A semi-Lagrangian scheme with radial basis approximation for surface reconstruction

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• 作者：E. Carlini ; R. Ferretti
• 关键词：Surface reconstruction ; Level set methods ; Mean curvature motion ; Semi ; Lagrangian schemes
• 刊名：Computing and Visualization in Science
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：18
• 期：2-3
• 页码：103-112
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Algorithms; Visualization; Numerical Analysis; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1433-0369
• 卷排序：18

文摘

We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. (Comput Vis Image Underst 80:295–319, 2000) to reconstruct unknown surfaces from sparse data sets. The main advantages of the proposed scheme are the possibility to solve the level set method on unstructured grids, as well as to concentrate the reconstruction points in the neighbourhood of the data set, with a consequent reduction of the computational effort. Moreover, the scheme is explicit. Numerical tests show the accuracy and robustness of our approach to reconstruct curves and surfaces from relatively sparse data sets.