Fast 8-Bit Median Filtering Based on Separability

We present a fast 8-bit median filter implementation based on a separability argument. Our strategy is to start with a naive separable implementation of the median filter which displays O(1) time complexity per pixel, and then optimize this implementation to reduce the time constant. The optimizations that we employ include (a) lowering the histogram memory requirements by using unsigned shorts or bytes as histogram elements, (b) consolidating operations by performing multiple short additions with a single integer addition, (c) employing SSE instructions to further speed up the histogram updates, and (d) updating only the part of the histogram that contains the median. We show that by employing these rather straightforward optimizations, we can achieve filter speeds that approach the performance of the fastest proprietary median filters currently in use.