],
                                   loss_function[alpha_index],
                                   pixels);
       }
     }
   }
 }

 // Solves the FoE problem using Ceres and post-processes it to make sure the
 // solution stays within [0, 255].
 void SolveProblem(Problem* problem, PGMImage<double>* solution) {
   // These parameters may be experimented with. For example, ceres::DOGLEG tends
   // to be faster for 2x2 filters, but gives solutions with slightly higher
   // objective function value.
   ceres::Solver::Options options;
   options.max_num_iterations = 100;
   if (FLAGS_verbose) {
     options.minimizer_progress_to_stdout = true;
   }

   if (FLAGS_line_search) {
     options.minimizer_type = ceres::LINE_SEARCH;
   }

   options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
   options.function_tolerance = 1e-3;  // Enough for denoising.

   ceres::Solver::Summary summary;
   ceres::Solve(options, problem, &summary);
   if (FLAGS_verbose) {
     std::cout << summary.FullReport() << "\n";
   }

   // Make the solution stay in [0, 255].
   for (int x = 0; x < solution->width(); ++x) {
     for (int y = 0; y < solution->height(); ++y) {
       *solution->MutablePixel(x, y) =
           std::min(255.0, std::max(0.0, solution->Pixel(x, y)));
     }
   }
 }
 }  // namespace examples
 }  // namespace ceres

 int main(int argc, char** argv) {
   using namespace ceres::examples;
   std::string
       usage("This program denoises an image using Ceres.  Sample usage:\n");
   usage += argv[0];
   usage += " --input=<noisy image PGM file> --foe_file=<FoE file name>";
   google::SetUsageMessage(usage);
   google::ParseCommandLineFlags(&argc, &argv, true);
   google::InitGoogleLogging(argv[0]);

   if (FLAGS_input.empty()) {
     std::cerr << "Please provide an image file name.\n";
     return 1;
   }

   if (FLAGS_foe_file.empty()) {
     std::cerr << "Please provide a Fields of Experts file name.\n";
     return 1;
   }

   // Load the Fields of Experts filters from file.
   FieldsOfExperts foe;
   if (!foe.LoadFromFile(FLAGS_foe_file)) {
     std::cerr << "Loading \"" << FLAGS_foe_file << "\" failed.\n";
     return 2;
   }

   // Read the images
   PGMImage<double> image(FLAGS_input);
   if (image.width() == 0) {
     std::cerr << "Reading \"" << FLAGS_input << "\" failed.\n";
     return 3;
   }
   PGMImage<double> solution(image.width(), image.height());
   solution.Set(0.0);

   ceres::Problem problem;
   CreateProblem(foe, image, &problem, &solution);

   SolveProblem(&problem, &solution);

   if (!FLAGS_output.empty()) {
     CHECK(solution.WriteToFile(FLAGS_output))
         << "Writing \"" << FLAGS_output << "\" failed.";
   }

   return 0;
 }
	// Ceres Solver - A fast non-linear least squares minimizer
	// Copyright 2012 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: strandmark@google.com (Petter Strandmark)
	//
	// Denoising using Fields of Experts and the Ceres minimizer.
	//
	// Note that for good denoising results the weighting between the data term
	// and the Fields of Experts term needs to be adjusted. This is discussed
	// in [1]. This program assumes Gaussian noise. The noise model can be changed
	// by substituing another function for QuadraticCostFunction.
	//
	// [1] S. Roth and M.J. Black. "Fields of Experts." International Journal of
	// Computer Vision, 82(2):205--229, 2009.

	#include <algorithm>
	#include <cmath>
	#include <iostream>
	#include <vector>
	#include <sstream>
	#include <string>

	#include "ceres/ceres.h"
	#include "gflags/gflags.h"
	#include "glog/logging.h"

	#include "fields_of_experts.h"
	#include "pgm_image.h"

	DEFINE_string(input, "", "File to which the output image should be written");
	DEFINE_string(foe_file, "", "FoE file to use");
	DEFINE_string(output, "", "File to which the output image should be written");
	DEFINE_double(sigma, 20.0, "Standard deviation of noise");
	DEFINE_bool(verbose, false, "Prints information about the solver progress.");
	DEFINE_bool(line_search, false, "Use a line search instead of trust region "
	"algorithm.");

	namespace ceres {
	namespace examples {

	// This cost function is used to build the data term.
	//
	// f_i(x) = a * (x_i - b)^2
	//
	class QuadraticCostFunction : public ceres::SizedCostFunction<1, 1> {
	public:
	QuadraticCostFunction(double a, double b)
	: sqrta_(std::sqrt(a)), b_(b) {}
	virtual bool Evaluate(double const* const* parameters,
	double* residuals,
	double** jacobians) const {
	const double x = parameters[0][0];
	residuals[0] = sqrta_ * (x - b_);
	if (jacobians != NULL && jacobians[0] != NULL) {
	jacobians[0][0] = sqrta_;
	}
	return true;
	}
	private:
	double sqrta_, b_;
	};

	// Creates a Fields of Experts MAP inference problem.
	void CreateProblem(const FieldsOfExperts& foe,
	const PGMImage<double>& image,
	Problem* problem,
	PGMImage<double>* solution) {
	// Create the data term
	CHECK_GT(FLAGS_sigma, 0.0);
	const double coefficient = 1 / (2.0 * FLAGS_sigma * FLAGS_sigma);
	for (unsigned index = 0; index < image.NumPixels(); ++index) {
	ceres::CostFunction* cost_function =
	new QuadraticCostFunction(coefficient,
	image.PixelFromLinearIndex(index));
	problem->AddResidualBlock(cost_function,
	NULL,
	solution->MutablePixelFromLinearIndex(index));
	}

	// Create Ceres cost and loss functions for regularization. One is needed for
	// each filter.
	std::vector<ceres::LossFunction*> loss_function(foe.NumFilters());
	std::vector<ceres::CostFunction*> cost_function(foe.NumFilters());
	for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
	loss_function[alpha_index] = foe.NewLossFunction(alpha_index);
	cost_function[alpha_index] = foe.NewCostFunction(alpha_index);
	}

	// Add FoE regularization for each patch in the image.
	for (int x = 0; x < image.width() - (foe.Size() - 1); ++x) {
	for (int y = 0; y < image.height() - (foe.Size() - 1); ++y) {
	// Build a vector with the pixel indices of this patch.
	std::vector<double*> pixels;
	const std::vector<int>& x_delta_indices = foe.GetXDeltaIndices();
	const std::vector<int>& y_delta_indices = foe.GetYDeltaIndices();
	for (int i = 0; i < foe.NumVariables(); ++i) {
	double* pixel = solution->MutablePixel(x + x_delta_indices[i],
	y + y_delta_indices[i]);
	pixels.push_back(pixel);
	}
	// For this patch with coordinates (x, y), we will add foe.NumFilters()
	// terms to the objective function.
	for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
	problem->AddResidualBlock(cost_function[alpha_index],
	loss_function[alpha_index],
	pixels);
	}
	}
	}
	}

	// Solves the FoE problem using Ceres and post-processes it to make sure the
	// solution stays within [0, 255].
	void SolveProblem(Problem* problem, PGMImage<double>* solution) {
	// These parameters may be experimented with. For example, ceres::DOGLEG tends
	// to be faster for 2x2 filters, but gives solutions with slightly higher
	// objective function value.
	ceres::Solver::Options options;
	options.max_num_iterations = 100;
	if (FLAGS_verbose) {
	options.minimizer_progress_to_stdout = true;
	}

	if (FLAGS_line_search) {
	options.minimizer_type = ceres::LINE_SEARCH;
	}

	options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
	options.function_tolerance = 1e-3; // Enough for denoising.

	ceres::Solver::Summary summary;
	ceres::Solve(options, problem, &summary);
	if (FLAGS_verbose) {
	std::cout << summary.FullReport() << "\n";
	}

	// Make the solution stay in [0, 255].
	for (int x = 0; x < solution->width(); ++x) {
	for (int y = 0; y < solution->height(); ++y) {
	*solution->MutablePixel(x, y) =
	std::min(255.0, std::max(0.0, solution->Pixel(x, y)));
	}
	}
	}
	} // namespace examples
	} // namespace ceres

	int main(int argc, char** argv) {
	using namespace ceres::examples;
	std::string
	usage("This program denoises an image using Ceres. Sample usage:\n");
	usage += argv[0];
	usage += " --input=<noisy image PGM file> --foe_file=<FoE file name>";
	google::SetUsageMessage(usage);
	google::ParseCommandLineFlags(&argc, &argv, true);
	google::InitGoogleLogging(argv[0]);

	if (FLAGS_input.empty()) {
	std::cerr << "Please provide an image file name.\n";
	return 1;
	}

	if (FLAGS_foe_file.empty()) {
	std::cerr << "Please provide a Fields of Experts file name.\n";
	return 1;
	}

	// Load the Fields of Experts filters from file.
	FieldsOfExperts foe;
	if (!foe.LoadFromFile(FLAGS_foe_file)) {
	std::cerr << "Loading \"" << FLAGS_foe_file << "\" failed.\n";
	return 2;
	}

	// Read the images
	PGMImage<double> image(FLAGS_input);
	if (image.width() == 0) {
	std::cerr << "Reading \"" << FLAGS_input << "\" failed.\n";
	return 3;
	}
	PGMImage<double> solution(image.width(), image.height());
	solution.Set(0.0);

	ceres::Problem problem;
	CreateProblem(foe, image, &problem, &solution);

	SolveProblem(&problem, &solution);

	if (!FLAGS_output.empty()) {
	CHECK(solution.WriteToFile(FLAGS_output))
	<< "Writing \"" << FLAGS_output << "\" failed.";
	}

	return 0;
	}