We consider the problem of creating a map between two arbitrary triangle meshes. Whereas previous approaches compose parametrizations over a simpler intermediate domain, we directly create and optimize a continuous map between the meshes. Map distortion is measured with a new symmetric metric, and is minimized during interleaved coarse-to-fine refinement of both meshes. By explicitly favoring low inter-surface distortion, we obtain maps that naturally align corresponding shape elements. Typically, the user need only specify a handful of feature correspondences for initial registration, and even these constraints can be removed during optimization. Our method robustly satisfies hard constraints if desired. Inter-surface mapping is shown using geometric and attribute morphs. Our general framework can also be applied to parametrize surfaces onto simplicial domains, such as coarse meshes (for semi-regular remeshing), and octahedron and toroidal domains (for geometry image remeshing). In these settings, we obtain better parametrizations than with previous specialized techniques, thanks to our fine-grain optimization.

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Abstract.Many applications benefit from surface parameterization, including texture mapping, morphing, remeshing, compression, object recognition, and detail transfer, because processing is easier on the domain than on the original irregular mesh. We present a method for simultaneously parameterizing several genus-0 meshes possibly with boundaries onto a common spherical domain, while ensuring that corresponding user-highlighted features on each of the meshes map to the same domain locations. We obtain visually smooth parameterizations without any cuts, and the constraints enable us to directly associate semantically important features such as animal limbs or facial detail. Our method is robust and works well with either sparse or dense sets of constraints.