This paper describes the problem of three-dimensional object correspondence and presents an algorithm for matching two three-dimensional colored surfaces using polygon reduction and the minimization of an energy function. At the core of this algorithm is a novel data-dependent multi-resolution pyramid for polygonal surfaces. The algorithm is general to correspondence between any two manifolds of the same dimension embedded in a higher dimensional space. Results demonstrating correspondences between various objects are presented and a method for incorporating user input is also detailed.