Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
}
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 -