Measuring Similarity Among Various Shapes Based on Geometric Matching

The purpose of this article is to examine how to measure the degree of similarity among various shapes, including for the first time those that are fragmented and perforated, by the overlap-based elongation index. It is argued that complete removal of the effects of position, size, and orientation on shape, which is essential for the calibration of shape similarity, can be achieved by a shape similarity index that varies continuously with changes in shape. After examining the characteristics of shape change, it is demonstrated that the elongation index is sensitive to changes in the shape of two spatial objects only when the centroids of the two objects are coincident. Two related rules of shape similarity are then presented. The applicability of the elongation index is evaluated by comparing several simple and complex shapes. The principal contribution of this article is that for the first time similarity among various shapes, fragmented or perforated, can be identified using the elongation index.