This is the first year of a three-year continuing award. The research addresses recovering the 3D shape of an object from its 2D image contour. Existing 3D shape recovery algorithms tend to rely on parametric models to uniquely constrain the underlying 3D surface. Often, real-world scenes are too general to describe using parametric models. This researcher has discovered that certain non-parametric shape models allow a much greater flexibilty while at the same time providing constraints that can be used in the shape recovery process. Using planar symmetry as a model, the PI has constructed a symmetry analyzer, SYMAN, that finds axes of symmetry from contour. In addition, he has developed algorithms that use symmetry and orthogonality as object-based heuristics to constrain or recover 3D shape from image contour. With this award, the research is extended to mathematical study of the surface and projective properties of curved symmetric surfaces as well as their application to the shape recovery problem, and use of "crystallographic" methods to describe and recover shape by viewing classes of shapes with similar structure as being equivalent, so that all "octally symmetric" objects (e.g., spheres, cubes, superquadrics) might be considered equivalent.
