#include <imageProcessing/ATu2v0.h>
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) |
| 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 |
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_over_4 |
| PrimalForm0 | l_1_over_4e |
| PrimalIdentity0 | l_1_over_4e_Id0 |
| bool | metric_average |
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.
Member Typedef Documentation
◆ Base
| typedef DECImage2D<TKSpace, TLinearAlgebra> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::Base |
◆ Calculus
| typedef DiscreteExteriorCalculus<2,2, LinearAlgebra> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Calculus |
Definition at line 753 of file DECImageHelpers.h.
◆ Domain
| typedef HyperRectDomain<Space> DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Domain |
Definition at line 752 of file DECImageHelpers.h.
◆ DualAntiderivative1
| typedef Calculus::DualAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative1 |
Definition at line 768 of file DECImageHelpers.h.
◆ DualAntiderivative2
| typedef Calculus::DualAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualAntiderivative2 |
Definition at line 769 of file DECImageHelpers.h.
◆ DualDerivative0
| typedef Calculus::DualDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative0 |
Definition at line 764 of file DECImageHelpers.h.
◆ DualDerivative1
| typedef Calculus::DualDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualDerivative1 |
Definition at line 765 of file DECImageHelpers.h.
◆ DualHodge0
| typedef Calculus::DualHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge0 |
Definition at line 773 of file DECImageHelpers.h.
◆ DualHodge1
| typedef Calculus::DualHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge1 |
Definition at line 774 of file DECImageHelpers.h.
◆ DualHodge2
| typedef Calculus::DualHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::DualHodge2 |
Definition at line 775 of file DECImageHelpers.h.
◆ Index
| typedef Calculus::Index DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Index |
Definition at line 755 of file DECImageHelpers.h.
◆ KSpace
| typedef TKSpace DGtal::ATu2v0< TKSpace, TLinearAlgebra >::KSpace |
◆ LinearAlgebra
| typedef TLinearAlgebra DGtal::ATu2v0< TKSpace, TLinearAlgebra >::LinearAlgebra |
◆ LinearAlgebraSolver
| typedef LinearAlgebra::SolverSimplicialLLT DGtal::ATu2v0< TKSpace, TLinearAlgebra >::LinearAlgebraSolver |
◆ Point
| typedef Space::Point DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Point |
Definition at line 746 of file DECImageHelpers.h.
◆ PrimalAntiderivative1
| typedef Calculus::PrimalAntiderivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative1 |
Definition at line 766 of file DECImageHelpers.h.
◆ PrimalAntiderivative2
| typedef Calculus::PrimalAntiderivative2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalAntiderivative2 |
Definition at line 767 of file DECImageHelpers.h.
◆ PrimalDerivative0
| typedef Calculus::PrimalDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative0 |
Definition at line 762 of file DECImageHelpers.h.
◆ PrimalDerivative1
| typedef Calculus::PrimalDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalDerivative1 |
Definition at line 763 of file DECImageHelpers.h.
◆ PrimalForm0
| typedef Calculus::PrimalForm0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm0 |
Definition at line 756 of file DECImageHelpers.h.
◆ PrimalForm1
| typedef Calculus::PrimalForm1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm1 |
Definition at line 757 of file DECImageHelpers.h.
◆ PrimalForm2
| typedef Calculus::PrimalForm2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalForm2 |
Definition at line 758 of file DECImageHelpers.h.
◆ PrimalHodge0
| typedef Calculus::PrimalHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge0 |
Definition at line 770 of file DECImageHelpers.h.
◆ PrimalHodge1
| typedef Calculus::PrimalHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge1 |
Definition at line 771 of file DECImageHelpers.h.
◆ PrimalHodge2
| typedef Calculus::PrimalHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalHodge2 |
Definition at line 772 of file DECImageHelpers.h.
◆ PrimalIdentity0
| typedef Calculus::PrimalIdentity0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity0 |
Definition at line 759 of file DECImageHelpers.h.
◆ PrimalIdentity1
| typedef Calculus::PrimalIdentity1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity1 |
Definition at line 760 of file DECImageHelpers.h.
◆ PrimalIdentity2
| typedef Calculus::PrimalIdentity2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::PrimalIdentity2 |
Definition at line 761 of file DECImageHelpers.h.
◆ RealVector
| typedef Space::RealVector DGtal::DECImage2D< TKSpace, TLinearAlgebra >::RealVector |
Definition at line 747 of file DECImageHelpers.h.
◆ Scalar
| typedef RealVector::Component DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Scalar |
Definition at line 748 of file DECImageHelpers.h.
◆ SCell
| typedef KSpace::SCell DGtal::DECImage2D< TKSpace, TLinearAlgebra >::SCell |
Definition at line 749 of file DECImageHelpers.h.
◆ SolverU
| typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 2, PRIMAL, 2, PRIMAL> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::SolverU |
◆ SolverV
| typedef DiscreteExteriorCalculusSolver<Calculus, LinearAlgebraSolver, 0, PRIMAL, 0, PRIMAL> DGtal::ATu2v0< TKSpace, TLinearAlgebra >::SolverV |
◆ Space
| typedef KSpace::Space DGtal::DECImage2D< TKSpace, TLinearAlgebra >::Space |
Definition at line 745 of file DECImageHelpers.h.
Constructor & Destructor Documentation
◆ ~ATu2v0()
|
default |
Destructor.
◆ ATu2v0() [1/3]
| 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]
|
delete |
Copy constructor.
- Parameters
-
other the object to clone.
◆ ATu2v0() [3/3]
|
delete |
Move constructor.
- Parameters
-
other the object to move.
Member Function Documentation
◆ addInput()
| 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
- Note
- For a color image stored with values
Color, should be called asAT.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()
| DGtal::ATu2v0< TKSpace, TLinearAlgebra >::BOOST_STATIC_ASSERT | ( | (KSpace::dimension==2) | ) |
◆ checkV()
| 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()
| Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::computeSNR | ( | ) | const |
Computes the SNR of u wrt ideal input (should have been given.
- See also
- addInput).
◆ computeVariation()
| 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()
|
inline |
- Returns
- the (global) alpha parameter.
Definition at line 276 of file ATu2v0.h.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::alpha.
◆ getEpsilon()
|
inline |
- Returns
- the epsilon parameter.
Definition at line 282 of file ATu2v0.h.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::epsilon.
◆ getG()
|
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.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::g2.
◆ getLambda()
|
inline |
- Returns
- the lambda parameter.
Definition at line 279 of file ATu2v0.h.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::lambda.
◆ getU()
|
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.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::u2.
◆ getV()
|
inline |
- Returns
- the v 0-form.
Definition at line 293 of file ATu2v0.h.
References DGtal::ATu2v0< TKSpace, TLinearAlgebra >::v0.
◆ init()
| void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::init | ( | Clone< KSpace > | K | ) |
Constructor from Khalimsky space, which specifies the domain of calculus.
◆ isValid()
| 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]
|
delete |
Move assignment operator.
- Parameters
-
other the object to move.
- Returns
- a reference on 'this'.
◆ operator=() [2/2]
|
delete |
Copy assignment operator.
- Parameters
-
other the object to copy.
- Returns
- a reference on 'this'.
◆ selfDisplay()
| 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]
| 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]
| 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()
| 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()
| 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()
| void DGtal::ATu2v0< TKSpace, TLinearAlgebra >::setMetricAverage | ( | bool | average | ) |
Use metric average to smooth L1-metric effects.
◆ setUFromInput()
| 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()
| 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.
◆ size0()
|
inline |
- Returns
- the size of a 0-form vector
Definition at line 296 of file ATu2v0.h.
References DGtal::KForm< TCalculus, order, duality >::myContainer, and DGtal::ATu2v0< TKSpace, TLinearAlgebra >::v0.
◆ solveU()
| 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()
| 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
|
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
|
protected |
◆ alpha_Id2
|
protected |
◆ calculus
| Calculus DGtal::DECImage2D< TKSpace, TLinearAlgebra >::calculus |
The discrete exterior calculus instance.
Definition at line 884 of file DECImageHelpers.h.
◆ D0
| PrimalDerivative0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D0 |
primal derivative: 0-form -> 1-form
Definition at line 890 of file DECImageHelpers.h.
◆ D1
| PrimalDerivative1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::D1 |
primal derivative: 1-form -> 2-form
Definition at line 892 of file DECImageHelpers.h.
◆ delta_v_l1
| Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_l1 |
◆ delta_v_l2
| Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_l2 |
◆ delta_v_loo
| Scalar DGtal::ATu2v0< TKSpace, TLinearAlgebra >::delta_v_loo |
◆ dual_D0
| 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
| 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
| DualHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h0 |
hodge star: dual 0-form -> 0-form
Definition at line 904 of file DECImageHelpers.h.
◆ dual_h1
| DualHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h1 |
hodge star: dual 1-form -> 1-form
Definition at line 906 of file DECImageHelpers.h.
◆ dual_h2
| DualHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::dual_h2 |
hodge star: dual 2-form -> 2-form
Definition at line 908 of file DECImageHelpers.h.
◆ 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
|
protected |
◆ g2
|
protected |
The g 2-forms.
Definition at line 359 of file ATu2v0.h.
Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getG().
◆ i2
|
protected |
◆ l_1_over_4
|
protected |
◆ l_1_over_4e
|
protected |
◆ l_1_over_4e_Id0
|
protected |
◆ 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
|
protected |
◆ M01
| PrimalDerivative0 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::M01 |
◆ M12
| PrimalDerivative1 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::M12 |
◆ metric_average
|
protected |
◆ primal_AD2
| PrimalAntiderivative2 DGtal::ATu2v0< TKSpace, TLinearAlgebra >::primal_AD2 |
◆ primal_h0
| PrimalHodge0 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h0 |
hodge star: 0-form -> dual 0-form
Definition at line 898 of file DECImageHelpers.h.
◆ primal_h1
| PrimalHodge1 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h1 |
hodge star: 1-form -> dual 1-form
Definition at line 900 of file DECImageHelpers.h.
◆ primal_h2
| PrimalHodge2 DGtal::DECImage2D< TKSpace, TLinearAlgebra >::primal_h2 |
hodge star: 2-form -> dual 2-form
Definition at line 902 of file DECImageHelpers.h.
◆ solver_u
|
protected |
◆ solver_v
|
protected |
◆ u2
|
protected |
The u 2-forms.
Definition at line 363 of file ATu2v0.h.
Referenced by DGtal::ATu2v0< TKSpace, TLinearAlgebra >::getU().
◆ 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
| 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:
