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We summarize recent work by the author and his colleagues aimed at generating rich representations of shape for two and three-dimensional objects. An implementation of the smoothed local symmetries representation of 2D shapes is described and its use for inspection and the recognition of occluded objects sketched. The implementation uses an edge finder developed by Canny that is optimal in a precisely defined sense. The curvature patch representation of 3D shape is based on ideas of differential geometry.