In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic dis- tances with applications to image segmentation. The key ingredient of the fronts propagation and the computation of the geodesic distances is the construction of the metrics. We make use of the Finsler metrics with Randers form, by which the asymmetric and anisotropic measures of the geodesic curve length are taken into account to avoid the shortcuts and leaking problems. This allows the fronts of the geodesic distance map to benefit from the asymmetric information derived from the image edges . The numerical implementations are carried out by the variant Finsler fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to  foreground and background segmentation implemented by the Voronoi index map. In addition,  the vessel extraction task can be carried out by identifying the level set lines of the distance map providing a thresholding value is given.
In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distances and Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distances is the geodesic metrics, which can govern the action of the geodesic distance propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow field . The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to the foreground and background segmentation implemented by the Voronoi index map. In addition, for the application of tubularity segmentation, we exploit the level set lines of the geodesic distance map associated to the proposed Finsler metric providing that a thresholding value is given.
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dis- tances with applications to image segmentation. The key ingredient of the fronts propagation and
distances and Eikonal partial differential equations. One of the key ingredients for
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construction of the metrics. We make use of the Finsler metrics with
geodesic metrics, which can govern the action of the geodesic distance propagation. We consider a Finsler metric with the
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by which the asymmetric and anisotropic measures of the geodesic curve length are
through which the asymmetry and anisotropy enhancements can be
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avoid the shortcuts and leaking problems. This allows the fronts of the geodesic distance map to benefit from the asymmetric information
prevent the fronts leaking problem during the fronts propagation. These enhancements can be
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edges
edge-dependent vector field such as the gradient vector flow field
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variant Finsler
Finsler variant of the
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the
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for the application of tubularity segmentation, we exploit
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vessel extraction task can be carried out by identifying the
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distance map providing
geodesic distance map associated to the proposed Finsler metric providing that