On characterizing ribbons and finding skewed symmetries

Abstract

Following Rosenfeld, we compare Blum, Brooks, and Brady ribbons. We prove that Blum and Brady ribbons are not, in general, Brooks ribbons. Conversely, we prove that Brooks ribbons are, in general, neither Blum nor Brady ribbons. For Blum and Brady 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. It is possible to characterize locally the pairs of contour points which form a Brooks ribbon pair? Using the curvature of the contour of a Brooks ribbon, we show that the answer to this question is yes 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.