(a) It was stated in Section 3.5.2 that isolated clusters of dark or light (with respect to the background) pixels whose area is less than one-half the area of a median filter are eliminated (forced to the median value of the neighbors) by the filter. Assume a filter of size n × n, with n odd, and explain why this is so.
(b) Consider an image having various sets of pixel clusters. Assume that all points in a cluster are lighter or darker than the background (but not both simultaneously in the same cluster), and that the area of each cluster is less than or equal to n2/2. In terms of n, under what condition would one or more of these clusters cease to be isolated in the sense described in part (a)?
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