geometry/meshes/vol-curvature-measures-icnc-3d.cpp

Computation of mean and Gaussiancurvatures on a mesh defined by a VOL digital file, using interpolated corrected curvature measures (based on the theory of corrected normal currents). It uses a digital normal vector estimator to improve curvature estimations.

# "Al" vol file
/examples/geometry/meshes/vol-curvature-measures-icnc-3d ../examples/samples/Al.100.vol 2.0 0 1 0.33 0.1

outputs

- Domain size is 100 x 100 x 100
- digital shape has 70413 voxels.
- surface has 21239 surfels.
[SurfaceMesh (OK) #V=21278 #VN=0 #E=42522 #F=21239 #FN=0 E[IF]=4.00151 E[IV]=3.9968 E[IFE]=1.99793]
- CTrivial normal t-ring=3 (discrete)
Computed mean curvatures: min=-0.223179 max=0.415828
Computed Gaussian curvatures: min=-0.215905 max=0.164086

It also produces several OBJ files to display curvature estimation results, example-cnc-H.obj and example-cnc-G.obj as well as the associated MTL file.

Interpolated corrected mean curvature measure, r=2

Interpolated corrected Gaussian curvature measure, r=2

See also

Curvature measures on meshes and digital surfaces

Note

In opposition with Normal Cycle curvature measures, (interpolated) corrected curvature measures can take into account an external normal vector field to estimate curvatures with better accuracy.

 
#include <iostream>
#include <fstream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/helpers/ShortcutsGeometry.h"
#include "DGtal/io/writers/SurfaceMeshWriter.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( int argc, char* argv[] )
{
  std::cout << "Usage: " << std::endl
            << "\t" << argv[ 0 ] << " <filename.vol> <R> <m> <M> <Hmax> <Gmax>" << std::endl
            << std::endl
            << "Computation of mean and Gaussian curvatures 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.vol>"      << 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
            << "- <Hmax> gives the colormap range [-Hmax,Hmax] for"      << std::endl
            << "  the output of mean curvature estimates"                << std::endl
            << "- <Gmax> gives the colormap range [-Gmax,Gmax] for"      << std::endl
            << "  the output of mean curvature estimates"                << std::endl
            << "It produces several OBJ files to display mean and"       << std::endl
            << "Gaussian curvature estimation results: `example-cnc-H.obj`" << std::endl
            << "and `example-cnc-G.obj` as well as the associated MTL file." << std::endl;
}
 
int main( int argc, char* argv[] )
{
  if ( argc <= 1 )
    {
      usage( argc, 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 Hmax = argc > 5 ? atof( argv[ 5 ] ) : 0.33; // range mean curvature colormap
  const double Gmax = argc > 6 ? atof( argv[ 6 ] ) : 0.1; // range Gaussian 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, mean and Gaussian curvature measures
  std::cout << "Compute mu0" << std::endl;
  auto mu0 = cnc.computeMu0();
  std::cout << "Compute mu1" << std::endl;
  auto mu1 = cnc.computeMu1();
  std::cout << "Compute mu2" << std::endl;
  auto mu2 = cnc.computeMu2();
 
  // estimates mean (H) and Gaussian (G) curvatures by measure normalization.
  std::vector< double > H( smesh.nbFaces() );
  std::vector< double > G( smesh.nbFaces() );
  for ( auto f = 0; f < smesh.nbFaces(); ++f )
    {
      const auto b    = smesh.faceCentroid( f );
      const auto area = mu0.measure( b, R, f );
      H[ f ] = cnc.meanCurvature    ( area, mu1.measure( b, R, f ) );
      G[ f ] = cnc.GaussianCurvature( area, mu2.measure( b, R, f ) );
    }
 
  auto H_min_max = std::minmax_element( H.cbegin(), H.cend() );
  auto G_min_max = std::minmax_element( G.cbegin(), G.cend() );
  std::cout << "Computed mean curvatures:"
            << " min=" << *H_min_max.first << " max=" << *H_min_max.second
            << std::endl;
  std::cout << "Computed Gaussian curvatures:"
            << " min=" << *G_min_max.first << " max=" << *G_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 colormapH = makeQuantifiedColorMap( makeColorMap( -Hmax, Hmax ) );
  const auto colormapG = makeQuantifiedColorMap( makeColorMap( -Gmax, Gmax ) );
  auto colorsH = SMW::Colors( smesh.nbFaces() );
  auto colorsG = SMW::Colors( smesh.nbFaces() );
  for ( auto i = 0; i < smesh.nbFaces(); i++ )
    {
      colorsH[ i ] = colormapH( H[ i ] );
      colorsG[ i ] = colormapG( G[ i ] );
    }
  SMW::writeOBJ( "example-cnc-H", smesh, colorsH );
  SMW::writeOBJ( "example-cnc-G", smesh, colorsG );
  return 0;
}