Near-Isometric Level Set Tracking

Implicit representations of geometry have found applications in shape modeling, simulation, and other graphics pipelines. These representations, however, do not provide information about the paths of individual points as shapes move and undergo deformation. For this reason, we reconsider the problem...

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Bibliographic Details
Published in:Computer graphics forum Vol. 35; no. 5; pp. 65 - 77
Main Authors: Tao, Michael, Solomon, Justin, Butscher, Adrian
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.08.2016
Subjects:
Algorithms
Analysis
and systems
Categories and Subject Descriptors (according to ACM CCS)
Computer graphics
Computer simulation
Deformation
Geometry
Graphical representations
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
Image processing systems
Information dissemination
languages
Mathematical analysis
Representations
Simulation
Studies
Tracking
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Implicit representations of geometry have found applications in shape modeling, simulation, and other graphics pipelines. These representations, however, do not provide information about the paths of individual points as shapes move and undergo deformation. For this reason, we reconsider the problem of tracking points on level set surfaces, with the goal of designing an algorithm that — unlike previous work — can recover rotational motion and nearly isometric deformation. We track points on level sets of a time‐varying function using approximate Killing vector fields (AKVFs), the velocity fields of near‐isometric motions. To this end, we provide suitable theoretical and discrete constructions for computing AKVFs in a narrow band surrounding an animated level set surface. Furthermore, we propose time integrators well‐suited to integrating AKVFs in time to track points. We demonstrate the theoretical and practical advantages of our proposed algorithms on synthetic and practical tasks.
Bibliography:istex:14E2DA7B6E35064AF9313082D6B6EEA817130208
ArticleID:CGF12964
Supporting Information
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SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12964