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Minimal Paths in 3D Images and Application to Virtual Endoscopy

  • Thomas Deschamps
  • Laurent D. Cohen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1843)

Abstract

This paper presents a new method to find minimal paths in 3D images, giving as initial data one or two endpoints. This is based on previous work [1] for extracting paths in 2D images using Fast Marching [4]. Our original contribution is to extend this technique to 3D, and give new improvements of the approach that are relevant in 2D as well as in 3D. We also introduce several methods to reduce the computation cost and the user interaction. This work finds its motivation in the particular case of 3D medical images. We show that this technique can be efficiently applied to the problem of finding a centered path in tubular anatomical structures with minimum interactivity, and we apply it to path construction for virtual endoscopy. Synthetic and real medical images are used to illustrate each contribution.

keywords

Deformable Models Minimal paths Level Set methods Medical image understanding Eikonal Equation Fast Marching 

References

  1. 1.
    Cohen, L.D., Kimmel, R.: Global Minimum for Active Contour Models: A Minimal Path Approach. International Journal of Computer Vision. 24 (1997) 57–78CrossRefGoogle Scholar
  2. 2.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision. 4 (1988) 321–331CrossRefGoogle Scholar
  3. 3.
    Malladi, R., Sethian, J.A.: A Real-Time Algorithm for Medical Shape Recovery. Proceedings of International Conference on Computer Vision. (1998) 304–310Google Scholar
  4. 4.
    Sethian J.A.: Level set methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Sciences. Cambridge University Press (1999)Google Scholar
  5. 5.
    Rouy, E., Tourin, A.: A Viscosity Solution Approach to Shape-From-Shading. SIAM Journal of Numerical Analysis. 29 (1992) 867–884zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Mathematic. 1 (1959) 269–271zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    McInerney, T., Terzopoulos, D.: Deformable Models in Medical Image Analysis, A Survey. Medical Image Analysis. 2 (1996)Google Scholar
  8. 8.
    Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Proceedings of International Conference on Computer Vision. (1995) 694–699Google Scholar
  9. 9.
    Deschamps, T., Cohen, L.D.: Minimal path in 3D images and application to virtual endoscopy. Les Cahiers du Cérémade, Université Paris Dauphine. (2000)Google Scholar
  10. 10.
    Yeorong, G., Stelts, D.R., Jie, W., Vining, D.J.: Computing the centerline of a colon: a robust and efficient method based on 3D skeletons. Proceedings of IEEE Nuclear Science Symposium Conference Record. 23 (1993) 786–794Google Scholar
  11. 11.
    Choiu, R.C.H., Kaufman, A.E., Zhengrong, L., Lichan, H., Achniotou, M.: An interactive fly-path planning using potential fields and cell decomposition for virtual endoscopy. Proceedings of IEEE Nuclear Science Symposium Conference Record. 46 (1999) 1045–1049Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas Deschamps
    • 1
    • 2
  • Laurent D. Cohen
    • 2
  1. 1.Medical Imaging Systems GroupLEPLimeil-BrévannesFrance
  2. 2.CEREMADE UMR CNRS 7534Université Paris IX DauphineParis Cedex 16France

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