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Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images

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Abstract

In this paper, we present a new method for segmenting closed contours and surfaces. Our work builds on a variant of the minimal path approach. First, an initial point on the desired contour is chosen by the user. Next, new keypoints are detected automatically using a front propagation approach. We assume that the desired object has a closed boundary. This a-priori knowledge on the topology is used to devise a relevant criterion for stopping the keypoint detection and front propagation. The final domain visited by the front will yield a band surrounding the object of interest. Linking pairs of neighboring keypoints with minimal paths allows us to extract a closed contour from a 2D image. This approach can also be used for finding an open curve giving extra information as stopping criteria. Detection of a variety of objects on real images is demonstrated. Using a similar idea, we can extract networks of minimal paths from a 3D image called Geodesic Meshing. The proposed method is applied to 3D data with promising results.

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References

  1. Ardon, R., Cohen, L.D., Yezzi, A.: A new implicit method for surface segmentation by minimal paths in 3d images. Appl. Math. Optim. 55(18), 127–144 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Benmansour, F., Bonneau, S., Cohen, L.D.: Finding a closed boundary by growing minimal paths from a single point on 2d or 3d images. In: MMBIA07, pp. 1–8 (2007)

  3. Bonneau, S.: Chemins minimaux en Analyse d’images: Nouvelles contributions et applications à l’imagerie biologique. PhD thesis, Université Paris-Dauphine, France (2006)

  4. Bonneau, S., Dahan, M., Cohen, L.D.: Single quantum dot tracking based on perceptual grouping using minimal paths in a spatiotemporal volume. IEEE Trans. Image Process. 14, 1384–1395 (2005)

    Article  Google Scholar 

  5. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22, 61–79 (1997)

    Article  MATH  Google Scholar 

  6. Cohen, L.D.: Multiple contour finding and perceptual grouping using minimal paths. J. Math. Imaging Vis. 14, 225–236 (2001)

    Article  MATH  Google Scholar 

  7. Cohen, L.D.: Minimal paths and fast marching methods for image analysis. In: Paragios, N., Chen, Y., Faugeras, O. (eds.) Mathematical Models in Computer Vision: The Handbook. Springer, Berlin (2005)

    Google Scholar 

  8. Cohen, L.D., Kimmel, R.: Global minimum for active contour models: a minimal path approach. Int. J. Comput. Vis. 24, 57–78 (1997)

    Article  Google Scholar 

  9. Deschamps, T., Cohen, L.D.: Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Med. Image Anal. 5, 281–299 (2001)

    Article  Google Scholar 

  10. Dijkstra, E.W.: A note on two problems in connection with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  11. Falcão, A.X., Udupa, J.K., Miyazawa, F.K.: An ultra-fast user-steered image segmentation paradigm: Live-wire-on-the-fly. IEEE Trans. Med. Imaging 19(1), 55–62 (2000)

    Article  Google Scholar 

  12. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1, 321–331 (1988)

    Article  Google Scholar 

  13. Kim, S.: An \(\mathcal{O}({N})\) level set method for Eikonal equations. SIAM J. Sci. Comput. 22, 2178–2193 (2001)

    Article  MATH  Google Scholar 

  14. Kimmel, R., Sethian, J.A.: Optimal algorithm for shape from shading and path planning. J. Math. Imaging Vis. 14, 237–244 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Peyré, G., Cohen, L.D.: Geodesic remeshing using front propagation. Int. J. Comput. Vis. 69, 145–156 (2006)

    Article  Google Scholar 

  16. Rouy, E., Tourin, A.: A viscosity solution approach to shape from shading. SIAM J. Numer. Anal. 29, 867–884 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Sethian, J.A.: A fast marching level set for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591–1595 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Sethian, J.A.: Fast marching methods. SIAM Rev. 41, 199–235 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  20. Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Autom. Control 40, 1528–1538 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  21. Yatziv, L., Bartesaghi, A., Sapiro, G.: \(\mathcal{O}({N})\) implementation of the fast marching algorithm. J. Comput. Phys. 212, 393–399 (2006)

    Article  MATH  Google Scholar 

  22. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A.: A geometric snake model for segmentation of medical imagery. IEEE Trans. Med. Imaging 16, 199–209 (1997)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Fethallah Benmansour & Laurent D. Cohen

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  1. Fethallah Benmansour
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  2. Laurent D. Cohen
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Correspondence to Fethallah Benmansour.

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Benmansour, F., Cohen, L.D. Fast Object Segmentation by Growing Minimal Paths from a Single Point on 2D or 3D Images. J Math Imaging Vis 33, 209–221 (2009). https://doi.org/10.1007/s10851-008-0131-0

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  • DOI: https://doi.org/10.1007/s10851-008-0131-0

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