Image Processing Reference
(1.1a) favite coral
(1.1b) near sets
FIGURE 1.1: Sample Near Sets
interest in comparing similarities between digital images. Unlike rough sets, the near set approach
does not require set approximation Peters and Wasilewski (2009). Simple examples of near sets can
sometimes be found in tolerance classes in pairs of image coverings, if, for instance, a subimage of
a class in one image has a description that is similar to the description of a subimage in a class in
the second image. In general, near sets are discovered by discerning objects-either within a single
set or across sets-with descriptions that are similar.
From the beginning, the near set approach to perception has had direct links to rough sets in its
approach to the perception of objects (Pawlak, 1981a; Orłowska, 1982) and the classification of ob-
jects (Pawlak, 1981a; Pawlak and Skowron, 2007c,b,a). This is evident in the early work on nearness
of objects and the extension of the approximation space model (see, e.g. , (Peters and Henry, 2006;
Peters et al., 2007)). Unlike the focus on the approximation boundary of a set, the study of near sets
focuses on the discovery of affinities between perceptual granules such as digital images viewed as
sets of points. In the context of near sets, the term affinity means close relationship between per-
ceptual granules (particularly images) based on common description . Affinities are discovered by
comparing the descriptions of perceptual granules, e.g. , descriptions of objects contained in classes
found in coverings defined by the tolerance relation = F , ε .
Near set theory provides methods that can be used to extract resemblance information from objects
contained in disjoint sets, i.e., it provides a formal basis for the observation, comparison, and clas-
sification of objects. The discovery of near sets begins with choosing the appropriate method to
describe observed objects. This is accomplished by the selection of probe functions representing
observable object features. A basic model for a probe function was introduced by M. Pavel (Pavel,
1993) in the text of image registration and image classification. In near set theory, a probe function is
a mapping from an object to a real number representing an observable feature value (Peters, 2007a).
For example, when comparing fruit such as apples, the redness of an apple (observed object) can be
described by a probe function representing colour, and the output of the probe function is a number
representing the degree of redness. Probe functions provide a basis for describing and discerning
affinities between objects as well as between groups of similar objects (Peters and Ramanna, 2009).
Objects that have, in some degree, affinities are considered near each other. Similarly, groups of
objects (i.e. sets) that have, in some degree, affinities are also considered near each other.