Adaptive grayscale morphological filters for image noise smoothing

The authors find an optimal solution for designing a gray-scale morphological filter. An adaptive algorithm is developed for determining, from a given class of gray-scale morphological filters, a filter which minimizes the mean square error between its output and a desired process. The adaptation using the conventional least mean square algorithm optimizes the gray-scale structuring element in a given search area. The noise removal performance is compared to that of another class of nonlinear filters, i.e., adaptive and nonadaptive stack-based filters