On characterizing ribbons and finding skewed symmetries

The author compares Blum, Brooks, and Brady ribbons, and proves that Blum and Brady ribbons are not, in general, Brooks ribbons. Conversely, he proves that Brook ribbons are, in general, neither Blum nor Brady ribbons. For Blum and Brooks ribbons, it is in principle trivial to decide whether two contour points may form a ribbon pair; they have to form a local symmetry. This property is not true for Brooks ribbons. Attention is also given to whether it is possible to characterize locally the pairs of contour points which form a Brooks ribbon pair. Using the curvature of a Brooks ribbon, it is shown that this is possible for some classes of Brooks ribbons, including skewed symmetries. This result is used in an implemented algorithm for finding skewed symmetries in an image, and examples of segmentation of real images are given