Title :
Orthogonal Least Squares in Partition of Unity Surface Reconstruction with Radial Basis Function
Author :
Xia, Qi ; Wang, Michael Yu ; Wu, Xiaojun
Author_Institution :
Chinese Univ. of Hong Kong, Shatin
Abstract :
In this paper, a least squares formulation with radial basis function for surface reconstruction is presented and OLS (orthogonal least squares) algorithm is proposed to select centers and eliminate numerical ill-conditioning. The two objectives are fused into a single iterative process in OLS algorithm, which makes the reconstruction fast and robust. In the end, in order to deal with large point sets, we organize a point set with an octree; reconstruct surfaces in octree cells and blend them into a global surface by partition of unity (POU) method. To sum up, the first method is dedicated to reconstructing a surface with a smaller number of RBFs, and the last one is a local method to bypass impractical global reconstructions. Effectiveness of our proposed methods is demonstrated with results of real world point sets
Keywords :
iterative methods; least squares approximations; octrees; set theory; surface fitting; iterative process; numerical ill-conditioning; octree; orthogonal least squares algorithm; partition of unity method; point sets; radial basis function; unity surface reconstruction; Image reconstruction; Iterative algorithms; Least squares approximation; Least squares methods; Linear systems; Measurement techniques; Partitioning algorithms; Robustness; Scattering; Surface reconstruction;
Conference_Titel :
Geometric Modeling and Imaging--New Trends, 2006
Conference_Location :
London, England
Print_ISBN :
0-7695-2604-7
DOI :
10.1109/GMAI.2006.40