Front Propagation: A Framework for Topology Independent Shape Modeling and Recovery

mportant goal of computational vision is to recover 3hapes of objects in 2D and 3D from various types of al data. One way to achieve this goal is via model:d techniques. Broadly speaking, these techniques, ~e name suggests, involve the use of a model whose adary representation is matched to the image to rer the object of interest. These models can either be I or nonrigid. In the former case, we have what are Jlarly known as correlation-based template match.echniques, while the later involves a dynamic model lg process to the data. In this paper we present a ~1 framework for shape modeling and shape recovbased on ideas developed by Osher ~ Sethian for t (solid-liquid boundary or boundary between burnt unburnt regions) propagation. In this framework, ,es are modeled by level sets of implicit functions are evolving over time. The dynamics of evolution ~verned by front propagation equations. This dyic shape modeling scheme retains the most attracfeatures of existing methods, and overcomes some eir prominent limitations. For the rest of this paper lill use the word shape model to mean a boundary "ace) representation of an object shape. tape recovery typically precedes the symbolic repltation of surfaces and shape models are expected id the recovery of detailed structure from noisy using only the weakest of the possible assumptions it the observed shape. To this end, several variafl shape recovery methods have been proposed and ; is abundant literature on the same [2]. Generalspline models with continuity constraints are well d for fulfilling the goals of shape recovery. Genzed splines are the key ingredient of the dynamic e modeling paradigm introduced by Terzopoulos ., [13]. Following the advent of the dynamic shape eling paradigm, there was a flurry of research acy in the area, with numerous application specific ifications to the modeling primitives, and external .s derived from data constraints [4, 14]. )wever, the aforementioned schemes for shape modcling have two noticeable limitationsthe dependence of the recovered surface shape on the initial guess used to start the numerical reconstruction procedure, and an assumption that the object is of a known topology. The first of these limitations stems from the fact that the nonconvex energy functionals used in the variational formulations have multiple local minima. As a consequence of this feature, the numerical procedures, for convergence to a satisfactory solution require an initim guess which is "reasonably" close to the desired solution (shape). Also, existing shape representation schemes lack the ability to dynamically sense the topological changes that may occur in the shape of interest (e.g., cell division) over time. In this paper, we present modeling scheme that makes no assumption about the object’s topology, and leads to a numerical algorithm whose convergence to the desired shape is independent of the shape initialization as long as the initialization is either completely enclosed by the shape of interest or vice-versa. Our method can also recover shapes whose topology changes over time, e.g., the cell boundary in cell division.