SoCooccurrenceQuantification2d Class Reference
[Statistics]

SoCooccurrenceQuantification2d engine provides texture indicators based on the co-occurrence matrix computation. More...

#include <ImageViz/Engines/ImageAnalysis/Statistics/SoCooccurrenceQuantification2d.h>

Inheritance diagram for SoCooccurrenceQuantification2d:

List of all members.

Classes
class	SbCoocurrrenceDetail
	Results details of cooccurrence global measure. More...
Public Member Functions
	SoCooccurrenceQuantification2d ()
Public Attributes
SoSFImageDataAdapter	inImage
SoSFImageDataAdapter	inMaskImage
SoSFInt32	offsetX
SoSFInt32	offsetY
SoImageVizEngineAnalysisOutput < SbCoocurrrenceDetail >	outResult

Detailed Description

SoCooccurrenceQuantification2d engine provides texture indicators based on the co-occurrence matrix computation.

The SoCooccurrenceQuantification2d engine provides some information concerning the texture thanks to the computation of a co-occurrence matrix. This command allow s to classify, given a direction $(dx,dy)$ , pairs of pixels by their gray level. The co-occurrence matrix components are given by :

$M(i,j)=number\left(\{x,y\}/(I(x,y)=i)\cap(I(x+dx,y+dy)=j)\right)$

Where $I(x,y)$ is the image graylevel for $(x,y)$ coordinates.
This formulation means that for a given pair $(i,j)$ , $M(i,j)$ contains the number of pixels verifying $I(x,y)=i$ and $I(x+dx,y+dy)=j$ .

This matrix is made symmetric and normalized such as :

$\forall(i,j),M(i,j)=M(j,i) ~\mbox{and} \sum_{i,j=1}^{N}M(i,j)=1$

These operations allow to be independent to the image size and to hold properties on a direction and its symmetric. Thirteen indicators are computed from this matrix :

an angular second moment indicator (ASM), also called uniformity. This indicator takes high values when image pixels present strong local uniformity.
$ASM= \sum_{i,j=1}^{N}{M(i,j)}^2$
a contrast indicator (Con). This indicator takes high values for great gray level variations.
$Con= \sum_{i,j=1}^{N}M(i,j)\times(i-j)^2$
a correlation indicator (Cor) which measures the dependency between gray levels and those of neighbouring pixels.
$Cor= \sum_{i,j=1}^{N}M(i,j)\times\frac{(i-\mu_i)(i-\mu_j)}{\sqrt{\sigma_i^2\sigma_j^2}}$
where :
$\mu_i=\mu_j=\sum_{i,j=1}^{N}i\times M(i,j) ~\mbox{and}~ \sigma_i^2=\sigma_j^2=\sum_{i,j=1}^{N}M(i,j)\times(i-\mu_i)^2$
a variance indicator (SSV) also called sum of squares. This indicator measures the dispersion of the combination of gray levels and their neighbour pixels around the mean.
$SSV=\sigma_i^2=\sigma_j^2=\sum_{i,j=1}^{N}M(i,j)\times(i-\mu_i)^2$
an inverse difference moment (IDM) also called homogeneity.
$IDM= \sum_{i,j=1}^{N}\frac{M(i,j)}{1+(i-j)^2}$
a sum average indicator (SAv).
$SAv=\sum_{i,j=1}^{N}M(i,j)\times(i+j)$
a sum variance indicator (SVa).
$SVa=\sum_{i,j=1}^{N}M(i,j)\times(i+j-SAv)^2$
a sum entropy indicator (SEn).
$SEn=-\sum_{k=2}^{2N}p_{x+y}(k)\times log(p_{x+y}(k)) ~\mbox{where}~ p_{x+y}(k)=\sum_{i+j=k}M(i,j)$
an entropy indicator (Ent).
$Ent=-\sum_{i,j=1}^{N}M(i,j)\times log(M(i,j))$
a difference variance indicator (DVa).
$DVa=variance(p_{x-y}) ~\mbox{where}~ p_{x-y}(k)=\sum_{|i-j|=k}M(i,j)$
a difference entropy indicator (DEn).
$DEn=-\sum_{k=0}^{N-1}p_{x-y}(k)\times log(p_{x-y}(k))$
two information measures of correlation (IC1 and IC2).
$IC1=\frac{HXY-HXY1}{max(HX,HY)} ~\mbox{where}~ IC2=\sqrt{1-e^{-2\times|HXY2-HXY|}}$
where HX and HY are entropies of px and py such as :
$p_x(i)=\sum_{j=1}^{N}M(i,j) ~\mbox{and}~ p_y(j)=\sum_{i=1}^{N}M(i,j)$
and
$HXY=-\sum_{i,j=1}^{N}M(i,j)\times log(M(i,j))$

$HXY1=-\sum_{i,j=1}^{N}M(i,j)\times log(p_x(i)\times p_y(j))$

$HXY2=-\sum_{i,j=1}^{N}p_x(i)\times p_y(j)\times log(p_x(i)\times p_y(j))$