MAP signal estimation in noisy sequences of morphologically smooth images

Sidiropoulos et al. (1994) demonstrated that morphological openings and closings can be viewed as maximum a posteriori (MAP) estimators of morphologically smooth signals in signal-independent i.i.d. noise. The present authors extend these results to the M-fold independent observation case, and show that the aforementioned estimators are strongly consistent. We also demonstrate the validity of a thresholding conjecture (Sidiropoulos et al., 1994) by simulation, and use it to evaluate estimator performance. Taken together, these results can help determine the least upper bound, M~, on M, which guarantees virtually error-free reconstruction of morphologically smooth images.