Curvature Estimation for Enhancement of Crossing Curves

In this paper we describe a method for estimating curva-ture of elongated structures in images. The curvature es-timation is performed on an invertible orientation score, which is a 3D entity obtained from a 2D image by con-volution with a rotating kernel. By considering the group structure we can define left-invariant derivatives, which are essential to construct operations on the orientation score that amount to rotationally invariant operations on the cor-responding image. The problem of estimating curvature of an oriented structure is stated as a minimization prob-lem, which can be solved by eigenvector analysis of a ma-trix constructed from the non-symmetric Hessian matrix. The experiments show the method performs well for a wide range of curvatures and noise levels. The method clearly outperforms a related curvature estimation method by Van Ginkel et al. that tends to give estimates that are too small. We show how we can incorporate the curvature estimate in our method for coherence-enhancing diffusion in orienta-tion scores. This method has superior performance in en-hancing crossing contours, which is demonstrated on medi-cal images. 1