DGtalTools  1.2.0
Public Types | Public Member Functions | Data Fields | Protected Attributes
DGtal::ATu0v1< TKSpace, TLinearAlgebra > Struct Template Reference

#include <imageProcessing/ATu0v1.h>

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Public Types

typedef TKSpace KSpace
 
typedef TLinearAlgebra LinearAlgebra
 
typedef DECImage2D< TKSpace, TLinearAlgebra > Base
 
typedef LinearAlgebra::SolverSimplicialLLT LinearAlgebraSolver
 
typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL > SolverU
 
typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL > SolverV
 
typedef KSpace::Space Space
 
typedef Space::Point Point
 
typedef Space::RealVector RealVector
 
typedef RealVector::Component Scalar
 
typedef KSpace::SCell SCell
 
typedef HyperRectDomain< Space > Domain
 
typedef DiscreteExteriorCalculus< 2, 2, LinearAlgebra > Calculus
 
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::PrimalHodge0 PrimalHodge0
 
typedef Calculus::PrimalHodge1 PrimalHodge1
 
typedef Calculus::PrimalHodge2 PrimalHodge2
 
typedef Calculus::DualHodge0 DualHodge0
 
typedef Calculus::DualHodge1 DualHodge1
 
typedef Calculus::DualHodge2 DualHodge2
 
- Public Types inherited from DGtal::DECImage2D< TKSpace, EigenLinearAlgebraBackend >
typedef TKSpace KSpace
 
typedef EigenLinearAlgebraBackend 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_STATIC_ASSERT ((KSpace::dimension==2))
 
 ~ATu0v1 ()=default
 
 ATu0v1 (int _verbose=1)
 
void init (Clone< KSpace > K)
 
 ATu0v1 (const ATu0v1 &other)=delete
 
 ATu0v1 (ATu0v1 &&other)=delete
 
ATu0v1 & operator= (const ATu0v1 &other)=delete
 
ATu0v1 & operator= (ATu0v1 &&other)=delete
 
template<typename Image , typename Function >
void addInput (const Image &image, const Function &f, bool perfect_data=false)
 
void setUFromInput ()
 
void setAlpha (Scalar _alpha)
 
void setAlpha (Scalar _alpha, const PrimalForm0 &m)
 
void setLambda (Scalar _lambda)
 
void setEpsilon (Scalar _epsilon)
 
Scalar computeSNR () const
 
Scalar getAlpha () const
 
Scalar getLambda () const
 
Scalar getEpsilon () const
 
const PrimalForm0 & getG (int i) const
 
const PrimalForm0 & getU (int i) const
 
const PrimalForm1 & getV () const
 
unsigned int size0 () const
 
unsigned int size1 () const
 
bool solveU ()
 
bool solveV ()
 
Scalar computeVariation ()
 
Scalar checkV ()
 
void selfDisplay (std::ostream &out) const
 
bool isValid () const
 
- Public Member Functions inherited from DGtal::DECImage2D< TKSpace, EigenLinearAlgebraBackend >
 BOOST_CONCEPT_ASSERT ((concepts::CCellularGridSpaceND< KSpace >))
 
 BOOST_STATIC_ASSERT ((KSpace::dimension==2))
 
 ~DECImage2D ()=default
 
 DECImage2D (int _verbose=1)
 
 DECImage2D (const DECImage2D &other)=delete
 
 DECImage2D (DECImage2D &&other)=delete
 
void init (Clone< KSpace > aKSpace)
 
DECImage2D & operator= (const DECImage2D &other)=delete
 
DECImage2D & operator= (DECImage2D &&other)=delete
 

Data Fields

Scalar delta_v_l1
 
Scalar delta_v_l2
 
Scalar delta_v_loo
 
PrimalIdentity1 L1
 
Calculus calculus
 
int verbose
 
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
 
- Data Fields inherited from DGtal::DECImage2D< TKSpace, EigenLinearAlgebraBackend >
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
 

Protected Attributes

std::vector< PrimalForm0 > g0
 
std::vector< PrimalForm0 > i0
 
std::vector< PrimalForm0 > u0
 
PrimalForm1 v1
 
PrimalForm1 former_v1
 
double alpha
 
double lambda
 
double epsilon
 
SolverU solver_u
 
SolverV solver_v
 
PrimalIdentity0 alpha_Id0
 
std::vector< PrimalForm0 > alpha_g0
 
PrimalIdentity1 l_L1
 
PrimalForm1 l_1_over_4
 
PrimalIdentity1 left_V1
 
PrimalForm1 l_1_over_4e
 

Detailed Description

template<typename TKSpace, typename TLinearAlgebra = EigenLinearAlgebraBackend>
struct DGtal::ATu0v1< TKSpace, TLinearAlgebra >

Aim: This class solves Ambrosio-Tortorelli functional in a plane for u a (vector of) 0-form(s) and v a 1-form. u is a regularized approximation of an input data g, while v represents the set of discontinuities of u.

Description of template class 'ATu0v1'

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

Definition at line 74 of file ATu0v1.h.

Member Typedef Documentation

◆ Base

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DECImage2D<TKSpace, TLinearAlgebra> DGtal::ATu0v1< TKSpace, TLinearAlgebra >::Base

Definition at line 78 of file ATu0v1.h.

◆ 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.

◆ Domain

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

Definition at line 752 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::ATu0v1< TKSpace, TLinearAlgebra >::KSpace

Definition at line 76 of file ATu0v1.h.

◆ LinearAlgebra

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef TLinearAlgebra DGtal::ATu0v1< TKSpace, TLinearAlgebra >::LinearAlgebra

Definition at line 77 of file ATu0v1.h.

◆ LinearAlgebraSolver

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef LinearAlgebra::SolverSimplicialLLT DGtal::ATu0v1< TKSpace, TLinearAlgebra >::LinearAlgebraSolver

Definition at line 116 of file ATu0v1.h.

◆ Point

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

Definition at line 746 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::ATu0v1< TKSpace, TLinearAlgebra >::SolverU

Definition at line 118 of file ATu0v1.h.

◆ SolverV

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 1, PRIMAL, 1, PRIMAL> DGtal::ATu0v1< TKSpace, TLinearAlgebra >::SolverV

Definition at line 120 of file ATu0v1.h.

◆ Space

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

Definition at line 745 of file DECImageHelpers.h.

Constructor & Destructor Documentation

◆ ~ATu0v1()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::ATu0v1< TKSpace, TLinearAlgebra >::~ATu0v1 ( )
default

Destructor.

◆ ATu0v1() [1/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::ATu0v1< TKSpace, TLinearAlgebra >::ATu0v1 ( int  _verbose = 1)

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

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

◆ ATu0v1() [2/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::ATu0v1< TKSpace, TLinearAlgebra >::ATu0v1 ( const ATu0v1< TKSpace, TLinearAlgebra > &  other)
delete

Copy constructor.

Parameters
otherthe object to clone.

◆ ATu0v1() [3/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::ATu0v1< TKSpace, TLinearAlgebra >::ATu0v1 ( ATu0v1< TKSpace, TLinearAlgebra > &&  other)
delete

Move constructor.

Parameters
otherthe object to move.

Member Function Documentation

◆ addInput()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
template<typename Image , typename Function >
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::addInput ( const Image &  image,
const Function &  f,
bool  perfect_data = false 
)

Adds an input 0-form by filtering an image values.

Parameters
imageany image such that the domain of this space is included in the domain of the image.
fany functor associating a scalar to an image value.
perfect_datawhen 'false', this is normal input data, otherwise this is perfect data only used for SNR computation.
Note
For a grey-level image stored with values unsigned char, should be called as
AT.addInput( image, [] (unsigned char c ) { return (double) c / 255.0; } );
Note
For a color image stored with values Color, should be called as
AT.addInput( image, [] ( Color c ) { return (double) c.red() / 255.0; } );
AT.addInput( image, [] ( Color c ) { return (double) c.green() / 255.0; } );
AT.addInput( image, [] ( Color c ) { return (double) c.blue() / 255.0; } );
Template Parameters
Imageany Image type.
Functionany function type ( typename Image::Value ) -> Scalar.

◆ BOOST_STATIC_ASSERT()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
DGtal::ATu0v1< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT ( (KSpace::dimension==2)  )

◆ checkV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::checkV ( )

Checks that form v is between 0 and 1 and forces v to be in-between.

Returns
the max of the deviation wrt 0 and 1.

◆ computeSNR()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::computeSNR ( ) const

Computes the SNR of u wrt ideal input (should have been given.

See also
addInput).

◆ computeVariation()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::computeVariation ( )

Computes the variation of v after a call to solveV.

See also
delta_v_l1, delta_v_l2, delta_v_loo.
Returns
the max of all variations (i.e. delta_v_loo).

◆ getAlpha()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getAlpha ( ) const
inline
Returns
the (global) alpha parameter.

Definition at line 262 of file ATu0v1.h.

262 { return alpha; }
DGtal::ATu0v1::alpha
double alpha
Smoothness parameter alpha of AT (in 1/area unit)
Definition: ATu0v1.h:351

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::alpha.

◆ getEpsilon()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getEpsilon ( ) const
inline
Returns
the epsilon parameter.

Definition at line 268 of file ATu0v1.h.

268 { return epsilon; }
DGtal::ATu0v1::epsilon
double epsilon
Thickness of discontinuity set (in length unit).
Definition: ATu0v1.h:355

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::epsilon.

◆ getG()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
const PrimalForm0& DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getG ( int  i) const
inline
Parameters
ian integer (between 0 and the number of input forms).
Returns
the i-th input g 0-form.

Definition at line 272 of file ATu0v1.h.

272 { return g0.at( i ); }
DGtal::ATu0v1::g0
std::vector< PrimalForm0 > g0
The g 0-forms.
Definition: ATu0v1.h:341

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::g0.

◆ getLambda()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getLambda ( ) const
inline
Returns
the lambda parameter.

Definition at line 265 of file ATu0v1.h.

265 { return lambda; }
DGtal::ATu0v1::lambda
double lambda
Amount of discontinuity parameter lambda (in 1/length unit).
Definition: ATu0v1.h:353

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::lambda.

◆ getU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
const PrimalForm0& DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getU ( int  i) const
inline
Parameters
ian integer (between 0 and the number of input forms).
Returns
the i-th u 0-form.

Definition at line 276 of file ATu0v1.h.

276 { return u0.at( i ); }
DGtal::ATu0v1::u0
std::vector< PrimalForm0 > u0
The u 0-forms.
Definition: ATu0v1.h:345

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::u0.

◆ getV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
const PrimalForm1& DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getV ( ) const
inline
Returns
the v 1-form.

Definition at line 279 of file ATu0v1.h.

279 { return v1; }
DGtal::ATu0v1::v1
PrimalForm1 v1
The v 1-form.
Definition: ATu0v1.h:347

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::v1.

◆ init()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::init ( Clone< KSpace >  K)

Constructor from Khalimsky space, which specifies the domain of calculus.

◆ isValid()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
bool DGtal::ATu0v1< TKSpace, TLinearAlgebra >::isValid ( ) const

Checks the validity/consistency of the object.

Returns
'true' if the object is valid, 'false' otherwise.

◆ operator=() [1/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
ATu0v1& DGtal::ATu0v1< TKSpace, TLinearAlgebra >::operator= ( ATu0v1< TKSpace, TLinearAlgebra > &&  other)
delete

Move assignment operator.

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

◆ operator=() [2/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
ATu0v1& DGtal::ATu0v1< TKSpace, TLinearAlgebra >::operator= ( const ATu0v1< TKSpace, TLinearAlgebra > &  other)
delete

Copy assignment operator.

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

◆ selfDisplay()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::selfDisplay ( std::ostream &  out) const

Writes/Displays the object on an output stream.

Parameters
outthe output stream where the object is written.

◆ setAlpha() [1/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::setAlpha ( Scalar  _alpha)

Sets the parameter \( alpha \) as global to the image. Should be set before setLambda and setEpsilon.

Parameters
_alphathe \( \alpha \) parameter in AT functional ( in term \( \int \alpha | u - g |^2 \) ). Dimension theory tells that it is in 1/area unit, the lower the smoother will be the output.

◆ setAlpha() [2/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::setAlpha ( Scalar  _alpha,
const PrimalForm0 &  m 
)

Sets the parameter \( alpha \) of the image, as well as a weight for each input data as the primal 0-form m. Should be set before setLambda and setEpsilon.

Note
Useful for inpainting applications where you indicate with m=0 that the specified pixel data is useless.
Parameters
_alphathe \( \alpha \) parameter in AT functional ( in term \( \int \alpha | u - g |^2 \) ). Dimension theory tells that it is in 1/area unit, the lower the smoother will be the output.
ma 0-form that specifies which input data is significant (1) or not be used (0).

◆ setEpsilon()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::setEpsilon ( Scalar  _epsilon)

Sets the parameter \( \epsilon \) of AT functional. Should be set after setAlpha and setLambda.

Parameters
_epsilonthe \( \epsilon \) parameter in AT functional ( in terms \( \int \lambda \epsilon | v \grad u |^2 + \int \frac{\lambda}{4\epsilon} |1-v|^2 \) ). Dimension theory tells that it is in length unit, the lower the thinner is the set of discontinuities.

◆ setLambda()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::setLambda ( Scalar  _lambda)

Sets the parameter \( \lambda \) of AT functional. Should be set after setAlpha and before setEpsilon.

Parameters
_lambdathe \( \lambda \) parameter in AT functional ( in terms \( \int \lambda \epsilon | v \grad u |^2 + \int \frac{\lambda}{4\epsilon} |1-v|^2 \) ). Dimension theory tells that it is in 1/length unit, the lower the longer is the set of discontinuities.

◆ setUFromInput()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
void DGtal::ATu0v1< TKSpace, TLinearAlgebra >::setUFromInput ( )

Sets approximation u to be equal to the input. Used for initializating u. Should be called once all addInput have been called.

◆ size0()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
unsigned int DGtal::ATu0v1< TKSpace, TLinearAlgebra >::size0 ( ) const
inline
Returns
the size of a 0-form vector

Definition at line 282 of file ATu0v1.h.

282 { return alpha_Id0.myContainer.columns(); }
DGtal::ATu0v1::alpha_Id0
PrimalIdentity0 alpha_Id0
alpha Id0
Definition: ATu0v1.h:363

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::alpha_Id0.

◆ size1()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
unsigned int DGtal::ATu0v1< TKSpace, TLinearAlgebra >::size1 ( ) const
inline
Returns
the size of a 1-form vector

Definition at line 285 of file ATu0v1.h.

285 { return v1.myContainer.rows(); }

References DGtal::ATu0v1< TKSpace, TLinearAlgebra >::v1.

◆ solveU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
bool DGtal::ATu0v1< TKSpace, TLinearAlgebra >::solveU ( )

Computes a solution to function(s) u given the input g and current v.

Returns
'true' iff the solver worked.

◆ solveV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
bool DGtal::ATu0v1< TKSpace, TLinearAlgebra >::solveV ( )

Computes a solution to function v given the input g and current u.

Returns
'true' iff the solver worked.

Field Documentation

◆ alpha

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
double DGtal::ATu0v1< TKSpace, TLinearAlgebra >::alpha
protected

Smoothness parameter alpha of AT (in 1/area unit)

Definition at line 351 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getAlpha().

◆ alpha_g0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
std::vector< PrimalForm0 > DGtal::ATu0v1< TKSpace, TLinearAlgebra >::alpha_g0
protected

alpha g0

Definition at line 365 of file ATu0v1.h.

◆ alpha_Id0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalIdentity0 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::alpha_Id0
protected

alpha Id0

Definition at line 363 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::size0().

◆ 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.

◆ 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.

◆ 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.

◆ delta_v_l1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::delta_v_l1

The L1-norm of variation of v.

Definition at line 328 of file ATu0v1.h.

◆ delta_v_l2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::delta_v_l2

The L2-norm of variation of v.

Definition at line 330 of file ATu0v1.h.

◆ delta_v_loo

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
Scalar DGtal::ATu0v1< TKSpace, TLinearAlgebra >::delta_v_loo

The Linfinity-norm of variation of v.

Definition at line 332 of file ATu0v1.h.

◆ 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.

◆ 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.

◆ 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.

◆ 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.

◆ 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.

◆ epsilon

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
double DGtal::ATu0v1< TKSpace, TLinearAlgebra >::epsilon
protected

Thickness of discontinuity set (in length unit).

Definition at line 355 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getEpsilon().

◆ former_v1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalForm1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::former_v1
protected

The v 1-form at the previous iteration.

Definition at line 349 of file ATu0v1.h.

◆ g0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
std::vector< PrimalForm0 > DGtal::ATu0v1< TKSpace, TLinearAlgebra >::g0
protected

The g 0-forms.

Definition at line 341 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getG().

◆ i0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
std::vector< PrimalForm0 > DGtal::ATu0v1< TKSpace, TLinearAlgebra >::i0
protected

The ideal input 0-forms (for snr computation).

Definition at line 343 of file ATu0v1.h.

◆ L1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalIdentity1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::L1

edge laplacien

Definition at line 335 of file ATu0v1.h.

◆ l_1_over_4

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalForm1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::l_1_over_4
protected

lambda 1/4 1

Definition at line 369 of file ATu0v1.h.

◆ l_1_over_4e

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalForm1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::l_1_over_4e
protected

lambda 1/(4*epsilon) 1

Definition at line 373 of file ATu0v1.h.

◆ l_L1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalIdentity1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::l_L1
protected

lambda * edge laplacien

Definition at line 367 of file ATu0v1.h.

◆ lambda

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
double DGtal::ATu0v1< TKSpace, TLinearAlgebra >::lambda
protected

Amount of discontinuity parameter lambda (in 1/length unit).

Definition at line 353 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getLambda().

◆ left_V1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalIdentity1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::left_V1
protected

epsilon * lambda * edge laplacien + (lambda / (4*epsilon)) * Id1

Definition at line 371 of file ATu0v1.h.

◆ 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.

◆ 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.

◆ 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.

◆ solver_u

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
SolverU DGtal::ATu0v1< TKSpace, TLinearAlgebra >::solver_u
protected

The solver for every 0-form u[i].

Definition at line 358 of file ATu0v1.h.

◆ solver_v

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
SolverV DGtal::ATu0v1< TKSpace, TLinearAlgebra >::solver_v
protected

The solver for 1-form v.

Definition at line 360 of file ATu0v1.h.

◆ u0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
std::vector< PrimalForm0 > DGtal::ATu0v1< TKSpace, TLinearAlgebra >::u0
protected

The u 0-forms.

Definition at line 345 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getU().

◆ v1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>
PrimalForm1 DGtal::ATu0v1< TKSpace, TLinearAlgebra >::v1
protected

The v 1-form.

Definition at line 347 of file ATu0v1.h.

Referenced by DGtal::ATu0v1< TKSpace, TLinearAlgebra >::getV(), and DGtal::ATu0v1< TKSpace, TLinearAlgebra >::size1().

◆ 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.

The documentation for this struct was generated from the following file:
Companion project associated to DGtal ; Generated on Wed Jun 2 2021 15:34:52 for DGtalTools by   doxygen 1.9.1