Dr. Christopher Henry, P. Eng.
Comparing the similarity of objects is a faculty characteristic of the human condition, performed seamlessly
and without effort. Comparison of objects begins with identification of features that are used, at
some level, for measuring similarity. Quantifying similarity inevitably leads to the question of nearness,
i.e. in terms of characteristic features, how near are pairs or sets of objects? It was only recently, relatively
speaking, that this idea of nearness was first explored mathematically. Frigyes Riesz first published
a paper in 1908 on the nearness of two sets, initiating the mathematical study of proximity spaces
and the eventual discovery of descriptively near sets. Inspired by this human ability to make feature-based
comparisons, the focus of my research is a formal and systematic process for considering and comparing
neighbourhoods of points in the context of near sets, rough sets, open sets, and general topology in solving
practical image analysis problems.
Image Analysis and Content-Based Image Retrieval
The problem considered in this work is one of establishing a theoretical framework on
which to build applications to produce results similar to a human performing the same task. While,
this work can be applied to any problem that can be formulated in terms of objects with associated
feature vectors, the focus is on finding and discerning patterns and similarities within single images
(image analysis), and between sets of images (content-based image retrieval).
J. F. Peters introduced the concept of near sets, which are disjoint sets containing objects with similar
descriptions. Similarity is determined quantitatively via some description of the objects. Near
set theory provides a formal basis for identifying, comparing, and measuring resemblance of objects based
on their descriptions, i.e. based on the features that describe the objects. The discovery of near sets begins
with identifying feature vectors for describing and discerning affinities between sample objects. Objects
that have, in some degree, affinities in their features are considered perceptually near each other. Groups
of these objects, extracted from the disjoint sets, provide information and reveal patterns of interest.
Rough sets were introduced by Z. Pawlak during the early 1980s. Briefly, a set X is considered a rough set if X
cannot be reproduced by the union of cells in a partition, where
the partition is defined by an equivalence relation on object attributes, called the indiscernibility relation.
Much work has been reported in the use of rough sets in image analysis. The focus here is on disjoint visual rough sets.