Curvature Estimation of Surfaces in 3D Grey-Value Images

Abstract

In this paper we present a novel method to estimate curvature of iso grey-level surfaces in grey-value images. Our method succeeds where isophote curvature fails. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation (normal vector) field of the surface. This orientation field and a description of local structure is obtained by the Gradient Structure Tensor. The estimated orientation field has discontinuities mod j. It is mapped via the Knutsson mapping to a continuous representation. The principal curvatures of the surface, a coordinate invariant property, are computed in this mapped representation. An evaluation shows that our curvature estimation is robust even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.