Deterministic properties of the recursive separable median filter

TLDR: Using threshold decomposition, the root structure of the recursive separable median filter is derived, where a root is a signal invariant to further filtering, and it is shown that these root structures differ from those of their nonrecursive counterparts.

Abstract: The recursive separable median filter has been successfully used to extract features from noisy two-dimensional signals. In many applications, it gives better noise suppression and edge preservation than the standard separable median filter. In this paper we use a new approach for studying the deterministic properties of separable median filters. In particular, using threshold decomposition, we derive the root structure of the recursive separable median filter, where a root is a signal invariant to further filtering. It is shown that these root structures differ from those of their nonrecursive counterparts. We also show that any two-dimensional signal will converge to a root after repeated passes of the recursive separable median filter.