Filtering and Gradient Estimation for Distance Fields by Quadratic Regression
Distance fields show up in many problems of 3D vision and rendering, for example, a volumetric fusion of depth images results in such a field. Distance fields obtained from measured values are inherently noisy, so its filtering is needed before isoparametric surfaces are extracted from them, and robust normal vector estimation also requires a local smoothing since differentiation is especially sensitive to noise. In this paper, we use regression to find a quadratic function that approximates the zero level surface of the distance field, and apply this both for filtering and normal vector estimation. We also present a computationally efficient method that exploits the regular structure of samples, the symmetry and separability of the weighting functions, and thus avoids the solution of larger linear equations, which otherwise would become necessary when regression is generally attacked. The algorithm is a part of a real-time volumetric fusion application running on the Graphics Processing Units (GPU).