Perceptual Systems Approach to Measuring Image Resemblance - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 150

8

Perceptual Systems Approach to
Measuring Image Resemblance

8.1 Introduction ........................................ 8-1

8.2 Perceptual Systems, Feature Based Relations and Near

Sets ................................................. 8-2

Perceptual Systems ￿ Perceptual Indiscernibility and
Tolerance Relations ￿ Nearness Relations and Near Sets

Amir H. Meghdadi
Computational Intelligence Laboratory,
University of Manitoba

8.3 Analysis and Comparison of Images Using Tolerance

Classes ..............................................

8-11

Tolerance Overlap Distribution nearness measure
(TOD)

James F. Peters
Computational Intelligence Laboratory,
University of Manitoba

8.4 Summary and Conclusions

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

8-19

Bibliography ............................................. 8-21

8.1 Introduction

Image resemblance is viewed as a form of nearness between sets of perceptual objects
as originally proposed in near set theory in (Peters, 2007b,c) and further elaborated
in (Peters, 2009, 2010; Peters and Wasilewski, 2009), where a nearness relation is
shown to be a tolerance relation on the family of near sets in a perceptual system.
The idea of using tolerance relations (Sossinsky, 1986) in formalizing the concept of
perceptual resemblance between images was introduced in 2008 (see, e.g. , (Peters,
2008b) and elaborated in (Peters, 2009, 2010; Peters and Wasilewski, 2009)) as
a result of a collaboration with Z. Pawlak in 2002 on describing the nearness of
perceived objects (Pawlak and Peters, 2002,2007). In this approach, images are
considered to be non-empty sets of perceptual objects

O (pixels or subimages).

Moreover, a set of probe functions is used to describe the objects by extracting

some of their perceivable features.

F

<O, F > is named as perceptual information

system (Peters and Ramanna, 2009).
Near set theory grew out of a generalization of the rough set approach (Pawlak,
1981a,b) in describing the anities between sample objects. The perceptual basis of
near set theory was inspired by Orlowska's suggestion that approximation spaces are
the formal counterpart of perception or observation (Orlowska and Pawlak, 1984).

8-1