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A wavelet function generated by a specially constructed symmetric scale function has been explored for use in edge detection. Experiments showed that relatively refined edge information was obtained in the coarse resolution levels. An edge detection algorithm based on regularization with space-varying parameters has been developed, where the values of the parameters are adaptively determined iteratively. A multiscale edge detection algorithm using a first order regularization filter has been developed. It is demonstrated experimentally that the high localization performance of the filter is combined with high detection performance by using a multiscale integration scheme. Time performances have been evaluated for different embeddings of the wavelet coefficients into two dimensional meshes over typical wavelet based algorithms. Parallel image processing algorithms are under study to identify fundamental parallel limits and to enable fully their parallel application in multiresolution application. Novel graph compounds which can be utilized to enhance communication bandwidth in mesh architectures have been evaluated and appear to offer some promise in image processing.