Generalization of geometrical flux maximizing flow on Riemannian manifolds for improved volumetric blood vessel segmentation

Geometric flux maximizing flow (FLUX) is an active contour based method which evolves an initial surface to maximize the flux of a vector field on the surface. For blood vessel segmentation, the vector field is defined as the vectors specified by vascular edge strengths and orientations. Hence, the segmentation performance depends on the quality of the detected edge vector field. In this paper, we propose a new method for level set based segmentation of blood vessels by generalizing the FLUX on a Riemannian manifold (R-FLUX). We consider a 3D scalar image I(x) as a manifold embedded in the 4D space (x, I(x)) and compute the image metric by pullback from the 4D space, whose metric tensor depends on the vessel enhancing diffusion (VED) tensor. This allows us to devise a non-linear filter which both projects and normalizes the original image gradient vectors under the inverse of local VED tensors. The filtered gradient vectors pertaining to the vessels are less sensitive to the local image contrast and more coherent with the local vessel orientation. The method has been applied to both synthetic and real TOF MRA data sets. Comparisons are made with the FLUX and vesselsness response based segmentations, indicating that the R-FLUX outperforms both methods in terms of leakage minimization and thiner vessel delineation.