Surface reconstruction from sparse data by a multiscale volumetric approach

This paper describes a method for surface reconstruction from sparse three-dimensional (3D) data that performs the reconstruction by building a sequence of surfaces approximating the data at increasing level of details (LOD). The method is simple, fast and suitable for a progressive 3D data/model representation, archiving, transmission. The surface reconstruction is obtained by a volumetric method that differs from other volumetric methods because it does not require implicitly or explicitly information on surface normals. This aspect is important in the case of noisy data sets, such as those coming from image based methods, because normals are often estimated unreliably from 3D 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 (RBFs). A hierarchy of surface approximations at different LOD is built by representing the voxels at the same octree level as RBFs having the same spatial support. At each scale, information related to the reconstruction error drives the reconstruction process at the following finer scale. Preliminary results on real data are presented and discussed. Key-Words: Surface reconstruction, sparse data, volumetric methods, radial basis functions, multiscale, octrees