fuzzy_entropy

fuzzy_entropy ( Regions, Image : : Apar, Cpar : Entropy )

Determine the fuzzy entropy of regions.

fuzzy_entropy calculates the fuzzy entropy of a fuzzy set. To do so, the image is regarded as a fuzzy set. The entropy then is a measure of how well the image approximates a white or black image. It is defined as follows:


             1     ----
  h(x) = --------- \    T (l) h(l)
         M N ln(2) /     e
                   ----

where MxN is the size of the image, and h(l) is the histogram of the image. Furthermore,

  T (l) = -u(l) ln(u(l)) - (1-u(l)) ln(1-u(l))
   e

Here, u(x(m,n)) is a fuzzy membership function defining the fuzzy set (see fuzzy_perimeter). The same restrictions hold as in fuzzy_perimeter.

Parameters

`Regions` (input_object)	region(-array) `->` object
Regions for which the fuzzy entropy is to be calculated.

`Image` (input_object)	image `->` object : byte
Input image containing the fuzzy membership values.

`Apar` (input_control)	integer `->` integer
Start of the fuzzy function.
Default value: 0
Suggested values: 0, 5, 10, 20, 50, 100
Typical range of values: `0 <= Apar <= 255` (lin)
Minimum increment: 1
Recommended increment: 5

`Cpar` (input_control)	integer `->` integer
End of the fuzzy function.
Default value: 255
Suggested values: 50, 100, 150, 200, 220, 255
Typical range of values: `0 <= Cpar <= 255` (lin)
Minimum increment: 1
Recommended increment: 5
Restriction: `Apar <= Cpar`

`Entropy` (output_control)	real(-array) `->` real
Fuzzy entropy of a region.

Example

/* To find a Fuzzy Entropy from an Image */
read_image(Image,'affe') 
fuzzy_entropy(Trans,Trans,0,255,Entro).

Result

The operator fuzzy_entropy returns the value 2 (H_MSG_TRUE) if the parameters are correct. Otherwise an exception is raised.

Parallelization Information

fuzzy_entropy is reentrant and automatically parallelized (on tuple level).

See also

fuzzy_perimeter

References

M.K. Kundu, S.K. Pal: `Äutomatic selection of object enhancement operator with quantitative justification based on fuzzy set theoretic measures''; Pattern Recognition Letters 11; 1990; pp. 811-829.

Module

Foundation