Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

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• 作者：Alberto Crivellaro^a ; Simona Perotto^b ; Stefano Zonca^b ; ^{stefano.zonca@polimi.it}
• 关键词：Multivariate interpolation ; Least-squares approximation ; Adaptive algorithm ; Radial basis functions ; 3D noisy and lacking scattered data
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：113
• 期：Complete
• 页码：93-108
• 全文大小：3417 K
• 卷排序：113

文摘

We propose new algorithms to overcome two of the most constraining limitations of surface reconstruction methods in use. In particular, we focus on the large amount of data characterizing standard acquisitions by scanner and the noise intrinsically introduced by measurements. The first algorithm represents an adaptive multi-level interpolating approach, based on an implicit surface representation via radial basis functions. The second algorithm is based on a least-squares approximation to filter noisy data. The third approach combines the two algorithms to merge the correspondent improvements. An extensive numerical validation is performed to check the performances of the proposed techniques.