From Tolerance Near Sets to Perceptual Image Analysis - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 173

9

From Tolerance Near Sets to
Perceptual Image Analysis

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-1

9.2 Perceptual systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-2

9.3 Perceptual Indiscernibility and Tolerance

Relations 9-3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.4 Near Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-5

9.5 Three Tolerance Near Set-based Nearness Measures for

Image Analysis and Comparison . . . . . . . . . . . . . . . . . . . .

Shabnam Shahfar
University of Manitoba

9-6

Tolerance Cardinality Distribution Nearness Measure
(TCD) • Tolerance Overlap Distribution nearness
measure (TOD) • Tolerance Nearness Measure (tNM)

Amir H. Meghdadi
University of Manitoba

9.6 Perceptual Image Analysis System 9-9

. . . . . . . . . . . . . . . . .

9.7 Conclusion 9-11

James F. Peters
University of Manitoba

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Bibliography 9-15

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9.1 Introduction

The problem considered in this chapter how is to find and measure the similarity between
two images. The image correspondence problem is a central and important area of research
in computer vision. To solve the image correspondence problem, a biologically inspired
approach using near sets and tolerance classes is proposed in this chapter. The proposed
method is developed in the context of perceptual systems (Peters and Ramanna, 2008),
where each image or parts of an image are considered as perceptual objects (Peters and
Wasilewski, 2009). ”A perceptual object is something presented to the senses or know-
able by human mind” (Peters and Wasilewski, 2009; Murray, Bradley, Craigie, and Onions,
1933). The perceptual system approach presented here is inspired by the early 1980s work
of Z. Pawlak (Pawlak, 1981) on the classification of objects by means of attributes and E.
Orlowska (Orlowska, 1982) on approximate spaces as formal counterparts of perception and
observation.

It has been shown in (Peters, 2007b) that near sets are a generalization of rough sets (Pawlak
and Skowron, 2007; Polkowski, 2002). Near sets provide a good basis for the classification
of perceptual objects. Near sets are disjoint sets that have matching descriptions to some
degree (Henry and Peters, 2009b). One set X is considered near another set Y in the
case where there is at least one x∈X with a description that matches the description of
y∈Y (Peters, 2007c,b). The proposed approach in this chapter also benefits from the idea
of tolerance classes introduced by Zeeman (Zeeman, 1961). Tolerance relations are viewed

9-1