Adjoint Map Representation for Shape Analysis and Matching

In 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...

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Vydané v:Computer graphics forum Ročník 36; číslo 5; s. 151 - 163
Hlavní autori: Huang, Ruqi, Ovsjanikov, Maks
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.08.2017
Wiley
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Categories and Subject Descriptors (according to ACM CCS)
Computer Science
Computer Vision and Pattern Recognition
Consistency
Distortion
I.3.3 [Computer Graphics]: —Shape Analysis
Matching
Operators
Shape recognition
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí:In 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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13253