Surface Reconstruction with Least Square Reproducing Kernel and Partition of Unity

We present a new scheme for the surface reconstruction of large noisy scattered points coming from laser range scanners. It is based on a combination of the two well-known methods: least square reproducing kernel (LSRK) and partition of unity (PoU). The input point datasets are broken into many subdomains with an error-controlled octree subdivision method, which adapts to variations in the complexity of the model. A local least square reproducing kernel function is constructed at each octree leaf cell. Finally, we blend these local shape functions together using weighting functions. Due to the separation of local approximation and local blending, the representation is not global and can be created and evaluated rapidly. Numerical experiments demonstrate robust and efficient performance of the proposed methods in processing a great variety of 2D and 3D reconstruction problems.