Azencot, OmriLai, RongjieDigne, Julie and Crane, Keenan2021-07-102021-07-1020211467-8659https://doi.org/10.1111/cgf.14360https://diglib.eg.org:443/handle/10.1111/cgf14360We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace-Beltrami operator and thus favor low-frequency eigenfunctions, we aim for a basis that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem allowing to better exploit non-smooth descriptors. To effectively search in this high-dimensional space of solutions, we incorporate into our minimization state-of-the-art regularizers. We solve the resulting highly non-linear and non-convex problem using an iterative scheme via the Alternating Direction Method of Multipliers. At each step, our optimization involves simple to solve linear or Sylvester-type equations. In practice, our method performs well in terms of convergence, and we additionally show that it is similar to a provably convergent problem. We show the advantages of our approach by extensively testing it on multiple datasets in a few applications including shape matching, consistent quadrangulation and scalar function transfer.Computing methodologiesShape analysis10.1111/cgf.1436097-110