void test_linear_ring()
{
trace.beginBlock("linear ring");
const Domain domain(Point(-5,-5), Point(5,5));
typedef DiscreteExteriorCalculus<1, 2, EigenLinearAlgebraBackend> Calculus;
Calculus calculus;
calculus.initKSpace<Domain>(domain);
for (int kk=-8; kk<10; kk++) calculus.insertSCell( calculus.myKSpace.sCell(Point(-8,kk), kk%2 == 0 ? Calculus::KSpace::POS : Calculus::KSpace::NEG) );
for (int kk=-8; kk<10; kk++) calculus.insertSCell( calculus.myKSpace.sCell(Point(kk,10), kk%2 == 0 ? Calculus::KSpace::POS : Calculus::KSpace::NEG) );
for (int kk=10; kk>-8; kk--) calculus.insertSCell( calculus.myKSpace.sCell(Point(10,kk)) );
for (int kk=10; kk>-8; kk--) calculus.insertSCell( calculus.myKSpace.sCell(Point(kk,-8)) );
calculus.updateIndexes();
{
trace.info() << calculus << endl;
Board2D board;
board << domain;
board << calculus;
board.saveSVG("ring_structure.svg");
}
const Calculus::PrimalDerivative0 d0 = calculus.derivative<0, PRIMAL>();
display_operator_info("d0", d0);
const Calculus::PrimalHodge0 h0 = calculus.hodge<0, PRIMAL>();
display_operator_info("h0", h0);
const Calculus::DualDerivative0 d0p = calculus.derivative<0, DUAL>();
display_operator_info("d0p", d0p);
const Calculus::PrimalHodge1 h1 = calculus.hodge<1, PRIMAL>();
display_operator_info("h1", h1);
const Calculus::PrimalIdentity0 laplace = calculus.laplace<PRIMAL>();
display_operator_info("laplace", laplace);
const int laplace_size = calculus.kFormLength(0, PRIMAL);
const Eigen::MatrixXd laplace_dense(laplace.myContainer);
for (int ii=0; ii<laplace_size; ii++)
FATAL_ERROR( laplace_dense(ii,ii) == 2 );
FATAL_ERROR( laplace_dense.array().rowwise().sum().abs().sum() == 0 );
FATAL_ERROR( laplace_dense.transpose() == laplace_dense );
trace.endBlock();
}
void
set_initial_phase_null(Calculus& calculus, Eigen::VectorXcd& initial_wave)
{
typedef typename Calculus::Cell Cell;
typedef typename Calculus::Index Index;
typedef typename Calculus::Point Point;
//! [time_phase_null]
for (int xx=9; xx<13; xx++)
for (int yy=13; yy<17; yy++)
{
const Point point(xx,yy);
const Cell cell = calculus.myKSpace.uSpel(point);
const Index index = calculus.getCellIndex(cell);
initial_wave(index) = 1;
}
//! [time_phase_null]
}
void
set_initial_phase_dir_yy(Calculus& calculus, Eigen::VectorXcd& initial_wave)
{
typedef typename Calculus::Cell Cell;
typedef typename Calculus::Index Index;
typedef typename Calculus::Point Point;
//! [time_phase_yy]
for (int xx=9; xx<13; xx++)
for (int yy=13; yy<17; yy++)
{
const Point point(xx,yy);
const Cell cell = calculus.myKSpace.uSpel(point);
const Index index = calculus.getCellIndex(cell);
initial_wave(index) = std::exp(std::complex<double>(0,2*M_PI*(yy-14.5)/8));
}
//! [time_phase_yy]
}
void test_linear_structure()
{
trace.beginBlock("creating dec problem with neumann border condition");
//! [neumann-creation]
typedef DiscreteExteriorCalculus<1, 2, EigenLinearAlgebraBackend> Calculus;
typedef std::list<Calculus::SCell> SCells;
SCells cells;
// fill cells container
{
const Calculus::KSpace kspace;
for (int kk=20; kk>0; kk--) cells.push_back( kspace.sCell(Point(0,kk), kk%2 != 0 ? Calculus::KSpace::NEG : Calculus::KSpace::POS) );
for (int kk=0; kk<10; kk++) cells.push_back( kspace.sCell(Point(kk,0)) );
for (int kk=0; kk<10; kk++) cells.push_back( kspace.sCell(Point(10,kk)) );
cells.push_back( kspace.sCell(Point(10,10)) );
cells.push_back( kspace.sCell(Point(9,10), Calculus::KSpace::NEG) );
for (int kk=10; kk<20; kk++) cells.push_back( kspace.sCell(Point(8,kk)) );
for (int kk=8; kk<12; kk++) cells.push_back( kspace.sCell(Point(kk,20)) );
for (int kk=20; kk>0; kk--) cells.push_back( kspace.sCell(Point(12,kk), kk%2 != 0 ? Calculus::KSpace::NEG : Calculus::KSpace::POS) );
cells.push_back( kspace.sCell(Point(12,0)) );
}
// fill calculus
const Domain domain(Point(-1,-1), Point(10,10));
// create DEC structure
Calculus calculus;
calculus.initKSpace<Domain>(domain);
for (SCells::const_iterator ci=cells.begin(), ce=cells.end(); ci!=ce; ci++) calculus.insertSCell( *ci );
calculus.updateIndexes();
//! [neumann-creation]
trace.info() << calculus << endl;
//! [input-dirac]
Calculus::PrimalForm0 dirac = Calculus::PrimalForm0::dirac(calculus, calculus.myKSpace.uCell(Point(10,4)));
//! [input-dirac]
{
Board2D board;
board << domain;
board << calculus;
board << dirac;
board.saveSVG("linear_structure_neumann_dirac.svg");
}
trace.endBlock();
{
trace.beginBlock("solving problem with neumann border condition using sparse qr solver");
//! [neumann-laplace-definition]
const Calculus::PrimalIdentity0 laplace = calculus.laplace<PRIMAL>();
//! [neumann-laplace-definition]
trace.info() << "laplace = " << laplace << endl;
const Calculus::PrimalIdentity0 reorder = calculus.reorder<0, PRIMAL>(cells.begin(), cells.end());
const Calculus::PrimalIdentity0 laplace_ordered = reorder * laplace * reorder.transpose();
trace.info() << Eigen::MatrixXd(laplace_ordered.myContainer) << endl;
//! [neumann-solve]
typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> Solver;
Solver solver;
solver.compute(laplace);
Calculus::PrimalForm0 solved_solution = solver.solve(dirac);
//! [neumann-solve]
solved_solution.myContainer.array() -= solved_solution.myContainer(38);
solved_solution.myContainer.array() /= solved_solution.myContainer.maxCoeff();
const Calculus::PrimalForm0 solved_solution_ordered = reorder * solved_solution;
Calculus::PrimalForm0 analytic_solution(calculus);
{
const Calculus::Index dirac_position = 17;
const Calculus::Index length = analytic_solution.length();
for (Calculus::Index kk=0; kk<length; kk++)
{
Calculus::Scalar alpha = 1. * (kk)/dirac_position * (kk+1.)/(dirac_position+1.);
if (kk>dirac_position)
{
alpha = 1. * (length-kk)/dirac_position * (length-kk-1.)/(dirac_position+1);
alpha -= 1. * (length-dirac_position)/dirac_position * (length-dirac_position-1.)/(dirac_position+1);
alpha += 1;
}
analytic_solution.myContainer(kk) = alpha;
}
}
trace.info() << solver.isValid() << " " << solver.myLinearAlgebraSolver.info() << endl;
{
std::ofstream handle("linear_structure_neumann.dat");
for (Calculus::Index kk=0; kk<analytic_solution.length(); kk++)
handle << solved_solution_ordered.myContainer(kk) << " " << analytic_solution.myContainer(kk) << endl;
}
FATAL_ERROR( (solved_solution_ordered-analytic_solution).myContainer.array().abs().maxCoeff() < 1e-5 );
{
Board2D board;
board << domain;
board << calculus;
board << solved_solution;
board.saveSVG("linear_structure_neumann_solution.svg");
}
{
Calculus::PrimalForm1 solved_solution_gradient = calculus.derivative<0, PRIMAL>() * solved_solution;
Board2D board;
board << domain;
board << calculus;
board << solved_solution_gradient;
board << CustomStyle("VectorField", new VectorFieldStyle2D(1));
board << calculus.sharp(solved_solution_gradient);
board.saveSVG("linear_structure_neumann_solution_gradient.svg");
}
trace.endBlock();
}
trace.beginBlock("creating dec problem with dirichlet border condition");
//! [dirichlet-creation]
calculus.insertSCell( calculus.myKSpace.sCell(Point(13,0)) );
calculus.insertSCell( calculus.myKSpace.sCell(Point(1,20), Calculus::KSpace::NEG) );
calculus.updateIndexes();
//! [dirichlet-creation]
{
Board2D board;
board << domain;
board << calculus;
board << dirac;
board.saveSVG("linear_structure_dirichlet_dirac.svg");
}
trace.endBlock();
{
trace.beginBlock("solving problem with dirichlet border condition using sparse qr solver");
//! [dirichlet-laplace-definition]
const Calculus::PrimalIdentity0 laplace = calculus.laplace<PRIMAL>();
//! [dirichlet-laplace-definition]
trace.info() << "laplace = " << laplace << endl;
const Calculus::PrimalIdentity0 reorder = calculus.reorder<0, PRIMAL>(cells.begin(), cells.end());
const Calculus::PrimalIdentity0 laplace_ordered = reorder * laplace * reorder.transpose();
trace.info() << Eigen::MatrixXd(laplace_ordered.myContainer) << endl;
//! [dirichlet-solve]
typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> Solver;
Solver solver;
solver.compute(laplace);
Calculus::PrimalForm0 solved_solution = solver.solve(dirac);
//! [dirichlet-solve]
solved_solution.myContainer.array() /= solved_solution.myContainer.maxCoeff();
const Calculus::PrimalForm0 solved_solution_ordered = reorder * solved_solution;
Calculus::PrimalForm0 analytic_solution(calculus);
{
const Calculus::Index dirac_position = 17;
const Calculus::Index length = analytic_solution.length();
for (Calculus::Index kk=0; kk<length; kk++)
{
Calculus::Scalar alpha = (kk+1.)/(dirac_position+1.);
if (kk>dirac_position)
{
alpha = 1. - (kk-dirac_position)/(1.*length-dirac_position);
}
analytic_solution.myContainer(kk) = alpha;
}
}
trace.info() << solver.isValid() << " " << solver.myLinearAlgebraSolver.info() << endl;
{
std::ofstream handle("linear_structure_dirichlet.dat");
for (Calculus::Index kk=0; kk<analytic_solution.length(); kk++)
handle << solved_solution_ordered.myContainer(kk) << " " << analytic_solution.myContainer(kk) << endl;
}
FATAL_ERROR( (solved_solution_ordered-analytic_solution).myContainer.array().abs().maxCoeff() < 1e-5 );
{
Board2D board;
board << domain;
board << calculus;
board << solved_solution;
board.saveSVG("linear_structure_dirichlet_solution.svg");
}
{
Calculus::PrimalForm1 solved_solution_gradient = calculus.derivative<0, PRIMAL>() * solved_solution;
Board2D board;
board << domain;
board << calculus;
board << solved_solution_gradient;
board << calculus.sharp(solved_solution_gradient);
board.saveSVG("linear_structure_dirichlet_solution_gradient.svg");
}
trace.endBlock();
}
}
void test_manual_operators_3d()
{
trace.beginBlock("testing 3d operators");
const Z3i::Domain domain(Z3i::Point(0,0,0), Z3i::Point(1,1,1));
typedef DiscreteExteriorCalculus<3, 3, EigenLinearAlgebraBackend> Calculus;
Calculus calculus;
calculus.initKSpace<Z3i::Domain>(domain);
{ // filling primal calculus
// 0-cells
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(0,0,0)) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(2,0,0)) );
// 1-cells
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(0,1,0), Calculus::KSpace::POS) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(0,0,1), Calculus::KSpace::POS) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(1,0,0), Calculus::KSpace::POS) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(2,1,0), Calculus::KSpace::NEG) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(2,0,1), Calculus::KSpace::NEG) );
// 2-cells
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(0,1,1), Calculus::KSpace::NEG) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(1,0,1), Calculus::KSpace::POS) ); //FIXME strange cell orientation
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(2,1,1), Calculus::KSpace::POS) );
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(1,1,0), Calculus::KSpace::NEG) );
// 3-cells
calculus.insertSCell( calculus.myKSpace.sCell(Z3i::Point(1,1,1)) );
calculus.updateIndexes();
trace.info() << calculus << endl;
}
trace.beginBlock("base operators");
{
const Calculus::PrimalDerivative0 d0 = calculus.derivative<0, PRIMAL>();
const Calculus::DualDerivative2 d2p = calculus.derivative<2, DUAL>();
display_operator_info("d0", d0);
display_operator_info("d2p", d2p);
Eigen::MatrixXd d0_th(5, 2);
d0_th <<
-1, 0,
-1, 0,
-1, 1,
0, 1,
0, 1;
FATAL_ERROR( Eigen::MatrixXd(d0.myContainer) == d0_th );
FATAL_ERROR( Eigen::MatrixXd(d2p.myContainer) == d0_th.transpose() );
}
{
const Calculus::PrimalDerivative1 d1 = calculus.derivative<1, PRIMAL>();
const Calculus::DualDerivative1 d1p = calculus.derivative<1, DUAL>();
display_operator_info("d1", d1);
display_operator_info("d1p", d1p);
Eigen::MatrixXd d1_th(4, 5);
d1_th <<
0, -1, 1, 0, -1,
1, 0, -1, 1, 0,
0, 0, 0, -1, 1,
-1, 1, 0, 0, 0;
FATAL_ERROR( Eigen::MatrixXd(d1.myContainer) == d1_th );
FATAL_ERROR( Eigen::MatrixXd(d1p.myContainer) == d1_th.transpose() );
}
{
const Calculus::PrimalDerivative2 d2 = calculus.derivative<2, PRIMAL>();
const Calculus::DualDerivative0 d0p = calculus.derivative<0, DUAL>();
display_operator_info("d2", d2);
display_operator_info("d0p", d0p);
Eigen::MatrixXd d2_th(1, 4);
d2_th << -1, -1, -1, -1;
FATAL_ERROR( Eigen::MatrixXd(d2.myContainer) == d2_th );
FATAL_ERROR( Eigen::MatrixXd(d0p.myContainer) == d2_th.transpose() );
}
trace.endBlock();
/*
QApplication app(0, NULL);
typedef Viewer3D<Z3i::Space, Z3i::KSpace> Viewer;
Viewer* viewer = new Viewer(calculus.myKSpace);
viewer->show();
viewer->setWindowTitle("structure");
(*viewer) << CustomColors3D(DGtal::Color(255,0,0), DGtal::Color(0,0,0));
(*viewer) << domain;
Display3DFactory<Z3i::Space, Z3i::KSpace>::draw(*viewer, calculus);
(*viewer) << Viewer::updateDisplay;
app.exec();
*/
trace.endBlock();
}
void propa_2d()
{
trace.beginBlock("2d propagation");
typedef DiscreteExteriorCalculus<2, 2, EigenLinearAlgebraBackend> Calculus;
typedef DiscreteExteriorCalculusFactory<EigenLinearAlgebraBackend> CalculusFactory;
{
trace.beginBlock("solving time dependent equation");
const Calculus::Scalar cc = 8; // px/s
trace.info() << "cc = " << cc << endl;
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(29,29));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
//! [time_laplace]
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>() + 1e-8 * calculus.identity<0, DUAL>();
//! [time_laplace]
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
//! [time_eigen]
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd eigen_vectors = eigen_solver.eigenvectors();
//! [time_eigen]
trace.info() << "eigen_values_range = " << eigen_values.minCoeff() << "/" << eigen_values.maxCoeff() << endl;
trace.endBlock();
//! [time_omega]
const Eigen::VectorXd angular_frequencies = cc * eigen_values.array().sqrt();
//! [time_omega]
Eigen::VectorXcd initial_wave = Eigen::VectorXcd::Zero(calculus.kFormLength(0, DUAL));
//set_initial_phase_null(calculus, initial_wave);
set_initial_phase_dir_yy(calculus, initial_wave);
{
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, initial_wave.real());
board.saveSVG("propagation_time_wave_initial_coarse.svg");
}
//! [time_init_proj]
Eigen::VectorXcd initial_projections = eigen_vectors.transpose() * initial_wave;
//! [time_init_proj]
// low pass
//! [time_low_pass]
const Calculus::Scalar lambda_cutoff = 4.5;
const Calculus::Scalar angular_frequency_cutoff = 2*M_PI * cc / lambda_cutoff;
int cutted = 0;
for (int kk=0; kk<initial_projections.rows(); kk++)
{
const Calculus::Scalar angular_frequency = angular_frequencies(kk);
if (angular_frequency < angular_frequency_cutoff) continue;
initial_projections(kk) = 0;
cutted ++;
}
//! [time_low_pass]
trace.info() << "cutted = " << cutted << "/" << initial_projections.rows() << endl;
{
const Eigen::VectorXcd wave = eigen_vectors * initial_projections;
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, wave.real());
board.saveSVG("propagation_time_wave_initial_smoothed.svg");
}
const int kk_max = 60;
trace.progressBar(0,kk_max);
for (int kk=0; kk<kk_max; kk++)
{
//! [time_solve_time]
const Calculus::Scalar time = kk/20.;
const Eigen::VectorXcd current_projections = (angular_frequencies * std::complex<double>(0,time)).array().exp() * initial_projections.array();
const Eigen::VectorXcd current_wave = eigen_vectors * current_projections;
//! [time_solve_time]
std::stringstream ss;
ss << "propagation_time_wave_solution_" << std::setfill('0') << std::setw(3) << kk << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-1, 1));
board << Calculus::DualForm0(calculus, current_wave.real());
board.saveSVG(ss.str().c_str());
trace.progressBar(kk+1,kk_max);
}
trace.info() << endl;
trace.endBlock();
}
{
trace.beginBlock("forced oscillations");
const Z2i::Domain domain(Z2i::Point(0,0), Z2i::Point(50,50));
const Calculus calculus = CalculusFactory::createFromDigitalSet(generateDiskSet(domain), false);
const Calculus::DualIdentity0 laplace = calculus.laplace<DUAL>();
trace.info() << "laplace = " << laplace << endl;
trace.beginBlock("finding eigen pairs");
typedef Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> EigenSolverMatrix;
const EigenSolverMatrix eigen_solver(laplace.myContainer);
const Eigen::VectorXd laplace_eigen_values = eigen_solver.eigenvalues();
const Eigen::MatrixXd laplace_eigen_vectors = eigen_solver.eigenvectors();
trace.info() << "eigen_values_range = " << laplace_eigen_values.minCoeff() << "/" << laplace_eigen_values.maxCoeff() << endl;
trace.endBlock();
Calculus::DualForm0 concentration(calculus);
{
const Z2i::Point point(25,25);
const Calculus::Cell cell = calculus.myKSpace.uSpel(point);
const Calculus::Index index = calculus.getCellIndex(cell);
concentration.myContainer(index) = 1;
}
{
Board2D board;
board << domain;
board << concentration;
board.saveSVG("propagation_forced_concentration.svg");
}
for (int ll=0; ll<6; ll++)
{
//! [forced_lambda]
const Calculus::Scalar lambda = 4*20.75/(1+2*ll);
//! [forced_lambda]
trace.info() << "lambda = " << lambda << endl;
//! [forced_dalembert_eigen]
const Eigen::VectorXd dalembert_eigen_values = (laplace_eigen_values.array() - (2*M_PI/lambda)*(2*M_PI/lambda)).array().inverse();
const Eigen::MatrixXd concentration_to_wave = laplace_eigen_vectors * dalembert_eigen_values.asDiagonal() * laplace_eigen_vectors.transpose();
//! [forced_dalembert_eigen]
//! [forced_wave]
Calculus::DualForm0 wave(calculus, concentration_to_wave * concentration.myContainer);
//! [forced_wave]
wave.myContainer /= wave.myContainer(calculus.getCellIndex(calculus.myKSpace.uSpel(Z2i::Point(25,25))));
{
trace.info() << "saving samples" << endl;
const Calculus::Properties properties = calculus.getProperties();
{
std::stringstream ss;
ss << "propagation_forced_samples_hv_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_horizontal(kk,25);
const Z2i::Point point_vertical(25,kk);
const Calculus::Scalar xx = 2 * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_horizontal) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_vertical) << endl;
}
}
{
std::stringstream ss;
ss << "propagation_forced_samples_diag_" << ll << ".dat";
std::ofstream handle(ss.str().c_str());
for (int kk=0; kk<=50; kk++)
{
const Z2i::Point point_diag_pos(kk,kk);
const Z2i::Point point_diag_neg(kk,50-kk);
const Calculus::Scalar xx = 2 * sqrt(2) * (kk/50. - .5);
handle << xx << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_pos) << " ";
handle << sample_dual_0_form<Calculus>(properties, wave, point_diag_neg) << endl;
}
}
}
{
std::stringstream ss;
ss << "propagation_forced_wave_" << ll << ".svg";
Board2D board;
board << domain;
board << CustomStyle("KForm", new KFormStyle2D(-.5, 1));
board << wave;
board.saveSVG(ss.str().c_str());
}
}
trace.endBlock();
}
trace.endBlock();
}
int main(int argc, char* argv[])
{
using DGtal::trace;
using std::endl;
using DGtal::PRIMAL;
using DGtal::DUAL;
const Options options = parse_options(argc, argv);
const KSpace kspace;
const Calculus calculus;
const FlatVector original_face_normals;
if (!ends_with(options.image_filename, ".csv"))
{
ASSERT( !options.image_filename.empty() );
typedef DGtal::Z3i::Domain Domain;
typedef DGtal::ImageSelector<Domain, unsigned char>::Type ImageUChar;
trace.info() << "image_filename=" << options.image_filename << endl;
ImageUChar image_uchar = DGtal::GenericReader<ImageUChar>::import(options.image_filename);
const Domain domain = image_uchar.domain();
trace.info() << "domain=" << domain << endl;
const Point center = (domain.upperBound()+domain.lowerBound())/2;
trace.info() << "center=" << center << endl;
const ImageShape<ImageUChar> shape(&image_uchar, center);
const_cast<KSpace&>(kspace).init(domain.lowerBound()-center-Point::diagonal(1), domain.upperBound()-center+Point::diagonal(1), true);
std::tie(const_cast<Calculus&>(calculus), const_cast<FlatVector&>(original_face_normals)) =
initCalculusAndNormalsWithNoise(kspace, shape, options.normal_radius, options.noise_level);
}
if (ends_with(options.image_filename, ".csv"))
{
ASSERT( !options.image_filename.empty() );
trace.info() << "csv_filename=" << options.image_filename << endl;
std::tie(const_cast<Calculus&>(calculus), const_cast<FlatVector&>(original_face_normals)) =
initCalculusAndNormalsFromSurfelNormalsCSV(options.image_filename);
}
const FlatVector original_vertex_normals = vertexNormals(calculus, original_face_normals);
const FlatVector original_positions;
const FlatVector regularized_positions;
const FlatVector original_centers;
const FlatVector regularized_centers;
std::tie(const_cast<FlatVector&>(original_positions),
const_cast<FlatVector&>(regularized_positions),
const_cast<FlatVector&>(original_centers),
const_cast<FlatVector&>(regularized_centers)) =
approximateSurface(calculus, original_face_normals,
ApproxParams({options.regularization_position, options.regularization_center, options.align, options.fairness, options.barycenter}));
ASSERT( original_positions.size() == 3*calculus.kFormLength(0, PRIMAL) );
ASSERT( regularized_positions.size() == 3*calculus.kFormLength(0, PRIMAL) );
ASSERT( original_centers.size() == 3*calculus.kFormLength(2, PRIMAL) );
ASSERT( regularized_centers.size() == 3*calculus.kFormLength(2, PRIMAL) );
{
trace.beginBlock( "computing energies" );
{
double position_energy = 0;
double align_energy = 0;
std::tie( position_energy, align_energy ) = approximateSurfaceEnergies(
calculus, original_face_normals, original_positions );
align_energy *= options.align;
position_energy *= options.regularization_position;
trace.info() << "original_energies=" << position_energy << " "
<< align_energy << " " << position_energy + align_energy
<< endl;
}
{
double position_energy = 0;
double align_energy = 0;
std::tie(position_energy, align_energy) = approximateSurfaceEnergies(calculus, original_face_normals, regularized_positions);
align_energy *= options.align;
position_energy *= options.regularization_position;
trace.info() << "regularized_energies=" << position_energy << " " << align_energy << " " << position_energy+align_energy << endl;
}
trace.endBlock();
}
{
ASSERT( !options.regularized_obj_filename.empty() );
trace.info() << "regularized_obj_filename=" << options.regularized_obj_filename << endl;
exportOBJ(calculus, regularized_positions, options.regularized_obj_filename);
}
if (!options.cubical_obj_filename.empty())
{
ASSERT( !options.cubical_obj_filename.empty() );
trace.info() << "cubical_obj_filename=" << options.cubical_obj_filename << endl;
exportOBJ(calculus, original_positions, options.cubical_obj_filename);
}
return 0;
}
int main( int argc, char* argv[] )
{
using namespace Z2i;
typedef ImageSelector<Domain, unsigned char>::Type Image;
// parse command line ----------------------------------------------
namespace po = boost::program_options;
po::options_description general_opt("Allowed options are: ");
general_opt.add_options()
("help,h", "display this message")
("input,i", po::value<string>(), "the input image filename." )
("output,o", po::value<string>()->default_value( "AT" ), "the output image basename." )
("lambda,l", po::value<double>(), "the parameter lambda." )
("lambda-1,1", po::value<double>()->default_value( 0.3125 ), "the initial parameter lambda (l1)." ) // 0.3125
("lambda-2,2", po::value<double>()->default_value( 0.00005 ), "the final parameter lambda (l2)." )
("lambda-ratio,q", po::value<double>()->default_value( sqrt(2) ), "the division ratio for lambda from l1 to l2." )
("alpha,a", po::value<double>()->default_value( 1.0 ), "the parameter alpha." )
("epsilon,e", po::value<double>()->default_value( 4.0/64.0 ), "the parameter epsilon." )
//("gridstep,g", po::value<double>()->default_value( 1.0 ), "the parameter h, i.e. the gridstep." )
("nbiter,n", po::value<int>()->default_value( 10 ), "the maximum number of iterations." )
("sigma,s", po::value<double>()->default_value( 2.0 ), "the parameter of the first convolution." )
("rho,r", po::value<double>()->default_value( 3.0 ), "the parameter of the second convolution." )
("image-size,t", po::value<double>()->default_value( 64.0 ), "the size of the image." )
;
bool parseOK=true;
po::variables_map vm;
try {
po::store(po::parse_command_line(argc, argv, general_opt), vm);
} catch ( const exception& ex ) {
parseOK = false;
cerr << "Error checking program options: "<< ex.what()<< endl;
}
po::notify(vm);
if ( ! parseOK || vm.count("help") || !vm.count("input") )
{
cerr << "Usage: " << argv[0] << " -i toto.pgm\n"
<< "Computes the Ambrosio-Tortorelli reconstruction/segmentation of an input image."
<< endl << endl
<< " / "
<< endl
<< " | a.(u-g)^2 + v^2 |grad u|^2 + le.|grad v|^2 + (l/4e).(1-v)^2 "
<< endl
<< " / "
<< endl << endl
<< general_opt << "\n";
return 1;
}
string f1 = vm[ "input" ].as<string>();
string f2 = vm[ "output" ].as<string>();
double l1 = vm[ "lambda-1" ].as<double>();
double l2 = vm[ "lambda-2" ].as<double>();
double lr = vm[ "lambda-ratio" ].as<double>();
if ( vm.count( "lambda" ) ) l1 = l2 = vm[ "lambda" ].as<double>();
if ( l2 > l1 ) l2 = l1;
if ( lr <= 1.0 ) lr = sqrt(2);
double a = vm[ "alpha" ].as<double>();
double e = vm[ "epsilon" ].as<double>();
double t = vm[ "image-size" ].as<double>();
//double h = vm[ "gridstep" ].as<double>();
double h = 1.0 / t;
e = 4.0*h;
int n = vm[ "nbiter" ].as<int>();
int s = vm[ "sigma" ].as<double>();
int r = vm[ "rho" ].as<double>();
trace.beginBlock("Reading image");
Image image = GenericReader<Image>::import( f1 );
trace.endBlock();
// MODIF : ouverture du fichier pour les resultats ***********************************************************************
const string file = f2 + ".txt";
ofstream f(file.c_str());
f << "# l \t" << " a \t" << " e \t" << "a(u-g)^2 \t" << "v^2|grad u|^2 \t" << " le|grad v|^2 \t" << " l(1-v)^2/4e \t" << " l.per \t" << "AT tot"<< endl;
// ***********************************************************************************************************************
trace.beginBlock("Creating calculus");
typedef DiscreteExteriorCalculus<2,2, EigenLinearAlgebraBackend> Calculus;
Domain domain = image.domain();
Point p0 = domain.lowerBound(); p0 *= 2;
Point p1 = domain.upperBound(); p1 *= 2;
Domain kdomain( p0, p1 );
Image dbl_image( kdomain );
Calculus calculus;
const KSpace& K = calculus.myKSpace;
// Les pixels sont des 0-cellules du primal.
for ( Domain::ConstIterator it = kdomain.begin(), itE = kdomain.end(); it != itE; ++it )
calculus.insertSCell( K.sCell( *it ) ); // ajoute toutes les cellules de Khalimsky.
calculus.updateIndexes();
trace.info() << calculus << endl;
Calculus::PrimalForm0 g( calculus );
for ( Calculus::Index index = 0; index < g.myContainer.rows(); index++)
{
const Calculus::SCell& cell = g.getSCell( index );
g.myContainer( index ) = ((double) image( K.sCoords( cell ) )) /
255.0;
}
// {
// Board2D board;
// board << calculus;
// board << CustomStyle( "KForm", new KFormStyle2D( 0.0, 1.0 ) )
// << g;
// string str_calculus = f2 + "-calculus.eps";
// board.saveEPS( str_calculus.c_str() );
// }
trace.endBlock();
trace.beginBlock("building AT functionnals");
trace.info() << "primal_D0" << endl;
const Calculus::PrimalDerivative0 primal_D0 = calculus.derivative<0,PRIMAL>();
trace.info() << "primal_h0" << endl;
const Calculus::PrimalHodge0 primal_h0 = calculus.hodge<0,PRIMAL>();
trace.info() << "primal_h1" << endl;
const Calculus::PrimalHodge1 primal_h1 = calculus.hodge<1,PRIMAL>();
trace.info() << "dual_D1" << endl;
const Calculus::DualDerivative1 dual_D1 = calculus.derivative<1,DUAL>();
trace.info() << "dual_h2" << endl;
const Calculus::DualHodge2 dual_h2 = calculus.hodge<2,DUAL>();
trace.info() << "primal_D1" << endl;
const Calculus::PrimalDerivative1 primal_D1 = calculus.derivative<1,PRIMAL>();
trace.info() << "primal_h2" << endl;
const Calculus::PrimalHodge2 primal_h2 = calculus.hodge<2,PRIMAL>();
trace.info() << "dual_D0" << endl;
const Calculus::DualDerivative0 dual_D0 = calculus.derivative<0,DUAL>();
trace.info() << "dual_h1" << endl;
const Calculus::DualHodge1 dual_h1 = calculus.hodge<1,DUAL>();
trace.info() << "ag" << endl;
const Calculus::PrimalForm0 ag = a * g;
trace.info() << "u" << endl;
Calculus::PrimalForm0 u = ag;
// trace.info() << "A^t*diag(v)^2*A = " << Av2A << endl;
trace.info() << "v" << endl;
Calculus::PrimalForm1 v( calculus );
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
v.myContainer( index ) = 1.0;
trace.endBlock();
// SparseLU is so much faster than SparseQR
// SimplicialLLT is much faster than SparsLU
// typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;
// typedef EigenLinearAlgebraBackend::SolverSparseLU LinearAlgebraSolver;
typedef EigenLinearAlgebraBackend::SolverSimplicialLLT LinearAlgebraSolver;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> SolverU;
SolverU solver_u;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL> SolverV;
SolverV solver_v;
SolverV solver_tBB;
const Calculus::PrimalIdentity1 tBB = -1.0 * ( primal_D0 * dual_h2 * dual_D1 * primal_h1 + dual_h1 * dual_D0 * primal_h2 * primal_D1 );
solver_tBB.compute( tBB );
while ( l1 >= l2 )
{
trace.info() << "************ lambda = " << l1 << " **************" << endl;
double l = l1;
trace.info() << "B'B'" << endl;
const Calculus::PrimalIdentity1 lBB = l * tBB;
// const Calculus::PrimalIdentity1 lBB = - l * ( primal_D0 * dual_h2 * dual_D1 * primal_h1 + dual_h1 * dual_D0 * primal_h2 * primal_D1 );
Calculus::PrimalForm1 l_4( calculus );
for ( Calculus::Index index = 0; index < l_4.myContainer.rows(); index++)
l_4.myContainer( index ) = l/4.0;
//Calculus::PrimalIdentity1 BB = eps * lBB + (l/(4*eps)) * calculus.identity<1, PRIMAL>();
//trace.info() << "le*B'^t*B' + l/(4e)Id" << BB << endl;
Calculus::PrimalIdentity1 BB = 0.0 * lBB;
double coef_eps = 2.0;
double eps = coef_eps*e;
for( int k = 0 ; k < 5 ; ++k )
{
if (eps/coef_eps < h*h)
break;
else
{
eps /= coef_eps;
BB = (h * eps) * lBB + (h*l/(4.0*eps)) * calculus.identity<1, PRIMAL>();
int i = 0;
for ( ; i < n; ++i )
{
trace.info() << "------ Iteration " << k << ":" << i << "/" << n << " ------" << endl;
trace.beginBlock("Solving for u");
trace.info() << "Building matrix Av2A" << endl;
Calculus::PrimalIdentity1 Mv2 = calculus.identity<1, PRIMAL>();
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
Mv2.myContainer.coeffRef( index, index ) = v.myContainer[ index ] * v.myContainer[ index ];
const Calculus::PrimalIdentity0 Av2A = ( - 1.0 * h ) * dual_h2 * dual_D1 * primal_h1 * Mv2 * primal_D0
+ ( a * h*h ) * calculus.identity<0, PRIMAL>();
trace.info() << "Prefactoring matrix Av2A" << endl;
solver_u.compute( Av2A );
trace.info() << "Solving Av2A u = ag" << endl;
u = solver_u.solve( (h*h) * ag );
trace.info() << ( solver_u.isValid() ? "OK" : "ERROR" ) << " " << solver_u.myLinearAlgebraSolver.info() << endl;
trace.endBlock();
trace.beginBlock("Solving for v");
trace.info() << "Building matrix BB+Mw2" << endl;
const Calculus::PrimalForm1 former_v = v;
const Calculus::PrimalForm1 w = primal_D0 * u;
Calculus::PrimalIdentity1 Mw2 = calculus.identity<1, PRIMAL>();
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
Mw2.myContainer.coeffRef( index, index ) = h * w.myContainer[ index ] * w.myContainer[ index ];
trace.info() << "Prefactoring matrix BB+Mw2" << endl;
solver_v.compute( BB + Mw2 );
trace.info() << "Solving (BB+Mw2)v = l_4e" << endl;
v = solver_v.solve( ( h * (1.0/eps) ) * l_4 );
trace.info() << ( solver_v.isValid() ? "OK" : "ERROR" ) << " " << solver_v.myLinearAlgebraSolver.info() << endl;
trace.endBlock();
double n_infty = 0.0;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
n_infty = max( n_infty, abs( v.myContainer( index ) - former_v.myContainer( index ) ) );
trace.info() << "Variation |v^k+1 - v^k|_oo = " << n_infty << endl;
if ( n_infty < 1e-4 ) break;
}
//BB = eps * lBB + (l/(4*eps)) * calculus.identity<1, PRIMAL>();
}
}
// *** MODIF : affichage des energies ***********************************************************************************
typedef Calculus::SparseMatrix SparseMatrix;
typedef Eigen::Matrix<double,Dynamic,Dynamic> Matrix;
trace.beginBlock("Computing energies");
// a(u-g)^2
trace.info() << "- a(u-g)^2 " << std::endl;
double UmG2 = 0.0;
for ( Calculus::Index index = 0; index < u.myContainer.rows(); index++)
UmG2 += a * (u.myContainer( index ) - g.myContainer( index )) * (u.myContainer( index ) - g.myContainer( index ));
// v^2|grad u|^2
trace.info() << "- v^2|grad u|^2" << std::endl;
double V2gradU2 = 0.0;
SolverU solver_Av2A;
trace.info() << " - Id" << std::endl;
Calculus::PrimalIdentity1 Mv2 = calculus.identity<1, PRIMAL>();
trace.info() << " - M := Diag(v^2)" << std::endl;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
Mv2.myContainer.coeffRef( index, index ) = v.myContainer[ index ] * v.myContainer[ index ];
trace.info() << " - * D_1 * M * D_0" << std::endl;
const Calculus::PrimalIdentity0 Av2A = - 1.0 * dual_h2 * dual_D1 * primal_h1 * Mv2 * primal_D0;
trace.info() << " - N := compute (* D_1 * M * D_0)" << std::endl;
solver_Av2A.compute( Av2A );
// JOL: 1000 * plus rapide !
trace.info() << " - u^t N u" << std::endl;
Calculus::PrimalForm0 u_prime = Av2A * u;
for ( Calculus::Index index = 0; index < u.myContainer.rows(); index++)
V2gradU2 += u.myContainer( index ) * u_prime.myContainer( index );
// for ( Calculus::Index index_i = 0; index_i < u.myContainer.rows(); index_i++)
// for ( Calculus::Index index_j = 0; index_j < u.myContainer.rows(); index_j++)
// V2gradU2 += u.myContainer( index_i ) * Av2A.myContainer.coeff( index_i,index_j ) * u.myContainer( index_j ) ;
// le|grad v|^2
trace.info() << "- le|grad v|^2" << std::endl;
Calculus::PrimalForm1 v_prime = tBB * v;
double gradV2 = 0.0;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
gradV2 += l * eps * v.myContainer( index ) * v_prime.myContainer( index );
// for ( Calculus::Index index_i = 0; index_i < v.myContainer.rows(); index_i++)
// for ( Calculus::Index index_j = 0; index_j < v.myContainer.rows(); index_j++)
// gradV2 += l * eps * v.myContainer( index_i ) * tBB.myContainer.coeff( index_i,index_j ) * v.myContainer( index_j );
// l(1-v)^2/4e
trace.info() << "- l(1-v)^2/4e" << std::endl;
double Vm12 = 0.0;
for ( Calculus::Index index_i = 0; index_i < v.myContainer.rows(); index_i++)
Vm12 += (l/(4*eps)) * (1 - 2*v.myContainer( index_i ) + v.myContainer( index_i )*v.myContainer( index_i ));
// l.per
trace.info() << "- l.per" << std::endl;
double Lper = h*gradV2 + h*Vm12;
// double per = 0.0;
// for ( Calculus::Index index_i = 0; index_i < v.myContainer.rows(); index_i++)
// {
// per += (1/(4*e)) * (1 - 2*v.myContainer( index_i ) + v.myContainer( index_i )*v.myContainer( index_i ));
// for ( Calculus::Index index_j = 0; index_j < v.myContainer.rows(); index_j++)
// per += e * v.myContainer( index_i ) * tBB.myContainer( index_i,index_j ) * v.myContainer( index_j );
// }
// AT tot
double ATtot = h*h*UmG2 + h*V2gradU2 + h*gradV2 + h*Vm12;
//f << "l " << " a " << " e " << " a(u-g)^2 " << " v^2|grad u|^2 " << " le|grad v|^2 " << " l(1-v)^2/4e " << " l.per " << " AT tot"<< endl;
f << tronc(l,8) << "\t" << a << "\t" << tronc(eps,4) << "\t" << tronc(UmG2,5) << "\t" << tronc(V2gradU2,5) << "\t" << tronc(gradV2,5) << "\t" << tronc(Vm12,5) << "\t" << tronc(Lper,5) << "\t" << tronc(ATtot,5) << endl;
trace.endBlock();
// ***********************************************************************************************************************
// int int_l = (int) floor(l);
// int dec_l = (int) (floor((l-floor(l))*10000));
// std::ostringstream ss;
// ss << (double) tronc(l,7);
// string s = ss.str();
// const int pos = s.find(".");
// string tronc_l = s.substr(0,pos) + "_" + s.substr(pos+1);
{
// Board2D board;
// board << calculus;
// board << CustomStyle( "KForm", new KFormStyle2D( 0.0, 1.0 ) ) << u;
// ostringstream oss;
// oss << f2 << "-u-" << i << ".eps";
// string str_u = oss.str(); //f2 + "-u-" + .eps";
// board.saveEPS( str_u.c_str() );
Image image2 = image;
PrimalForm0ToImage( calculus, u, image2 );
ostringstream oss2;
// oss2 << f2 << "-l" << int_l << "_" << dec_l << "-u.pgm";
// oss2 << f2 << "-l" << tronc_l << "-u.pgm";
oss2 << boost::format("%s-l%.7f-u.pgm") %f2 %l;
string str_image_u = oss2.str();
// boost::regex re("\\.");
// str_image_u = boost::regex_replace(str_image_u, re , "_");
// const int pos = str_image_u.find(".");
// str_image_u = str_image_u.substr(0,pos) + "_" + str_image_u.substr(pos+1);
image2 >> str_image_u.c_str();
}
{
// Board2D board;
// board << calculus;
// board << CustomStyle( "KForm", new KFormStyle2D( 0.0, 1.0 ) )
// << v;
// ostringstream oss;
// oss << f2 << "-v-" << i << ".eps";
// string str_v = oss.str();
// board.saveEPS( str_v.c_str() );
PrimalForm1ToImage( calculus, v, dbl_image );
ostringstream oss3;
//oss3 << f2 << "-l" << tronc_l << "-v.pgm";
oss3 << boost::format("%s-l%.7f-v.pgm") %f2 %l;
string str_image_v = oss3.str();
dbl_image >> str_image_v.c_str();
}
l1 /= lr;
} // while ( l1 >= l2 )
// typedef SelfAdjointEigenSolver<MatrixXd> EigenSolverMatrix;
// const EigenSolverMatrix eigen_solver(laplace.myContainer);
// const VectorXd eigen_values = eigen_solver.eigenvalues();
// const MatrixXd eigen_vectors = eigen_solver.eigenvectors();
// for (int kk=0; kk<laplace.myContainer.rows(); kk++)
// {
// Calculus::Scalar eigen_value = eigen_values(kk, 0);
// const VectorXd eigen_vector = eigen_vectors.col(kk);
// const Calculus::DualForm0 eigen_form = Calculus::DualForm0(calculus, eigen_vector);
// std::stringstream ss;
// ss << "chladni_eigen_" << kk << ".svg";
// const std::string filename = ss.str();
// ss << "chladni_eigen_vector_" << kk << ".svg";
// trace.info() << kk << " " << eigen_value << " " << sqrt(eigen_value) << " " << eigen_vector.minCoeff() << " " << eigen_vector.maxCoeff() << " " << standard_deviation(eigen_vector) << endl;
// Board2D board;
// board << domain;
// board << calculus;
// board << CustomStyle("KForm", new KFormStyle2D(eigen_vectors.minCoeff(),eigen_vectors.maxCoeff()));
// board << eigen_form;
// board.saveSVG(filename.c_str());
// }
f.close();
return 0;
}
int main( int argc, char* argv[] )
{
using namespace Z2i;
typedef ImageContainerBySTLVector<Domain, unsigned char> Image;
typedef ImageContainerBySTLVector<Domain, double> ImageDouble;
typedef ImageContainerBySTLVector<Domain,
SimpleMatrix<double,2,2> > ImageSimpleMatrix2d;
typedef ImageContainerBySTLVector<Domain, RealVector> ImageVector;
typedef std::vector< unsigned char >::iterator ImageIterator;
typedef std::vector< double >::iterator ImageDoubleIterator;
typedef std::vector< SimpleMatrix<double,2,2> >::iterator ImageSimpleMatrix2dIterator;
typedef std::vector< RealVector >::iterator ImageVectorIterator;
// parse command line ----------------------------------------------
namespace po = boost::program_options;
po::options_description general_opt("Allowed options are: ");
general_opt.add_options()
("help,h", "display this message")
("input,i", po::value<string>(), "the input image filename." )
("output,o", po::value<string>()->default_value( "AT" ), "the output image basename." )
("lambda,l", po::value<double>(), "the parameter lambda." )
("lambda-1,1", po::value<double>()->default_value( 0.3125 ), "the initial parameter lambda (l1)." ) // 0.3125
("lambda-2,2", po::value<double>()->default_value( 0.00005 ), "the final parameter lambda (l2)." )
("lambda-ratio,q", po::value<double>()->default_value( sqrt(2) ), "the division ratio for lambda from l1 to l2." )
("alpha,a", po::value<double>()->default_value( 1.0 ), "the parameter alpha." )
("epsilon,e", po::value<double>()->default_value( 1.0 ), "the initial and final parameter epsilon of AT functional at the same time." )
("epsilon-1", po::value<double>(), "the initial parameter epsilon." )
("epsilon-2", po::value<double>(), "the final parameter epsilon." )
("epsilon-r", po::value<double>()->default_value( 2.0 ), "sets the ratio between two consecutive epsilon values of AT functional." )
//("gridstep,g", po::value<double>()->default_value( 1.0 ), "the parameter h, i.e. the gridstep." )
("nbiter,n", po::value<int>()->default_value( 10 ), "the maximum number of iterations." )
//("sigma,s", po::value<double>()->default_value( 2.0 ), "the parameter of the first convolution." )
//("rho,r", po::value<double>()->default_value( 3.0 ), "the parameter of the second convolution." )
("image-size,t", po::value<double>()->default_value( 64.0 ), "the size of the image." )
;
bool parseOK=true;
po::variables_map vm;
try {
po::store(po::parse_command_line(argc, argv, general_opt), vm);
} catch ( const exception& ex ) {
parseOK = false;
cerr << "Error checking program options: "<< ex.what()<< endl;
}
po::notify(vm);
if ( ! parseOK || vm.count("help") || !vm.count("input") )
{
cerr << "Usage: " << argv[0] << " -i toto.pgm\n"
<< "Computes the Ambrosio-Tortorelli reconstruction/segmentation of an input image."
<< endl << endl
<< " / "
<< endl
<< " | a.(u-g)^2 + v^2 |grad u|^2 + le.|grad v|^2 + (l/4e).(1-v)^2 "
<< endl
<< " / "
<< endl
<< "Discretized as (u 0-form, v 1-form, A vertex-edge bdry, B edge-face bdy)" << endl
<< "E(u,v) = a(u-g)^t (u-g) + u^t A^t diag(v)^2 A^t u + l e v^t (A A^t + B^t B) v + l/(4e) (1-v)^t (1-v)" << endl
<< endl
<< general_opt << "\n"
<< "Example: ./at-u0-v1 -i ../Images/cerclesTriangle64b02.pgm -o tmp -a 0.05 -e 1 -1 0.1 -2 0.00001 -t 64"
<< endl;
return 1;
}
string f1 = vm[ "input" ].as<string>();
string f2 = vm[ "output" ].as<string>();
double l1 = vm[ "lambda-1" ].as<double>();
double l2 = vm[ "lambda-2" ].as<double>();
double lr = vm[ "lambda-ratio" ].as<double>();
if ( vm.count( "lambda" ) ) l1 = l2 = vm[ "lambda" ].as<double>();
if ( l2 > l1 ) l2 = l1;
if ( lr <= 1.0 ) lr = sqrt(2);
double a = vm[ "alpha" ].as<double>();
double e = vm[ "epsilon" ].as<double>();
double e1 = vm.count( "epsilon-1" ) ? vm[ "epsilon-1" ].as<double>() : e;
double e2 = vm.count( "epsilon-2" ) ? vm[ "epsilon-2" ].as<double>() : e;
double er = vm[ "epsilon-r" ].as<double>();
double t = vm[ "image-size" ].as<double>();
//double h = vm[ "gridstep" ].as<double>();
double h = 1.0 / t;
int n = vm[ "nbiter" ].as<int>();
//double s = vm[ "sigma" ].as<double>();
//double r = vm[ "rho" ].as<double>();
trace.beginBlock("Reading image");
Image image = GenericReader<Image>::import( f1 );
Image end_image = image;
trace.endBlock();
// opening file
const string file = f2 + ".txt";
ofstream f(file.c_str());
f << "# l \t" << " a \t" << " e \t" << "a(u-g)^2 \t" << "v^2|grad u|^2 \t" << " le|grad v|^2 \t" << " l(1-v)^2/4e \t" << " l.per \t" << "AT tot"<< endl;
trace.beginBlock("Creating calculus");
typedef DiscreteExteriorCalculus<2,2, EigenLinearAlgebraBackend> Calculus;
Domain domain = image.domain();
Point p0 = domain.lowerBound(); p0 *= 2;
Point p1 = domain.upperBound(); p1 *= 2;
Domain kdomain( p0, p1 );
Image dbl_image( kdomain );
Calculus calculus;
calculus.initKSpace( ConstAlias<Domain>( domain ) );
const KSpace& K = calculus.myKSpace;
// Les pixels sont des 0-cellules du primal.
for ( Domain::ConstIterator it = kdomain.begin(), itE = kdomain.end(); it != itE; ++it )
calculus.insertSCell( K.sCell( *it ) ); // ajoute toutes les cellules de Khalimsky.
calculus.updateIndexes();
trace.info() << calculus << endl;
Calculus::PrimalForm0 g( calculus );
double min_g = 300.0, max_g = 0.0;
for ( Calculus::Index index = 0; index < g.myContainer.rows(); index++)
{
const Calculus::SCell& cell = g.getSCell( index );
g.myContainer( index ) = ((double) image( K.sCoords( cell ) )) /
255.0;
min_g = std::min( min_g , g.myContainer( index ) );
max_g = std::max( max_g , g.myContainer( index ) );
}
trace.info() << "min_g= " << min_g << " max_g= " << max_g << std::endl;
trace.endBlock();
// u = g at the beginning
trace.info() << "u" << endl;
Calculus::PrimalForm0 u = g;
// v = 1 at the beginning
trace.info() << "v" << endl;
Calculus::PrimalForm1 v( calculus );
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
v.myContainer( index ) = 1;
trace.beginBlock("building AT functionnals");
trace.info() << "primal_D0" << endl;
const Calculus::PrimalDerivative0 primal_D0 = calculus.derivative<0,PRIMAL>();
trace.info() << "primal_D1" << endl;
const Calculus::PrimalDerivative1 primal_D1 = calculus.derivative<1,PRIMAL>();
trace.info() << "dual_D0" << endl;
const Calculus::DualDerivative0 dual_D0 = calculus.derivative<0,DUAL>();
trace.info() << "dual_D1" << endl;
const Calculus::DualDerivative1 dual_D1 = calculus.derivative<1,DUAL>();
trace.info() << "primal_h0" << endl;
const Calculus::PrimalHodge0 primal_h0 = calculus.hodge<0,PRIMAL>();
trace.info() << "primal_h1" << endl;
const Calculus::PrimalHodge1 primal_h1 = calculus.hodge<1,PRIMAL>();
trace.info() << "primal_h2" << endl;
const Calculus::PrimalHodge2 primal_h2 = calculus.hodge<2,PRIMAL>();
trace.info() << "dual_h1" << endl;
const Calculus::DualHodge1 dual_h1 = calculus.hodge<1,DUAL>();
trace.info() << "dual_h2" << endl;
const Calculus::DualHodge2 dual_h2 = calculus.hodge<2,DUAL>();
const DGtal::Dimension dimX = 0, dimY = 1;
// BEG JOL
// Calculus::PrimalIdentity1 tSS = calculus.identity<1, PRIMAL>();
// for ( Calculus::Index index_i = 0; index_i < tSS.myContainer.rows(); index_i++ )
// for ( Calculus::Index index_j = 0; index_j < tSS.myContainer.cols(); index_j++ )
// {
// tSS.myContainer.coeffRef( index_i, index_j ) = 0.0;
// for ( Calculus::Index index_k = 0; index_k < tSS.myContainer.rows(); index_k++ )
// tSS.myContainer.coeffRef( index_i, index_j ) += sharp_x.myContainer.coeffRef( index_k, index_i ) * sharp_x.myContainer.coeffRef( index_k, index_j )
// + sharp_y.myContainer.coeffRef( index_k, index_i ) * sharp_y.myContainer.coeffRef( index_k, index_j ) ;
// }
// END JOL
trace.endBlock();
const Calculus::PrimalIdentity0 Id0 = calculus.identity<0, PRIMAL>();
const Calculus::PrimalIdentity1 Id1 = calculus.identity<1, PRIMAL>();
const Calculus::PrimalIdentity2 Id2 = calculus.identity<2, PRIMAL>();
// Weight matrices
// Calculus::DualIdentity2 G0 = ( 1.0/(h*h) ) * calculus.identity<2, DUAL>();
Calculus::PrimalIdentity0 G0 = Id0; // = ( 1.0/(h*h) ) * calculus.identity<0, PRIMAL>();
Calculus::PrimalIdentity0 invG0 = Id0; // = (h*h) * calculus.identity<0, PRIMAL>();
// Calculus::DualIdentity1 G1 = calculus.identity<1, DUAL>();
Calculus::PrimalIdentity1 G1 = Id1; // = calculus.identity<1, PRIMAL>();
Calculus::PrimalIdentity1 invG1 = Id1; // = calculus.identity<1, PRIMAL>();
// Calculus::DualIdentity0 G2 = (h*h) * calculus.identity<0, DUAL>();
Calculus::PrimalIdentity2 G2 = Id2; // = (h*h) * calculus.identity<2, PRIMAL>();
Calculus::PrimalIdentity2 invG2 = Id2; // = ( 1.0/(h*h) ) * calculus.identity<2, PRIMAL>();
// Building alpha_G0_1
Calculus::PrimalIdentity0 alpha_iG0 = a * Id0; // a * calculus.identity<0, PRIMAL>(); // a * invG0; //diag_alpha;
Calculus::PrimalForm0 alpha_iG0_g = alpha_iG0 * g;
// Builds a Laplacian but at distance 2 !
// const Matrix& M = tA_tS_S_A.myContainer;
// for (int k = 0; k < M.outerSize(); ++k)
// {
// trace.info() << "-----------------------------------------------------------------------" << endl;
// for ( Matrix::InnerIterator it( M, k ); it; ++it )
// trace.info() << "[" << it.row() << "," << it.col() << "] = " << it.value() << endl;
// }
// Building iG1_A_G0_tA_iG1 + tB_iG2_B
// // A.tA
// const Calculus::PrimalIdentity1 lap_operator_v = -1.0 * ( invG1 * primal_D0 * G0 * dual_h2 * dual_D1 * primal_h1 * invG1 );
// // tB.B
// const Calculus::PrimalIdentity1 lap_operator_v = -1.0 * ( dual_h1 * dual_D0 * primal_h2 * invG2 * primal_D1 );
// tB.B + A.tA
const Calculus::PrimalIdentity1 lap_operator_v = -1.0 * ( invG1 * primal_D0 * G0 * dual_h2 * dual_D1 * primal_h1 * invG1
+ dual_h1 * dual_D0 * primal_h2 * invG2 * primal_D1 );
// SparseLU is so much faster than SparseQR
// SimplicialLLT is much faster than SparseLU
// typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;
// typedef EigenLinearAlgebraBackend::SolverSparseLU LinearAlgebraSolver;
typedef EigenLinearAlgebraBackend::SolverSimplicialLLT LinearAlgebraSolver;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> SolverU;
SolverU solver_u;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL> SolverV;
SolverV solver_v;
while ( l1 >= l2 )
{
trace.info() << "************ lambda = " << l1 << " **************" << endl;
double l = l1;
trace.info() << "B'B'" << endl;
const Calculus::PrimalIdentity1 lBB = l * lap_operator_v;
Calculus::PrimalForm1 l_sur_4( calculus );
for ( Calculus::Index index = 0; index < l_sur_4.myContainer.rows(); index++)
l_sur_4.myContainer( index ) = l/4.0;
l_sur_4 = Id1 * l_sur_4; //tS_S * l_sur_4; //
double epsilon = 0.0;
for( int i = 0; i < 2; ++i ) // change alpha
{
g = u;
alpha_iG0 = a * Id0;
alpha_iG0_g = alpha_iG0 * g;
for ( double eps = e1; eps >= e2; eps /= er )
{
Calculus::PrimalIdentity1 BB = eps * lBB + ( l/(4.0*eps) ) * Id1; // tS_S;
int i = 0;
for ( ; i < n; ++i )
{
trace.info() << "------ Iteration " << i << "/" << n << " ------" << endl;
trace.beginBlock("Solving for u");
trace.info() << "Building matrix Av2A" << endl;
//double tvtSSv = 0.0;
Calculus::PrimalIdentity1 diag_v = diag( calculus, v );
Calculus::PrimalDerivative0 v_A = diag_v * primal_D0;
Calculus::PrimalIdentity0 Av2A = square( calculus, v_A ) + alpha_iG0;
trace.info() << "Prefactoring matrix Av2A := tA_v_tv_A + alpha_iG0" << endl;
trace.info() << "-------------------------------------------------------------------------------" << endl;
// const Matrix& M = Av2A.myContainer;
// for (int k = 0; k < M.outerSize(); ++k)
// for ( Matrix::InnerIterator it( M, k ); it; ++it )
// trace.info() << "[" << it.row() << "," << it.col() << "] = " << it.value() << endl;
solver_u.compute( Av2A );
trace.info() << "Solving Av2A u = ag" << endl;
u = solver_u.solve( alpha_iG0_g );
trace.info() << ( solver_u.isValid() ? "OK" : "ERROR" ) << " " << solver_u.myLinearAlgebraSolver.info() << endl;
trace.info() << "-------------------------------------------------------------------------------" << endl;
trace.endBlock();
const Calculus::PrimalForm1 former_v = v;
trace.beginBlock("Solving for v");
trace.info() << "Building matrix BB+Mw2" << endl;
const Calculus::PrimalIdentity1 A_u = diag( calculus, primal_D0 * u );
const Calculus::PrimalIdentity1 tu_tA_A_u = square( calculus, A_u );
solver_v.compute( tu_tA_A_u + BB );
v = solver_v.solve( (1.0/eps) * l_sur_4 );
trace.info() << ( solver_v.isValid() ? "OK" : "ERROR" ) << " " << solver_v.myLinearAlgebraSolver.info() << endl;
trace.endBlock();
trace.beginBlock("Checking v, computing norms");
double m1 = 1.0;
double m2 = 0.0;
double ma = 0.0;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
{
double val = v.myContainer( index );
m1 = std::min( m1, val );
m2 = std::max( m2, val );
ma += val;
}
trace.info() << "1-form v: min=" << m1 << " avg=" << ( ma/ v.myContainer.rows() )
<< " max=" << m2 << std::endl;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
v.myContainer( index ) = std::min( std::max(v.myContainer( index ), 0.0) , 1.0 );
double n_infty = 0.0;
double n_2 = 0.0;
double n_1 = 0.0;
for ( Calculus::Index index = 0; index < v.myContainer.rows(); index++)
{
n_infty = max( n_infty, fabs( v.myContainer( index ) - former_v.myContainer( index ) ) );
n_2 += ( v.myContainer( index ) - former_v.myContainer( index ) )
* ( v.myContainer( index ) - former_v.myContainer( index ) );
n_1 += fabs( v.myContainer( index ) - former_v.myContainer( index ) );
}
n_1 /= v.myContainer.rows();
n_2 = sqrt( n_2 / v.myContainer.rows() );
trace.info() << "Variation |v^k+1 - v^k|_oo = " << n_infty << endl;
trace.info() << "Variation |v^k+1 - v^k|_2 = " << n_2 << endl;
trace.info() << "Variation |v^k+1 - v^k|_1 = " << n_1 << endl;
trace.endBlock();
if ( n_infty < 1e-4 ) break;
}
epsilon = eps;
}
a = 0.5;
}
// affichage des energies ********************************************************************
trace.beginBlock("Computing energies");
// a(u-g)^2
Calculus::PrimalIdentity0 diag_alpha = a * Id0;
const Calculus::PrimalForm0 u_minus_g = u - g;
double alpha_square_u_minus_g = innerProduct( calculus, diag_alpha * u_minus_g, u_minus_g );
trace.info() << "- a(u-g)^2 = " << alpha_square_u_minus_g << std::endl;
// v^2|grad u|^2
const Calculus::PrimalIdentity1 diag_v = diag( calculus, v );
const Calculus::PrimalForm1 v_A_u = diag_v * primal_D0 * u;
double square_v_grad_u = innerProduct( calculus, v_A_u, v_A_u );
trace.info() << "- v^2|grad u|^2 = " << square_v_grad_u << std::endl;
// // JOL: 1000 * plus rapide !
// trace.info() << " - u^t N u" << std::endl;
// Calculus::PrimalForm0 u_prime = Av2A * u;
// for ( Calculus::Index index = 0; index < u.myContainer.rows(); index++)
// V2gradU2 += u.myContainer( index ) * u_prime.myContainer( index );
// // for ( Calculus::Index index_i = 0; index_i < u.myContainer.rows(); index_i++)
// // for ( Calculus::Index index_j = 0; index_j < u.myContainer.rows(); index_j++)
// // V2gradU2 += u.myContainer( index_i ) * Av2A.myContainer.coeff( index_i,index_j ) * u.myContainer( index_j ) ;
// // le|grad v|^2
Calculus::PrimalForm1 v_prime = lap_operator_v * v;
double le_square_grad_v = l * epsilon * innerProduct( calculus, v, v_prime );
trace.info() << "- le|grad v|^2 = " << le_square_grad_v << std::endl;
// l(1-v)^2/4e
Calculus::PrimalForm1 one_minus_v = v;
for ( Calculus::Index index_i = 0; index_i < v.myContainer.rows(); index_i++)
one_minus_v.myContainer( index_i ) = 1.0 - one_minus_v.myContainer( index_i );
double l_over_4e_square_1_minus_v
= l / (4*epsilon) * innerProduct( calculus, one_minus_v, one_minus_v );
trace.info() << "- l(1-v)^2/4e = " << l_over_4e_square_1_minus_v << std::endl;
// l.per
double Lper = 2.0* l_over_4e_square_1_minus_v; //le_square_grad_v + l_over_4e_square_1_minus_v;
trace.info() << "- l.per = " << Lper << std::endl;
// AT tot
double ATtot = alpha_square_u_minus_g + square_v_grad_u + Lper;
// f << "l " << " a " << " e " << " a(u-g)^2 " << " v^2|grad u|^2 " << " le|grad v|^2 " << " l(1-v)^2/4e " << " l.per " << " AT tot"<< endl;
f << tronc(l,8) << "\t" << a << "\t" << tronc(epsilon,4)
<< "\t" << tronc(alpha_square_u_minus_g,5)
<< "\t" << tronc(square_v_grad_u,5)
<< "\t" << tronc(le_square_grad_v,5)
<< "\t" << tronc(l_over_4e_square_1_minus_v,5)
<< "\t" << tronc(Lper,5)
<< "\t" << tronc(ATtot,5) << endl;
trace.endBlock();
// ***********************************************************************************************************************
int int_l = (int) floor(l);
int dec_l = (int) (floor((l-floor(l))*10000000));
ostringstream ossU;
ossU << boost::format("%s-l%.7f-u.pgm") %f2 %l;
string str_image_u = ossU.str();
savePrimalForm0ToImage( calculus, end_image, u, str_image_u);
ostringstream ossV;
ossV << boost::format("%s-l%.7f-v.pgm") %f2 %l;
string str_image_v = ossV.str();
savePrimalForm1ToImage( calculus, dbl_image, v, str_image_v );
l1 /= lr;
}
f.close();
return 0;
}
int main( int argc, char** argv )
{
// parse command line ----------------------------------------------
po::options_description general_opt("Allowed options are");
general_opt.add_options()
("help,h", "display this message")
("input,i", po::value< std::string >(), ".vol file")
("trivial-radius,t", po::value<double>()->default_value( 3 ), "the parameter t defining the radius for the Trivial estimator, which is used for reorienting II or VCM normal estimations." )
("r-radius,r", po::value< double >(), "Kernel radius r for IntegralInvariant estimator" )
("noise,k", po::value< double >()->default_value(0.5), "Level of Kanungo noise ]0;1[" )
("min,l", po::value< int >()->default_value(0), "set the minimal image threshold to define the image object (object defined by the voxel with intensity belonging to ]min, max ] )." )
("max,u", po::value< int >()->default_value(255), "set the minimal image threshold to define the image object (object defined by the voxel with intensity belonging to ]min, max] )." )
("lambda,L", po::value<double>()->default_value( 0.05 ), "the parameter lambda of AT functional." )
("alpha,a", po::value<double>()->default_value( 0.1 ), "the parameter alpha of AT functional." )
("epsilon,e", po::value<double>()->default_value( 4.0 ), "the initial parameter epsilon of AT functional." );
bool parseOK = true;
po::variables_map vm;
try
{
po::store( po::parse_command_line( argc, argv, general_opt ), vm );
}
catch( const std::exception & ex )
{
parseOK = false;
trace.error() << " Error checking program options: " << ex.what() << std::endl;
}
bool neededArgsGiven=true;
if (parseOK && !(vm.count("input"))){
missingParam("--input");
neededArgsGiven=false;
}
if (parseOK && !(vm.count("r-radius"))){
missingParam("--r-radius");
neededArgsGiven=false;
}
double noiseLevel = vm["noise"].as< double >();
if( noiseLevel < 0.0 || noiseLevel > 1.0 )
{
parseOK = false;
trace.error() << "The noise level should be in the interval: [0, 1]"<< std::endl;
}
if(!neededArgsGiven || !parseOK || vm.count("help") || argc <= 1 )
{
trace.info()<< "Vol file viewer, with normals regularized by Ambrosio-Tortorelli functionnal" <<std::endl
<< general_opt << "\n"
<< "Basic usage: "<<std::endl
<< "\t at-3d-normals -i file.vol -r 5 --noise 0.1"<<std::endl
<< std::endl;
return 0;
}
QApplication application(argc,argv);
int min = vm["min"].as< int >();
int max = vm["max"].as< int >();
const double h = 1.0; // not pertinent for now.
//-----------------------------------------------------------------------------
// Types.
typedef Z3i::Space Space;
typedef Z3i::KSpace KSpace;
typedef Space::RealVector RealVector;
typedef KSpace::SCell SCell;
typedef KSpace::Cell Cell;
typedef KSpace::Surfel Surfel;
typedef Z3i::Domain Domain;
typedef ImageSelector<Domain, unsigned char>::Type Image;
typedef IntervalForegroundPredicate< Image > Object;
typedef KanungoNoise< Object, Domain > KanungoPredicate;
typedef BinaryPointPredicate<DomainPredicate<Domain>, KanungoPredicate, AndBoolFct2 > NoisyObject;
typedef KSpace::SurfelSet SurfelSet;
typedef SetOfSurfels< KSpace, SurfelSet > MySetOfSurfels;
typedef DigitalSurface< MySetOfSurfels > MyDigitalSurface;
typedef MyDigitalSurface::ConstIterator ConstIterator;
//-----------------------------------------------------------------------------
// Loading vol file.
trace.beginBlock( "Loading vol file." );
std::string inputFile = vm[ "input" ].as< std::string >();
std::string extension = inputFile.substr(inputFile.find_last_of(".") + 1);
if(extension!="vol" && extension != "p3d" && extension != "pgm3D" && extension != "pgm3d" && extension != "sdp" && extension != "pgm" )
{
trace.info() << "File extension not recognized: "<< extension << std::endl;
return 0;
}
Image image = GenericReader<Image>::import (inputFile );
trace.endBlock();
//-----------------------------------------------------------------------------
// Extracting object with possible noise.
trace.beginBlock( "Extracting object with possible noise." );
Object object( image, min, max );
KanungoPredicate kanungo_pred( object, image.domain(), noiseLevel );
DomainPredicate<Domain> domain_pred( image.domain() );
AndBoolFct2 andF;
NoisyObject noisy_object(domain_pred, kanungo_pred, andF );
Domain domain = image.domain();
KSpace K;
bool space_ok = K.init( domain.lowerBound()-Z3i::Domain::Point::diagonal(),
domain.upperBound()+Z3i::Domain::Point::diagonal(), true );
if (!space_ok)
{
trace.error() << "Error in the Khalimsky space construction."<<std::endl;
return 2;
}
CanonicSCellEmbedder< KSpace > embedder( K );
SurfelAdjacency< KSpace::dimension > surfAdj( true );
trace.endBlock();
//-----------------------------------------------------------------------------
//! [3dVolBoundaryViewer-ExtractingSurface]
trace.beginBlock( "Extracting boundary by scanning the space. " );
MySetOfSurfels theSetOfSurfels( K, surfAdj );
Surfaces<KSpace>::sMakeBoundary( theSetOfSurfels.surfelSet(),
K, image,
domain.lowerBound(),
domain.upperBound() );
MyDigitalSurface digSurf( theSetOfSurfels );
trace.info() << "Digital surface has " << digSurf.size() << " surfels."
<< std::endl;
trace.endBlock();
//! [3dVolBoundaryViewer-ExtractingSurface]
// Map surfel -> estimated normals.
std::map<SCell,RealVector> n_estimations;
//-----------------------------------------------------------------------------
// Estimating orientation of normals
trace.beginBlock( "Estimating orientation of normals by simple convolutions of trivial surfel normals." );
double t = vm["trivial-radius"].as<double>();
typedef RealVector::Component Scalar;
typedef functors::HatFunction<Scalar> Functor;
typedef functors::ElementaryConvolutionNormalVectorEstimator< Surfel, CanonicSCellEmbedder<KSpace> > SurfelFunctor;
typedef ExactPredicateLpSeparableMetric<Space,2> Metric;
typedef LocalEstimatorFromSurfelFunctorAdapter< MySetOfSurfels, Metric, SurfelFunctor, Functor> NormalEstimator;
Functor fct( 1.0, t );
CanonicSCellEmbedder<KSpace> canonic_embedder( K );
SurfelFunctor surfelFct( canonic_embedder, 1.0 );
NormalEstimator nt_estimator;
Metric aMetric;
std::vector<RealVector> nt_estimations;
nt_estimator.attach( digSurf );
nt_estimator.setParams( aMetric, surfelFct, fct, t );
nt_estimator.init( h, digSurf.begin(), digSurf.end());
nt_estimator.eval( digSurf.begin(), digSurf.end(), std::back_inserter( nt_estimations ) );
trace.endBlock();
//-----------------------------------------------------------------------------
// Estimating normals
trace.beginBlock( "Estimating normals with II." );
typedef typename Domain::ConstIterator DomainConstIterator;
typedef functors::IINormalDirectionFunctor<Space> IINormalFunctor;
typedef IntegralInvariantCovarianceEstimator<KSpace, NoisyObject, IINormalFunctor> IINormalEstimator;
std::vector<RealVector> nii_estimations;
const double r = vm["r-radius"].as<double>();
IINormalEstimator nii_estimator( K, noisy_object );
trace.info() << " r=" << r << std::endl;
nii_estimator.setParams( r );
nii_estimator.init( h, digSurf.begin(), digSurf.end() );
nii_estimator.eval( digSurf.begin(), digSurf.end(), std::back_inserter( nii_estimations ) );
// Fix orientations of ii.
for ( unsigned int i = 0; i < nii_estimations.size(); ++i )
{
if ( nii_estimations[ i ].dot( nt_estimations[ i ] ) < 0.0 )
nii_estimations[ i ] *= -1.0;
}
trace.info() << "- nb estimations = " << nii_estimations.size() << std::endl;
trace.endBlock();
// The chosen estimator is II.
{
unsigned int i = 0;
for ( ConstIterator it = digSurf.begin(), itE = digSurf.end(); it != itE; ++it, ++i )
{
RealVector nii = nii_estimations[ i ];
nii /= nii.norm();
n_estimations[ *it ] = nii;
}
}
//-----------------------------------------------------------------------------
//! [3dVolBoundaryViewer-ViewingSurface]
trace.beginBlock( "Displaying everything. " );
Viewer3D<Space,KSpace> viewer( K );
viewer.setWindowTitle("Simple boundary of volume Viewer");
viewer.show();
viewer << SetMode3D(K.unsigns( *(digSurf.begin()) ).className(), "Basic");
unsigned int i = 0;
for ( ConstIterator it = digSurf.begin(), itE = digSurf.end(); it != itE; ++it, ++i )
{
viewer.setFillColor( Color( 200, 200, 250 ) );
Display3DFactory<Space,KSpace>::drawOrientedSurfelWithNormal( viewer, *it, n_estimations[ *it ], false );
}
viewer << Viewer3D<>::updateDisplay;
trace.endBlock();
//-----------------------------------------------------------------------------
// Defining Discrete Calculus.
typedef CubicalComplex< KSpace > CComplex;
typedef DiscreteExteriorCalculus<2,3, EigenLinearAlgebraBackend> Calculus;
typedef Calculus::Index Index;
typedef Calculus::PrimalForm0 PrimalForm0;
typedef Calculus::PrimalForm1 PrimalForm1;
typedef Calculus::PrimalForm2 PrimalForm2;
typedef Calculus::PrimalIdentity0 PrimalIdentity0;
typedef Calculus::PrimalIdentity1 PrimalIdentity1;
typedef Calculus::PrimalIdentity2 PrimalIdentity2;
trace.beginBlock( "Creating Discrete Exterior Calculus. " );
Calculus calculus;
calculus.initKSpace<Domain>( domain );
const KSpace& Kc = calculus.myKSpace; // should not be used.
// Use a cubical complex to find all lower incident cells easily.
CComplex complex( K );
for ( ConstIterator it = digSurf.begin(), itE = digSurf.end(); it != itE; ++it )
complex.insertCell( 2, K.unsigns( *it ) );
complex.close();
for ( CComplex::CellMapIterator it = complex.begin( 0 ), itE = complex.end( 0 ); it != itE; ++it )
calculus.insertSCell( K.signs( it->first, K.POS ) );
for ( CComplex::CellMapIterator it = complex.begin( 1 ), itE = complex.end( 1 ); it != itE; ++it )
{
SCell linel = K.signs( it->first, K.POS );
Dimension k = * K.sDirs( linel );
bool pos = K.sDirect( linel, k );
calculus.insertSCell( pos ? linel : K.sOpp( linel ) );
// calculus.insertSCell( K.signs( it->first, K.POS ) );
}
// for ( CComplex::CellMapIterator it = complex.begin( 2 ), itE = complex.end( 2 ); it != itE; ++it )
// calculus.insertSCell( K.signs( it->first, K.POS ) );
for ( ConstIterator it = digSurf.begin(), itE = digSurf.end(); it != itE; ++it )
{
calculus.insertSCell( *it );
// SCell surfel = *it;
// Dimension k = K.sOrthDir( surfel );
// bool pos = K.sDirect( surfel, k );
// calculus.insertSCell( pos ? *it : K.sOpp( *it ) );
}
calculus.updateIndexes();
trace.info() << calculus << endl;
std::vector<PrimalForm2> g;
g.reserve( 3 );
g.push_back( PrimalForm2( calculus ) );
g.push_back( PrimalForm2( calculus ) );
g.push_back( PrimalForm2( calculus ) );
Index nb2 = g[ 0 ].myContainer.rows();
for ( Index index = 0; index < nb2; index++)
{
const Calculus::SCell& cell = g[ 0 ].getSCell( index );
if ( theSetOfSurfels.isInside( cell ) )
{
const RealVector& n = n_estimations[ cell ];
g[ 0 ].myContainer( index ) = n[ 0 ];
g[ 1 ].myContainer( index ) = n[ 1 ];
g[ 2 ].myContainer( index ) = n[ 2 ];
}
else
{
const RealVector& n = n_estimations[ K.sOpp( cell ) ];
g[ 0 ].myContainer( index ) = n[ 0 ];
g[ 1 ].myContainer( index ) = n[ 1 ];
g[ 2 ].myContainer( index ) = n[ 2 ];
}
}
cout << endl;
trace.info() << "primal_D0" << endl;
const Calculus::PrimalDerivative0 primal_D0 = calculus.derivative<0,PRIMAL>();
trace.info() << "primal_D1" << endl;
const Calculus::PrimalDerivative1 primal_D1 = calculus.derivative<1,PRIMAL>();
trace.info() << "dual_D0" << endl;
const Calculus::DualDerivative0 dual_D0 = calculus.derivative<0,DUAL>();
trace.info() << "dual_D1" << endl;
const Calculus::DualDerivative1 dual_D1 = calculus.derivative<1,DUAL>();
trace.info() << "primal_h0" << endl;
const Calculus::PrimalHodge0 primal_h0 = calculus.hodge<0,PRIMAL>();
trace.info() << "primal_h1" << endl;
const Calculus::PrimalHodge1 primal_h1 = calculus.hodge<1,PRIMAL>();
trace.info() << "primal_h2" << endl;
const Calculus::PrimalHodge2 primal_h2 = calculus.hodge<2,PRIMAL>();
trace.info() << "dual_h1" << endl;
const Calculus::DualHodge1 dual_h1 = calculus.hodge<1,DUAL>();
trace.info() << "dual_h2" << endl;
const Calculus::DualHodge2 dual_h2 = calculus.hodge<2,DUAL>();
trace.endBlock();
//-----------------------------------------------------------------------------
// Building AT functional.
trace.beginBlock( "Building AT functional. " );
double a = vm[ "alpha" ].as<double>();
double e = vm[ "epsilon" ].as<double>();
double l = vm[ "lambda" ].as<double>();
// u = g at the beginning
trace.info() << "u[0,1,2]" << endl;
std::vector<PrimalForm2> u;
u.push_back( g[ 0 ] ); u.push_back( g[ 1 ] ); u.push_back( g[ 2 ] );
// v = 1 at the beginning
trace.info() << "v" << endl;
PrimalForm1 v( calculus );
Index nb1 = v.myContainer.rows();
for ( Index index = 0; index < nb1; index++) v.myContainer( index ) = 1.0;
const PrimalIdentity0 Id0 = calculus.identity<0, PRIMAL>();
const PrimalIdentity1 Id1 = calculus.identity<1, PRIMAL>();
const PrimalIdentity2 Id2 = calculus.identity<2, PRIMAL>();
// Building alpha_
trace.info() << "alpha_g" << endl;
const PrimalIdentity2 alpha_Id2 = a * Id2; // a * invG0;
vector<PrimalForm2> alpha_g;
alpha_g.push_back( alpha_Id2 * g[ 0 ] );
alpha_g.push_back( alpha_Id2 * g[ 1 ] );
alpha_g.push_back( alpha_Id2 * g[ 2 ] );
trace.info() << "lap_operator_v" << endl;
const PrimalIdentity1 lap_operator_v = -1.0 * ( primal_D0 * dual_h2 * dual_D1 * primal_h1
+ dual_h1 * dual_D0 * primal_h2 * primal_D1 );
// SparseLU is so much faster than SparseQR
// SimplicialLLT is much faster than SparseLU
// typedef EigenLinearAlgebraBackend::SolverSparseQR LinearAlgebraSolver;
// typedef EigenLinearAlgebraBackend::SolverSparseLU LinearAlgebraSolver;
typedef EigenLinearAlgebraBackend::SolverSimplicialLLT LinearAlgebraSolver;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL> SolverU;
SolverU solver_u;
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL> SolverV;
SolverV solver_v;
trace.info() << "lB'B'" << endl;
const PrimalIdentity1 lBB = l * lap_operator_v;
PrimalForm1 l_sur_4( calculus );
for ( Index index = 0; index < nb1; index++)
l_sur_4.myContainer( index ) = l / 4.0;
double coef_eps = 2.0;
double eps = 2.0 * e;
const int n = 10;
trace.endBlock();
//-----------------------------------------------------------------------------
// Solving AT functional.
trace.beginBlock( "Solving AT functional. " );
while ( eps / coef_eps >= h )
{
eps /= coef_eps;
trace.info() << "************** epsilon = " << eps << "***************************************" << endl;
const PrimalIdentity1 BB = eps * lBB + ( l/(4.0*eps) ) * Id1; // tS_S;
for ( int i = 0; i < n; ++i )
{
trace.info() << "---------- Iteration " << i << "/" << n << " ------------------------------" << endl;
trace.info() << "-------------------------------------------------------------------------------" << endl;
trace.beginBlock("Solving for u");
trace.info() << "Building matrix Av2A" << endl;
PrimalIdentity1 diag_v = diag( calculus, v );
PrimalIdentity2 U_Id2 = -1.0 * primal_D1 * diag_v * diag_v * dual_h1 * dual_D0 * primal_h2
+ alpha_Id2;
trace.info() << "Prefactoring matrix Av2A + alpha_iG0" << endl;
solver_u.compute( U_Id2 );
for ( unsigned int d = 0; d < 3; ++d )
{
trace.info() << "Solving (Av2A + alpha_iG0) u[" << d << "] = ag[" << d << "]" << endl;
u[ d ] = solver_u.solve( alpha_g[ d ] );
trace.info() << " => " << ( solver_u.isValid() ? "OK" : "ERROR" )
<< " " << solver_u.myLinearAlgebraSolver.info() << endl;
}
trace.info() << "-------------------------------------------------------------------------------" << endl;
trace.endBlock();
trace.beginBlock("Solving for v");
const PrimalForm1 former_v = v;
trace.info() << "Building matrix tu_tA_A_u + BB + Mw2" << endl;
PrimalIdentity1 V_Id1 = BB;
for ( unsigned int d = 0; d < 3; ++d )
{
const PrimalIdentity1 A_u = diag( calculus, dual_h1 * dual_D0 * primal_h2 * u[ d ] );
V_Id1.myContainer += square( calculus, A_u ).myContainer;
}
trace.info() << "Prefactoring matrix tu_tA_A_u + BB + Mw2" << endl;
solver_v.compute( V_Id1 );
trace.info() << "Solving (tu_tA_A_u + BB + Mw2) v = 1/(4eps) * l" << endl;
v = solver_v.solve( (1.0/eps) * l_sur_4 );
trace.info() << " => " << ( solver_v.isValid() ? "OK" : "ERROR" )
<< " " << solver_v.myLinearAlgebraSolver.info() << endl;
trace.info() << "-------------------------------------------------------------------------------" << endl;
trace.endBlock();
for ( Index index = 0; index < nb2; index++)
{
double n2 = 0.0;
for ( unsigned int d = 0; d < 3; ++d )
n2 += u[ d ].myContainer( index ) * u[ d ].myContainer( index );
double norm = sqrt( n2 );
for ( unsigned int d = 0; d < 3; ++d )
u[ d ].myContainer( index ) /= norm;
}
trace.beginBlock("Checking v, computing norms");
double m1 = 1.0;
double m2 = 0.0;
double ma = 0.0;
for ( Index index = 0; index < nb1; index++)
{
double val = v.myContainer( index );
m1 = std::min( m1, val );
m2 = std::max( m2, val );
ma += val;
}
trace.info() << "1-form v: min=" << m1 << " avg=" << ( ma / nb1 ) << " max=" << m2 << std::endl;
for ( Index index = 0; index < nb1; index++)
v.myContainer( index ) = std::min( std::max(v.myContainer( index ), 0.0) , 1.0 );
double n_infty = 0.0;
double n_2 = 0.0;
double n_1 = 0.0;
for ( Index index = 0; index < nb1; index++)
{
n_infty = std::max( n_infty, fabs( v.myContainer( index ) - former_v.myContainer( index ) ) );
n_2 += ( v.myContainer( index ) - former_v.myContainer( index ) )
* ( v.myContainer( index ) - former_v.myContainer( index ) );
n_1 += fabs( v.myContainer( index ) - former_v.myContainer( index ) );
}
n_1 /= v.myContainer.rows();
n_2 = sqrt( n_2 / v.myContainer.rows() );
trace.info() << "Variation |v^k+1 - v^k|_oo = " << n_infty << endl;
trace.info() << "Variation |v^k+1 - v^k|_2 = " << n_2 << endl;
trace.info() << "Variation |v^k+1 - v^k|_1 = " << n_1 << endl;
trace.endBlock();
if ( n_infty < 1e-4 ) break;
} // for ( int i = 0; i < n; ++i )
}
trace.endBlock();
//-----------------------------------------------------------------------------
// Displaying regularized normals
trace.beginBlock( "Displaying regularized normals. " );
Viewer3D<Space,KSpace> viewerR( K );
viewerR.setWindowTitle("Regularized normals");
viewerR.show();
viewerR << SetMode3D(K.unsigns( *(digSurf.begin()) ).className(), "Basic");
viewerR.setFillColor( Color( 200, 200, 250 ) );
for ( Index index = 0; index < nb2; index++)
{
const SCell& cell = u[ 0 ].getSCell( index );
// const RealVector& n = n_estimations[ cell ];
RealVector nr = RealVector( u[ 0 ].myContainer( index ),
u[ 1 ].myContainer( index ),
u[ 2 ].myContainer( index ) );
nr /= nr.norm();
if ( theSetOfSurfels.isInside( cell ) )
Display3DFactory<Space,KSpace>::drawOrientedSurfelWithNormal( viewerR, cell, nr, false );
else
Display3DFactory<Space,KSpace>::drawOrientedSurfelWithNormal( viewerR, K.sOpp( cell ), nr, false );
}
viewerR.setLineColor( Color( 255, 0, 0 ) );
for ( Index index = 0; index < nb1; index++)
{
const SCell& cell = v.getSCell( index );
Dimension k = * K.sDirs( cell );
const SCell p0 = K.sIncident( cell, k, true );
const SCell p1 = K.sIncident( cell, k, false );
if ( v.myContainer( index ) >= 0.5 ) continue;
viewerR.addLine( embedder.embed( p0 ), embedder.embed( p1 ), (0.5 - v.myContainer( index ))/ 5.0 );
}
viewerR << Viewer3D<>::updateDisplay;
trace.endBlock();
return application.exec();
}