Correspondence is a very fundamental notion in computer vision and related fields. Given two objects, a correspondence is a mapping from any point on one object to the "corresponding" point on the other object. For images, correspondence falls under the names optical flow, mosaicing, registration, and disparity.
Correspondence can also be found for other classes of objects. The main purpose behind this work is to find correspondences between two three-dimensional surfaces (by this I mean a 2D surface embedded in R3). However, the work is general to surface of any dimension embedded in any Euclidean space.
We seek such correspondences in order to build morphable models of a class of objects. Such models allow synthesis, analysis, and constraints on other objects of the same class.