Hierarchical 3D surface reconstruction based on Radial Basis Functions

Volumetric methods based on implicit surfaces are commonly used in surface reconstruction from uniformly distributed sparse 3D data. The case of non-uniform distributed data has recently deserved much attention, because it occurs frequently in practice. This paper describes a volumetric approach to surface reconstruction from non-uniform data which is based on a hierarchical partitioning of the volume data set. The working volume is split and classified at different scales of spatial resolution into surface, internal and external voxels and this hierarchy is described by an octree structure in a multiscale framework. The octree structure is used to build a multiresolution description of the surface by means of compact support radial basis funtions (RBF). Volumetric functions at different level of details are built by representing the voxels at the same octree level as RBF of similar spatial support. Information related to the reconstruction error propagates along the scales to drive the reconstruction at the following finer scales. The method described in this paper is suitable to convey visual information into the reconstruction process. Preliminary results and perspectives are presented.