Correspondence between n-dimensional surface: vector fields that are defined by surfaces and that generate surfaces which preserve characteristics of the defining surfaces

Abstract

Techniques for finding a correspondence between a source object and a target object, the objects having n>2 dimensions, such that a vector field based on the correspondence generates objects which tend to preserve the characteristics of both the source object and the target object. The techniques result in vector fields which maximize the generated object's similarity to the target object while minimizing structural changes to the source object. Minimization of structural changes is done by associating directional spring functions with points in the source object and finding a vector which generates an object for which changes in the directional spring functions are minimized. Further included are techniques for reducing the computational cost of finding a correspondence by making a set of pairs of increasingly-simplified representations of the source object and the target object and then finding pair vector fields for the pairs, beginning with the most simplified pair and ending with the original representations of the source object and the target object. The increasingly-simplified representations have the property that they preserve the large-scale structure of the original representations of the source object and the target object. The pair vector field for a given pair is found by extending the pair vector field found for the next simpler pair so that it applies to the pair's source object and then using the extended pair vector field as the initial vector field in finding the pair vector field. The techniques may be applied to images and to surfaces in which color is represented by means of additional dimensions. Vector fields found using the techniques may be used to generate objects belonging to a class of objects defined by the source object and at least the target object.