We establish a theoretical link between the 3D edge detection and the local surface approximation using uncertainty. As a practical application of the theory, we present a method for computing typical curvature features from 3D medical images. We use the uncertainties inherent in edge (and surface) detection in 2- and 3-dimensional images determined by quantitatively analyzing the uncertainty in edge position, orientation and magnitude produced by the multidimensional (2-D and 3-D) versions of the Monga-Deriche-Canny recursive separable edge-detector. These uncertainties allow to compute local geometric models (quadric surface patches) of the surface, which are suitable for reliably estimating local surface characteristics, for example, Gaussian and Mean curvature. We demonstrate the effectiveness of our methods compared to previous techniques. These curvatures are then used to obtain more structured features such as curvature extrema and lines of curvature extrema. The final goal is to extract robust geometric features on which registration and/or tracking procedures can rely.