A scale-space approach to shape similarity

In this paper we develop a definition of "shape similarity" applied to contours and 2D shapes. The similarity is established within a particular scale-space whose characteristics are determined by the shapes themselves. The fundamental principle is that two contours or 2D shapes are similar at a given scale if they can give rise to identical area sampled images at the given scale with respect to a given sampling regime. The usefulness of the concept is that it can be used to build a formal theory of shape simplification, based on migration of the shape through the induced scale-space, to assist object recognition.