Show simple item record

dc.contributor.authorRen, Jing
dc.contributor.authorPanine, Mikhail
dc.contributor.authorWonka, Peter
dc.contributor.authorOvsjanikov, Maks
dc.date.accessioned2019-08-21T08:23:17Z
dc.date.available2019-08-21T08:23:17Z
dc.date.issued2019-08-12
dc.identifier.citationRen, J., Panine, M., Wonka, P., & Ovsjanikov, M. (2019). Structured Regularization of Functional Map Computations. Computer Graphics Forum, 38(5), 39–53. doi:10.1111/cgf.13788
dc.identifier.doi10.1111/cgf.13788
dc.identifier.urihttp://hdl.handle.net/10754/656562
dc.description.abstractWe consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to commute with the Laplace-Beltrami operators on the source and target shapes. We show that this approach has certain undesirable fundamental theoretical limitations, and can be undefined even for trivial maps in the smooth setting. Instead we propose a novel, theoretically well-justified approach for regularizing functional maps, by using the notion of the resolvent of the Laplacian operator. In addition, we provide a natural one-parameter family of regularizers, that can be easily tuned depending on the expected approximate isometry of the input shape pair. We show on a wide range of shape correspondence scenarios that our novel regularization leads to an improvement in the quality of the estimated functional, and ultimately pointwise correspondences before and after commonly-used refinement techniques.
dc.description.sponsorshipThe authors would like to thank the anonymous reviewers for their valuable comments and helpful suggestions. Parts of this work were supported by the KAUST OSR Awards No. CRG2017-3426 and CRG2018-3730, a gift from the NVIDIA Corporation, and the ERC Starting Grant No. 758800 (EXPROTEA).
dc.publisherWiley
dc.relation.urlhttps://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13788
dc.rightsArchived with thanks to Computer Graphics Forum
dc.subjectCCS Concepts
dc.subjectComputing methodologies → Shape analysis
dc.titleStructured Regularization of Functional Map Computations
dc.typeArticle
dc.contributor.departmentComputer Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalComputer Graphics Forum
dc.rights.embargodate2020-08-12
dc.eprint.versionPost-print
dc.contributor.institutionLIX, École Polytechnique, CNRS
dc.identifier.arxivid2009.14624
kaust.personRen, Jing
kaust.personWonka, Peter
kaust.grant.numberCRG2017
kaust.grant.numberCRG2018-3730
refterms.dateFOA2019-08-21T12:49:05Z
kaust.acknowledged.supportUnitOSR
dc.date.published-online2019-08-12
dc.date.published-print2019-08


Files in this item

Thumbnail
Name:
SGP19_Structured_Regularization_fMap.pdf
Size:
23.47Mb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record