vol-curvature-measures-icnc-XY-3d.cpp

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#include <iostream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/math/linalg/EigenDecomposition.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/helpers/ShortcutsGeometry.h"
#include "DGtal/io/readers/SurfaceMeshReader.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
 
DGtal::GradientColorMap< double >
makeColorMap( double min_value, double max_value )
{
  DGtal::GradientColorMap< double > gradcmap( min_value, max_value );
  gradcmap.addColor( DGtal::Color( 0, 0, 255 ) );
  gradcmap.addColor( DGtal::Color( 0, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 0 ) );
  gradcmap.addColor( DGtal::Color( 255, 0, 0 ) );
  return gradcmap;
}
 
void usage( char* argv[] )
{
  std::cout << "Usage: " << std::endl
            << "\t" << argv[ 0 ] << " <filename.vol> <R> <m> <M> <Kmax>" << std::endl
            << std::endl
            << "Computation of principal curvatures and directions on a vol file, " << std::endl
            << "using interpolated corrected curvature measures (based " << std::endl
            << "on the theory of corrected normal currents)."            << std::endl
            << "- builds the surface mesh from file <filename.obj>"      << std::endl
            << "- <R> is the radius of the measuring balls."             << std::endl
            << "- <m> is the min threshold value for the vol file"       << std::endl
            << "- <M> is the max threshold value for the vol file"       << std::endl
            << "- <Kmax> gives the colormap range [-Kmax,Kmax] for"      << std::endl
            << "  the output of principal curvatures estimates"          << std::endl
            << "It produces several OBJ files to display principal "     << std::endl
            << "curvatures and directions estimations: `example-cnc-K1.obj`" << std::endl
            << "`example-cnc-K2.obj`, `example-cnc-D1.obj`, and"         << std::endl
            << "`example-cnc-D2.obj` as well as associated MTL files."   << std::endl;
}
 
int main( int argc, char* argv[] )
{
  if ( argc <= 1 )
    {
      usage( argv );
      return 0;
    }
  using namespace DGtal;
  using namespace DGtal::Z3i;
  typedef SurfaceMesh< RealPoint, RealVector >                    SM;
  typedef CorrectedNormalCurrentComputer< RealPoint, RealVector > CNC;
  typedef Shortcuts< KSpace >          SH;
  typedef ShortcutsGeometry< KSpace > SHG;
  // VOL file
  std::string input = argv[ 1 ];
  const double    R = argc > 2 ? atof( argv[ 2 ] ) : 2.0; // radius of measuring ball
  const int       m = argc > 3 ? atoi( argv[ 3 ] ) : 0; // min threshold
  const int       M = argc > 4 ? atoi( argv[ 4 ] ) : 1; // max threshold
  const double Kmax = argc > 5 ? atof( argv[ 5 ] ) : 0.33; // range mean curvature colormap

  // Read VOL file and build digital surface
  auto params = SH::defaultParameters() | SHG::defaultParameters();
  params( "thresholdMin", m )( "thresholdMax", M )( "closed", 1);
  params( "t-ring", 3 )( "surfaceTraversal", "Default" );
  auto bimage = SH::makeBinaryImage( input.c_str(), params );
  if ( bimage == nullptr ) 
    {
      trace.error() <<  "Unable to read file <" << input.c_str() << ">" << std::endl;
      return 1;
    }
  auto K      = SH::getKSpace( bimage, params );
  auto sembedder   = SH::getSCellEmbedder( K );
  auto embedder    = SH::getCellEmbedder( K );
  auto surface     = SH::makeDigitalSurface( bimage, K, params );
  auto surfels     = SH::getSurfelRange( surface, params );
  trace.info() << "- surface has " << surfels.size()<< " surfels." << std::endl;

  SM smesh;
  std::vector< SM::Vertices > faces;
  SH::Cell2Index c2i;
  auto pointels = SH::getPointelRange( c2i, surface );
  auto vertices = SH::RealPoints( pointels.size() );
  std::transform( pointels.cbegin(), pointels.cend(), vertices.begin(),
                  [&] (const SH::Cell& c) { return embedder( c ); } ); 
  for ( auto&& surfel : *surface )
    {
      const auto primal_surfel_vtcs = SH::getPointelRange( K, surfel );
      SM::Vertices face;              
      for ( auto&& primal_vtx : primal_surfel_vtcs )
        face.push_back( c2i[ primal_vtx ] );
      faces.push_back( face );
    }
  smesh.init( vertices.cbegin(), vertices.cend(),
              faces.cbegin(),    faces.cend() );
  trace.info() << smesh << std::endl;

  // Builds a CorrectedNormalCurrentComputer object onto the SurfaceMesh object
  CNC cnc( smesh );
  // Estimates normal vectors using Convolved Trivial Normal estimator 
  auto face_normals = SHG::getCTrivialNormalVectors( surface, surfels, params );
  smesh.setFaceNormals( face_normals.cbegin(), face_normals.cend() );
  if ( smesh.vertexNormals().empty() )
    smesh.computeVertexNormalsFromFaceNormals();
  // computes area, anisotropic XY curvature measures
  auto mu0  = cnc.computeMu0();
  auto muXY = cnc.computeMuXY();

  // estimates principal curvatures (K1,K2) and directions (D1,D2) by
  // measure normalization.
  std::vector< double > K1( smesh.nbFaces() );
  std::vector< double > K2( smesh.nbFaces() );
  std::vector< RealVector > D1( smesh.nbFaces() );
  std::vector< RealVector > D2( smesh.nbFaces() );
  for ( auto f = 0; f < smesh.nbFaces(); ++f )
    {
      const auto b    = smesh.faceCentroid( f );
      const auto N    = smesh.faceNormals()[ f ];
      const auto area = mu0 .measure( b, R, f );
      const auto M2   = muXY.measure( b, R, f );
      std::tie( K1[ f ], K2[ f ], D1[ f ], D2[ f ] )
        = cnc.principalCurvatures( area, M2, N );
    }

  auto K1_min_max = std::minmax_element( K1.cbegin(), K1.cend() );
  auto K2_min_max = std::minmax_element( K2.cbegin(), K2.cend() );
  std::cout << "Computed k1 curvatures:"
            << " min=" << *K1_min_max.first << " max=" << *K1_min_max.second
            << std::endl;
  std::cout << "Computed k2 curvatures:"
            << " min=" << *K2_min_max.first << " max=" << *K2_min_max.second
            << std::endl;

  // Remove normals for better blocky display.
  smesh.vertexNormals() = SH::RealVectors();
  smesh.faceNormals()   = SH::RealVectors();
  typedef SurfaceMeshWriter< RealPoint, RealVector > SMW;
  const auto colormapK1 = makeQuantifiedColorMap( makeColorMap( -Kmax, Kmax ) );
  const auto colormapK2 = makeQuantifiedColorMap( makeColorMap( -Kmax, Kmax ) );
  auto colorsK1 = SMW::Colors( smesh.nbFaces() );
  auto colorsK2 = SMW::Colors( smesh.nbFaces() );
  for ( auto i = 0; i < smesh.nbFaces(); i++ )
    {
      colorsK1[ i ] = colormapK1( K1[ i ] );
      colorsK2[ i ] = colormapK2( K2[ i ] );
    }
  SMW::writeOBJ( "example-cnc-K1", smesh, colorsK1 );
  SMW::writeOBJ( "example-cnc-K2", smesh, colorsK2 );
  const auto avg_e = smesh.averageEdgeLength();
  SH::RealPoints positions( smesh.nbFaces() );
  for ( auto f = 0; f < positions.size(); ++f )
    {
      D1[ f ] *= smesh.localWindow( f );
      positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D1[ f ];
    }
  SH::saveVectorFieldOBJ( positions, D1, 0.05 * avg_e, SH::Colors(),
                          "example-cnc-D1",
                          SH::Color::Black, SH::Color( 0, 128, 0 ) );
  for ( auto f = 0; f < positions.size(); ++f )
    {
      D2[ f ] *= smesh.localWindow( f );
      positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D2[ f ];
    }
  SH::saveVectorFieldOBJ( positions, D2, 0.05 * avg_e, SH::Colors(),
                          "example-cnc-D2",
                          SH::Color::Black, SH::Color(128, 0,128 ) );
  return 0;
}