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Curvature-aware regularization on Riemannian submanifolds

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

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Curvature-aware regularization on Riemannian submanifolds. / Kim, Kwang In; Tompkin, James; Theobalt, Christian.

Proc. International Conference on Computer Vision (ICCV) 2013. 2013. p. 881-888.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

Harvard

Kim, KI, Tompkin, J & Theobalt, C 2013, Curvature-aware regularization on Riemannian submanifolds. in Proc. International Conference on Computer Vision (ICCV) 2013. pp. 881-888.

APA

Kim, K. I., Tompkin, J., & Theobalt, C. (2013). Curvature-aware regularization on Riemannian submanifolds. In Proc. International Conference on Computer Vision (ICCV) 2013 (pp. 881-888)

Vancouver

Kim KI, Tompkin J, Theobalt C. Curvature-aware regularization on Riemannian submanifolds. In Proc. International Conference on Computer Vision (ICCV) 2013. 2013. p. 881-888

Author

Kim, Kwang In ; Tompkin, James ; Theobalt, Christian. / Curvature-aware regularization on Riemannian submanifolds. Proc. International Conference on Computer Vision (ICCV) 2013. 2013. pp. 881-888

Bibtex

@inbook{d1f3b15cbd434bee96e6691f65cfb485,
title = "Curvature-aware regularization on Riemannian submanifolds",
abstract = "One fundamental assumption in object recognition as well as in other computer vision and pattern recognition problems is that the data generation process lies on a manifold and that it respects the intrinsic geometry of the manifold.This assumption is held in several successful algorithms for diffusion and regularization, in particular, in graph-Laplacian-based algorithms. We claim that the performance of existing algorithms can be improved if we additionallyaccount for how the manifold is embedded within the ambient space, i.e., if we consider the extrinsic geometry of the manifold. We present a procedure for characterizing the extrinsic (as well as intrinsic) curvature of a manifold M which is described by a sampled point cloud in a high-dimensional Euclidean space. Once estimated, we use this characterization in general diffusion and regularization on M, and form a new regularizer on a point cloud. The resulting re-weighted graph Laplacian demonstrates superior performance over classical graph Laplacian in semi supervised learning and spectral clustering.",
author = "Kim, {Kwang In} and James Tompkin and Christian Theobalt",
year = "2013",
language = "English",
pages = "881--888",
booktitle = "Proc. International Conference on Computer Vision (ICCV) 2013",

}

RIS

TY - CHAP

T1 - Curvature-aware regularization on Riemannian submanifolds

AU - Kim, Kwang In

AU - Tompkin, James

AU - Theobalt, Christian

PY - 2013

Y1 - 2013

N2 - One fundamental assumption in object recognition as well as in other computer vision and pattern recognition problems is that the data generation process lies on a manifold and that it respects the intrinsic geometry of the manifold.This assumption is held in several successful algorithms for diffusion and regularization, in particular, in graph-Laplacian-based algorithms. We claim that the performance of existing algorithms can be improved if we additionallyaccount for how the manifold is embedded within the ambient space, i.e., if we consider the extrinsic geometry of the manifold. We present a procedure for characterizing the extrinsic (as well as intrinsic) curvature of a manifold M which is described by a sampled point cloud in a high-dimensional Euclidean space. Once estimated, we use this characterization in general diffusion and regularization on M, and form a new regularizer on a point cloud. The resulting re-weighted graph Laplacian demonstrates superior performance over classical graph Laplacian in semi supervised learning and spectral clustering.

AB - One fundamental assumption in object recognition as well as in other computer vision and pattern recognition problems is that the data generation process lies on a manifold and that it respects the intrinsic geometry of the manifold.This assumption is held in several successful algorithms for diffusion and regularization, in particular, in graph-Laplacian-based algorithms. We claim that the performance of existing algorithms can be improved if we additionallyaccount for how the manifold is embedded within the ambient space, i.e., if we consider the extrinsic geometry of the manifold. We present a procedure for characterizing the extrinsic (as well as intrinsic) curvature of a manifold M which is described by a sampled point cloud in a high-dimensional Euclidean space. Once estimated, we use this characterization in general diffusion and regularization on M, and form a new regularizer on a point cloud. The resulting re-weighted graph Laplacian demonstrates superior performance over classical graph Laplacian in semi supervised learning and spectral clustering.

M3 - Chapter

SP - 881

EP - 888

BT - Proc. International Conference on Computer Vision (ICCV) 2013

ER -