Carleton University
Technical Report TR-18
January 1983
A Geometrical Approach to Polygonal Dissimilarity and the Classification of Closed Boundaries
R.L. Kashyap & B.J. Oommen
Abstract
The problem of quantizing the dissimilarity between two irregular polygons has been considered. Two measures which are geometrical in nature and which capture the intuitive notion of the dissimilarity between shapes have been presented. Both these measures are related to the minimum value of the common area of the polygons when they are superposed on one another in various configurations. The first of these measures is edge based and the second is vertex based. Both are pseudo-metrics and are equally informative. An alternative measure of dissimilarity, referred to as the minimum integral square error between the polygons has also been proposed. The Latter is closely related to the the area based dissimilarity measures, but is more easily computable. Using the minimum integral square error as a criterion, pattern classification of closed boundaries can be performed. Experimental results involving the boundaries of the four Great Lakes, Erie, Huron, Michigan and Superior justify the theoretical results presented in this paper.