Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects

We introduce techniques for the processing of motion and animations of non‐rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in ℝn to the processing of motion o...

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Vydáno v:Computer graphics forum Ročník 35; číslo 2; s. 295 - 305
Hlavní autoři: Brandt, Christopher, von Tycowicz, Christoph, Hildebrandt, Klaus
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.05.2016
Témata:
Algorithms
Analysis
Animation
Categories and Subject Descriptors (according to ACM CCS)
Computation
Computer animation
Curves (geometry)
Deformation
Formability
Geodesy
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Physically based modeling
Image processing systems
Smoothing
Studies
ISSN:0167-7055, 1467-8659
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Popis
Shrnutí:We introduce techniques for the processing of motion and animations of non‐rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in ℝn to the processing of motion of non‐rigid shapes. Following this principle, we introduce a discrete geometric flow for curves in shape space. The flow iteratively replaces every shape with a weighted average shape of a local neighborhood and thereby globally decreases an energy whose minimizers are discrete geodesics in shape space. Based on the flow, we devise a novel smoothing filter for motions and animations of deformable shapes. By shortening the length in shape space of an animation, it systematically regularizes the deformations between consecutive frames of the animation. The scheme can be used for smoothing and noise removal, e.g., for reducing jittering artifacts in motion capture data. We introduce a reduced‐order method for the computation of the flow. In addition to being efficient for the smoothing of curves, it is a novel scheme for computing geodesics in shape space. We use the scheme to construct non‐linear “Bézier curves” by executing de Casteljau's algorithm in shape space.
Bibliografie:ark:/67375/WNG-W2161KMG-D
istex:BECFF88764CA89601CE2D3A25B125BAFB26128E3
ArticleID:CGF12832
Supporting Information
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12832