DGtal::ATVu2v0< TKSpace, TLinearAlgebra > Struct Template Reference

#include <imageProcessing/ATVu2v0.h>

Inheritance diagram for DGtal::ATVu2v0< TKSpace, TLinearAlgebra >:

Collaboration diagram for DGtal::ATVu2v0< TKSpace, TLinearAlgebra >:

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, 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))
	~ATVu2v0 ()=default
	ATVu2v0 (int _verbose=1)
void	init (Clone< KSpace > K)
	ATVu2v0 (const ATVu2v0 &other)=delete
	ATVu2v0 (ATVu2v0 &&other)=delete
ATVu2v0 &	operator= (const ATVu2v0 &other)=delete
ATVu2v0 &	operator= (ATVu2v0 &&other)=delete
template<typename Image , typename Function >
void	addInput (const Image &image, const Function &f, bool perfect_data=false)
void	setMetricAverage (bool average)
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
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, 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
PrimalDerivative0	M01
PrimalDerivative1	M12
PrimalAntiderivative2	primal_AD2
PrimalIdentity0	primal_L0
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< PrimalForm2 >	g2
std::vector< PrimalForm2 >	i2
std::vector< PrimalForm2 >	u2
PrimalForm0	v0
PrimalForm0	former_v0
double	alpha
double	lambda
double	epsilon
SolverU	solver_u
SolverV	solver_v
PrimalIdentity2	alpha_Id2
std::vector< PrimalForm2 >	alpha_g2
PrimalIdentity0	left_V0
PrimalForm0	l_1
PrimalForm0	l_over_e_1
PrimalIdentity0	l_over_e_Id0
bool	metric_average

Detailed Description

template<typename TKSpace, typename TLinearAlgebra = EigenLinearAlgebraBackend>
struct DGtal::ATVu2v0< TKSpace, TLinearAlgebra >

Aim: This class solves a variant of 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. Instead of using \( \epsilon \| \nabla v \|^2 + \frac{1}{4\epsilon}(1-v)^2\) as a penalizer, it uses \( \epsilon^3 \| \Delta v \|^2 + \frac{1}{\epsilon}(1-v)^2\).

Description of template class 'ATVu2v0'

Template Parameters

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

Definition at line 77 of file ATVu2v0.h.

Member Typedef Documentation

Base

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DECImage2D<TKSpace, TLinearAlgebra> DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::Base

Definition at line 81 of file ATVu2v0.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::ATVu2v0< TKSpace, TLinearAlgebra >::KSpace

Definition at line 79 of file ATVu2v0.h.

LinearAlgebra

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef TLinearAlgebra DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::LinearAlgebra

Definition at line 80 of file ATVu2v0.h.

LinearAlgebraSolver

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef LinearAlgebra::SolverSimplicialLLT DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::LinearAlgebraSolver

Definition at line 123 of file ATVu2v0.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::ATVu2v0< TKSpace, TLinearAlgebra >::SolverU

Definition at line 125 of file ATVu2v0.h.

SolverV

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::SolverV

Definition at line 127 of file ATVu2v0.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

~ATVu2v0()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::~ATVu2v0 ( )

default

Destructor.

ATVu2v0() [1/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::ATVu2v0

(

int

_verbose = 1

)

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

Parameters

_verbose

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

ATVu2v0() [2/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::ATVu2v0 ( const ATVu2v0< TKSpace, TLinearAlgebra > &  other )

delete

Copy constructor.

Parameters

other

the object to clone.

ATVu2v0() [3/3]

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::ATVu2v0 ( ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT

(

(KSpace::dimension==2)

)

checkV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< TKSpace, TLinearAlgebra >::getAlpha ( ) const

inline

Returns

the (global) alpha parameter.

Definition at line 279 of file ATVu2v0.h.

{ return alpha; }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::alpha.

getEpsilon()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getEpsilon ( ) const

inline

Returns

the epsilon parameter.

Definition at line 285 of file ATVu2v0.h.

{ return epsilon; }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::epsilon.

getG()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm2& DGtal::ATVu2v0< 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 289 of file ATVu2v0.h.

{ return g2.at( i ); }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::g2.

getLambda()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getLambda ( ) const

inline

Returns

the lambda parameter.

Definition at line 282 of file ATVu2v0.h.

{ return lambda; }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::lambda.

getU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm2& DGtal::ATVu2v0< 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 293 of file ATVu2v0.h.

{ return u2.at( i ); }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::u2.

getV()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

const PrimalForm0& DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getV ( ) const

inline

Returns

the v 0-form.

Definition at line 296 of file ATVu2v0.h.

{ return v0; }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::v0.

init()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATVu2v0< 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::ATVu2v0< 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>

ATVu2v0& DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::operator= ( ATVu2v0< 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>

ATVu2v0& DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::operator= ( const ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< TKSpace, TLinearAlgebra >::setMetricAverage

(

bool

average

)

Use metric average to smooth L1-metric effects.

setUFromInput()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

void DGtal::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< TKSpace, TLinearAlgebra >::size0 ( ) const

inline

Returns

the size of a 0-form vector

Definition at line 299 of file ATVu2v0.h.

{ return v0.myContainer.rows(); }

References DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::v0.

solveU()

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

bool DGtal::ATVu2v0< 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::ATVu2v0< 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::ATVu2v0< TKSpace, TLinearAlgebra >::alpha

protected

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

Definition at line 374 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getAlpha().

alpha_g2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::alpha_g2

protected

alpha g2

Definition at line 388 of file ATVu2v0.h.

alpha_Id2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity2 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::alpha_Id2

protected

alpha Id2

Definition at line 386 of file ATVu2v0.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::ATVu2v0< TKSpace, TLinearAlgebra >::delta_v_l1

The L1-norm of variation of v.

Definition at line 345 of file ATVu2v0.h.

delta_v_l2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::delta_v_l2

The L2-norm of variation of v.

Definition at line 347 of file ATVu2v0.h.

delta_v_loo

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

Scalar DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::delta_v_loo

The Linfinity-norm of variation of v.

Definition at line 349 of file ATVu2v0.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::ATVu2v0< TKSpace, TLinearAlgebra >::epsilon

protected

Thickness of discontinuity set (in length unit).

Definition at line 378 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getEpsilon().

former_v0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::former_v0

protected

The v 0-form at the previous iteration.

Definition at line 372 of file ATVu2v0.h.

g2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::g2

protected

The g 2-forms.

Definition at line 364 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getG().

i2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::i2

protected

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

Definition at line 366 of file ATVu2v0.h.

l_1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::l_1

protected

lambda 1

Definition at line 392 of file ATVu2v0.h.

l_over_e_1

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::l_over_e_1

protected

lambda/epsilon 1

Definition at line 394 of file ATVu2v0.h.

l_over_e_Id0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::l_over_e_Id0

protected

lambda/epsilon Id0

Definition at line 396 of file ATVu2v0.h.

lambda

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

double DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::lambda

protected

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

Definition at line 376 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getLambda().

left_V0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::left_V0

protected

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

Definition at line 390 of file ATVu2v0.h.

M01

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalDerivative0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::M01

point_to_edge average operator

Definition at line 352 of file ATVu2v0.h.

M12

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalDerivative1 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::M12

edge_to_face average operator

Definition at line 354 of file ATVu2v0.h.

metric_average

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

bool DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::metric_average

protected

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

Definition at line 399 of file ATVu2v0.h.

primal_AD2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalAntiderivative2 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::primal_AD2

Antiderivative 2-form -> to 1-form.

Definition at line 356 of file ATVu2v0.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.

primal_L0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalIdentity0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::primal_L0

primal laplace operator on 0-forms

Definition at line 358 of file ATVu2v0.h.

solver_u

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

SolverU DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::solver_u

protected

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

Definition at line 381 of file ATVu2v0.h.

solver_v

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

SolverV DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::solver_v

protected

The solver for 0-form v.

Definition at line 383 of file ATVu2v0.h.

u2

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

std::vector< PrimalForm2 > DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::u2

protected

The u 2-forms.

Definition at line 368 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getU().

v0

template<typename TKSpace , typename TLinearAlgebra = EigenLinearAlgebraBackend>

PrimalForm0 DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::v0

protected

The v 0-form.

Definition at line 370 of file ATVu2v0.h.

Referenced by DGtal::ATVu2v0< TKSpace, TLinearAlgebra >::getV(), and DGtal::ATVu2v0< 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:

• ATVu2v0.h