A Data-Driven Approach to Functional Map Construction and Bases Pursuit

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dc.contributor.authorAzencot, Omrien_US
dc.contributor.authorLai, Rongjieen_US
dc.contributor.editorDigne, Julie and Crane, Keenanen_US
dc.date.accessioned2021-07-10T07:46:18Z
dc.date.available2021-07-10T07:46:18Z
dc.date.issued2021
dc.description.abstractWe 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.en_US
dc.description.number5
dc.description.sectionheadersShape Matching
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume40
dc.identifier.doi10.1111/cgf.14360
dc.identifier.issn1467-8659
dc.identifier.pages97-110
dc.identifier.urihttps://doi.org/10.1111/cgf.14360
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14360
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectComputing methodologies
dc.subjectShape analysis
dc.titleA Data-Driven Approach to Functional Map Construction and Bases Pursuiten_US
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