A preliminary step in image analysis is detection of edges to extract structures of interest from an image for subsequent processing. Numerous edge detection algorithms are based on convolution of the image data with one or more 2-dimensional kernels. The coefficients for these kernels are selected by analytical, heuristic, or ad hoc methods. Because convolution is a timeconsuming process, it is important that such implementations are as efficient as possible. In this paper, common 2-dimensional kernels are decomposed into basic elements to minimize their complexity and to demonstrate how they are related. Decomposition of the popular SOBEL filter kernels shows that they can be replaced by functionally identical simpler kernels. This result is significant because it proves that the SOBEL filter can be implemented with faster software or hardware than is currently possible.
In this paper we describe progress toward the development of an X-ray image analysis system for industrial inspection. Here the goal is to check part dimensions and identify geometric flaws against known tolerance specifications. From an image analysis standpoint this poses challenges to devise robust methods to extract low level features; develop deformable parameterized templates; and perform statistical tolerancing tests for geometry verification. We illustrate aspects of our current system and how knowledge of expected object geometry is used to guide the interpretation of geometry from images.
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