Parallel Computation Of 2-D Wavelet Transform For Image Processing And Computer `vision

The wavelet multiresolution representation warrants a hierarchical approach to image processing and computer vision that can be made parallel in both pixels and scales. To start we need to generate the midtiresolution representation on the network of processing elements, which should be done as fast as the information can be further processed. We present two parallelized versions of the Mallat algorithm [l] for t8he 2-D orthogonal wavelet transform on mesh and pyramid networks, and experimental results for both algorithms implemented on the Connection Machine. The mesh algorithm adopts a strategy similar to Maresca and Li's Snake Sweeping [2] to superimpose image sub-frames which are contributions associated with individual filter coefficients in the 2-D convolution. This approach is appealing because the computational time of the 2-D convolution can be made a constant independent of the image size if sufficient number of processors are given, which behaves like the human visual system in the low-level processing. Special treatments are designed io accommodate the data symmetry assumption and take advantage of filter symmetries. The mesh algorithm has a time complexity of O ( K L + ZogN IT2) compared to O ( N z K L ) of Mallat's fast sequential algorithm for a IC-scale orthogonal wavelet transform of an A' x N image with a filter of length L. In the case of small-sized filters, the mesh algorithm is communicationdominant. The pyramid algorithm better solves the inter-scale communications and has a time complexity of O ( K L ) ! , which is independent of the ima ge size. Both algorithms have been iinplemented on the Connection Machine and experiments have been done for image sizes from 8x8 to 1024x1024 with 8K and 16K physical processors. The experimental results produced by the Connection Machine agree with the estimated complexities. When the virtual processor(VP) ratio [3] is below 1, the run time of parallel programs is almost constant ancl independent of the image sizle. The superiority of the pyramid algorithm over the mesh algorithm can be clearly seen only when the smallsized filters are used. In such a aituation the run time of the pyramid algorithm remains constant while the run time of t:he mesh algorithm slightly goes up with the image size. For a standard image size of 256x256, the actual speed of paralllel programs executed on the Connection Machine with 8K or 16K physical processors is over 1000 times faster than that of a sequential program executed on an IBM RT workstation.