Advertisement

Multi-Label Simple Points Definition for 3D Images Digital Deformable Model

  • Alexandre Dupas
  • Guillaume Damiand
  • Jacques-Olivier Lachaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

The main contribution of this paper is the definition of multi-label simple points that ensures that the partition topology remains invariant during a deformable partition process. The definition is based on simple intervoxel properties and is easy to implement. A deformation process is carried out with a greedy energy minimization algorithm. A discrete area estimator is used to approach at best standard regularizers classically used in continuous energy minimizing methods. The effectiveness of our approach is shown on several 3D image segmentations.

Keywords

Simple Point Deformable Model Multi-Label Image 

References

  1. 1.
    Ardon, R., Cohen, L.D.: Fast constrained surface extraction by minimal paths. International Journal on Computer Vision 69(1), 127–136 (2006)CrossRefGoogle Scholar
  2. 2.
    Bazin, P.-L., Ellingsen, L.M., Pham, D.L.: Digital homeomorphisms in deformable registration. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 211–222. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Bertrand, G.: Simple points, topological numbers and geodesic neighborhoods in cubic grids. Pattern Recognition Letters 15(10), 1003–1011 (1994)CrossRefGoogle Scholar
  4. 4.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1222–1239 (2001)CrossRefGoogle Scholar
  5. 5.
    Caselles, V., Catte, F., Coll, T., Dibos, F.: A geometric model for active contours. Numerische Mathematik 66, 1–31 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Caselles, V., Kimmel, R., Sapiro, G., Sbert, C.: Minimal surfaces based object segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 19(4), 394–398 (1997)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. on Image Processing 10(2), 266–277 (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Cocosco, C.A., Kollokian, V., Kwan, R.K.-S., Evans, A.C.: Brainweb: Online interface to a 3d MRI simulated brain database. In: Proc. of 3-rd Int. Conference on Functional Mapping of the Human Brain, Copenhagen, Denmark (May 1997)Google Scholar
  9. 9.
    Cohen, L.D., Kimmel, R.: Global minimum for active contour models: a minimal path approach. Int. Journal of Computer Vision 24(1), 57–78 (1997)CrossRefGoogle Scholar
  10. 10.
    de Vieilleville, F., Lachaud, J.-O.: Toward a digital deformable model simulating open active contours. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 156–167. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Greig, D., Porteous, B., Seheult, A.: Exact maximum a posteriori estimation for binary images. Journal of the Royal Statistical Society (B) 51(2), 271–279 (1989)Google Scholar
  12. 12.
    Guigues, L., Cocquerez, J.-P., Le Men, H.: Scale-sets image analysis. International Journal on Computer Vision 68(3), 289–317 (2006)CrossRefGoogle Scholar
  13. 13.
    Han, X., Xu, C., Prince, J.L.: A topology preserving level set method for geometric deformable models. IEEE Trans. on Pattern Analysis and Machine Intelligence 25(6), 755–768 (2003)CrossRefGoogle Scholar
  14. 14.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1(4), 321–331 (1988)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kovalevsky, V.A.: Finite topology as applied to image analysis 46, 141–161 (1989)Google Scholar
  16. 16.
    Lachaud, J.-O., Vialard, A.: Discrete deformable boundaries for the segmentation of multidimensional images. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 542–551. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Lachaud, J.-O., Vialard, A.: Geometric measures on arbitrary dimensional digital surfaces. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 434–443. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape Modelling with Front Propagation: A Level Set Approach. IEEE Trans. on Pattern Analysis and Machine Intelligence 17(2), 158–174 (1995)CrossRefGoogle Scholar
  19. 19.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–684 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Pons, J.-P., Boissonnat, J.-D.: Delaunay deformable models: Topology-adaptive meshes based on the restricted Delaunay triangulation. In: Proc. IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)Google Scholar
  21. 21.
    Pruvot, J.H., Brun, L.: Scale set representation for image segmentation. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 126–137. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Ségonne, F.: Active contours under topology control - genus preserving level sets. Int. Journal of Computer Vision 79, 107–117 (2008)CrossRefGoogle Scholar
  23. 23.
    Ségonne, F., Pons, J.-P., Grimson, W.E.L., Fischl, B.: Active contours under topology control genus preserving level sets. In: Int. Workshop Computer Vision for Biomedical Image Applications, pp. 135–145 (2005)Google Scholar
  24. 24.
    Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50(3), 271–293 (2002)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alexandre Dupas
    • 1
  • Guillaume Damiand
    • 2
  • Jacques-Olivier Lachaud
    • 3
  1. 1.Université de Poitiers, CNRS, SIC-XLIM, UMR6172France
  2. 2.Université de Lyon, CNRS, LIRIS, UMR5205France
  3. 3.Université de Savoie, CNRS, LAMA, UMR5127France

Personalised recommendations