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Some Remarks on the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours

Abstract

Recently, Caselles et al. have shown the equivalence between a classical snake problem of Kass et al. and a geodesic active contour model. The PDE derived from the geodesic problem gives an evolution equation for active contours which is very powerfull for image segmentation since changes of topology are allowed using the level set implementation. However in Caselles' paper the equivalence with classical snake is only shown for 2D images and 1D curves, by using concepts of Hamiltonian theory which have no meanings for active surfaces. This paper propose to examine the notion of equivalence and to revisite Caselles et al. arguments. Then a notion equivalence is introduced and shown for classical snakes and geodesic active contours in the 2D (active contour) and 3D (active surface) case.

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References

  1. Caselles, V., Catte, F., Coll. T., and Dibos, F. 1993. A geometric model for active contours. Numerische Mathematik, 66:1–31.

    Google Scholar 

  2. Caselles, V., Kimmel, R., and Sapiro, G. 1997. On geodesic active contours. Int. Journal of Computer Vision, 22(1):61–79.

    Google Scholar 

  3. Kass, M., Witkin, A., and Terzopoulos, D. 1987. Snakes: Active contour models. International Journal of Computer Vision, 1:321–331.

    Google Scholar 

  4. Malladi, R., Sethian, J.A., and Vermuri, B.C. 1995. Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2).

  5. Osher, S. and Sethian, J.A. 1988. Front propagating with curvature dependant speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79:12–49.

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Aubert, G., Blanc-Féraud, L. Some Remarks on the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours. International Journal of Computer Vision 34, 19–28 (1999). https://doi.org/10.1023/A:1008168219878

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  • geodesic active contours
  • active surfaces
  • Hamiltonian
  • snakes
  • optimization