Improves the basic tensor voting formalism to infer the 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, nor oriented normal vector recovery is performed in our method. These approaches are known to be noise-sensitive, since accurate partial derivative information is often required, which is usually unavailable from real data. Also, unlike approaches that detect signs of Gaussian curvature, we can handle points with zero Gaussian curvature uniformly, without first localizing them in a separate process. The tensor-voting curvature estimation is non-iterative, does not require initialization, and is robust to a considerable amount of outlier noise, as its effect is reduced by collecting a large number of tensor votes. Qualitative and quantitative results on synthetic and real complex data are presented.