Adjoint Map Representation for Shape Analysis and Matching

dc.contributor.authorHuang, Ruqien_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.editorBærentzen, Jakob Andreas and Hildebrandt, Klausen_US
dc.date.accessioned2017-07-02T17:37:54Z
dc.date.available2017-07-02T17:37:54Z
dc.date.issued2017
dc.description.abstractIn this paper, we propose to consider the adjoint operators of functional maps, and demonstrate their utility in several tasks in geometry processing. Unlike a functional map, which represents a correspondence simply using the pull-back of function values, the adjoint operator reflects both the map and its distortion with respect to given inner products. We argue that this property of adjoint operators and especially their relation to the map inverse under the choice of different inner products, can be useful in applications including bi-directional shape matching, shape exploration, and pointwise map recovery among others. In particular, in this paper, we show that the adjoint operators can be used within the cycle-consistency framework to encode and reveal the presence or lack of consistency between distortions in a collection, in a way that is complementary to the previously used purely map-based consistency measures.We also show how the adjoint can be used for matching pairs of shapes, by accounting for maps in both directions, can help in recovering point-to-point maps from their functional counterparts, and describe how it can shed light on the role of functional basis selection.en_US
dc.description.number5
dc.description.sectionheadersShape Analysis and Variation
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13253
dc.identifier.issn1467-8659
dc.identifier.pages151-163
dc.identifier.urihttps://doi.org/10.1111/cgf.13253
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13253
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.3 [Computer Graphics]
dc.subject
dc.subjectShape Analysis
dc.titleAdjoint Map Representation for Shape Analysis and Matchingen_US
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