Anisotropic Haralick Edge Detection Scheme with Application to Vessel Segmentation

In this paper, detection of edges in oriented fields is addressed. Haralick edge detection is an accurate scheme for estimation of the edge in a Euclidean space. However, in some applications such as edge detection for vessel segmentation because of the intrinsic orientation of structures, accuracy is only demanded in a particular subspace. This is specially usefull when a curve evolution is chosen for segmentation since gradients in parallel to vessel orientation stops evolution. Haralick edge detection is generalized on a Riemannian space using the inner product of the vectors under a space metric tensor. This eliminates the spurious gradients and preserves the accuracy on the vessel border. Examples are given and the comparison is made with the state-of-the-art flux maximizing flow indicating that significant improvements in terms of leakage minimization and thiner vessel delineation is achievable using our methodology.