Constructing Implicit Shape Models from Boundary Data

Abstract We develop a method to construct an implicit shape model that approximates a solid object from its characteristic function. The method is based on multiresolution edge detection and reconstruction using dyadic wavelets. It synthesizes edges at multiple resolutions such that the reconstructed function preserves the shape boundary, and the gradient of the function gives the normal vector field at the boundary. Several examples and applications of the procedure are given. One of the applications consists of the procedure of obtaining a rough estimate of the tubular neighborhood of a shape. We also apply this procedure to obtain an approximate, but accurate, conversion from a parametric to an implicit surface.