Testing Hypotheses About Contours in Images

Abstract

We consider the problem of testing hypotheses about the contours in binary images observed on the regular grid. We propose a simple goodness-of-fit test of the hypothesis that a contour belongs to a given parametric family against a nonparametric alternative. We analyze the behavior of the test under the null hypothesis, and under the alternative separated from the null parametric family by a distance of order n À1=2 (n is the total number of observations and the distance is defined as the measure of symmetric difference between the sets whose boundaries are the contours of interest). Finally, we prove the lower bound showing that no test can be consistent if the distance between the hypothesis and the alternative is of the order smaller than n À1=2 .