TY - UNPB
T1 - Shape Analysis via Functional Map Construction and Bases Pursuit
AU - Azencot, Omri
AU - Lai, Rongjie
N1 - 12 pages, 16 figures
PY - 2019
Y1 - 2019
N2 - We 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 spectrum that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem which we exploit to improve the accuracy of our computed correspondences. 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.
AB - We 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 spectrum that allows for better feature matching. This change of perspective introduces many degrees of freedom into the problem which we exploit to improve the accuracy of our computed correspondences. 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.
KW - cs.GR
M3 - Preprint
BT - Shape Analysis via Functional Map Construction and Bases Pursuit
ER -