A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modeling

• Main Authors: ZHU, Jianke, HOI, Steven C. H., LYU, Michael R.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: Algorithms; Factorization; Linear equations; Problem solving; Support vector machines; Tikhonov regularization; Kernel machines; Computer Sciences; Databases and Information Systems; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/2385; https://ink.library.smu.edu.sg/context/sis_research/article/3385/viewcontent/Multi_scale_Tikhonov_regularization_scheme_2007_afv.pdf
• Institution: Singapore Management University

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.