Kd-tree based OLS in implicit surface reconstruction with radial basis function

Authors:
Peizhi Wen;Xiaojun Wu;Tao Gao;Chengke Wu
Affiliations:
Guilin University of Electronic Technology, Guilin, China;HIT Shenzhen Graduate School, Shenzhen, China;Xi’an Jiaotong University, Xi’an, China;Xidian University, Xi’an, China
Venue:
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Year:
2006

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Abstract

In this paper, we propose a new method for surface reconstruction from scattered point set based on least square radial basis function (LSRBF) and orthogonal least square forward selection procedure. Firstly, the traditional RBF formulation is rewritten into least square formula. A implicit surface can be represented with fewer centers. Then, the orthogonal least square procedure is utilized to select significant centers from original point data set. The RBF coefficients can be solved from the triangular matrix from OLS selection through backward substitution method. So, this scheme can offer a fast surface reconstruction tool and can overcome the numerical ill-conditioning of coefficient matrix and over-fitting problem. Some examples are presented to show the effectiveness of our algorithm in 2D and 3D cases.