Surfaces can be described locally and classified by their cur- vature values at every point. In this paper we investigate a grey-level based curvature estimator in combination with a sampling-error free inte- gration technique of the curvature image. We compute shape descriptors as the bending energy and a global topological invariant, the Euler char- acterization. The integration of curvature values over the surface area is done by grey-volume integration. Our curvature estimator works on the orientation field of the surface, which does not require a segmentation of the surface. The estimated orientation fields has discontinuities mod . It is mapped via the Knutsson mapping to a continuous representation in which the curvatures are computed.