Informative Descriptor Preservation via Commutativity for Shape Matching

dc.contributor.authorNogneng, Dorianen_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorLoic Barthe and Bedrich Benesen_US
dc.date.accessioned2017-04-22T16:26:36Z
dc.date.available2017-04-22T16:26:36Z
dc.date.issued2017
dc.description.abstractWe consider the problem of non-rigid shape matching, and specifically the functional maps framework that was recently proposed to find correspondences between shapes. A key step in this framework is to formulate descriptor preservation constraints that help to encode the information (e.g., geometric or appearance) that must be preserved by the unknown map. In this paper, we show that considering descriptors as linear operators acting on functions through multiplication, rather than as simple scalar-valued signals, allows to extract significantly more information from a given descriptor and ultimately results in a more accurate functional map estimation. Namely, we show that descriptor preservation constraints can be formulated via commutativity with respect to the unknown map, which can be conveniently encoded by considering relations between matrices in the discrete setting. As a result, when the vector space spanned by the descriptors has a dimension smaller than that of the reduced basis, our optimization may still provide a fully-constrained system leading to accurate point-to-point correspondences, while previous methods might not. We demonstrate on a wide variety of experiments that our approach leads to significant improvement for functional map estimation by helping to reduce the number of necessary descriptor constraints by an order of magnitude, even given an increase in the size of the reduced basis.en_US
dc.description.number2
dc.description.sectionheadersShape Matching
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13124
dc.identifier.issn1467-8659
dc.identifier.pages259-267
dc.identifier.urihttps://doi.org/10.1111/cgf.13124
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13124
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]
dc.subjectComputational Geometry and Object Modeling
dc.subject[Geometric algorithms
dc.subjectlanguages
dc.subjectand systems]
dc.titleInformative Descriptor Preservation via Commutativity for Shape Matchingen_US
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