Physical Sciences and Mathematics Commons^™

A Multi-Scale Tikhonov Regularization Scheme For Implicit Surface Modeling, Jianke Zhu, Steven C. H. Hoi, Michael R. Lyu

Research Collection School Of Computing and Information Systems

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 …