A multiscale volumetric approach to surface reconstruction

The inference of a three-dimensional (3D) surface from its sparse data samples is one of the most challenging problems in computer vision and in computer graphics. This paper describes a surface reconstruction method based on a volumetric approach where the reconstruction is obtained by building a sequence of surfaces approximating the data at increasing level of details. 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 represented in a multiscale framework by an octree structure. A volumetric description of the surface is build from the octree structure by representing the octree voxels as volumetric Radial Basis Functions (RBFs) of compact support. A hierarchy of surface approximations at different levels of details is then built from the octree scales. At each scale, information related to the reconstruction error drives the reconstruction process at the following finer scale. Differently from other volumetric methods, this method does not require information on surface normals. This aspect is important in the case of noisy data sets, such as those coming from image processing, because in this case normals are often estimated unreliably from the data. The method is simple, fast and suitable for a progressive 3D data/model representation, archiving, transmission. Preliminary results on synthetic and real data are presented and discussed.