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We design rank filtering algorithms using the threshold decomposition and radix splitting techniques. We map an n x n image onto an n x n single-bit mesh array with one pixel per processing element (PE). Suppose that the maximum pixel value is L. Using threshold decomposition technique, we can implement any rank filter in O((m log m + log L)L) time on a mesh processor array with O(log L + log m) bits of space on each PE. Using the radix splitting technique, we can implement any rank order filter in O(m2 log m log L ) time on a mesh processor array with O(log L + m2) bits of space on each PE. If the local space in each PE is limited to O(log L + log m) bits, we can have an O(m2 (log L + log m) log L) implementation. We also present some experimental results of the implementation of those algorithms on the PAL computer.