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Fast Asymmetric Fronts Propagation for Image Segmentation

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Abstract

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set 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. 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 image segmentation applications. Specifically, the foreground and background segmentation is 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 with the proposed Finsler metric providing that a thresholding value is given.

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Notes

  1. Initially, each source point \(\mathbf {x}\in \mathfrak {s}\) is tagged as Trial and the remaining grid points are tagged as Far.

  2. These ellipses are the boundaries of the control sets.

  3. Note that metrics \(\mathcal {G}_\mathfrak {g}^{\varvec{\alpha }}\) and \({\tilde{\mathcal {G}}}_\mathfrak {g}^{\varvec{\alpha }}\) have the identical anisotropy and asymmetry properties to \(\mathcal {F}_{\mathfrak {g}}^{\varvec{\alpha }}\) and \({\tilde{\mathcal {F}}}_{\mathfrak {g}}^{\varvec{\alpha }}\), respectively.

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Acknowledgements

The authors would like to thank all the anonymous reviewers for their detailed remarks that helped us improve the presentation of this paper. The authors thank Dr. Jean-Marie Mirebeau from Université Paris-Sud for his fruitful discussion and creative suggestions. The first author also thanks Dr. Gabriel Peyré from ENS Paris for his financial support. This work was partially supported by the European Research Council (ERC project SIGMA-Vision).

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  1. CEREMADE, CNRS, UMR 7534, University Paris Dauphine, PSL Research University, 75016, Paris, France

    Da Chen & Laurent D. Cohen

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Chen, D., Cohen, L.D. Fast Asymmetric Fronts Propagation for Image Segmentation. J Math Imaging Vis 60, 766–783 (2018). https://doi.org/10.1007/s10851-017-0776-7

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