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We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.
Isometric embedding, minimum-distortion mapping, generalized multidimensional scaling, correspondence problem, texture mapping, face animation, expression exaggeration, morphing, virtual dressing, virtual body painting, calculus of surfaces

A. Bronstein, R. Kimmel and M. Bronstein, "Calculus of Nonrigid Surfaces for Geometry and Texture Manipulation," in IEEE Transactions on Visualization & Computer Graphics, vol. 13, no. , pp. 902-913, 2007.
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