A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modeling
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.
In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR2007)
ZHU, Jianke; HOI, Steven; and Lyu, Michael R..
A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modeling. (2007). In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR2007). Research Collection School Of Information Systems.
Available at: http://ink.library.smu.edu.sg/sis_research/2385