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This research was conducted to obtain better methods for image processing. It focused on several aspects of this problem, including parallel algorithms for image processing, knowledge-based techniques for image understanding, and modeling images using shape and texture. Eighteen technical reports were produced which will also appear as published papers in journals. In the paper Holes and Genus of 3D images, it was shown that certain geometric invariants of a digital image (number of components, number of holes, and number of cavities) do not determine the topology (in the sense of connectivity) of the image refuting the commonly believed assumption that they do. This research lays the groundwork for research on digital and computational geometry of 3D images. In the paper Hough Transform Algorithms for Mesh-Connected for Mesh-Connected SIMD Parallel Processors, several methods of Hough transform computation are studied in terms of suitability for implementation on a parallel processor, providing a valuable tool for straight-line detection.