Computation of 2-D Wavelet Transforms on the Connection Machine-2

An important step in image processing tasks involves the identiication of certain desired attributes in an image. Traditionally, this is done by transforming the image into a domain where the desired attributes or features are easily identiiable. In this paper, we discuss the parallel implementation of one such image transform{the 2-D Gabor based Wavelet Transform. Individual components of this transform are sensitive to particular ranges of frequencies and the orientation of features in an image. The transform is formed by computing convolutions of the image with a family of wavelets. Each member of the wavelet family is a 2-D Gabor Function. We describe how this 2-D Wavelet Transform can be computed eeciently on a ne-grained, Single Instruction, Multiple Data Stream (SIMD) computer, the Connection Machine (CM-2). The transform of a 128 128 pixel image using 40 wavelets (sensitive to diierent frequency levels and orientations of features) takes 2.43 seconds on the CM-2 as compared to 240 seconds on a Sun 4/200 and 55 seconds on a SPARCsystem 10. The gains achieved by these speed-ups are even more dramatic when hundreds of images have to be transformed (as in the Face Recognition problem 1]).