A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modelling

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 c...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Jianke Zhu, Steven C. H. Hoi, Michael R. Lyu
• Keywords: Computer Vision, CVPR 2007, Implicit Shape Models, Implicit Surface Modelling, Implicit Surfaces, Promising Solution, Tikhonov Regularization Scheme