A shape representation for computer vision based on differential topology

We describe a shape representation for use in computer vision, after a brief review of shape representation and object recognition in general. Our shape representation is based on graph structures derived from level sets whose characteristics are understood from differential topology, particularly singularity theory. This leads to a representation which is both stable and whose changes under deformation are simple. The latter allows smoothing in the representation domain (‘symbolic smoothing’), which in turn can be used for coarse-to-fine strategies, or as a discrete analog of scale space. Essentially the same representation applies to an object embedded in 3-dimensional space as to one in the plane, and likewise for a 3D object and its silhouette. We suggest how this can be used for recognition.