Folding spatial image filters on the CM-5

This paper presents an eecient data-parallel algorithm for general convolutions, and compares its performance on the CM-5 to FFT frequency ltering. Sequential FFT lters are faster than sequential convo-lutions for windows beyond a very small size, typically 6 6 pixels. Our folded convolution algorithm shifts the convolution/FFT performance crossover to much larger lter sizes. For 256256 images on a 512 node CM-5, the folded convolution is faster than FFT lter-ing up to 36 36 windows. Results are reported for a naively implemented convolution, our folded convolu-tion with default and optimized memory layouts, and FFT ltering using FFTs from the CM-5 scientiic library (CMSSL). The data yield two important results: 1. Parallel convolutions on the CM-5 are faster than FFT ltering for a substantial and important range of window sizes. This is in contrast to sequential systems, where convolutions are more ef-cient only for very small windows. 2. Considerable performance gains are realized by folding the convolution and optimizing layout.