L_2 Vector Median Filters on Arrays with Reconfigurable Optical Buses

• Authors: Chin-Hsiung Wu;Shi-Jinn Horng
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 2001

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\times N image and a W\times W window, the computational complexity of vector median filter is O(W^{4} N^{2}). In this paper, we design three fast and efficient parallel algorithms for vector median filtering based on the 2\hbox{-}{\rm{norm}} (L_2) on the arrays with reconfigurable optical buses (AROB). For 1\leq p\leq W\leq q \leq N, our algorithms run in O(W^{4}\log W/p^{4}), O({\frac{W^{4}N^{2}}{p^{4}q^{2}}}\log W) and O(1) times using p^{4}N^{2}/\log W, p^{4}q^{2}/\log W, and W^{4}N^{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.