Robust Estimation of Curvature Information from Noisy 3D Data for Shape Description

We describe an effective and novel approach to infer sign and direction of principal curvatures at each input site from noisy 3D data. Unlike most previous approaches, no local surface fitting, partial derivative computation of any kind, nor oriented normal vector recovery is performed in our method. These approaches are noise-sensitive since accurate, local, partial derivative information is often required, which is usually unavailable from real data because of the unavoidable outlier noise inherent in many measurement phases. Also, we can handle points with zero Gaussian curvature uniformly (i.e., without the need to localize and handle them first as a separate process). Our approach is based on Tensor Voting, a unified, salient structure inference process. Both the sign and the direction of principal curvatures are inferred directly from the input. Each input is first transformed into a synthetic tensor. A novel and robust approach based on tensor voting is proposed for curvature information estimation. With faithfully inferred curvature information, each input ellipsoid is aligned with curvature-based dense tensor kernels to produce a dense tensor field. Surfaces and crease curves are extracted from this dense field, by using an extremal feature extraction process. The computation is non-iterative, does not require initialization, and robust to considerable amounts of outlier noise as its effect is reduced by collecting a large number of tensor votes. Qualitative and quantitative results on synthetic as well as real and complex data are presented.