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.
Copyright © 1996-1997 MVTec Software GmbH