Invariant Signatures for Planar Shape Recognition under Partial Occlusion

Abstract

A planar shape distorted by a projective viewing transformation can be recognized under partial occlusion if an invariant description of its boundary is available. Invariant boundary descriptions should be based solely on the local properties of the boundary curve, perhaps relying on further information on the viewing transformation. Recent research in this area has provided a theory for invariant boundary descriptions based on an interplay of differential, local, and global invariants. Differential invariants require high-order derivatives. However, the use of global invariances and point match information on the distorting transformations enables the derivation of invariant signatures for planar shapes using lower order derivatives. Trade-offs between the highest order derivatives required and the quantity of additional information constraining the distorting viewing transformations are made explicit. Once an invariant is established, recognition of the equivalence of two objects requires only partial function matching. Uses of these invariants include the identification of planar surfaces in varying orientations and resolving the outline of a cluster for planar objects into individual components.