pentropyquadtree

Synopsis

Description

pentropyquadtree segments the input image im_in into homogeneous regions. Homogeneous regions are regions that have an inner entropy degree ≤ threshold.

The principle of the algorithm is as follows:

• At the begin consider the image as the first block.
• If the block violates the uniformity predicate (i.e. inner entropy ≤ threshold) then split the block into four equally sized sub-blocks and then apply the algorithm recursively on each sub-blocks.

Therefore, the result is composed of rectangular regions.

The entropy in the sense of Shannon is the quantity of information held by the input image. The more seldom a pixel value is, the more information it holds and the greater the entropy is.

The entropy for a region is calculated as follows:

   entropy= - SUM { Pi * log2(Pi) }

where Pi is the probability of pixel i. (Pi is computed from the normalized histogram.)

Notice: This operator cannot worked on float image since related probabilities are not significant.

For 3D image, the output region map is composed of octree regions.

Parameters

• threshold is the maximum entropy value to decide if a region is homogeneous or not. Values are between 0 and the maximum value approximated by ln(N)/ln(2) (where N is the number of pixels).

Inputs

• im_in: a grayscale image.

Outputs

• rg_out: a region map.

Result

Returns the number of regions.

Examples

Builds the quadtree of tangram.pan:

   pentropyquadtree 4 tangram.pan a.pan

See also

C++ prototype

Version française

Segmentation d'une image par quadtree (ou octree) selon l'entropie.