Functionals::PhaseField Class Reference

Two Phase-Field for segmentation, see [1]. [1] Shen. Gamma-Convergence Approximation to Piecewise Constant Mumford-Shah Segmentation. International Conference on Advanced Concepts of Intelligent Vision Systems, 2005. More...

#include <functionals.h>

Static Public Member Functions
static float	f (const Eigen::MatrixXf &x, float epsilon)
	Differentiable but non-convex part: 9 | z|^2 + (1-z^2)^2/(64) dx. More...
static void	df (const Eigen::MatrixXf &x, Eigen::MatrixXf &df_x, float epsilon)
	Derivative of f. More...
static float	g (const Eigen::MatrixXf &x, const Eigen::MatrixXf &x_0, float Cp, float Cm, float lambda)
	Non-differentiable but convex part: (1 +- z)^2/4 (x_0 + Cpm)^2 dx. More...
static void	prox_g (const Eigen::MatrixXf &x, const Eigen::MatrixXf &x_0, Eigen::MatrixXf &prox_g_x, float Cp, float Cm, float lambda, float alpha)
	Proximal map of g. More...
static float	g_absolute (const Eigen::MatrixXf &x, const Eigen::MatrixXf &X_0, float Cp, float Cm, float lambda)
	Non-differentiable but convex part: |1 +- z| |x_0 + Cpm| dx. More...
static void	prox_g_absolute (const Eigen::MatrixXf &x, const Eigen::MatrixXf &x_0, Eigen::MatrixXf &prox_g_x, float Cp, float Cm, float lambda, float alpha)
	Proximal map of g_absolute. More...
static float	Cp (const Eigen::MatrixXf &x, const Eigen::MatrixXf &x_0)
	Compute Cp from the given labels x and the image x_0. More...
static float	Cm (const Eigen::MatrixXf &x, const Eigen::MatrixXf &x_0)
	Compute Cp::m from the given labels x and the image x_0. More...

Detailed Description

Two Phase-Field for segmentation, see [1]. [1] Shen. Gamma-Convergence Approximation to Piecewise Constant Mumford-Shah Segmentation. International Conference on Advanced Concepts of Intelligent Vision Systems, 2005.

Member Function Documentation

float Functionals::PhaseField::Cm ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  x_0  )

static

Compute Cp::m from the given labels x and the image x_0.

Parameters

[in]	x
[in]	x_0

float Functionals::PhaseField::Cp ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  x_0  )

static

Compute Cp from the given labels x and the image x_0.

Parameters

[in]	x
[in]	x_0

void Functionals::PhaseField::df ( const Eigen::MatrixXf &  x, Eigen::MatrixXf &  df_x, float  epsilon  )

static

Derivative of f.

Parameters

[in]	x
[out]	df_x
[in]	epsilon

float Functionals::PhaseField::f ( const Eigen::MatrixXf &  x, float  epsilon  )

static

Differentiable but non-convex part: 9 | z|^2 + (1-z^2)^2/(64) dx.

Parameters

[in]	x
[in]	epsilon

float Functionals::PhaseField::g ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  x_0, float  Cp, float  Cm, float  lambda  )

static

Non-differentiable but convex part: (1 +- z)^2/4 (x_0 + Cpm)^2 dx.

Parameters

[in]	x
[in]	x_0
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda

float Functionals::PhaseField::g_absolute ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  X_0, float  Cp, float  Cm, float  lambda  )

static

Non-differentiable but convex part: |1 +- z| |x_0 + Cpm| dx.

Parameters

[in]	x
[in]	x_0
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda

void Functionals::PhaseField::prox_g ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  x_0, Eigen::MatrixXf &  prox_g_x, float  Cp, float  Cm, float  lambda, float  alpha  )

static

Proximal map of g.

Parameters

[in]	x
[in]	x_0
[out]	prox_g_x
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda
[in]	alpha

void Functionals::PhaseField::prox_g_absolute ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  x_0, Eigen::MatrixXf &  prox_g_x, float  Cp, float  Cm, float  lambda, float  alpha  )

static

Proximal map of g_absolute.

Parameters

[in]	x
[in]	x_0
[out]	prox_g_x
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda
[in]	alpha

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The documentation for this class was generated from the following file:

• lib_ipiano/functionals.h