A reflective symmetry descriptor

Michael Kazhdan; Bernard Chazelle; David Dobkin; Adam Finkelstein; Thomas Funkhouser

doi:10.1007/3-540-47967-8_43

A reflective symmetry descriptor

Michael Kazhdan, Bernard Chazelle, David Dobkin, Adam Finkelstein, Thomas Funkhouser

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

95 Scopus citations

Abstract

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N⁴ logN) time for an N × N × N voxel grid, and computes a multiresolution approximation in O(N³ logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.

Original language	English (US)
Title of host publication	Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings
Editors	Anders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen
Publisher	Springer Verlag
Pages	642-656
Number of pages	15
ISBN (Print)	9783540437444
DOIs	https://doi.org/10.1007/3-540-47967-8_43
State	Published - 2002
Event	7th European Conference on Computer Vision, ECCV 2002 - Copenhagen, Denmark Duration: May 28 2002 → May 31 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2351
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th European Conference on Computer Vision, ECCV 2002
Country/Territory	Denmark
City	Copenhagen
Period	5/28/02 → 5/31/02

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-47967-8_43

Cite this

Kazhdan, M., Chazelle, B., Dobkin, D., Finkelstein, A., & Funkhouser, T. (2002). A reflective symmetry descriptor. In A. Heyden, G. Sparr, M. Nielsen, & P. Johansen (Eds.), Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings (pp. 642-656). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2351). Springer Verlag. https://doi.org/10.1007/3-540-47967-8_43

Kazhdan, Michael ; Chazelle, Bernard ; Dobkin, David et al. / A reflective symmetry descriptor. Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. editor / Anders Heyden ; Gunnar Sparr ; Mads Nielsen ; Peter Johansen. Springer Verlag, 2002. pp. 642-656 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model{\textquoteright}s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N4 logN) time for an N × N × N voxel grid, and computes a multiresolution approximation in O(N3 logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.",

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Kazhdan, M, Chazelle, B, Dobkin, D, Finkelstein, A & Funkhouser, T 2002, A reflective symmetry descriptor. in A Heyden, G Sparr, M Nielsen & P Johansen (eds), Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2351, Springer Verlag, pp. 642-656, 7th European Conference on Computer Vision, ECCV 2002, Copenhagen, Denmark, 5/28/02. https://doi.org/10.1007/3-540-47967-8_43

A reflective symmetry descriptor. / Kazhdan, Michael; Chazelle, Bernard; Dobkin, David et al.
Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. ed. / Anders Heyden; Gunnar Sparr; Mads Nielsen; Peter Johansen. Springer Verlag, 2002. p. 642-656 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2351).

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

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T1 - A reflective symmetry descriptor

AU - Kazhdan, Michael

AU - Chazelle, Bernard

AU - Dobkin, David

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AU - Funkhouser, Thomas

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N4 logN) time for an N × N × N voxel grid, and computes a multiresolution approximation in O(N3 logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.

AB - Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N4 logN) time for an N × N × N voxel grid, and computes a multiresolution approximation in O(N3 logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Kazhdan M, Chazelle B, Dobkin D, Finkelstein A, Funkhouser T. A reflective symmetry descriptor. In Heyden A, Sparr G, Nielsen M, Johansen P, editors, Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. Springer Verlag. 2002. p. 642-656. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-47967-8_43

A reflective symmetry descriptor

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