<title>Correlators for rank order shape similarity measurement</title>

Abstract

Correlators have been used for detecting shapes but not as often for measuring shape similarity. The complex inner product (CIP) has been used in various formulations as a shape similarity measure. The CIP is essentially a one-dimensional correlation approach to measuring similarity. One-dimensional variants of the correlation techniques including the matched filter (MF), phase-only filter (POF), and amplitude-modulated phase only filter (AMPOF) are shown to measure shape similarity in a trend that approaches human perception, however, clear performance differences are noted. The results show that the best correlator for measuring shape similarity is not the best correlator for detecting a shape. It is suggested that detection and shape similarity are fundamentally different functions that are in opposition to some degree. Ideal detection and ideal similarity measurement functions are explored. The degree to which various formulations of correlators approach the ideal functions of detection and similarity measurement are shown as well as results from human psychophysical experiments.