Anisotropic diffusion of surface normals for feature preserving surface reconstruction

For 3D surface reconstruction problems with noisy and incomplete range data measured from complex scenes with arbitrary topologies, a low-level representation, such as level set surfaces, is used. Such surface reconstruction is typically accomplished by minimizing a weighted sum of datamodel discrepancy and model smoothness terms. We introduce a new nonlinear model smoothness term for surface reconstruction based on variations of the surface normals. A direct solution requires solving a fourth-order partial differential equation (PDE), which is very difficult with; conventional numerical techniques. Our solution is based on processing the normals separately from the surface, which allows us to separate the problem into two second-order PDEs. The proposed method can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion.