Comparison of the maximum likelihood ratio test algorithm and linear filters for target location in binary images

Abstract

We consider the problem of estimating the position of objects in binary images corrupted with nonoverlapping and spatially nonhomogeneous noise. For this application, we compare classical linear filters with the recently proposed maximum likelihood ratio test (MLRT) algorithm, which is optimal in the maximum likelihood sense for object detection. We first demonstrate that the MLRT algorithm can be approximated with a good precision by the square of a correlation product. We then compare the MLRT with the Classical Matched, Phase-only and Optimal Tradeoff filters in terms of probability of correct location. We conclude that if they are properly regularized, linear filters can achieve a performance level comparable to that of the MLRT. This result is important in the design of optical correlators, which often implement linear filters with binary input spatial light modulators.