Grant: Discovery Grants Program - Individual

The aim of this work is based on the observation that comparing the similarity of objects is a faculty characteristic of the human condition, performed seamlessly and without effort. At a young age, we become adept at identifying the similarity of objects in our environment, and can quickly assess the degree of similarity. In fact, our day-to-day conversations are full of adverbs and adjectives used to encapsulate the nearness of ""things"" in our environment. Phrases like ""he was about as tall as you are"" or ""those suits look similar"" serve to demonstrate the frequency with which we are making analogies to objects that are not the same, but share some common characteristics. 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. The proposed approach is based on an intuitive view of assessing nearness and apartness grounded in theory based on near sets, rough sets, open sets, and general topology. Specifically, this work investigates neighbourhoods of points formed based on extracted feature values. In general, the contribution of this work is different methods of finding and assessing the most similar pairs of neighbourhoods. In particular, this approach can be applied to many problems in engineering and mathematical sciences, such as using regions-of-interest (ROI) within digital images to measure image correspondence to facilitate image retrieval. Here, image ROIs can be viewed as collections of point sets called neighbourhoods, that are usually open sets. By investigating different properties and structures of similar objects within these neighbourhoods, as well as developing and improving similarity-detection algorithms, it is possible to develop nearness-based applications. This will lead to improvements in the standard of living and quality of life for Canadians, through, e.g., new applications in security surveillance, defense, and remote sensing, based on the contributions of this work to the areas of image analysis, image correspondence, and content-based image retrieval systems.