Optimal scale selection for circular edge extraction

Abstract

This paper addresses the issue of optimal scale selection for circular edge extraction in the context of higher dimensional multiscale edge extraction. Based on a classification of higher dimensional edges according to local curvature, we exemplarily establish a 2-D circular edge model. Through a careful mathematical derivation, we transform the circular edge model from Cartesian coordinates for which the analytical solution is unknown into polar coordinates. Utilizing this edge model we develop a novel theoretical framework for optimal scale selection for circular edge extraction through which the effects of curvature as related to scale can be analyzed. Moreover, we carry out a validation study in order to investigate on the level of principal performance how well the experimental results obtained from application of the developed framework to 2-D synthetic images match the theoretical results. © Springer-Verlag Berlin Heidelberg 2003.