Aim: This class solves Ambrosio-Tortorelli functional in a plane for u a (vector of) 2-form(s) and v a 0-form. u is a regularized approximation of an input image data g (grey-level or color image), while v represents the set of discontinuities of u. More...

#include <imageProcessing/ATu2v0.h>

Inheritance diagram for DGtal::ATu2v0< TKSpace, TLinearAlgebra >:

[legend]

Public Types
typedef TKSpace	KSpace

typedef TLinearAlgebra	LinearAlgebra

typedef DECImage2D< TKSpace, TLinearAlgebra >	Base

typedef LinearAlgebra::SolverSimplicialLLT	LinearAlgebraSolver

typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL >	SolverU

typedef DiscreteExteriorCalculusSolver< Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, 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::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

Public Types inherited from DGtal::DECImage2D< TKSpace, TLinearAlgebra >
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_STATIC_ASSERT ((KSpace::dimension==2))

	~ATu2v0 ()=default

	ATu2v0 (int _verbose=1)

void	init (Clone< KSpace > K)

	ATu2v0 (const ATu2v0 &other)=delete

	ATu2v0 (ATu2v0 &&other)=delete

ATu2v0 &	operator= (const ATu2v0 &other)=delete

ATu2v0 &	operator= (ATu2v0 &&other)=delete

template<typename Image , typename Function >
void	addInput (const Image &image, const Function &f, bool perfect_data=false)

void	setMetricAverage (bool average)
	Use metric average to smooth L1-metric effects.

void	setUFromInput ()

void	setUFromInputAndMask ()

void	setAlpha (Scalar _alpha)

void	setAlpha (Scalar _alpha, const PrimalForm2 &m)

void	setLambda (Scalar _lambda)

void	setEpsilon (Scalar _epsilon)

Scalar	computeSNR () const
	Computes the SNR of u wrt ideal input (should have been given.

Scalar	getAlpha () const

Scalar	getLambda () const

Scalar	getEpsilon () const

const PrimalForm2 &	getG (int i) const

const PrimalForm2 &	getU (int i) const

const PrimalForm0 &	getV () const

unsigned int	size0 () 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, TLinearAlgebra >
	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
Scalar	delta_v_l1
	The L1-norm of variation of v.

Scalar	delta_v_l2
	The L2-norm of variation of v.

Scalar	delta_v_loo
	The Linfinity-norm of variation of v.

PrimalDerivative0	M01
	point_to_edge average operator

PrimalDerivative1	M12
	edge_to_face average operator

PrimalAntiderivative2	primal_AD2
	Antiderivative 2-form -> to 1-form.

Calculus	calculus
	The discrete exterior calculus instance.

int	verbose
	The verbose level (0: silent).

PrimalDerivative0	D0
	primal derivative: 0-form -> 1-form

PrimalDerivative1	D1
	primal derivative: 1-form -> 2-form

DualDerivative0	dual_D0
	dual derivative dual 0-form -> dual 1-form

DualDerivative1	dual_D1
	dual derivative dual 1-form -> dual 2-form

PrimalHodge0	primal_h0
	hodge star: 0-form -> dual 0-form

PrimalHodge1	primal_h1
	hodge star: 1-form -> dual 1-form

PrimalHodge2	primal_h2
	hodge star: 2-form -> dual 2-form

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

Data Fields inherited from DGtal::DECImage2D< TKSpace, TLinearAlgebra >
int	verbose
	The verbose level (0: silent).

Calculus	calculus
	The discrete exterior calculus instance.

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

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

PrimalDerivative0	D0
	primal derivative: 0-form -> 1-form

PrimalDerivative1	D1
	primal derivative: 1-form -> 2-form

DualDerivative0	dual_D0
	dual derivative dual 0-form -> dual 1-form

DualDerivative1	dual_D1
	dual derivative dual 1-form -> dual 2-form

PrimalHodge0	primal_h0
	hodge star: 0-form -> dual 0-form

PrimalHodge1	primal_h1
	hodge star: 1-form -> dual 1-form

PrimalHodge2	primal_h2
	hodge star: 2-form -> dual 2-form

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

Protected Attributes
std::vector< PrimalForm2 >	g2
	The g 2-forms.

std::vector< PrimalForm2 >	i2
	The ideal input 2-forms (for snr computation).

std::vector< PrimalForm2 >	u2
	The u 2-forms.

PrimalForm0	v0
	The v 0-form.

PrimalForm0	former_v0
	The v 0-form at the previous iteration.

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

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

double	epsilon
	Thickness of discontinuity set (in length unit).

SolverU	solver_u
	The solver for every 2-form u[i].

SolverV	solver_v
	The solver for 0-form v.

PrimalIdentity2	alpha_Id2
	alpha Id2

std::vector< PrimalForm2 >	alpha_g2
	alpha g2

PrimalIdentity0	left_V0
	(lambda / (4epsilon)) Id0 + lambda epsilon D0^t D0

PrimalForm0	l_1_over_4
	lambda 1/4 1

PrimalForm0	l_1_over_4e
	lambda 1/(4*epsilon) 1

PrimalIdentity0	l_1_over_4e_Id0
	lambda 1/(4_epsilon) Id0

bool	metric_average
	When 'true', use metric average, otherwise use identity.

Detailed Description

template<typename TKSpace, typename TLinearAlgebra = EigenLinearAlgebraBackend>
struct DGtal::ATu2v0< TKSpace, TLinearAlgebra >

Aim: This class solves Ambrosio-Tortorelli functional in a plane for u a (vector of) 2-form(s) and v a 0-form. u is a regularized approximation of an input image data g (grey-level or color image), while v represents the set of discontinuities of u.

Description of template class 'ATu2v0'

Template Parameters

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

Definition at line 74 of file ATu2v0.h.

Member Typedef Documentation

◆ Base

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DECImage2D<TKSpace, TLinearAlgebra> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::Base

Definition at line 78 of file ATu2v0.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.

◆ 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::ATu2v0< TKSpace, TLinearAlgebra >::KSpace

Definition at line 76 of file ATu2v0.h.

◆ LinearAlgebra

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef TLinearAlgebra DGtal::ATu2v0< TKSpace, TLinearAlgebra >::LinearAlgebra

Definition at line 77 of file ATu2v0.h.

◆ LinearAlgebraSolver

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef LinearAlgebra::SolverSimplicialLLT DGtal::ATu2v0< TKSpace, TLinearAlgebra >::LinearAlgebraSolver

Definition at line 120 of file ATu2v0.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, 2, PRIMAL, 2, PRIMAL> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::SolverU

Definition at line 122 of file ATu2v0.h.

◆ SolverV

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::SolverV

Definition at line 124 of file ATu2v0.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

◆ ~ATu2v0()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATu2v0< TKSpace, TLinearAlgebra >::~ATu2v0 ( )

default

Destructor.

◆ ATu2v0() [1/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATu2v0< TKSpace, TLinearAlgebra >::ATu2v0 ( int _verbose = 1 )

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

Parameters

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

◆ ATu2v0() [2/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATu2v0< TKSpace, TLinearAlgebra >::ATu2v0 ( const ATu2v0< TKSpace, TLinearAlgebra > & other )

delete

Copy constructor.

Parameters

other the object to clone.

◆ ATu2v0() [3/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATu2v0< TKSpace, TLinearAlgebra >::ATu2v0 ( ATu2v0< TKSpace, TLinearAlgebra > && other )

delete

Move constructor.

Parameters

other the object to move.

Member Function Documentation

◆ addInput()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

template<typename Image , typename Function >

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::addInput	(	const Image &	image,
		const Function &	f,
		bool	perfect_data = `false`
	)

Adds an input 2-form by filtering an image values.

Parameters

image	any image such that the domain of this space is included in the domain of the image.
f	any functor associated a scalar to an image value.
perfect_data	when '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

Image	any Image type.
Function	any function type ( typename Image::Value ) -> Scalar.

◆ BOOST_STATIC_ASSERT()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATu2v0< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT ( (KSpace::dimension==2) )

◆ checkV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATu2v0< 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::ATu2v0< 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::ATu2v0< 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::ATu2v0< TKSpace, TLinearAlgebra >::getAlpha ( ) const

inline

Returns: the (global) alpha parameter.

Definition at line 276 of file ATu2v0.h.

276{ return alpha; }

DGtal::ATu2v0::alpha

double alpha

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

Definition ATu2v0.h:369

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::alpha.

◆ getEpsilon()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getEpsilon ( ) const

inline

Returns: the epsilon parameter.

Definition at line 282 of file ATu2v0.h.

282{ return epsilon; }

DGtal::ATu2v0::epsilon

double epsilon

Thickness of discontinuity set (in length unit).

Definition ATu2v0.h:373

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::epsilon.

◆ getG()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm2 & DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getG ( int i ) const

inline

Parameters

i	an integer (between 0 and the number of input forms).

Returns: the i-th input g 2-form.

Definition at line 286 of file ATu2v0.h.

286{ return g2.at( i ); }

DGtal::ATu2v0::g2

std::vector< PrimalForm2 > g2

The g 2-forms.

Definition ATu2v0.h:359

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::g2.

◆ getLambda()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getLambda ( ) const

inline

Returns: the lambda parameter.

Definition at line 279 of file ATu2v0.h.

279{ return lambda; }

DGtal::ATu2v0::lambda

double lambda

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

Definition ATu2v0.h:371

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::lambda.

◆ getU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm2 & DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getU ( int i ) const

inline

Parameters

i	an integer (between 0 and the number of input forms).

Returns: the i-th u 2-form.

Definition at line 290 of file ATu2v0.h.

290{ return u2.at( i ); }

DGtal::ATu2v0::u2

std::vector< PrimalForm2 > u2

The u 2-forms.

Definition ATu2v0.h:363

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::u2.

◆ getV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm0 & DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getV ( ) const

inline

Returns: the v 0-form.

Definition at line 293 of file ATu2v0.h.

293{ return v0; }

DGtal::ATu2v0::v0

PrimalForm0 v0

The v 0-form.

Definition ATu2v0.h:365

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::v0.

◆ init()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< 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::ATu2v0< 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>

ATu2v0 & DGtal::ATu2v0< TKSpace, TLinearAlgebra >::operator= ( ATu2v0< TKSpace, TLinearAlgebra > && other )

delete

Move assignment operator.

Parameters

other the object to move.

Returns: a reference on 'this'.

◆ operator=() [2/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

ATu2v0 & DGtal::ATu2v0< TKSpace, TLinearAlgebra >::operator= ( const ATu2v0< TKSpace, TLinearAlgebra > & other )

delete

Copy assignment operator.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ selfDisplay()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ setAlpha() [1/2]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::setAlpha ( Scalar _alpha )

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

Parameters

_alpha the \( \alpha \) 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::ATu2v0< TKSpace, TLinearAlgebra >::setAlpha	(	Scalar	_alpha,
		const PrimalForm2 &	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

_alpha	the \( \alpha \) 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.
m	a 0-form that specifies which input data is significant (1) or not be used (0).

◆ setEpsilon()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::setEpsilon ( Scalar _epsilon )

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

Parameters

_epsilon the \( \epsilon \) 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::ATu2v0< TKSpace, TLinearAlgebra >::setLambda ( Scalar _lambda )

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

Parameters

_lambda the \( \lambda \) 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.

◆ setMetricAverage()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::setMetricAverage ( bool average )

Use metric average to smooth L1-metric effects.

◆ setUFromInput()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< 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.

◆ setUFromInputAndMask()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::setUFromInputAndMask ( )

Sets approximation u to be equal to the input. Used for initializating u. Should be called once all addInput have been called. Note that it initializes u with random values wherever an inpainting mask was applied.

See also: setAlpha( Scalar _alpha, const PrimalForm2& m )

◆ size0()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

unsigned int DGtal::ATu2v0< TKSpace, TLinearAlgebra >::size0 ( ) const

inline

Returns: the size of a 0-form vector

Definition at line 296 of file ATu2v0.h.

296{ return v0.myContainer.rows(); }

References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::v0.

◆ solveU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

bool DGtal::ATu2v0< 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::ATu2v0< 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::ATu2v0< TKSpace, TLinearAlgebra >::alpha

protected

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

Definition at line 369 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getAlpha().

◆ alpha_g2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATu2v0< TKSpace, TLinearAlgebra >::alpha_g2

protected

alpha g2

Definition at line 383 of file ATu2v0.h.

◆ alpha_Id2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity2 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::alpha_Id2

protected

alpha Id2

Definition at line 381 of file ATu2v0.h.

◆ 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::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_l1

The L1-norm of variation of v.

Definition at line 342 of file ATu2v0.h.

◆ delta_v_l2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_l2

The L2-norm of variation of v.

Definition at line 344 of file ATu2v0.h.

◆ delta_v_loo

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_loo

The Linfinity-norm of variation of v.

Definition at line 346 of file ATu2v0.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::ATu2v0< TKSpace, TLinearAlgebra >::epsilon

protected

Thickness of discontinuity set (in length unit).

Definition at line 373 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getEpsilon().

◆ former_v0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::former_v0

protected

The v 0-form at the previous iteration.

Definition at line 367 of file ATu2v0.h.

◆ g2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATu2v0< TKSpace, TLinearAlgebra >::g2

protected

The g 2-forms.

Definition at line 359 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getG().

◆ i2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATu2v0< TKSpace, TLinearAlgebra >::i2

protected

The ideal input 2-forms (for snr computation).

Definition at line 361 of file ATu2v0.h.

◆ l_1_over_4

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::l_1_over_4

protected

lambda 1/4 1

Definition at line 387 of file ATu2v0.h.

◆ l_1_over_4e

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::l_1_over_4e

protected

lambda 1/(4*epsilon) 1

Definition at line 389 of file ATu2v0.h.

◆ l_1_over_4e_Id0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::l_1_over_4e_Id0

protected

lambda 1/(4_epsilon) Id0

Definition at line 391 of file ATu2v0.h.

◆ lambda

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

double DGtal::ATu2v0< TKSpace, TLinearAlgebra >::lambda

protected

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

Definition at line 371 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getLambda().

◆ left_V0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::left_V0

protected

(lambda / (4*epsilon)) * Id0 + lambda epsilon D0^t D0

Definition at line 385 of file ATu2v0.h.

◆ M01

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalDerivative0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::M01

point_to_edge average operator

Definition at line 349 of file ATu2v0.h.

◆ M12

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalDerivative1 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::M12

edge_to_face average operator

Definition at line 351 of file ATu2v0.h.

◆ metric_average

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

bool DGtal::ATu2v0< TKSpace, TLinearAlgebra >::metric_average

protected

When 'true', use metric average, otherwise use identity.

Definition at line 394 of file ATu2v0.h.

◆ primal_AD2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalAntiderivative2 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::primal_AD2

Antiderivative 2-form -> to 1-form.

Definition at line 353 of file ATu2v0.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::ATu2v0< TKSpace, TLinearAlgebra >::solver_u

protected

The solver for every 2-form u[i].

Definition at line 376 of file ATu2v0.h.

◆ solver_v

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

SolverV DGtal::ATu2v0< TKSpace, TLinearAlgebra >::solver_v

protected

The solver for 0-form v.

Definition at line 378 of file ATu2v0.h.

◆ u2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATu2v0< TKSpace, TLinearAlgebra >::u2

protected

The u 2-forms.

Definition at line 363 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getU().

◆ v0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::v0

protected

The v 0-form.

Definition at line 365 of file ATu2v0.h.

Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getV(), and DGtal::ATu2v0< TKSpace, TLinearAlgebra >::size0().

◆ 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:

ATu2v0.h

Public Types

Public Member Functions

Data Fields

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ Calculus

◆ Domain

◆ DualAntiderivative1

◆ DualAntiderivative2

◆ DualDerivative0

◆ DualDerivative1

◆ DualHodge0

◆ DualHodge1

◆ DualHodge2

◆ Index

◆ KSpace

◆ LinearAlgebra

◆ LinearAlgebraSolver

◆ Point

◆ PrimalAntiderivative1

◆ PrimalAntiderivative2

◆ PrimalDerivative0

◆ PrimalDerivative1

◆ PrimalForm0

◆ PrimalForm1

◆ PrimalForm2

◆ PrimalHodge0

◆ PrimalHodge1

◆ PrimalHodge2

◆ PrimalIdentity0

◆ PrimalIdentity1

◆ PrimalIdentity2

◆ RealVector

◆ Scalar

◆ SCell

◆ SolverU

◆ SolverV

◆ Space

Constructor & Destructor Documentation

◆ ~ATu2v0()

◆ ATu2v0() [1/3]

◆ ATu2v0() [2/3]

◆ ATu2v0() [3/3]

Member Function Documentation

◆ addInput()

◆ BOOST_STATIC_ASSERT()

◆ checkV()

◆ computeSNR()

◆ computeVariation()

◆ getAlpha()

◆ getEpsilon()

◆ getG()

◆ getLambda()

◆ getU()

◆ getV()

◆ init()

◆ isValid()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ selfDisplay()

◆ setAlpha() [1/2]

◆ setAlpha() [2/2]

◆ setEpsilon()

◆ setLambda()

◆ setMetricAverage()

◆ setUFromInput()

◆ setUFromInputAndMask()

◆ size0()

◆ solveU()

◆ solveV()

Field Documentation

◆ alpha

◆ alpha_g2

◆ alpha_Id2

◆ calculus

◆ D0

◆ D1

◆ delta_v_l1