Abstract
A recursive maximum filter (RMF) is an algorithm devised to solve the problem of detecting small moving targets in noisy image sequences. RMF is simple and effective for the enhancement of small moving targets with a low signal-to-noise ratio; however, its principle and performance limit are not clear because the algorithm was derived heuristically. In this paper, we reformulate RMF based on a Bayes estimation and show that it can be interpreted as a Bellman equation of dynamic programming (DP). Although some DP-based algorithms have already been proposed, RMF requires much less computation than previous algorithms because its state space is much smaller. RMF includes two design parameters: neighborhood size and a forgetting factor. We derive approximation formulae of the distributions of RMF outputs for various parameter values. By using the formulae, we show a minimum SNR with which targets are detectable for each neighborhood size. We also show the conditions under which targets can be detected by RMF with various parameter values.
