L/sub 2/ vector median filters on arrays with reconfigurable optical buses

Abstract

In spite of their good filtering characteristics for vector-valued image processing, the usability of vector median filters is limited by their high computational complexity. Given an N /spl times/ N image and a W /spl times/ W window, the computational complexity of vector median filter is O(W/sup 4/N/sup 2/). In this paper, we design three fast and efficient parallel algorithms for vector median filtering based on the 2-norm (L/sub 2/) on the arrays with reconfigurable optical buses (AROB). For 1 /spl les/ p /spl les/ W /spl les/ q /spl les/ N, our algorithms run in O(W/sup 4/ log W/p/sup 4/), O(W/sup 2/N/sup 2//p/sup 4/q/sup 2/ log W) and O(1) times using p/sup 4/N/sup 2/ / log W, p/sup 4/q/sup 2/ / log W, and W/sup 4/N/sup 2/ log N processors, respectively. In the sense of the product of time and the number of processors used, the first two results are cost optimal and the last one is time optimal.