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Two new approaches of 3D implicit surfaces reconstruction with radial basis functions (RBFs) are proposed in this paper. With the first method, a point set is organized by a balanced binary tree. The cells are controlled to be mildly overlapped and to contain adequate number of points for efficiency and stability. In each subdomain, only one off-surface point in the quasi-normal direction which is estimated by an eigen analysis is used in RBF interpolation. Another method is least square RBFs. This method can overcome the problem of numerical ill-conditioning and over-fitting of traditional RBF reconstruction and it offers a methodology for reconstruction with less centers. These method are versatile and with topological flexibility and numerical efficiency.

3D Reconstruction Methods Based on Radial Basis Functions for Laser Scanned Data Point Sets