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 nonuniform distributed data has recently deserved more attention, because it occurs frequently in practice. This work describes a volumetric approach to surface reconstruction from nonuniform data which is suitable for the reconstruction of surfaces from images, in particular from multiple views. Differently from volumetric methods which use both 3D surface points and surface normals, the approach does not use the surface normals because they are often unreliable when estimated from image data. The method 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 functions (RBF). A hierarchy of surface approximations at different levels of details is built by representing the voxels at the same octree level as RBF of similar spatial support. At each scale, information related to the reconstruction error drives the reconstruction process at the following finer scale. Preliminary results on synthetic data and future perspectives are presented.