fuzzy_perimeter ( Regions, Image : : Apar, Cpar : Perimeter )
Calculate the fuzzy perimeter of a region.
The operator fuzzy_perimeter is used to determine the
differences of fuzzy membership between an image point and its
neighbor points. The right and lower neighbor are taken into
account. The fuzzy perimeter is then defined as follows:
M-1 N-1
---- ----
\ \
p(x) = / / |u(x(m,n)) - u(x(m,n+1))| +
---- ----
m=1 n=1
M-1 N-1
---- ----
\ \
/ / |u(x(m,n)) - u(x(m+1,n))|
---- ----
m=1 n=1
where MxN is the size of the image, and
u(x(m,n)) is the fuzzy membership function (i.e., the input
image). This implementation uses Zadeh's Standard-S function, which
is defined as follows:
/ 0, x <= a
u(x) = | 2((x-a)/(c-a))**2, a < x <= b
| 1-2((x-a)/(c-a))**2, b < x < c
\ 1, c <= x.
The parameters a, b and c obey the following restrictions: b
= (a+c)/2 is the inflection point of the
function, Db = b - a = c - b is the
bandwith, and for x = b u(x) = 0.5
holds. In fuzzy_perimeter, the parameters
Apar and Cpar are defined as follows: b is
(Apar + Cpar)/2.
Parameters
Regions (input_object)
|
region(-array) -> object
|
Regions for which the fuzzy perimeter 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 |
Perimeter (output_control)
|
real(-array) -> real
|
Fuzzy perimeter of a region. |
Example
/* To find a Fuzzy Entropy from an Image */
read_image(:Image:'affe':) >
fuzzy_perimeter(Trans,Trans::0,255:Per) >
Result
The operator fuzzy_perimeter returns the value TRUE if
the parameters are correct. Otherwise an exception is raised.
See also
fuzzy_entropy
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