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
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
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 TRUE if the parameters are correct. Otherwise an exception is raised.


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.



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