Hypersurface fitting via jacobian nonlinear PCA on riemannian space

Authors:
Jun Fujiki;Shotaro Akaho
Affiliations:
National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan;National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

Citing 3
Cited 1

Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Fitting of Surfaces to Data with Covariances

IEEE Transactions on Pattern Analysis and Machine Intelligence
Unified Computation of Strict Maximum Likelihood for Geometric Fitting

Journal of Mathematical Imaging and Vision

Robust hypersurface fitting based on random sampling approximations

ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III

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Abstract

The subspace fitting method based on usual nonlinear principle component analysis (NLPCA), which minimizes the square distance in feature space, sometimes derives bad estimation because it does not reflect themetric on input space. To alleviate this problem, authors proposed the subspace fitting method based on NLPCA with considering the metric on input space, which is called Jacobian NLPCA. The proposed method is efficient when the metric of input space is defined. The proposed method can be rewritten as kernel method as explained in the paper.