Order structure, correspondence, and shape based categories

We propose a general method for finding pointwise correspondence between 2- D shapes based on the concept of order structure and using geometric hashin g. The problem of finding correspondence and the problem of establishing sh ape equivalence can be considered as one and the same problem. Given shape equivalence, we can in general find pointwise correspondence and the existe nce of a unambiguous correspondence mapping can be used as a rule for decid ing shape equivalence. As a measure of shape equivalence we will use the co ncept of order structure which in principle can be defined for arbitrary ge ometric configurations such as points lines and curves. The order structure equivalence of subsets of points and tangent directions of a shape is will be used to establish pointwise correspondence. The finding of corresponden ce between different views of the same object and different instances of th e same object category can be used as a foundation for establishment and re cognition of visual categories.