MAP signal estimation in noisy sequences of morphologically smooth images

In a recent paper 111, it has been demonstrated that morphological openings and closings can be viewed as Maximum U potrrrrorr (MAP) estimators of morphologically smooth signals in signalindependent i.i.d. noise. In this correspondence, we extend these results to the .\l-fold independent observation case, and show that the aforementioned estimators are strongly consistent. We also demonstrate the validity of a thresholding conjecture [Z] by simulation, and use it to evaluate estimator performance. Taken together, these results can help determine the least upper hound, ,cf, on M, which guarantees virtually error-free reconstruction of morphologically smooth images.