Multiscale Spectral Manifold Wavelet Regularizer for Unsupervised Deep Functional Maps

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dc.contributor.authorWang, Haiboen_US
dc.contributor.authorMeng, Jingen_US
dc.contributor.authorLi, Qinsongen_US
dc.contributor.authorHu, Lingen_US
dc.contributor.authorGuo, Yueyuen_US
dc.contributor.authorLiu, Xinruen_US
dc.contributor.authorYang, Xiaoxiaen_US
dc.contributor.authorLiu, Shengjunen_US
dc.contributor.editorChen, Renjieen_US
dc.contributor.editorRitschel, Tobiasen_US
dc.contributor.editorWhiting, Emilyen_US
dc.date.accessioned2024-10-13T18:08:33Z
dc.date.available2024-10-13T18:08:33Z
dc.date.issued2024
dc.description.abstractIn deep functional maps, the regularizer computing the functional map is especially crucial for ensuring the global consistency of the computed pointwise map. As the regularizers integrated into deep learning should be differentiable, it is not trivial to incorporate informative axiomatic structural constraints into the deep functional map, such as the orientation-preserving term. Although commonly used regularizers include the Laplacian-commutativity term and the resolvent Laplacian commutativity term, these are limited to single-scale analysis for capturing geometric information. To this end, we propose a novel and theoretically well-justified regularizer commuting the functional map with the multiscale spectral manifold wavelet operator. This regularizer enhances the isometric constraints of the functional map and is conducive to providing it with better structural properties with multiscale analysis. Furthermore, we design an unsupervised deep functional map with the regularizer in a fully differentiable way. The quantitative and qualitative comparisons with several existing techniques on the (near-)isometric and non-isometric datasets show our method's superior accuracy and generalization capabilities. Additionally, we illustrate that our regularizer can be easily inserted into other functional map methods and improve their accuracy.en_US
dc.description.number7
dc.description.sectionheadersGeometric Processing II
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume43
dc.identifier.doi10.1111/cgf.15230
dc.identifier.issn1467-8659
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.15230
dc.identifier.urihttps://diglib.eg.org/handle/10.1111/cgf15230
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Computing methodologies → Shape analysis; Theory of computation → Computational geometry
dc.subjectComputing methodologies → Shape analysis
dc.subjectTheory of computation → Computational geometry
dc.titleMultiscale Spectral Manifold Wavelet Regularizer for Unsupervised Deep Functional Mapsen_US
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