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(); }