[1] N. Litke, M. Droske, M. Rumpf, and P. Schröder. An image processing approach to surface matching. In Proc. of Eurographics Symposium on Geometry Processing, pages 207-216, 2005.
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Establishing a correspondence between two surfaces is a basic ingredient in many geometry processing applications. Existing approaches, which attempt to match two embedded meshes directly, can be cumbersome to implement and it is often hard to produce accurate results in reasonable time. In this paper, we present a new variational method for matching surfaces that addresses these issues. Instead of matching two surfaces via a non-rigid deformation directly in R3, we apply well established matching methods from image processing in the parameter domains of the surfaces. A matching energy is introduced which may depend on curvature, feature demarcations or surface textures, and a regularization energy controls length and area changes in the induced deformation between the two surfaces. The metric on both surfaces is properly incorporated into the formulation of the energy. This approach reduces all computations to the 2D setting while accounting for the original geometries. Consequently a fast multiresolution numerical algorithm for regular image grids can be applied to solve the global optimization problem. The final algorithm is robust, generically much simpler than direct matching methods, and computationally very fast for highly resolved triangle meshes.