The operator fuzzy_perimeterfuzzy_perimeterFuzzyPerimeterfuzzy_perimeterFuzzyPerimeterFuzzyPerimeter 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:
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:
The parameters a, b and c obey the following restrictions: is the inflection point of the
function, is the
bandwith, and for x = b
holds. In fuzzy_perimeterfuzzy_perimeterFuzzyPerimeterfuzzy_perimeterFuzzyPerimeterFuzzyPerimeter, the parameters
AparAparAparAparAparapar and CparCparCparCparCparcpar are defined as follows: b is
.
Note that for fuzzy_perimeterfuzzy_perimeterFuzzyPerimeterfuzzy_perimeterFuzzyPerimeterFuzzyPerimeter, the RegionsRegionsRegionsRegionsRegionsregions must lie
completely within the previously defined domain. Otherwise an exception
is raised.
The operator fuzzy_perimeterfuzzy_perimeterFuzzyPerimeterfuzzy_perimeterFuzzyPerimeterFuzzyPerimeter returns the value 2 (H_MSG_TRUE) if
the parameters are correct. Otherwise an exception is raised.
M.K. Kundu, S.K. Pal: “Automatic selection of object enhancement
operator with quantitative justification based on fuzzy set theoretic
measures”; Pattern Recognition Letters 11; 1990; pp. 811-829.