Estimation of Curvature Based Shape Properties of Surfaces in 3D Grey-Value Images

Surfaces can be described locally and classified by their curvature values at every point. In this paper we investigate a grey-level based curvature estimator in combination with a sampling-error free integration technique of the curvature image. We compute shape descriptors as the bending energy and a global topological invariant, the Euler characterization. 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 π. It is mapped via the Knutsson mapping to a continuous representation in which the curvatures are computed.