Discovering Image Similarities.Tolerance Near Set Approach - Rough Fuzzy Image Analysis: Foundations and Methodologies - page 229

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Discovering Image Similarities.
Tolerance Near Set Approach

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1

12.2 Tolerance Near Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-3

Probe Function • Perceptual Systems • L 2 norm-based
Object Description • Perceptual Tolerance Relation
12.3 Resemblance Measures 12-5

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

Description-based Set Intersection Nearness Measure •
Tolerance Class Overlap Distribution Nearness
Measure (Meghdadi, Peters, and Ramanna, 2009) •
Tolerance Class Size-Based Nearness Measure (Henry
and Peters, 2008) • Hausdorff Distance and Image
Correspondence Measure
12.4 Illustration: Image Nearness Measures with Microfossil
Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-9
12.5 Image Retrieval Experiments with Meghdadi Image
Nearness Toolset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-11
tNM-measure Results • Hausdorff-measure Results
12.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-13
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-13
Bibliography

Sheela Ramanna
University of Winnipeg, Dept. Applied
Computer Science, 515 Portage Ave.,
Winnipeg, Manitoba, R3B 2E9, Canada

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12.1 Introduction

This chapter proposes an approach to detecting chains of a nities between perceptual ob-
jects contained in tolerance classes in digital image coverings. A perceptual object is some-
thing perceptible to the senses or knowable by the mind. Perceptual objects that have
similar appearance are considered perceptually near each other, i.e., perceived objects that
have perceived a nities or, at least, similar descriptions. Similarities between digital im-
ages are measured within the context of tolerance spaces with measurable similarities. This
form of tolerance space is inspired by E.C. Zeeman's work on visual perception and H.
Poincare's work on the contrast between mathematical continua and the physical continua
in a pragmatic philosophy of science that laid the foundations for tolerance spaces. Com-
parison of pairs of tolerance spaces that are in some sense close to each other originated in
E.C. Zeeman's work on visual accuity spaces and a topological model for visual sensation.
The perception of nearness or closeness that underlies tolerance near relations is rooted in
M. Merleau-Ponty's work on the phenomenology of perception during the mid-1940s, and,
especially, philosophical reflections on description of perceived objects and the perception
of nearness. Pairs of disjoint sets such as sets of points represening digital images are con-
sidered near each other to the extent that elements of tolerance classes in image coverings

12-1