Image Processing Reference

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homogeneity approach (Cheng, Chen, Chiu, and Xu, 1998) and the histon based approach

(Mohabey and Ray, 2000) exploit this correlation to improve the quality of segmentation.

The concept of histon, introduced by Mohabey and Ray (Mohabey and Ray, 2000), is an

encrustation of the histogram that visualizes the multi-dimensional color information in an

integrated fashion. The concept has found applicability towards boundary region analysis

problems. The histon encapsulates the fundamentals of color image segmentation in a

rough-set theoretic sense and provides a direct means of segregating pool of inhomogeneous

regions into its components.

In this chapter, we present a new technique for color image segmentation using a rough-

set theoretic approach. The roughness index, obtained by correlating histon with the upper

approximation and the histogram to the lower approximation of a rough set, has been used

as a basis for segmentation (Mushrif and Ray, 2008).

In the next section we present the basic concepts of the rough set theory and some im-

portant properties of rough sets. In section 1.3, we describe the concept of histon and

calculation of roughness measure. Section 1.4 describes segmentation algorithm and exper-

imental results are given in section 1.5, followed by concluding remarks in section 1.6.

Rough set theory, introduced by Z. Pawlak (Pawlak, 1991), represents a new mathemati-

cal approach to vagueness and uncertainty. The theory is especially useful in discovery of

patterns in data in real life applications such as medical diagnosis (Tanaka, Ishibuchi, and

Shigenaga, 1992), pharmacology, industry (Szladow and Ziarko, 1992), image analysis (Pal,

Shankar, and Mitra, 2005) and others.

Rough set theory provides a possibilistic approach towards classication and extraction

of knowledge from a data set. It supports granularity in knowledge and concerns with

understanding knowledge, nding means of representation of knowledge and automation of

the process of extraction of information from knowledge bases. Rough set theory addresses

the issue of indiscernibility and is a formal framework for the automated transformation of

of data into knowledge. The knowledge is primarily dened by the ability of the system to

classify data or objects. Thus, it is necessarily connected with the variety of classication

patterns related to specic parts of the real or abstract world, called universe of discourse.

In this section, we introduce some preliminary concepts of rough-set theory that are relevant

to this chapter.

Given a nite set U 6= ; (the universe) of objects, any subset X U of the universe

is called aconcept or acategoryinUand any family of concepts inUis referred to as

abstractknowledgeaboutU. Categories lead to the classication or partition of a certain

universe U, i.e. in families C = fX
1
;X
2
;:::;X
n
g such that X
i
U; X
i
6= ;; X
i
\X
j
= ;

for i 6= j; i;j = 1; 2;:::;n and
S
X
i
= U.

A knowledge base is a relational system K = (U;R), where U 6= ; andRis a family of

equivalence relations overU. IfPRandP6= ;, then \Pis also an equivalence relation,

and is denoted by IND (P), and is known asindiscernibilityrelation overP. Moreover

[x]
IND(
P
)
=
\

R
2P

[x]
R

(10.1)

Thus, U=IND (P) or simply U=Pdenotes the knowledge associated with the family of

equivalence relationsP, calledP-basic knowledge aboutUin the knowledge baseK. The

equivalence classes of IND (P) are called basic categories of knowledgeP. TheP-basic

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