Volumetric Methods for Surface Reconstruction and Manipulation

The RBF method (introduced in the previous chapter) involves solving a dense linear system. For huge numbers of points, this becomes too computationally demanding. Like the RBF method, volumetric methods for reconstruction produce an implicit representation of the reconstructed surface, but instead of solving a linear system, these methods proceed by solving a partial differential equation discretized on a 3D grid. Volumetric reconstruction algorithms become rather simple: essentially it boils down to repeatedly smoothing data on a 3D grid while keeping the values at some grid points constant. Having discussed the basic approach, we also explain how normals for point data can be estimated, since point normal estimates are generally required for volumetric reconstruction.