In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in most previous approaches.
In this paper we develop an in-depth theoretical investigation of the discrete Hamiltonian eigenbasis, which remains quite unexplored in the geometry processing community. This choice is supported by the fact that Dirichlet eigenfunctions can be equivalently computed by defining a Hamiltonian operator, whose potential energy and localization region can be controlled with ease. We vary with continuity the potential energy and study the relationship between the Dirichlet Laplacian and the Hamiltonian eigenbases with the functional map formalism.
© Università degli Studi di Roma "La Sapienza" - Piazzale Aldo Moro 5, 00185 Roma
