Near Set Evaluation And Recognition (NEAR) System - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 142

FIGURE 7.14: Sample run of the tolerance class frame using a window size of 10×10,
B={φ ,φ

H Shannon }, and ε = 0.05. NormG

7.7 Segmentation evaluation frame

This frame performs segmentation evaluation using perceptual morphology as described
in (Henry and Peters, 2008, 2009c), where the evaluation is labelled the Near Set Index
(NSI). Briefly, the NSI uses perceptual morphology (a form of morphological image pro-
cessing based on traditional mathematical morphology (Henry and Peters, 2009c)) to eval-
uate the quality of an image segmentation. As is given in (Henry and Peters, 2009c), the
perception-based dilation is defined as

A⊕B ={x /∼ B ∈B|x /∼ B ∩A 6=∅},

and the perception-based erosion is defined as
A · B = [
x /∼ B ∈B

{x /∼ B ∩A},

where the set A⊆O is selected such that it has some a priori perceptual meaning associated
with it, i.e. this set has definite meaning in a perceptual sense outside of the probe functions
inB. Furthermore, the structuring element B is the quotient set given in Eq. 7.1, i.e.,
B = O /∼ B

∗ . As was reported in (Henry and Peters, 2009c), the quotient set is used as
the SE in perceptual morphology, since it contains the perceptual information necessary to
augment the set A in a perceptually meaningful way. This perceptual information is in the
form of elementary sets (collections of objects with the same descriptions) since, we perceive

∗ The quotient set is being relabelled only to be notationally consistent with traditional mathematical
morphology.