Supplementary Material: Articulation-aware Canonical Surface Mapping


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Parameterizing surface of a mesh. The surface S of a mesh is 2D manifold in 3D space hence we can construct a mapping φ : [0, 1) − → S. We deal with triangular meshes as they are the most general form of mesh representation. Given the mapping from 2D square to a spherical mesh and another from the sphere to our template shape, our mapping from 2D manifold to the template shape is their composition. Constructing a mapping between 2D square and sphere can be understood to one analogous to latitudes and longitudes on the globe. All our template shapes are genus-0 (isomorphic to a sphere – without holes). They have been pre-processed to have 642 vertices and 1280 faces using Meshlab’s [1] quadratic vertex decimation [3]. Constructing a mapping between a sphere and a template shape corresponds to finding a mapping between faces of the spherical mesh and the faces of the template shape. To find such a mapping we need to deform the sphere to ensure that the corresponding faces have similar areas. We to do this by minimizing the squared difference of logarithm of triangle areas as the objective using Adam [7] optimizer. This optimization is an offline process and is part of preprocessing for the given category.
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