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A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modelling

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3 Author(s)
Jianke Zhu ; Department of Computer Science & Engineering, Chinese University of Hong Kong, Shatin, Hong Kong. jkzhu@cse.cuhk.edu.hk ; Steven C. H. Hoi ; Michael R. Lyu

Kernel machines have recently been considered as a promising solution for implicit surface modelling. A key challenge of machine learning solutions is how to fit implicit shape models from large-scale sets of point cloud samples efficiently. In this paper, we propose a fast solution for approximating implicit surfaces based on a multi-scale Tikhonov regularization scheme. The optimization of our scheme is formulated into a sparse linear equation system, which can be efficiently solved by factorization methods. Different from traditional approaches, our scheme does not employ auxiliary off-surface points, which not only saves the computational cost but also avoids the problem of injected noise. To further speedup our solution, we present a multi-scale surface fitting algorithm of coarse to fine modelling. We conduct comprehensive experiments to evaluate the performance of our solution on a number of datasets of different scales. The promising results show that our suggested scheme is considerably more efficient than the state-of-the-art approach.

Published in:

2007 IEEE Conference on Computer Vision and Pattern Recognition

Date of Conference:

17-22 June 2007