The weighted median filter

The median filter is well-known [1, 2]. However, if a user wishes to predefine a set of feature types to remove or retain, the median filter does not necessarily satisfy the requirements. A more general filter, called the Weighted Median Filter, of which the median filter is a special case, is described. It enables filters to be designed with a wide variety of properties. Particular cases of filter requirements are discussed and the corresponding filters are derived. The notion of a minimal weighted median filter, of a subclass that act identically, is introduced and discussed. The question of finding the number of distinct ways a class of filters can act is considered and solved for some classes.

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