From voxel to curvature

A theoretical link is established between the 3D edge detection and the local surface approximation using uncertainty. As a practical application of the theory, a method is presented for computing typical curvature features from 3D medical images. The authors determine the uncertainties inherent in edge (and surface) detection and 2D and 3D images by quantitatively analyzing the uncertainty in edge position, orientation, and magnitude produced by the multidimensional (2D and 3D) versions of the Monga-Deriche-Canny recursive separable edge-detector. The uncertainty is shown to depend on edge orientation, e.g. the position uncertainty may vary with a ratio larger than 2.8 in the 2D case, and 3.5 in the 3D case. These uncertainties are then used 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. The authors demonstrate the effectiveness of these methods compared to previous techniques