pderavi

Performs multi-thresholding on image using Deravi algorithm.

Synopsis

pderavi length [-m mask] [im_in|-] [im_out|-]

Description

pderavi classifies the input image pixels into a small number of clusters according to their value. Every pixel p of the input image is assigned to a cluster identified by the related threshold value:

   if threshold[k-1]<im_out[p]<=threshold[k].
   then im_out[p]=threshold[k]

The last threshold is equal to 255.

The number of clusters and the value of the thresholds are determined from the Deravi algorithm. It is based on the measure of the conditional probability of transition. For each gray level i the busyness ratio is:

   P(i) = (P1(i) + P2(i) ) / 2;

   P1(i) = [SUM(SUM((Tkl)*(Tkl))] / [SUM(SUM(Tkl))+ SUM(SUM(Tpq))]	
   with k=[0..i], l=[i+1..N-1], p=[0..i], q=[0..i]
 
   P2(i) = [SUM(SUM((Tkl)*(Tkl))] / [SUM(SUM(Tkl))+ SUM(SUM(Tpq))]
   with k=[i+1..N-1], l=[0..i], p=[i+1..N-1], q=[i+1..N-1]

The co-occurrence matrix Tkl contains the number of times the gray level k is a neighbor of the gray level l considering the neighborhood Nxy={ (x,y+1), (x+1,y) }.

Then the thresholds are located as regional minima of the conditional probability of transition function. The minima are searched in the space of length gray levels around the gray level i.

Notice: This operator can only work on grayscale image of bytes (Img2duc, Img3duc).

Parameters

length defined the length of the search space of the regional minima. It is defined in gray level unit. The greater is the length, the less there are thresholds. A typical value is 10.

Inputs

im_in: a grayscale image of bytes (Img2duc, Img3duc).

Outputs

im_out: a grayscale image of bytes (Img2duc, Img3duc).

Result

Returns the number of thresholds.

Examples

Segments tangram.pan and displays the number of thresholds:

   pderavi 15 tangram.pan out.pan
   pstatus

C++ prototype

Errc PDeravi( const Img2duc &im_in, Img2duc &im_out, int length );

Version française

Multiseuillage de l'image par analyse de la matrice de co-occurences selon Deravi.

Reference

F. Deravi et al., "Gray level thresholding using second-order statistics", Pattern Recognition Letter, Vol. 1, No. 5-6, pp. 417-422, 1983.

Author: Régis Clouard