Isometric Multi-Shape Matching

Figure 1 . Left: We present a novel approach for isometric multi-shape matching based on matching each shape to a (virtual) universe shape (shown semi-transparent). Our formulation represents point-to-point correspondences between shapes i and j as the composition of the shape-to-universe permutation matrix Pi and the universe-to-shape permutation matrix P T j . By doing so, the pairwise matchings Pij = PiP ⊤ j are by construction cycle-consistent. Middle: Our formulation successfully solves isometric multi-matching of partial shapes. Right: Due to the cycle-consistency we can use our correspondences to faithfully transfer textures across a shape collection.