DGtalTools  0.9.4
DECImageHelpers.h
1 
17 #pragma once
18 
33 #if defined(DECImageHelpers_RECURSES)
34 #error Recursive header files inclusion detected in DECImageHelpers.h
35 #else // defined(DECImageHelpers_RECURSES)
36 
37 #define DECImageHelpers_RECURSES
38 
39 #if !defined DECImageHelpers_h
40 
41 #define DECImageHelpers_h
42 
44 // Inclusions
45 #include <iostream>
46 #include "DGtal/base/Common.h"
47 #include "DGtal/images/CImage.h"
48 #include "DGtal/topology/CCellularGridSpaceND.h"
49 #include "DGtal/math/linalg/CLinearAlgebra.h"
50 #include "DGtal/dec/DiscreteExteriorCalculus.h"
51 
53 
54 namespace DGtal {
55  namespace functions {
56  namespace dec {
57 
70  template <typename Calculus, DGtal::Dimension dim, DGtal::Duality duality>
71  DGtal::LinearOperator<Calculus, dim, duality, dim, duality>
72  diagonal(const DGtal::KForm<Calculus, dim, duality>& kform)
73  {
74  typedef DGtal::LinearOperator<Calculus,dim, duality, dim, duality> Operator;
75  typedef typename Calculus::LinearAlgebraBackend::Triplet Triplet;
76  typedef typename Calculus::Index Index;
77  typedef std::vector<Triplet> Triplets;
78 
79  Triplets triplets;
80  for (Index index=0; index<kform.length(); index++)
81  triplets.push_back(Triplet(index, index, kform.myContainer(index)));
82 
83  Operator op( kform.myCalculus );
84  op.myContainer.setFromTriplets( triplets.begin(), triplets.end() );
85  return op;
86  }
87 
97  template <typename Calculus, DGtal::Dimension dim, DGtal::Duality duality>
98  void
99  squares(DGtal::KForm<Calculus, dim, duality>& kform)
100  {
101  kform.myContainer.array() = kform.myContainer.array().square();
102  }
103 
116  template <typename Calculus, DGtal::Dimension dim, DGtal::Duality duality>
117  DGtal::LinearOperator<Calculus, dim, duality, dim, duality>
118  squaredDiagonal(const DGtal::KForm<Calculus, dim, duality>& kform)
119  {
120  auto v2 = kform;
121  squares( v2 );
122  return diagonal( v2 );
123  }
124 
137  template <typename Image>
138  void writePixel( Image& image, typename Image::Point pt, typename Image::Value val,
139  int pixel_size = 1 )
140  {
141  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
142  typedef typename Image::Point Point;
143  typedef typename Point::Coordinate Coordinate;
144  pt *= pixel_size;
145  for ( int y = 0; y < pixel_size; y++ )
146  for ( int x = 0; x < pixel_size; x++ )
147  {
148  Point q( (Coordinate) x, (Coordinate) y );
149  image.setValue( pt + q, val );
150  }
151  }
152 
165  template <typename Image>
166  void writePrimalLinel( Image& image, typename Image::Point pt, typename Image::Value val,
167  int pixel_size = 1 )
168  {
169  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
170  typedef typename Image::Point Point;
171  typedef typename Point::Coordinate Coordinate;
172  int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 1 : pixel_size;
173  int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 1 : pixel_size;
174  pt /= 2;
175  pt *= pixel_size;
176  for ( int y = 0; y < pixel_size_y; y++ )
177  for ( int x = 0; x < pixel_size_x; x++ )
178  {
179  Point q( (Coordinate) x, (Coordinate) y );
180  image.setValue( pt + q, val );
181  }
182  }
183 
196  template <typename Image>
197  void writeDualLinel( Image& image, typename Image::Point pt, typename Image::Value val,
198  int pixel_size = 1 )
199  {
200  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
201  typedef typename Image::Point Point;
202  typedef typename Point::Coordinate Coordinate;
203  int pixel_size_x = NumberTraits<Coordinate>::even( pt[ 0 ] ) ? 0 : pixel_size-1;
204  int pixel_size_y = NumberTraits<Coordinate>::even( pt[ 1 ] ) ? 0 : pixel_size-1;
205  pt /= 2;
206  pt *= pixel_size;
207  for ( int y = pixel_size_y; y < pixel_size; y++ )
208  for ( int x = pixel_size_x; x < pixel_size; x++ )
209  {
210  Point q( (Coordinate) x, (Coordinate) y );
211  image.setValue( pt + q, val );
212  }
213  }
214 
236  template <typename Calculus, typename AnyForm2, typename Image, typename Function>
237  void form2ToImage
238  ( const Calculus& calculus,
239  const AnyForm2& u,
240  Image& image,
241  const Function& functor,
242  double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )
243  {
244  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
245  typedef typename Calculus::Index Index;
246  typedef typename Calculus::SCell SCell;
247  typedef typename Calculus::Scalar Scalar;
248  typedef typename Calculus::KSpace KSpace;
249  typedef typename KSpace::Point Point;
250  typedef typename KSpace::Integer Integer;
251  double min_u = NumberTraits<Scalar>::castToDouble( u.myContainer[ 0 ] );
252  double max_u = min_u;
253  for ( Index index = 0; index < u.myContainer.rows(); index++)
254  {
255  double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
256  min_u = std::min( min_u, v );
257  max_u = std::max( max_u, v );
258  }
259  if ( min_u < cut_low ) min_u = cut_low;
260  if ( max_u > cut_up ) max_u = cut_up;
261  for ( Index index = 0; index < u.myContainer.rows(); index++)
262  {
263  SCell cell = u.getSCell( index );
264  double v = NumberTraits<Scalar>::castToDouble( u.myContainer[ index ] );
265  double w = std::min( cut_up, std::max( cut_low, v ) );
266  if ( min_u != max_u ) w = ( w - min_u ) / ( max_u - min_u );
267  writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w ), pixel_size );
268  }
269  }
270 
296  template <typename Calculus, typename Form1, typename Image, typename Function, typename Predicate>
297  void form1ToImage
298  ( const Calculus& calculus,
299  const Form1& v, bool primal,
300  Image& image,
301  const Function& functor,
302  const Predicate& predicate,
303  double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )
304  {
305  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
306  typedef typename Calculus::Index Index;
307  typedef typename Calculus::SCell SCell;
308  typedef typename Calculus::Scalar Scalar;
309  typedef typename Calculus::KSpace KSpace;
310  typedef typename KSpace::Point Point;
311  typedef typename KSpace::Integer Integer;
312  double min_v = NumberTraits<Scalar>::castToDouble( v.myContainer[ 0 ] );
313  double max_v = min_v;
314  for ( Index index = 0; index < v.myContainer.rows(); index++)
315  {
316  double w = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
317  min_v = std::min( min_v, w );
318  max_v = std::max( max_v, w );
319  }
320  if ( min_v < cut_low ) min_v = cut_low;
321  if ( max_v > cut_up ) max_v = cut_up;
322  for ( Index index = 0; index < v.myContainer.rows(); index++)
323  {
324  SCell cell = v.getSCell( index );
325  double u = NumberTraits<Scalar>::castToDouble( v.myContainer[ index ] );
326  if ( ! predicate( u ) ) continue;
327  double w = std::min( cut_up, std::max( cut_low, u ) );
328  if ( min_v != max_v ) w = ( w - min_v ) / ( max_v - min_v );
329  Point kpt = calculus.myKSpace.sKCoords( cell );
330  if ( primal ) writePrimalLinel( image, kpt, functor( w ), pixel_size );
331  else writeDualLinel ( image, kpt, functor( w ), pixel_size );
332  }
333  }
334 
358  template <typename Calculus, typename Image, typename Function, typename Predicate>
359  void dualForm1ToImage
360  ( const Calculus& calculus,
361  const typename Calculus::DualForm1& v,
362  Image& image,
363  const Function& functor,
364  const Predicate& predicate,
365  double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )
366  {
367  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
368  form1ToImage( calculus, v, false, image, functor, predicate,
369  cut_low, cut_up, pixel_size );
370  }
371 
395  template <typename Calculus, typename Image, typename Function, typename Predicate>
396  void primalForm1ToImage
397  ( const Calculus& calculus,
398  const typename Calculus::PrimalForm1& v,
399  Image& image,
400  const Function& functor,
401  const Predicate& predicate,
402  double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )
403  {
404  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
405  form1ToImage( calculus, v, true, image, functor, predicate,
406  cut_low, cut_up, pixel_size );
407  }
408 
432  template <typename Calculus, typename AnyForm2, typename Image, typename Function>
433  void threeForms2ToImage
434  ( const Calculus& calculus,
435  const AnyForm2& u0,
436  const AnyForm2& u1,
437  const AnyForm2& u2,
438  Image& image,
439  const Function& functor,
440  double cut_low = 0.0, double cut_up = 1.0, int pixel_size = 1 )
441  {
442  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
443  typedef typename Calculus::Index Index;
444  typedef typename Calculus::SCell SCell;
445  typedef typename Calculus::Scalar Scalar;
446  double min_u = NumberTraits<Scalar>::castToDouble( u0.myContainer[ 0 ] );
447  double max_u = min_u;
448  for ( Index index = 0; index < u0.myContainer.rows(); index++)
449  {
450  double v = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
451  min_u = std::min( min_u, v );
452  max_u = std::max( max_u, v );
453  }
454  for ( Index index = 0; index < u1.myContainer.rows(); index++)
455  {
456  double v = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
457  min_u = std::min( min_u, v );
458  max_u = std::max( max_u, v );
459  }
460  for ( Index index = 0; index < u2.myContainer.rows(); index++)
461  {
462  double v = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
463  min_u = std::min( min_u, v );
464  max_u = std::max( max_u, v );
465  }
466  if ( min_u < cut_low ) min_u = cut_low;
467  if ( max_u > cut_up ) max_u = cut_up;
468  for ( Index index = 0; index < u0.myContainer.rows(); index++)
469  {
470  SCell cell = u0.getSCell( index );
471  double v0 = NumberTraits<Scalar>::castToDouble( u0.myContainer[ index ] );
472  double w0 = std::min( cut_up, std::max( cut_low, v0 ) );
473  if ( min_u != max_u ) w0 = ( w0 - min_u ) / ( max_u - min_u );
474  double v1 = NumberTraits<Scalar>::castToDouble( u1.myContainer[ index ] );
475  double w1 = std::min( cut_up, std::max( cut_low, v1 ) );
476  if ( min_u != max_u ) w1 = ( w1 - min_u ) / ( max_u - min_u );
477  double v2 = NumberTraits<Scalar>::castToDouble( u2.myContainer[ index ] );
478  double w2 = std::min( cut_up, std::max( cut_low, v2 ) );
479  if ( min_u != max_u ) w2 = ( w2 - min_u ) / ( max_u - min_u );
480  writePixel( image, calculus.myKSpace.sCoords( cell ), functor( w0, w1, w2 ), pixel_size );
481  }
482  }
483 
504  template <typename Calculus, typename AnyForm2, typename Image>
505  void form2ToGreyLevelImage
506  ( const Calculus& calculus,
507  const AnyForm2& u,
508  Image& image,
509  double cut_low = 0.0, double cut_up = 1.0,
510  int pixel_size = 1 )
511  {
512  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
513  form2ToImage( calculus, u, image,
514  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
515  cut_low, cut_up, pixel_size );
516  }
517 
538  template <typename Calculus, typename Image>
539  void primalForm1ToGreyLevelImage
540  ( const Calculus& calculus,
541  const typename Calculus::PrimalForm1& v,
542  Image& image,
543  double cut_low = 0.0, double cut_up = 1.0,
544  int pixel_size = 1 )
545  {
546  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
547  // Threshold is 0.25 instead of 0.5 because an edge connecting
548  // two vertices with v=0 and v=1 should not belong to the
549  // discontinuity set.
550  primalForm1ToImage( calculus, v, image,
551  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
552  [] ( double x ) { return x < 0.25; },
553  cut_low, cut_up, pixel_size );
554  }
555 
576  template <typename Calculus, typename Image>
577  void dualForm1ToGreyLevelImage
578  ( const Calculus& calculus,
579  const typename Calculus::DualForm1& v,
580  Image& image,
581  double cut_low = 0.0, double cut_up = 1.0,
582  int pixel_size = 1 )
583  {
584  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
585  // Threshold is 0.25 instead of 0.5 because an edge connecting
586  // two vertices with v=0 and v=1 should not belong to the
587  // discontinuity set.
588  dualForm1ToImage( calculus, v, image,
589  [] ( double x ) { return (unsigned char) ( round( x * 255.0 ) ); },
590  [] ( double x ) { return x < 0.25; },
591  cut_low, cut_up, pixel_size );
592  }
593 
615  template <typename Calculus, typename Image>
616  void primalForm1ToRGBColorImage
617  ( const Calculus& calculus,
618  const typename Calculus::PrimalForm1& v,
619  Image& image, Color color,
620  double cut_low = 0.0, double cut_up = 1.0,
621  int pixel_size = 1 )
622  {
623  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
624  // Threshold is 0.25 instead of 0.5 because an edge connecting
625  // two vertices with v=0 and v=1 should not belong to the
626  // discontinuity set.
627  primalForm1ToImage( calculus, v, image,
628  [color] ( double x ) { return color; },
629  [] ( double x ) { return x < 0.25; },
630  cut_low, cut_up, pixel_size );
631  }
632 
654  template <typename Calculus, typename Image>
655  void dualForm1ToRGBColorImage
656  ( const Calculus& calculus,
657  const typename Calculus::DualForm1& v,
658  Image& image, Color color,
659  double cut_low = 0.0, double cut_up = 1.0,
660  int pixel_size = 1 )
661  {
662  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
663  // Threshold is 0.25 instead of 0.5 because an edge connecting
664  // two vertices with v=0 and v=1 should not belong to the
665  // discontinuity set.
666  dualForm1ToImage( calculus, v, image,
667  [color] ( double x ) { return color; },
668  [] ( double x ) { return x < 0.25; },
669  cut_low, cut_up, pixel_size );
670  }
671 
697  template <typename Calculus, typename AnyForm2, typename Image>
698  void threeForms2ToRGBColorImage
699  ( const Calculus& calculus,
700  const AnyForm2& u0,
701  const AnyForm2& u1,
702  const AnyForm2& u2,
703  Image& image,
704  double cut_low = 0.0, double cut_up = 1.0,
705  int pixel_size = 1 )
706  {
707  BOOST_CONCEPT_ASSERT(( concepts::CImage<Image> ));
708  threeForms2ToImage
709  ( calculus, u0, u1, u2, image,
710  [] ( double r, double g, double b )
711  { return Color( (unsigned char) ( round( r * 255.0 ) ),
712  (unsigned char) ( round( g * 255.0 ) ),
713  (unsigned char) ( round( b * 255.0 ) ) ); },
714  cut_low, cut_up, pixel_size );
715  }
716 
717  } // namespace dec
718  } // namespace functions
719 
720 
722  // template class DECImage2D
739  template < typename TKSpace,
740  typename TLinearAlgebra = EigenLinearAlgebraBackend >
741  struct DECImage2D {
742  typedef TKSpace KSpace;
743  typedef TLinearAlgebra LinearAlgebra;
744  BOOST_CONCEPT_ASSERT(( concepts::CCellularGridSpaceND< KSpace > ));
745  typedef typename KSpace::Space Space;
746  typedef typename Space::Point Point;
747  typedef typename Space::RealVector RealVector;
748  typedef typename RealVector::Component Scalar;
749  typedef typename KSpace::SCell SCell;
750  typedef typename KSpace::Cell Cell;
751  typedef typename KSpace::Surfel Surfel;
752  typedef HyperRectDomain<Space> Domain;
753  typedef DiscreteExteriorCalculus<2,2, LinearAlgebra> Calculus;
754  typedef DiscreteExteriorCalculusFactory<LinearAlgebra> CalculusFactory;
755  typedef typename Calculus::Index Index;
756  typedef typename Calculus::PrimalForm0 PrimalForm0;
757  typedef typename Calculus::PrimalForm1 PrimalForm1;
758  typedef typename Calculus::PrimalForm2 PrimalForm2;
759  typedef typename Calculus::PrimalIdentity0 PrimalIdentity0;
760  typedef typename Calculus::PrimalIdentity1 PrimalIdentity1;
761  typedef typename Calculus::PrimalIdentity2 PrimalIdentity2;
762  typedef typename Calculus::PrimalDerivative0 PrimalDerivative0;
763  typedef typename Calculus::PrimalDerivative1 PrimalDerivative1;
764  typedef typename Calculus::DualDerivative0 DualDerivative0;
765  typedef typename Calculus::DualDerivative1 DualDerivative1;
766  typedef typename Calculus::PrimalAntiderivative1 PrimalAntiderivative1;
767  typedef typename Calculus::PrimalAntiderivative2 PrimalAntiderivative2;
768  typedef typename Calculus::DualAntiderivative1 DualAntiderivative1;
769  typedef typename Calculus::DualAntiderivative2 DualAntiderivative2;
770  typedef typename Calculus::PrimalHodge0 PrimalHodge0;
771  typedef typename Calculus::PrimalHodge1 PrimalHodge1;
772  typedef typename Calculus::PrimalHodge2 PrimalHodge2;
773  typedef typename Calculus::DualHodge0 DualHodge0;
774  typedef typename Calculus::DualHodge1 DualHodge1;
775  typedef typename Calculus::DualHodge2 DualHodge2;
776  typedef typename LinearAlgebra::SolverSimplicialLLT LinearAlgebraSolver;
777  typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL>
778  SolverU;
779  typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL>
780  SolverV;
781 
782  BOOST_STATIC_ASSERT(( KSpace::dimension == 2 ));
783 
784  // ----------------------- Standard services ------------------------------
785  public:
786 
790  ~DECImage2D() = default;
791 
796  DECImage2D( int _verbose = 1 )
797  : verbose( _verbose ),
798  calculus(),
799  D0( calculus ), D1( calculus ),
800  dual_D0( calculus ), dual_D1( calculus ),
801  primal_h0( calculus ), primal_h1( calculus ), primal_h2( calculus ),
802  dual_h0( calculus ), dual_h1( calculus ), dual_h2( calculus )
803  {}
804 
812  void init( Clone<KSpace> aKSpace )
813  {
814  calculus.myKSpace = aKSpace;
815  const KSpace & K = calculus.myKSpace;
816  domain = Domain( K.lowerBound(), K.upperBound() );
817  Point p0 = K.uKCoords( K.lowerCell() );
818  Point p1 = K.uKCoords( K.upperCell() );
819  cell_domain = Domain( p0, p1 );
820 
821  if ( verbose > 0 ) trace.beginBlock("building AT functionnals");
822  // Adds all the cell
823  for ( typename Domain::ConstIterator it = cell_domain.begin(), itE = cell_domain.end();
824  it != itE; ++it )
825  calculus.insertSCell( K.sCell( *it ) ); // ajoute toutes les cellules de Khalimsky.
826  calculus.updateIndexes();
827  if ( verbose > 1 ) trace.info() << calculus << std::endl;
828  // Precomputes operators.
829  if ( verbose > 1 ) trace.info() << "primal_D0" << std::endl;
830  D0 = calculus.template derivative<0,PRIMAL>();
831  if ( verbose > 1 ) trace.info() << "primal_D1" << std::endl;
832  D1 = calculus.template derivative<1,PRIMAL>();
833  if ( verbose > 1 ) trace.info() << "dual_D0" << std::endl;
834  dual_D0 = calculus.template derivative<0,DUAL>();
835  if ( verbose > 1 ) trace.info() << "dual_D1" << std::endl;
836  dual_D1 = calculus.template derivative<1,DUAL>();
837  if ( verbose > 1 ) trace.info() << "primal_h1" << std::endl;
838  primal_h0 = calculus.template hodge<0,PRIMAL>();
839  if ( verbose > 1 ) trace.info() << "primal_h1" << std::endl;
840  primal_h1 = calculus.template hodge<1,PRIMAL>();
841  if ( verbose > 1 ) trace.info() << "primal_h2" << std::endl;
842  primal_h2 = calculus.template hodge<2,PRIMAL>();
843  if ( verbose > 1 ) trace.info() << "dual_h1" << std::endl;
844  dual_h0 = calculus.template hodge<0,DUAL>();
845  if ( verbose > 1 ) trace.info() << "dual_h1" << std::endl;
846  dual_h1 = calculus.template hodge<1,DUAL>();
847  if ( verbose > 1 ) trace.info() << "dual_h2" << std::endl;
848  dual_h2 = calculus.template hodge<2,DUAL>();
849  if ( verbose > 0 ) trace.endBlock();
850  }
851 
856  DECImage2D ( const DECImage2D & other ) = delete;
857 
862  DECImage2D ( DECImage2D && other ) = delete;
863 
869  DECImage2D & operator= ( const DECImage2D & other ) = delete;
870 
876  DECImage2D & operator= ( DECImage2D && other ) = delete;
877 
878  // ------------------------- Public Datas ------------------------------
879  public:
880 
882  int verbose;
884  Calculus calculus;
886  Domain domain;
888  Domain cell_domain;
890  PrimalDerivative0 D0;
892  PrimalDerivative1 D1;
894  DualDerivative0 dual_D0;
896  DualDerivative1 dual_D1;
898  PrimalHodge0 primal_h0;
900  PrimalHodge1 primal_h1;
902  PrimalHodge2 primal_h2;
904  DualHodge0 dual_h0;
906  DualHodge1 dual_h1;
908  DualHodge2 dual_h2;
909 
910  };
911 
912 } // namespace DGtal
913 
915 // Includes inline functions.
916 
917 // //
919 
920 #endif // !defined DECImageHelpers_h
921 
922 #undef DECImageHelpers_RECURSES
923 #endif // else defined(DECImageHelpers_RECURSES)
DGtal::Trace::beginBlock
void beginBlock(const std::string &keyword="")
DGtal::DECImage2D::DECImage2D
DECImage2D(int _verbose=1)
Definition: DECImageHelpers.h:796
DGtal::functions::dec::dualForm1ToGreyLevelImage
void dualForm1ToGreyLevelImage(const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:578
DGtal::DECImage2D::PrimalHodge0
Calculus::PrimalHodge0 PrimalHodge0
Definition: DECImageHelpers.h:770
DGtal::DECImage2D::Point
Space::Point Point
Definition: DECImageHelpers.h:746
DGtal::DECImage2D::BOOST_CONCEPT_ASSERT
BOOST_CONCEPT_ASSERT((concepts::CCellularGridSpaceND< KSpace >))
DGtal::HyperRectDomain::begin
const ConstIterator & begin() const
DGtal::HyperRectDomain::end
const ConstIterator & end() const
DGtal::functions::dec::primalForm1ToImage
void primalForm1ToImage(const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:397
DGtal::DiscreteExteriorCalculus::Scalar
LinearAlgebraBackend::DenseVector::Scalar Scalar
DGtal::KhalimskySpaceND::sKCoords
const Point & sKCoords(const SCell &c) const
DGtal::functions::dec::primalForm1ToRGBColorImage
void primalForm1ToRGBColorImage(const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:617
DGtal::DECImage2D::~DECImage2D
~DECImage2D()=default
DGtal::functions::dec::diagonal
DGtal::LinearOperator< Calculus, dim, duality, dim, duality > diagonal(const DGtal::KForm< Calculus, dim, duality > &kform)
Definition: DECImageHelpers.h:72
DGtal::DECImage2D::DualHodge0
Calculus::DualHodge0 DualHodge0
Definition: DECImageHelpers.h:773
DGtal::NumberTraits::castToDouble
static double castToDouble(const T &aT)
DGtal::Image::Point
TImageContainer::Point Point
DGtal::DECImage2D::PrimalDerivative0
Calculus::PrimalDerivative0 PrimalDerivative0
Definition: DECImageHelpers.h:762
DGtal::DECImage2D::dual_D0
DualDerivative0 dual_D0
dual derivative dual 0-form -> dual 1-form
Definition: DECImageHelpers.h:894
DGtal::DECImage2D::DualDerivative1
Calculus::DualDerivative1 DualDerivative1
Definition: DECImageHelpers.h:765
DGtal::Trace::endBlock
double endBlock()
DGtal::DECImage2D::PrimalAntiderivative1
Calculus::PrimalAntiderivative1 PrimalAntiderivative1
Definition: DECImageHelpers.h:766
DGtal::functions::dec::threeForms2ToImage
void threeForms2ToImage(const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:434
DGtal::DECImage2D
Aim: This class simplifies the development of 2D image processing tools using discrete exterior calcu...
Definition: DECImageHelpers.h:741
DGtal::Image::setValue
void setValue(const Point &aPoint, const Value &aValue)
DGtal::DECImage2D::PrimalHodge1
Calculus::PrimalHodge1 PrimalHodge1
Definition: DECImageHelpers.h:771
DGtal::DECImage2D::primal_h2
PrimalHodge2 primal_h2
hodge star: 2-form -> dual 2-form
Definition: DECImageHelpers.h:902
DGtal::DECImage2D::dual_D1
DualDerivative1 dual_D1
dual derivative dual 1-form -> dual 2-form
Definition: DECImageHelpers.h:896
DGtal::DECImage2D::init
void init(Clone< KSpace > aKSpace)
Definition: DECImageHelpers.h:812
DGtal::KForm::myContainer
Container myContainer
DGtal::DECImage2D::dual_h0
DualHodge0 dual_h0
hodge star: dual 0-form -> 0-form
Definition: DECImageHelpers.h:904
DGtal::DECImage2D::CalculusFactory
DiscreteExteriorCalculusFactory< LinearAlgebra > CalculusFactory
Definition: DECImageHelpers.h:754
DGtal::functions::dec::threeForms2ToRGBColorImage
void threeForms2ToRGBColorImage(const Calculus &calculus, const AnyForm2 &u0, const AnyForm2 &u1, const AnyForm2 &u2, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:699
DGtal::DECImage2D::PrimalHodge2
Calculus::PrimalHodge2 PrimalHodge2
Definition: DECImageHelpers.h:772
DGtal::DECImage2D::LinearAlgebra
TLinearAlgebra LinearAlgebra
Definition: DECImageHelpers.h:743
DGtal::DECImage2D::DualAntiderivative2
Calculus::DualAntiderivative2 DualAntiderivative2
Definition: DECImageHelpers.h:769
DGtal::DECImage2D::PrimalForm2
Calculus::PrimalForm2 PrimalForm2
Definition: DECImageHelpers.h:758
DGtal::functions::dec::squaredDiagonal
DGtal::LinearOperator< Calculus, dim, duality, dim, duality > squaredDiagonal(const DGtal::KForm< Calculus, dim, duality > &kform)
Definition: DECImageHelpers.h:118
DGtal::DECImage2D::PrimalIdentity2
Calculus::PrimalIdentity2 PrimalIdentity2
Definition: DECImageHelpers.h:761
DGtal::functions::dec::dualForm1ToImage
void dualForm1ToImage(const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:360
DGtal::functions::dec::writeDualLinel
void writeDualLinel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
Definition: DECImageHelpers.h:197
DGtal::DECImage2D::DualAntiderivative1
Calculus::DualAntiderivative1 DualAntiderivative1
Definition: DECImageHelpers.h:768
DGtal::DECImage2D::RealVector
Space::RealVector RealVector
Definition: DECImageHelpers.h:747
DGtal::DECImage2D::PrimalForm1
Calculus::PrimalForm1 PrimalForm1
Definition: DECImageHelpers.h:757
DGtal::DECImage2D::Calculus
DiscreteExteriorCalculus< 2, 2, LinearAlgebra > Calculus
Definition: DECImageHelpers.h:753
DGtal::DECImage2D::dual_h1
DualHodge1 dual_h1
hodge star: dual 1-form -> 1-form
Definition: DECImageHelpers.h:906
DGtal::DECImage2D::DualHodge2
Calculus::DualHodge2 DualHodge2
Definition: DECImageHelpers.h:775
DGtal::DECImage2D::PrimalIdentity1
Calculus::PrimalIdentity1 PrimalIdentity1
Definition: DECImageHelpers.h:760
DGtal::functions::dec::writePixel
void writePixel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
Definition: DECImageHelpers.h:138
DGtal::functions::dec::dualForm1ToRGBColorImage
void dualForm1ToRGBColorImage(const Calculus &calculus, const typename Calculus::DualForm1 &v, Image &image, Color color, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:656
DGtal::DECImage2D::PrimalDerivative1
Calculus::PrimalDerivative1 PrimalDerivative1
Definition: DECImageHelpers.h:763
DGtal::KhalimskySpaceND::sCoords
Point sCoords(const SCell &c) const
DGtal::NumberTraits::even
static bool even(ParamType aT)
DGtal::DECImage2D::SCell
KSpace::SCell SCell
Definition: DECImageHelpers.h:749
DGtal::DECImage2D::DualHodge1
Calculus::DualHodge1 DualHodge1
Definition: DECImageHelpers.h:774
DGtal::DECImage2D::verbose
int verbose
The verbose level (0: silent).
Definition: DECImageHelpers.h:882
DGtal::functions::dec::writePrimalLinel
void writePrimalLinel(Image &image, typename Image::Point pt, typename Image::Value val, int pixel_size=1)
Definition: DECImageHelpers.h:166
DGtal::trace
Trace trace(traceWriterTerm)
DGtal::Trace::info
std::ostream & info()
DGtal::DECImage2D::Surfel
KSpace::Surfel Surfel
Definition: DECImageHelpers.h:751
DGtal::DECImage2D::PrimalIdentity0
Calculus::PrimalIdentity0 PrimalIdentity0
Definition: DECImageHelpers.h:759
DGtal::functions::dec::form1ToImage
void form1ToImage(const Calculus &calculus, const Form1 &v, bool primal, Image &image, const Function &functor, const Predicate &predicate, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:298
DGtal::HyperRectDomain_Iterator
DGtal::functions::dec::primalForm1ToGreyLevelImage
void primalForm1ToGreyLevelImage(const Calculus &calculus, const typename Calculus::PrimalForm1 &v, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:540
Point
typename Self::Point Point
DGtal::DECImage2D::calculus
Calculus calculus
The discrete exterior calculus instance.
Definition: DECImageHelpers.h:884
DGtal::functions::dec::form2ToGreyLevelImage
void form2ToGreyLevelImage(const Calculus &calculus, const AnyForm2 &u, Image &image, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:506
DGtal::functions::dec::squares
void squares(DGtal::KForm< Calculus, dim, duality > &kform)
Definition: DECImageHelpers.h:99
DGtal::DECImage2D::primal_h0
PrimalHodge0 primal_h0
hodge star: 0-form -> dual 0-form
Definition: DECImageHelpers.h:898
DGtal::DECImage2D::DualDerivative0
Calculus::DualDerivative0 DualDerivative0
Definition: DECImageHelpers.h:764
DGtal::DECImage2D::PrimalAntiderivative2
Calculus::PrimalAntiderivative2 PrimalAntiderivative2
Definition: DECImageHelpers.h:767
DGtal::DECImage2D::dual_h2
DualHodge2 dual_h2
hodge star: dual 2-form -> 2-form
Definition: DECImageHelpers.h:908
DGtal::DiscreteExteriorCalculus::insertSCell
bool insertSCell(const SCell &signed_cell)
DGtal::DECImage2D::cell_domain
Domain cell_domain
The cell domain (i.e. all the cells)
Definition: DECImageHelpers.h:888
DGtal::functions::dec::form2ToImage
void form2ToImage(const Calculus &calculus, const AnyForm2 &u, Image &image, const Function &functor, double cut_low=0.0, double cut_up=1.0, int pixel_size=1)
Definition: DECImageHelpers.h:238
DGtal::DECImage2D::Space
KSpace::Space Space
Definition: DECImageHelpers.h:745
DGtal::Image::Value
TImageContainer::Value Value
DGtal::KForm::length
Index length() const
DGtal::DECImage2D::SolverU
DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL > SolverU
Definition: DECImageHelpers.h:778
DGtal::DECImage2D::D0
PrimalDerivative0 D0
primal derivative: 0-form -> 1-form
Definition: DECImageHelpers.h:890
DGtal::DECImage2D::LinearAlgebraSolver
LinearAlgebra::SolverSimplicialLLT LinearAlgebraSolver
Definition: DECImageHelpers.h:776
DGtal::DECImage2D::BOOST_STATIC_ASSERT
BOOST_STATIC_ASSERT((KSpace::dimension==2))
DGtal::KhalimskySpaceND::dimension
static const constexpr Dimension dimension
DGtal::DECImage2D::D1
PrimalDerivative1 D1
primal derivative: 1-form -> 2-form
Definition: DECImageHelpers.h:892
DGtal::DECImage2D::primal_h1
PrimalHodge1 primal_h1
hodge star: 1-form -> dual 1-form
Definition: DECImageHelpers.h:900
DGtal::DECImage2D::SolverV
DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL > SolverV
Definition: DECImageHelpers.h:780
DGtal::DECImage2D::operator=
DECImage2D & operator=(const DECImage2D &other)=delete
DGtal::DECImage2D::domain
Domain domain
The image domain (i.e. all the pixels)
Definition: DECImageHelpers.h:886
DGtal::DECImage2D::Index
Calculus::Index Index
Definition: DECImageHelpers.h:755
DGtal::DECImage2D::PrimalForm0
Calculus::PrimalForm0 PrimalForm0
Definition: DECImageHelpers.h:756
DGtal::DECImage2D::Domain
HyperRectDomain< Space > Domain
Definition: DECImageHelpers.h:752
DGtal::KForm::myCalculus
const Calculus * myCalculus
DGtal::DECImage2D::Scalar
RealVector::Component Scalar
Definition: DECImageHelpers.h:748
DGtal::DiscreteExteriorCalculus::Index
LinearAlgebraBackend::DenseVector::Index Index
DGtal::PointVector::Component
TEuclideanRing Component
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