A dynamic balanced flow for filtering point-sampled geometry

3D point data acquisition has become a practical approach for generating complex 3D shapes. Subsequent smoothing or denoising operations on these raw data sets are required before performing sophisticated modeling operations. Based on covariance analysis and constructed directional curvature, a new approach of anisotropic curvature flow is developed for filtering the point data set. By introducing a forcing term, a balanced flow equation is constructed, which allows the anisotropic diffusion flow to be restricted in the flow diffusion band of the original surface. Thus, the common problem of shape shrinkage that puzzles most current denoising approaches for point-sampled geometry is avoided. Applying dynamic balance techniques, the equation converges to the solution quickly with appealing physical interpretations. The algorithms operate directly on the discrete sample points, requiring no vertex connectivity information. They are shown to be computationally efficient, robust and simple to implement.