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International Conference on Geometric Science of Information

GSI 2017: Geometric Science of Information pp 782–790Cite as

Anisotropic Edge-Based Balloon Eikonal Active Contours

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

Abstract

In this paper, we propose a new edge-based active contour model for image segmentation and curve evolution by an asymmetric Finsler metric and the corresponding minimal paths. We consider the edge anisotropy information and the balloon force term to build a Finsler metric comprising of a symmetric quartic term and an asymmetric linear term. Unlike the traditional geodesic active contour model where the curve evolution is carried out by the level set framework, we search for a more robust optimal curve by solving an Eikonal partial differential equation (PDE) associated to the Finsler metrics. Moreover, we present an interactive way for geodesics extraction and closed contour evolution. Compared to the level set-based geodesic active contour model, our model is more robust to spurious edges, and also more efficient in numerical solution.

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Notes

  1. 1.

    This is because is the bounded connected component of .

  2. 2.

    We use the distance preserving method [18] to avoid level set reinitialization.

References

  1. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. IJCV 1(4), 321–331 (1988)

    Article  MATH  Google Scholar 

  2. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. IJCV 22(1), 61–79 (1997)

    Article  MATH  Google Scholar 

  3. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A.: A geometric snake model for segmentation of medical imagery. TMI 16(2), 199–209 (1997)

    Google Scholar 

  4. Melonakos, J., Pichon, E., Angenent, S., Tannenbaum, A.: Finsler active contours. TPAMI 30(3), 412–423 (2008)

    Article  Google Scholar 

  5. Jbabdi, S., Bellec, P., et al.: Accurate anisotropic fast marching for diffusion-based geodesic tractography. JBI 2008, 2 (2008)

    Google Scholar 

  6. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. JCP 79(1), 12–49 (1988)

    MATH  MathSciNet  Google Scholar 

  7. Cohen, L.D., Kimmel, R.: Global minimum for active contour models: a minimal path approach. IJCV 24(1), 57–78 (1997)

    Article  Google Scholar 

  8. Appia, V., Yezzi, A.: Active geodesics: region-based active contour segmentation with a global edge-based constraint. In: Proceedings of ICCV 2011, pp. 1975–1980 (2011)

    Google Scholar 

  9. Mille, J., Bougleux, S., Cohen, L.: Combination of piecewise-geodesic paths for interactive segmentation. IJCV 112(1), 1–22 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  10. Chen, D., Mirebeau, J.M., Cohen, L.D.: Finsler geodesic evolution model for region-based active contours. In: Proceedings of BMVC 2016 (2016)

    Google Scholar 

  11. Cohen, L.D.: On active contour models and balloons. CVGIP Image Underst. 53(2), 211–218 (1991)

    Article  MATH  Google Scholar 

  12. Chen, D., Mirebeau, J.M., Cohen, L.D.: Global minimum for a Finsler elastica minimal path approach. IJCV 122(3), 458–483 (2017)

    Article  MathSciNet  Google Scholar 

  13. Mirebeau, J.M.: Efficient fast marching with Finsler metrics. Numer. Math. 126(3), 515–557 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sethian, J.A., Vladimirsky, A.: Ordered upwind methods for static Hamilton-Jacobi equations: theory and algorithms. SINUM 41(1), 325–363 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chen, D., Cohen, L.D.: Fast asymmetric fronts propagation for image segmentation (2017, preprint)

    Google Scholar 

  16. Randers, G.: On an asymmetrical metric in the four-space of general relativity. Phys. Rev. 59(2), 195 (1941)

    Article  MATH  MathSciNet  Google Scholar 

  17. Chan, T.F., Vese, L.A.: Active contours without edges. TIP 10(2), 266–277 (2001)

    MATH  Google Scholar 

  18. Li, C., Xu, C., et al.: Distance regularized level set evolution and its application to image segmentation. TIP 19(12), 3243–3254 (2010)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

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

    Da Chen & Laurent D. Cohen

Authors
  1. Da Chen
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  2. Laurent D. Cohen
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Corresponding author

Correspondence to Da Chen .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Chen, D., Cohen, L.D. (2017). Anisotropic Edge-Based Balloon Eikonal Active Contours. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_90

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_90

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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