Curvature morphology

Abstract:
The notion of curvature of planar curves has emerged as one of the most powerful for the representation and interpretation of objects in an image. Although curvature extraction from a digitized object contour would seem to be a rather simple task, few methods exist that are at the same time easy to implement, fast, and reliable in the presence of noise. In this paper we first briefly present a scheme for obtaining the discrete curvature function of planar contours based on the chain-code representation of a boundary. Secondly, we propose a method for extracting important features from the curvature function such as extrema or peaks, and segments of constant curvature. We use mathematical morphological operations on functions to achieve this. Finally, on the basis of these morphological operations, we suggest a new scale-space representation for curvature named the Morphological Curvature Scale-Space. Advantages over the usual scale-space approaches are shown.

Index terms: Shape Representation, Curvature Representation and Analysis, Morphological Operators, Multiscale Description, Multi-Dimensional Scale-Space.