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      1 // Ceres Solver - A fast non-linear least squares minimizer
      2 // Copyright 2012 Google Inc. All rights reserved.
      3 // http://code.google.com/p/ceres-solver/
      4 //
      5 // Redistribution and use in source and binary forms, with or without
      6 // modification, are permitted provided that the following conditions are met:
      7 //
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     17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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     28 //
     29 // Author: strandmark (at) google.com (Petter Strandmark)
     30 //
     31 // Denoising using Fields of Experts and the Ceres minimizer.
     32 //
     33 // Note that for good denoising results the weighting between the data term
     34 // and the Fields of Experts term needs to be adjusted. This is discussed
     35 // in [1]. This program assumes Gaussian noise. The noise model can be changed
     36 // by substituing another function for QuadraticCostFunction.
     37 //
     38 // [1] S. Roth and M.J. Black. "Fields of Experts." International Journal of
     39 //     Computer Vision, 82(2):205--229, 2009.
     40 
     41 #include <algorithm>
     42 #include <cmath>
     43 #include <iostream>
     44 #include <vector>
     45 #include <sstream>
     46 #include <string>
     47 
     48 #include "ceres/ceres.h"
     49 #include "gflags/gflags.h"
     50 #include "glog/logging.h"
     51 
     52 #include "fields_of_experts.h"
     53 #include "pgm_image.h"
     54 
     55 DEFINE_string(input, "", "File to which the output image should be written");
     56 DEFINE_string(foe_file, "", "FoE file to use");
     57 DEFINE_string(output, "", "File to which the output image should be written");
     58 DEFINE_double(sigma, 20.0, "Standard deviation of noise");
     59 DEFINE_bool(verbose, false, "Prints information about the solver progress.");
     60 
     61 namespace ceres {
     62 namespace examples {
     63 
     64 // This cost function is used to build the data term.
     65 //
     66 //   f_i(x) = a * (x_i - b)^2
     67 //
     68 class QuadraticCostFunction : public ceres::SizedCostFunction<1, 1> {
     69  public:
     70   QuadraticCostFunction(double a, double b)
     71     : sqrta_(std::sqrt(a)), b_(b) {}
     72   virtual bool Evaluate(double const* const* parameters,
     73                         double* residuals,
     74                         double** jacobians) const {
     75     const double x = parameters[0][0];
     76     residuals[0] = sqrta_ * (x - b_);
     77     if (jacobians != NULL && jacobians[0] != NULL) {
     78       jacobians[0][0] = sqrta_;
     79     }
     80     return true;
     81   }
     82  private:
     83   double sqrta_, b_;
     84 };
     85 
     86 // Creates a Fields of Experts MAP inference problem.
     87 void CreateProblem(const FieldsOfExperts& foe,
     88                    const PGMImage<double>& image,
     89                    Problem* problem,
     90                    PGMImage<double>* solution) {
     91   // Create the data term
     92   CHECK_GT(FLAGS_sigma, 0.0);
     93   const double coefficient = 1 / (2.0 * FLAGS_sigma * FLAGS_sigma);
     94   for (unsigned index = 0; index < image.NumPixels(); ++index) {
     95     ceres::CostFunction* cost_function =
     96         new QuadraticCostFunction(coefficient,
     97                                   image.PixelFromLinearIndex(index));
     98     problem->AddResidualBlock(cost_function,
     99                               NULL,
    100                               solution->MutablePixelFromLinearIndex(index));
    101   }
    102 
    103   // Create Ceres cost and loss functions for regularization. One is needed for
    104   // each filter.
    105   std::vector<ceres::LossFunction*> loss_function(foe.NumFilters());
    106   std::vector<ceres::CostFunction*> cost_function(foe.NumFilters());
    107   for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
    108     loss_function[alpha_index] = foe.NewLossFunction(alpha_index);
    109     cost_function[alpha_index] = foe.NewCostFunction(alpha_index);
    110   }
    111 
    112   // Add FoE regularization for each patch in the image.
    113   for (int x = 0; x < image.width() - (foe.Size() - 1); ++x) {
    114     for (int y = 0; y < image.height() - (foe.Size() - 1); ++y) {
    115       // Build a vector with the pixel indices of this patch.
    116       std::vector<double*> pixels;
    117       const std::vector<int>& x_delta_indices = foe.GetXDeltaIndices();
    118       const std::vector<int>& y_delta_indices = foe.GetYDeltaIndices();
    119       for (int i = 0; i < foe.NumVariables(); ++i) {
    120         double* pixel = solution->MutablePixel(x + x_delta_indices[i],
    121                                                y + y_delta_indices[i]);
    122         pixels.push_back(pixel);
    123       }
    124       // For this patch with coordinates (x, y), we will add foe.NumFilters()
    125       // terms to the objective function.
    126       for (int alpha_index = 0; alpha_index < foe.NumFilters(); ++alpha_index) {
    127         problem->AddResidualBlock(cost_function[alpha_index],
    128                                   loss_function[alpha_index],
    129                                   pixels);
    130       }
    131     }
    132   }
    133 }
    134 
    135 // Solves the FoE problem using Ceres and post-processes it to make sure the
    136 // solution stays within [0, 255].
    137 void SolveProblem(Problem* problem, PGMImage<double>* solution) {
    138   // These parameters may be experimented with. For example, ceres::DOGLEG tends
    139   // to be faster for 2x2 filters, but gives solutions with slightly higher
    140   // objective function value.
    141   ceres::Solver::Options options;
    142   options.max_num_iterations = 100;
    143   if (FLAGS_verbose) {
    144     options.minimizer_progress_to_stdout = true;
    145   }
    146   options.trust_region_strategy_type = ceres::LEVENBERG_MARQUARDT;
    147   options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
    148   options.function_tolerance = 1e-3;  // Enough for denoising.
    149 
    150   ceres::Solver::Summary summary;
    151   ceres::Solve(options, problem, &summary);
    152   if (FLAGS_verbose) {
    153     std::cout << summary.FullReport() << "\n";
    154   }
    155 
    156   // Make the solution stay in [0, 255].
    157   for (int x = 0; x < solution->width(); ++x) {
    158     for (int y = 0; y < solution->height(); ++y) {
    159       *solution->MutablePixel(x, y) =
    160           std::min(255.0, std::max(0.0, solution->Pixel(x, y)));
    161     }
    162   }
    163 }
    164 }  // namespace examples
    165 }  // namespace ceres
    166 
    167 int main(int argc, char** argv) {
    168   using namespace ceres::examples;
    169   std::string
    170       usage("This program denoises an image using Ceres.  Sample usage:\n");
    171   usage += argv[0];
    172   usage += " --input=<noisy image PGM file> --foe_file=<FoE file name>";
    173   google::SetUsageMessage(usage);
    174   google::ParseCommandLineFlags(&argc, &argv, true);
    175   google::InitGoogleLogging(argv[0]);
    176 
    177   if (FLAGS_input.empty()) {
    178     std::cerr << "Please provide an image file name.\n";
    179     return 1;
    180   }
    181 
    182   if (FLAGS_foe_file.empty()) {
    183     std::cerr << "Please provide a Fields of Experts file name.\n";
    184     return 1;
    185   }
    186 
    187   // Load the Fields of Experts filters from file.
    188   FieldsOfExperts foe;
    189   if (!foe.LoadFromFile(FLAGS_foe_file)) {
    190     std::cerr << "Loading \"" << FLAGS_foe_file << "\" failed.\n";
    191     return 2;
    192   }
    193 
    194   // Read the images
    195   PGMImage<double> image(FLAGS_input);
    196   if (image.width() == 0) {
    197     std::cerr << "Reading \"" << FLAGS_input << "\" failed.\n";
    198     return 3;
    199   }
    200   PGMImage<double> solution(image.width(), image.height());
    201   solution.Set(0.0);
    202 
    203   ceres::Problem problem;
    204   CreateProblem(foe, image, &problem, &solution);
    205 
    206   SolveProblem(&problem, &solution);
    207 
    208   if (!FLAGS_output.empty()) {
    209     CHECK(solution.WriteToFile(FLAGS_output))
    210         << "Writing \"" << FLAGS_output << "\" failed.";
    211   }
    212 
    213   return 0;
    214 }
    215