Growth Guided Shape Recovery

A central problem in computer vision is to detect, delineate (segment) and recognize objects in an image. One reason why this is diicult is that very little information speciic to given types of objects is used during segmentation. Making use of information about an object's shape, for example, should facilitate and improve the segmentation of that object. This paper introduces a 2D discrete growth model for shape from a point on a Cartesian grid, based on notions related to biological growth. By \growth" is meant an accretionary process occurring at the boundary of the shape. We discuss two types of growth models: probabilistic models and deterministic (periodic) models. A probabilistic model on the Cartesian grid, which associates probabilities of growth with each of the eight directions, is considered. While such models empirically have been shown to describe many natural growth phenomena, complete quantitative characterizations do not yet exist. We introduce a new type of deterministic growth model based on the notion of \time delay". Associating a delay with each direction deenes a time delay kernel (TDK); we show that such kernels produce classes of convex octagons, and that sequences of TDKs can give rise to arbitrary convex polygons. We introduce an environment consisting of promoters and inhibitors that facilitate and impede growth, respectively. We investigate several types of nonhomogeneous environments, and show their eeects on kernel-based growth. We also show that TDK-based growth in an environment can model the gross morphology of multiple sclerosis lesions in magnetic resonance images (MRI).