DGtalTools  1.2.0
Public Types | Public Member Functions | Data Fields
DGtal::DECImage2D< TKSpace, TLinearAlgebra > Struct Template Reference

#include <imageProcessing/DECImageHelpers.h>

Inheritance diagram for DGtal::DECImage2D< TKSpace, TLinearAlgebra >:
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Public Types

typedef TKSpace KSpace
 
typedef TLinearAlgebra LinearAlgebra
 
typedef KSpace::Space Space
 
typedef Space::Point Point
 
typedef Space::RealVector RealVector
 
typedef RealVector::Component Scalar
 
typedef KSpace::SCell SCell
 
typedef KSpace::Cell Cell
 
typedef KSpace::Surfel Surfel
 
typedef HyperRectDomain< SpaceDomain
 
typedef DiscreteExteriorCalculus< 2, 2, LinearAlgebraCalculus
 
typedef DiscreteExteriorCalculusFactory< LinearAlgebraCalculusFactory
 
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
 
typedef Calculus::PrimalDerivative0 PrimalDerivative0
 
typedef Calculus::PrimalDerivative1 PrimalDerivative1
 
typedef Calculus::DualDerivative0 DualDerivative0
 
typedef Calculus::DualDerivative1 DualDerivative1
 
typedef Calculus::PrimalAntiderivative1 PrimalAntiderivative1
 
typedef Calculus::PrimalAntiderivative2 PrimalAntiderivative2
 
typedef Calculus::DualAntiderivative1 DualAntiderivative1
 
typedef Calculus::DualAntiderivative2 DualAntiderivative2
 
typedef Calculus::PrimalHodge0 PrimalHodge0
 
typedef Calculus::PrimalHodge1 PrimalHodge1
 
typedef Calculus::PrimalHodge2 PrimalHodge2
 
typedef Calculus::DualHodge0 DualHodge0
 
typedef Calculus::DualHodge1 DualHodge1
 
typedef Calculus::DualHodge2 DualHodge2
 
typedef LinearAlgebra::SolverSimplicialLLT LinearAlgebraSolver
 
typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL > SolverU
 
typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL > SolverV
 

Public Member Functions

 BOOST_CONCEPT_ASSERT ((concepts::CCellularGridSpaceND< KSpace >))
 
 BOOST_STATIC_ASSERT ((KSpace::dimension==2))
 
 ~DECImage2D ()=default
 
 DECImage2D (int _verbose=1)
 
void init (Clone< KSpace > aKSpace)
 
 DECImage2D (const DECImage2D &other)=delete
 
 DECImage2D (DECImage2D &&other)=delete
 
DECImage2Doperator= (const DECImage2D &other)=delete
 
DECImage2Doperator= (DECImage2D &&other)=delete
 

Data Fields

int verbose
 
Calculus calculus
 
Domain domain
 
Domain cell_domain
 
PrimalDerivative0 D0
 
PrimalDerivative1 D1
 
DualDerivative0 dual_D0
 
DualDerivative1 dual_D1
 
PrimalHodge0 primal_h0
 
PrimalHodge1 primal_h1
 
PrimalHodge2 primal_h2
 
DualHodge0 dual_h0
 
DualHodge1 dual_h1
 
DualHodge2 dual_h2
 

Detailed Description

template<typename TKSpace, typename TLinearAlgebra = EigenLinearAlgebraBackend>
struct DGtal::DECImage2D< TKSpace, TLinearAlgebra >

Aim: This class simplifies the development of 2D image processing tools using discrete exterior calculus. Most notably it take care of initializing correctly a discrete exterior calculus in some 2D domain, and precomputes derivative and Hodge star operators. You may have a look at module Image restoration and inpainting with Ambrosio-Tortorelli functional for such image processing tools and more explanation on discrete calculus.

Description of template class 'DECImage2D'

Template Parameters
TKSpaceany model of CCellularGridSpaceND, e.g KhalimskySpaceND
TLinearAlgebraany back-end for performing linear algebra, default is EigenLinearAlgebraBackend.
See also
ATu0v1
ATu2v0

Definition at line 741 of file DECImageHelpers.h.

Member Typedef Documentation

◆ Calculus

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DiscreteExteriorCalculus<2,2, LinearAlgebra> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Calculus

Definition at line 753 of file DECImageHelpers.h.

◆ CalculusFactory

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DiscreteExteriorCalculusFactory<LinearAlgebra> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::CalculusFactory

Definition at line 754 of file DECImageHelpers.h.

◆ Cell

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef KSpace::Cell DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Cell

Definition at line 750 of file DECImageHelpers.h.

◆ Domain

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef HyperRectDomain<Space> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Domain

Definition at line 752 of file DECImageHelpers.h.

◆ DualAntiderivative1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative1

Definition at line 768 of file DECImageHelpers.h.

◆ DualAntiderivative2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative2

Definition at line 769 of file DECImageHelpers.h.

◆ DualDerivative0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative0

Definition at line 764 of file DECImageHelpers.h.

◆ DualDerivative1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative1

Definition at line 765 of file DECImageHelpers.h.

◆ DualHodge0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge0

Definition at line 773 of file DECImageHelpers.h.

◆ DualHodge1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge1

Definition at line 774 of file DECImageHelpers.h.

◆ DualHodge2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::DualHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge2

Definition at line 775 of file DECImageHelpers.h.

◆ Index

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::Index DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Index

Definition at line 755 of file DECImageHelpers.h.

◆ KSpace

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef TKSpace DGtal::DECImage2D< TKSpace, TLinearAlgebra >::KSpace

Definition at line 742 of file DECImageHelpers.h.

◆ LinearAlgebra

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef TLinearAlgebra DGtal::DECImage2D< TKSpace, TLinearAlgebra >::LinearAlgebra

Definition at line 743 of file DECImageHelpers.h.

◆ LinearAlgebraSolver

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef LinearAlgebra::SolverSimplicialLLT DGtal::DECImage2D< TKSpace, TLinearAlgebra >::LinearAlgebraSolver

Definition at line 776 of file DECImageHelpers.h.

◆ Point

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Space::Point DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Point

Definition at line 746 of file DECImageHelpers.h.

◆ PrimalAntiderivative1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative1

Definition at line 766 of file DECImageHelpers.h.

◆ PrimalAntiderivative2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative2

Definition at line 767 of file DECImageHelpers.h.

◆ PrimalDerivative0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative0

Definition at line 762 of file DECImageHelpers.h.

◆ PrimalDerivative1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative1

Definition at line 763 of file DECImageHelpers.h.

◆ PrimalForm0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalForm0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm0

Definition at line 756 of file DECImageHelpers.h.

◆ PrimalForm1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalForm1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm1

Definition at line 757 of file DECImageHelpers.h.

◆ PrimalForm2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalForm2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm2

Definition at line 758 of file DECImageHelpers.h.

◆ PrimalHodge0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge0

Definition at line 770 of file DECImageHelpers.h.

◆ PrimalHodge1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge1

Definition at line 771 of file DECImageHelpers.h.

◆ PrimalHodge2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge2

Definition at line 772 of file DECImageHelpers.h.

◆ PrimalIdentity0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalIdentity0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity0

Definition at line 759 of file DECImageHelpers.h.

◆ PrimalIdentity1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalIdentity1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity1

Definition at line 760 of file DECImageHelpers.h.

◆ PrimalIdentity2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Calculus::PrimalIdentity2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity2

Definition at line 761 of file DECImageHelpers.h.

◆ RealVector

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef Space::RealVector DGtal::DECImage2D< TKSpace, TLinearAlgebra >::RealVector

Definition at line 747 of file DECImageHelpers.h.

◆ Scalar

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef RealVector::Component DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Scalar

Definition at line 748 of file DECImageHelpers.h.

◆ SCell

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef KSpace::SCell DGtal::DECImage2D< TKSpace, TLinearAlgebra >::SCell

Definition at line 749 of file DECImageHelpers.h.

◆ SolverU

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::SolverU

Definition at line 778 of file DECImageHelpers.h.

◆ SolverV

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::SolverV

Definition at line 780 of file DECImageHelpers.h.

◆ Space

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef KSpace::Space DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Space

Definition at line 745 of file DECImageHelpers.h.

◆ Surfel

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef KSpace::Surfel DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Surfel

Definition at line 751 of file DECImageHelpers.h.

Constructor & Destructor Documentation

◆ ~DECImage2D()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::~DECImage2D ( )
default

Destructor.

◆ DECImage2D() [1/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DECImage2D ( int  _verbose = 1)
inline

Default constructor. The object needs to be initialized with init.

Parameters
_verbosespecifies the verbose level (0: silent, 1: more info ... ).

Definition at line 796 of file DECImageHelpers.h.

797  : verbose( _verbose ),
798  calculus(),
799  D0( calculus ), D1( calculus ),
803  {}
int verbose
The verbose level (0: silent).
DualDerivative0 dual_D0
dual derivative dual 0-form -> dual 1-form
PrimalHodge2 primal_h2
hodge star: 2-form -> dual 2-form
PrimalDerivative0 D0
primal derivative: 0-form -> 1-form
Calculus calculus
The discrete exterior calculus instance.
DualHodge0 dual_h0
hodge star: dual 0-form -> 0-form
DualHodge1 dual_h1
hodge star: dual 1-form -> 1-form
DualHodge2 dual_h2
hodge star: dual 2-form -> 2-form
PrimalHodge0 primal_h0
hodge star: 0-form -> dual 0-form
PrimalHodge1 primal_h1
hodge star: 1-form -> dual 1-form
PrimalDerivative1 D1
primal derivative: 1-form -> 2-form
DualDerivative1 dual_D1
dual derivative dual 1-form -> dual 2-form

◆ DECImage2D() [2/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DECImage2D ( const DECImage2D< TKSpace, TLinearAlgebra > &  other)
delete

Copy constructor.

Parameters
otherthe object to clone.

◆ DECImage2D() [3/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DECImage2D ( DECImage2D< TKSpace, TLinearAlgebra > &&  other)
delete

Move constructor.

Parameters
otherthe object to move.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::BOOST_CONCEPT_ASSERT ( (concepts::CCellularGridSpaceND< KSpace >)  )

◆ BOOST_STATIC_ASSERT()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::DECImage2D< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT ( (KSpace::dimension==2)  )

◆ init()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init ( Clone< KSpace aKSpace)
inline

Constructor from cellular grid space, which specifies the domain of calculus.

Parameters
aKSpacethe cellular grid space specifies the domain of calculus (i.e. all the cells and incidence), which is cloned inside the class.

Definition at line 812 of file DECImageHelpers.h.

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  }
HyperRectDomain< Space > Domain
Domain cell_domain
The cell domain (i.e. all the cells)
Domain domain
The image domain (i.e. all the pixels)

References DGtal::DECImage2D< TKSpace, TLinearAlgebra >::calculus, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::cell_domain, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D0, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D1, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::domain, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_D0, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_D1, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h0, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h1, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h2, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h0, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h1, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h2, and DGtal::DECImage2D< TKSpace, TLinearAlgebra >::verbose.

◆ operator=() [1/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DECImage2D& DGtal::DECImage2D< TKSpace, TLinearAlgebra >::operator= ( const DECImage2D< TKSpace, TLinearAlgebra > &  other)
delete

Copy assignment operator.

Parameters
otherthe object to copy.
Returns
a reference on 'this'.

◆ operator=() [2/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DECImage2D& DGtal::DECImage2D< TKSpace, TLinearAlgebra >::operator= ( DECImage2D< TKSpace, TLinearAlgebra > &&  other)
delete

Move assignment operator.

Parameters
otherthe object to move.
Returns
a reference on 'this'.

Field Documentation

◆ calculus

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Calculus DGtal::DECImage2D< TKSpace, TLinearAlgebra >::calculus

The discrete exterior calculus instance.

Definition at line 884 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ cell_domain

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Domain DGtal::DECImage2D< TKSpace, TLinearAlgebra >::cell_domain

The cell domain (i.e. all the cells)

Definition at line 888 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ D0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D0

primal derivative: 0-form -> 1-form

Definition at line 890 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ D1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D1

primal derivative: 1-form -> 2-form

Definition at line 892 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ domain

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Domain DGtal::DECImage2D< TKSpace, TLinearAlgebra >::domain

The image domain (i.e. all the pixels)

Definition at line 886 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ dual_D0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DualDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_D0

dual derivative dual 0-form -> dual 1-form

Definition at line 894 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ dual_D1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DualDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_D1

dual derivative dual 1-form -> dual 2-form

Definition at line 896 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ dual_h0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DualHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h0

hodge star: dual 0-form -> 0-form

Definition at line 904 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ dual_h1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DualHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h1

hodge star: dual 1-form -> 1-form

Definition at line 906 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ dual_h2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DualHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h2

hodge star: dual 2-form -> 2-form

Definition at line 908 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ primal_h0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h0

hodge star: 0-form -> dual 0-form

Definition at line 898 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ primal_h1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h1

hodge star: 1-form -> dual 1-form

Definition at line 900 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ primal_h2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h2

hodge star: 2-form -> dual 2-form

Definition at line 902 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().

◆ verbose

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
int DGtal::DECImage2D< TKSpace, TLinearAlgebra >::verbose

The verbose level (0: silent).

Definition at line 882 of file DECImageHelpers.h.

Referenced by DGtal::DECImage2D< TKSpace, TLinearAlgebra >::init().


The documentation for this struct was generated from the following file: