Orthogonal Least Squares in Partition of Unity Surface Reconstruction with Radial Basis Function

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.