DGtal::DECImage2D< TKSpace, TLinearAlgebra > Struct Template Reference

#include <imageProcessing/DECImageHelpers.h>

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

Collaboration diagram for DGtal::DECImage2D< TKSpace, TLinearAlgebra >:

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< Space >	Domain
typedef DiscreteExteriorCalculus< 2, 2, LinearAlgebra >	Calculus
typedef DiscreteExteriorCalculusFactory< LinearAlgebra >	CalculusFactory
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
DECImage2D &	operator= (const DECImage2D &other)=delete
DECImage2D &	operator= (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

TKSpace	any model of CCellularGridSpaceND, e.g KhalimskySpaceND
TLinearAlgebra	any back-end for performing linear algebra, default is EigenLinearAlgebraBackend.

See also

ATu0v1

ATu2v0

Definition at line 741 of file DECImageHelpers.h.

Member Typedef Documentation

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DiscreteExteriorCalculus<2,2, LinearAlgebra> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Calculus

Definition at line 753 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DiscreteExteriorCalculusFactory<LinearAlgebra> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::CalculusFactory

Definition at line 754 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef KSpace::Cell DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Cell

Definition at line 750 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef HyperRectDomain<Space> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Domain

Definition at line 752 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative1

Definition at line 768 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative2

Definition at line 769 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative0

Definition at line 764 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative1

Definition at line 765 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge0

Definition at line 773 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge1

Definition at line 774 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::DualHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge2

Definition at line 775 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::Index DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Index

Definition at line 755 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef TKSpace DGtal::DECImage2D< TKSpace, TLinearAlgebra >::KSpace

Definition at line 742 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef TLinearAlgebra DGtal::DECImage2D< TKSpace, TLinearAlgebra >::LinearAlgebra

Definition at line 743 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef LinearAlgebra::SolverSimplicialLLT DGtal::DECImage2D< TKSpace, TLinearAlgebra >::LinearAlgebraSolver

Definition at line 776 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Space::Point DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Point

Definition at line 746 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative1

Definition at line 766 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative2

Definition at line 767 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative0

Definition at line 762 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative1

Definition at line 763 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalForm0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm0

Definition at line 756 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalForm1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm1

Definition at line 757 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalForm2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm2

Definition at line 758 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge0

Definition at line 770 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge1

Definition at line 771 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge2

Definition at line 772 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalIdentity0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity0

Definition at line 759 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalIdentity1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity1

Definition at line 760 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Calculus::PrimalIdentity2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity2

Definition at line 761 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef Space::RealVector DGtal::DECImage2D< TKSpace, TLinearAlgebra >::RealVector

Definition at line 747 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef RealVector::Component DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Scalar

Definition at line 748 of file DECImageHelpers.h.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef KSpace::SCell DGtal::DECImage2D< TKSpace, TLinearAlgebra >::SCell

Definition at line 749 of file DECImageHelpers.h.

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.

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.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef KSpace::Space DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Space

Definition at line 745 of file DECImageHelpers.h.

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

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::DECImage2D< TKSpace, TLinearAlgebra >::~DECImage2D ( )

default

Destructor.

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

_verbose

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

Definition at line 796 of file DECImageHelpers.h.

      : verbose( _verbose ), 
        calculus(), 
        D0( calculus ), D1( calculus ), 
        dual_D0( calculus ), dual_D1( calculus ),
        primal_h0( calculus ), primal_h1( calculus ), primal_h2( calculus ),
        dual_h0( calculus ), dual_h1( calculus ), dual_h2( calculus )
    {}

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DECImage2D ( const DECImage2D< TKSpace, TLinearAlgebra > &  other )

delete

Copy constructor.

Parameters

other

the object to clone.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DECImage2D ( DECImage2D< TKSpace, TLinearAlgebra > &&  other )

delete

Move constructor.

Parameters

other

the object to move.

Member Function Documentation

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::DECImage2D< TKSpace, TLinearAlgebra >::BOOST_CONCEPT_ASSERT

(

(concepts::CCellularGridSpaceND< KSpace >)

)

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::DECImage2D< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT

(

(KSpace::dimension==2)

)

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

aKSpace

the 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.

References DGtal::HyperRectDomain< TSpace >::begin(), DGtal::Trace::beginBlock(), 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::HyperRectDomain< TSpace >::end(), DGtal::Trace::endBlock(), DGtal::Trace::info(), DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::insertSCell(), DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::myKSpace, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h0, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h1, DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h2, DGtal::trace, DGtal::DiscreteExteriorCalculus< dimEmbedded, dimAmbient, TLinearAlgebraBackend, TInteger >::updateIndexes(), and DGtal::DECImage2D< TKSpace, TLinearAlgebra >::verbose.

    {
      calculus.myKSpace = aKSpace;
      const KSpace & K  = calculus.myKSpace;
      domain            = Domain( K.lowerBound(), K.upperBound() );
      Point  p0         = K.uKCoords( K.lowerCell() );
      Point  p1         = K.uKCoords( K.upperCell() );
      cell_domain       = Domain( p0, p1 );

      if ( verbose > 0 ) trace.beginBlock("building AT functionnals");
      // Adds all the cell
      for ( typename Domain::ConstIterator it = cell_domain.begin(), itE = cell_domain.end(); 
            it != itE; ++it )
        calculus.insertSCell( K.sCell( *it ) ); // ajoute toutes les cellules de Khalimsky.
      calculus.updateIndexes();
      if ( verbose > 1 ) trace.info() << calculus << std::endl;
      // Precomputes operators.
      if ( verbose > 1 ) trace.info() << "primal_D0" << std::endl;
      D0 = calculus.template derivative<0,PRIMAL>();
      if ( verbose > 1 ) trace.info() << "primal_D1" << std::endl;
      D1 = calculus.template derivative<1,PRIMAL>();
      if ( verbose > 1 ) trace.info() << "dual_D0" << std::endl;
      dual_D0   = calculus.template derivative<0,DUAL>();
      if ( verbose > 1 ) trace.info() << "dual_D1" << std::endl;
      dual_D1   = calculus.template derivative<1,DUAL>();
      if ( verbose > 1 ) trace.info() << "primal_h1" << std::endl;
      primal_h0 = calculus.template hodge<0,PRIMAL>();
      if ( verbose > 1 ) trace.info() << "primal_h1" << std::endl;
      primal_h1 = calculus.template hodge<1,PRIMAL>();
      if ( verbose > 1 ) trace.info() << "primal_h2" << std::endl;
      primal_h2 = calculus.template hodge<2,PRIMAL>();
      if ( verbose > 1 ) trace.info() << "dual_h1" << std::endl;
      dual_h0   = calculus.template hodge<0,DUAL>();
      if ( verbose > 1 ) trace.info() << "dual_h1" << std::endl;
      dual_h1   = calculus.template hodge<1,DUAL>();
      if ( verbose > 1 ) trace.info() << "dual_h2" << std::endl;
      dual_h2   = calculus.template hodge<2,DUAL>();
      if ( verbose > 0 ) trace.endBlock();
    }

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DECImage2D& DGtal::DECImage2D< TKSpace, TLinearAlgebra >::operator= ( const DECImage2D< TKSpace, TLinearAlgebra > &  other )

delete

Copy assignment operator.

Parameters

other

the object to copy.

Returns

a reference on 'this'.

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DECImage2D& DGtal::DECImage2D< TKSpace, TLinearAlgebra >::operator= ( DECImage2D< TKSpace, TLinearAlgebra > &&  other )

delete

Move assignment operator.

Parameters

other

the object to move.

Returns

a reference on 'this'.

Field Documentation

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.

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().

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().

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().

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().

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().

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().

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().

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().

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().

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().

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().

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().

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:

• DECImageHelpers.h