Symmetrization

Niloy J. Mitra; Leonidas J. Guibas; Mark Pauly

doi:10.1145/1275808.1276456

Symmetrization

Niloy J. Mitra^*, Leonidas J. Guibas, Mark Pauly

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.

Original language	English (US)
Title of host publication	Proceedings of ACM SIGGRAPH 2007
DOIs	https://doi.org/10.1145/1275808.1276456
State	Published - 2007
Externally published	Yes
Event	34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics - San Diego, CA, United States Duration: Aug 5 2007 → Aug 9 2007

Other

Other	34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics
Country/Territory	United States
City	San Diego, CA
Period	08/5/07 → 08/9/07

Keywords

Correspondence
Matching
Shape analysis
Shape optimization
Symmetry

ASJC Scopus subject areas

General Computer Science

Access to Document

10.1145/1275808.1276456

Cite this

@inproceedings{79b63d6c824849febefd7e81e029e1d8,

title = "Symmetrization",

abstract = "We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.",

keywords = "Correspondence, Matching, Shape analysis, Shape optimization, Symmetry",

author = "Mitra, {Niloy J.} and Guibas, {Leonidas J.} and Mark Pauly",

year = "2007",

doi = "10.1145/1275808.1276456",

language = "English (US)",

booktitle = "Proceedings of ACM SIGGRAPH 2007",

note = "34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics ; Conference date: 05-08-2007 Through 09-08-2007",

}

TY - GEN

T1 - Symmetrization

AU - Mitra, Niloy J.

AU - Guibas, Leonidas J.

AU - Pauly, Mark

PY - 2007

Y1 - 2007

N2 - We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.

AB - We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.

KW - Correspondence

KW - Matching

KW - Shape analysis

KW - Shape optimization

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=36948998773&partnerID=8YFLogxK

U2 - 10.1145/1275808.1276456

DO - 10.1145/1275808.1276456

M3 - Conference contribution

BT - Proceedings of ACM SIGGRAPH 2007

T2 - 34th Annual Meeting of the Association for Computing Machinery's Special Interest Group on Graphics

Y2 - 5 August 2007 through 9 August 2007

ER -

Symmetrization

Abstract

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Keywords

ASJC Scopus subject areas

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