The Proximity System is an application developed to demonstrate descriptive-based topological approaches to nearness and proximity within the context of digital image analysis. The Proximity System grew out of the work of S. Naimpally and J. Peters on Topological Spaces. The Proximity System was written in Java and is intended to run in two different operating environments, namely on Android smartphones and tablets, as well as desktop platforms running the Java Virtual Machine. With respect to the desktop environment, the Proximity System is a cross-platform Java application for Windows, OSX, and Linux systems, which has been tested on Windows 7 and Debian Linux using the Sun Java 6 Runtime. In terms of the implementation of the theoretical approaches, both the Android and the desktop based applications use the same back-end libraries to perform the description-based calculations, where the only differences are the user interface and the Android version has less available features due to restrictions on system resources.
The inspiration for the approach implemented in the Proximity System is an observation that the concept of nearness is a generalization of set intersection. The idea follows from the notion of set description, which is a collection of the unique feature vectors (n-dimensional real-valued feature vectors representing characteristics of the objects) associated with all the objects in the set. Describing sets in this manner, at some level, matches the human approach to describing sets of objects. Furthermore, in comparing disjoint sets of objects, we must at some level be performing a comparison of the descriptions we associate with the objects within the sets. Thus, a natural approach for quantifying the degree of similarity (i.e. the nearness or apartness) between two sets would be to look at the intersection of the sets containing their unique feature vectors.
The sets considered in the Proximity System are obtained from digital images. For instance, Regions Of Interest (ROI) play an important role in discerning perceptual similarity within a single image, or between a pair of images. In this work, four different ROIs are considered. Namely, a simple set of pixels, a spatial neighbourhood, a descriptive neighbourhood, and a hybrid approach in which the neighbourhood is formed by spatial and descriptive characteristics of the objects. In terms of pixels, closeness between ROIs can be assessed in light of the traditional closeness between points and sets and closeness between sets using topology or proximity theory.
Finally, the code for the Proximity System was written by Garrett Smith and a technical report detailing the theory behind and the operation of the Proximity System is available at the University of Manitoba's Computational Intelligence Laboratory website (located at: http://wren.ee.umanitoba.ca/)