Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

Dan Raviv; Michael M. Bronstein; Alexander M. Bronstein; Ron Kimmel; Nir Sochen

doi:https://doi.org/10.1109/CVPR.2011.5995486

Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

Dan Raviv, Michael M. Bronstein, Alexander M. Bronstein, Ron Kimmel, Nir Sochen

Tel Aviv University, Technion - Israel Institute of Technology

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

Abstract

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

Original language	English
Title of host publication	2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011
Publisher	IEEE Computer Society
Pages	2361-2367
Number of pages	7
ISBN (Print)	9781457703942
DOIs	https://doi.org/10.1109/CVPR.2011.5995486
State	Published - 2011

Publication series

Name	Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

All Science Journal Classification (ASJC) codes

Software
Computer Vision and Pattern Recognition

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https://doi.org/10.1109/CVPR.2011.5995486

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Raviv, D., Bronstein, M. M., Bronstein, A. M., Kimmel, R., & Sochen, N. (2011). Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. In 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011 (pp. 2361-2367). Article 5995486 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). IEEE Computer Society. https://doi.org/10.1109/CVPR.2011.5995486

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title = "Affine-invariant diffusion geometry for the analysis of deformable 3D shapes",

abstract = "We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.",

author = "Dan Raviv and Bronstein, {Michael M.} and Bronstein, {Alexander M.} and Ron Kimmel and Nir Sochen",

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publisher = "IEEE Computer Society",

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Raviv, D, Bronstein, MM, Bronstein, AM , Kimmel, R & Sochen, N 2011, Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. in 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011., 5995486, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society, pp. 2361-2367. https://doi.org/10.1109/CVPR.2011.5995486

Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. / Raviv, Dan; Bronstein, Michael M.; Bronstein, Alexander M. et al.
2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011. IEEE Computer Society, 2011. p. 2361-2367 5995486 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).

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

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Raviv D, Bronstein MM, Bronstein AM , Kimmel R , Sochen N. Affine-invariant diffusion geometry for the analysis of deformable 3D shapes. In 2011 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2011. IEEE Computer Society. 2011. p. 2361-2367. 5995486. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). doi: https://doi.org/10.1109/CVPR.2011.5995486

Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

Abstract

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