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// Ceres Solver - A fast non-linear least squares minimizer
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// 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 substituting 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 <random>
#include <sstream>
#include <string>
#include <vector>
#include "ceres/ceres.h"
#include "fields_of_experts.h"
#include "gflags/gflags.h"
#include "glog/logging.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_string(trust_region_strategy,
"levenberg_marquardt",
"Options are: levenberg_marquardt, dogleg.");
DEFINE_string(dogleg,
"traditional_dogleg",
"Options are: traditional_dogleg,"
"subspace_dogleg.");
DEFINE_string(linear_solver,
"sparse_normal_cholesky",
"Options are: "
"sparse_normal_cholesky and cgnr.");
DEFINE_string(preconditioner,
"jacobi",
"Options are: "
"identity, jacobi, subset");
DEFINE_string(sparse_linear_algebra_library,
"suite_sparse",
"Options are: suite_sparse, cx_sparse and eigen_sparse");
DEFINE_double(eta,
1e-2,
"Default value for eta. Eta determines the "
"accuracy of each linear solve of the truncated newton step. "
"Changing this parameter can affect solve performance.");
DEFINE_int32(num_threads, 1, "Number of threads.");
DEFINE_int32(num_iterations, 10, "Number of iterations.");
DEFINE_bool(nonmonotonic_steps,
false,
"Trust region algorithm can use"
" nonmonotic steps.");
DEFINE_bool(inner_iterations,
false,
"Use inner iterations to non-linearly "
"refine each successful trust region step.");
DEFINE_bool(mixed_precision_solves, false, "Use mixed precision solves.");
DEFINE_int32(max_num_refinement_iterations,
0,
"Iterative refinement iterations");
DEFINE_bool(line_search,
false,
"Use a line search instead of trust region "
"algorithm.");
DEFINE_double(subset_fraction,
0.2,
"The fraction of residual blocks to use for the"
" subset preconditioner.");
namespace ceres::examples {
namespace {
// 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) {}
bool Evaluate(double const* const* parameters,
double* residuals,
double** jacobians) const override {
const double x = parameters[0][0];
residuals[0] = sqrta_ * (x - b_);
if (jacobians != nullptr && jacobians[0] != nullptr) {
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(CERES_GET_FLAG(FLAGS_sigma), 0.0);
const double coefficient =
1 / (2.0 * CERES_GET_FLAG(FLAGS_sigma) * CERES_GET_FLAG(FLAGS_sigma));
for (int index = 0; index < image.NumPixels(); ++index) {
ceres::CostFunction* cost_function = new QuadraticCostFunction(
coefficient, image.PixelFromLinearIndex(index));
problem->AddResidualBlock(
cost_function, nullptr, 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);
}
}
}
}
void SetLinearSolver(Solver::Options* options) {
CHECK(StringToLinearSolverType(CERES_GET_FLAG(FLAGS_linear_solver),
&options->linear_solver_type));
CHECK(StringToPreconditionerType(CERES_GET_FLAG(FLAGS_preconditioner),
&options->preconditioner_type));
CHECK(StringToSparseLinearAlgebraLibraryType(
CERES_GET_FLAG(FLAGS_sparse_linear_algebra_library),
&options->sparse_linear_algebra_library_type));
options->use_mixed_precision_solves =
CERES_GET_FLAG(FLAGS_mixed_precision_solves);
options->max_num_refinement_iterations =
CERES_GET_FLAG(FLAGS_max_num_refinement_iterations);
}
void SetMinimizerOptions(Solver::Options* options) {
options->max_num_iterations = CERES_GET_FLAG(FLAGS_num_iterations);
options->minimizer_progress_to_stdout = true;
options->num_threads = CERES_GET_FLAG(FLAGS_num_threads);
options->eta = CERES_GET_FLAG(FLAGS_eta);
options->use_nonmonotonic_steps = CERES_GET_FLAG(FLAGS_nonmonotonic_steps);
if (CERES_GET_FLAG(FLAGS_line_search)) {
options->minimizer_type = ceres::LINE_SEARCH;
}
CHECK(StringToTrustRegionStrategyType(
CERES_GET_FLAG(FLAGS_trust_region_strategy),
&options->trust_region_strategy_type));
CHECK(
StringToDoglegType(CERES_GET_FLAG(FLAGS_dogleg), &options->dogleg_type));
options->use_inner_iterations = CERES_GET_FLAG(FLAGS_inner_iterations);
}
// 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;
SetMinimizerOptions(&options);
SetLinearSolver(&options);
options.function_tolerance = 1e-3; // Enough for denoising.
if (options.linear_solver_type == ceres::CGNR &&
options.preconditioner_type == ceres::SUBSET) {
std::vector<ResidualBlockId> residual_blocks;
problem->GetResidualBlocks(&residual_blocks);
// To use the SUBSET preconditioner we need to provide a list of
// residual blocks (rows of the Jacobian). The denoising problem
// has fairly general sparsity, and there is no apriori reason to
// select one residual block over another, so we will randomly
// subsample the residual blocks with probability subset_fraction.
std::default_random_engine engine;
std::uniform_real_distribution<> distribution(0, 1); // rage 0 - 1
for (auto residual_block : residual_blocks) {
if (distribution(engine) <= CERES_GET_FLAG(FLAGS_subset_fraction)) {
options.residual_blocks_for_subset_preconditioner.insert(
residual_block);
}
}
}
ceres::Solver::Summary summary;
ceres::Solve(options, problem, &summary);
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
} // namespace ceres::examples
int main(int argc, char** argv) {
using namespace ceres::examples;
GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true);
google::InitGoogleLogging(argv[0]);
if (CERES_GET_FLAG(FLAGS_input).empty()) {
std::cerr << "Please provide an image file name using -input.\n";
return 1;
}
if (CERES_GET_FLAG(FLAGS_foe_file).empty()) {
std::cerr << "Please provide a Fields of Experts file name using -foe_file."
"\n";
return 1;
}
// Load the Fields of Experts filters from file.
FieldsOfExperts foe;
if (!foe.LoadFromFile(CERES_GET_FLAG(FLAGS_foe_file))) {
std::cerr << "Loading \"" << CERES_GET_FLAG(FLAGS_foe_file)
<< "\" failed.\n";
return 2;
}
// Read the images
PGMImage<double> image(CERES_GET_FLAG(FLAGS_input));
if (image.width() == 0) {
std::cerr << "Reading \"" << CERES_GET_FLAG(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 (!CERES_GET_FLAG(FLAGS_output).empty()) {
CHECK(solution.WriteToFile(CERES_GET_FLAG(FLAGS_output)))
<< "Writing \"" << CERES_GET_FLAG(FLAGS_output) << "\" failed.";
}
return 0;
}