A ne Invariant Deformation Curves CONTENTSContents

A ne Invariant Deformation Curves A Tool for Shape Characterization Rein van den Boomgaard Dept. of Computer Science University of Amsterdam The Netherlands In this paper we describe a combination of two well-known concepts: morphological deformation curves and a ne invariant evolution processes. A morphological deformation curve is a shape descriptor obtained by continuously deforming the shape and in the meantime measuring some geometric parameter. This measurement as a function of the deformation provides a characterization of the shape that can be used for shape classi cation and recognition. In classical morphology the deformation process is taken to be a morphological operator (erosions, dilations and combinations thereof). Most of the morphological operators are only invariant under the Euclidean symmetry group (translation and rotation) and (relative) invariant under isotropic rescalings. Only recently in the context of computer vision, an a ne invariant shape deformation process has been identi ed. When we measure the area of the object while it is deformed in this way we obtain a function that provides a characterization of a shape in an a ne invariant way. In this paper an a ne invariant deformation curve is introduced and its application for shape and texture characterization is illustrated.