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In this paper, we introduce a generalized asymmetric fronts propagation modelbased on the geodesic distance maps and the Eikonal partial differentialequations. One of the key ingredients for the computation of the geodesicdistance map is the geodesic metric, which can govern the action of thegeodesic distance level set propagation. We consider a Finsler metric with theRanders form, through which the asymmetry and anisotropy enhancements can betaken into account to prevent the fronts leaking problem during the frontspropagation. These enhancements can be derived from the image edge-dependentvector field such as the gradient vector flow. The numerical implementationsare carried out by the Finsler variant of the fast marching method, leading tovery efficient interactive segmentation schemes. We apply the proposed Finslerfronts propagation model to image segmentation applications. Specifically, theforeground and background segmentation is implemented by the Voronoi index map.In addition, for the application of tubularity segmentation, we exploit thelevel set lines of the geodesic distance map associated to the proposed Finslermetric providing that a thresholding value is given.

Fast Asymmetric Fronts Propagation for Image Segmentation