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Non-rigid surface registration, particularly registration of human faces, finds a wide variety of applications in computer vision and graphics. We present a new automatic surface registration method which utilizes both attraction forces originating from geometrical and textural similarities, and stresses due to non-linear elasticity of the surfaces. Reference and target surfaces are first mapped onto their feature image planes, then these images are registered by subjecting them to local deformations, and finally 3D correspondences are established. Surfaces are assumed to be elastic sheets and are represented by triangular meshes. The internal elastic forces act as a regularizer in this ill-posed problem. Furthermore, the non-linear elasticity model allows us to handle large deformations, which can be essential, for instance, for facial expressions. The method has been tested successfully on 3D scanned human faces, with and without expressions. The algorithm runs quite efficiently using a multiresolution approach.