Skip to main content
Log in

Automatic active contour segmentation approach via vector field convolution

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Among the segmentation methods proposed in the literature, the active contour models have been widely used in medical images segmentation. This is due to their efficiency to capture complex shapes. Nevertheless, the adequate set of the initial curves for active contours is needed to lead to good automatic segmentation results. An adequate initialization method should set the initial active contour model close enough, to the final targeted boundary, to avoid local minima and to improve computational efficiency. In this paper, we present a new approach, based on the divergence of vector field and the Dijkstra’s algorithm to automatically initialize and give the B-Snake the ability to change topology in presence of multiple objects very close to each other. The divergence of vector fields informs about the vectors spread. Negative divergence indicates that the vectors converge and positive divergence indicates that the vectors diverge. Thus, we used the negative region of the divergence of the vector field convolution (VFC) to set the initial active contour near the objects and the positive divergence region was used to split the B-Snake via Dijkstra algorithm. To demonstrate the effectiveness of the proposed method, we use computed tomography (CT) images of close bones. This method gives good segmentation results, especially on CT images presenting proximities, compared to results obtained by other automatic segmentation methods from the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Amini, A.A., Weymouth, T.E., Jain, R.C.: Using dynamic programming for solving variational problems in vision. IEEE Trans. Anal. Mach. Intell. 12(9), 855–867 (1990)

    Article  Google Scholar 

  3. Kang, D.J.: A fast and stable snake algorithm for medical images. Pattern Recognit. 20(5), 507–512 (1999)

    Article  Google Scholar 

  4. Menet, S., Saint-Marc, P., Medioni, G.: B-Snakes: Implementation and application to stereo. In: Proceedings of the Image Understanding Workshop, Sept. 1990, pp. 720–726 (1990)

  5. Charfi, M., Zrida, J.: Speed improvement of B-Snake algorithm using dynamic programming optimization. IEEE Trans. Image Process. 20(10), 2848–2855 (2011)

    Article  MathSciNet  Google Scholar 

  6. Cohen, L.D.: On active contours models and balloons. Comput. Vis. Graph. Image Process. Image Underst. 53, 211–218 (1991)

    MATH  Google Scholar 

  7. Cohen, L.D., Cohen, I.: Finite-element methods for active contour models and balloons for 2-d and 3-d images. IEEE Trans. Pattern Anal. Mach. Intell. 5(11), 1131–1147 (1993)

  8. Xu, C., Prince, J.L.: Generalized gradient vector flow external forces for active contours. Signal Process. 71, 131–139 (1998)

    Article  MATH  Google Scholar 

  9. Xu, C.: Deformable Models with Application to Human Cerebral Cortex Reconstruction from Magnetic Resonance Images. Phd thesis, Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA (1999)

  10. Hsu, C.Y., Chen, S.H., Wang, K.L.: Active contour model with a novel image force field. In: 16th IPPR Conference on Computer Vision, Graphics and Image Processing, 17–19 Aug, pp. 477–483 (2003)

  11. Li, C., Liu, J., Foxa, M.D.: Segmentation of external force field for automatic initialization and splitting of snakes. Pattern Recognit. 38, 1947–1960 (2005)

    Article  Google Scholar 

  12. Li, B., Acton, S.T.: Active contour external force using vector field convolution for image segmentation. IEEE Trans. Image Process. 16(8), 2069–2106 (2007)

    Article  MathSciNet  Google Scholar 

  13. Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on the Hamilton-Jacobi formulation. J. Comput. Phys. 79, 12–49 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  14. Caselles, V., Catte, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numer. Math. 66(1), 1–31 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: a level set approach. IEEE Trans. Pattern. Anal. Mach. Intell. 17(2), 158–175 (1995)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Adalsteinsson, D., Sethian, J.: A fast level set method for propagating interfaces. J. Comput. Phys. 118(2), 269–277 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Adalsteinsson, D., Sethian, J.: The fast construction of extension velocities in level set methods. J. Comput. Phys. 148(1), 2–22 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  20. Min, C.: On reinitializing level set functions. J. Comput. Phys. 229(8), 2764–2772 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Li, C., Xu, C., Gui, C., Fox, M.D.: Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process. 19(12), 3243–3254 (2010)

    Article  MathSciNet  Google Scholar 

  22. Ge, X., Tian, J.: An automatic active contour model for multiple objects. In: Proceedings 16th International Conference on Pattern Recognition, vol. 2, pp. 881–884 (2002)

  23. Tauber, C., Batatia, H., Ayache, A.: A general Quasi-automatic initialization for Snakes: application to ultrasound images. IEEE Int. Conf. Image Process. 2, 806–809 (2005)

    Google Scholar 

  24. Li, B., Acton, S.T.: Automatic active model initialization via Poisson inverse gradient. IEEE Trans. Image Process. 17(8), 1406–1420 (2008)

    Article  MathSciNet  Google Scholar 

  25. Selvadurai, A.P.S.: Partial Differential Equations in Mechanics 1: Fundamentals, Laplace’s Equation, Diffusion Equation, Wave Equation, Chapter 1.1. Springer, Berlin (2000)

  26. Margolin, L.G., Shashkova, M., Smolarkiewiczb, P.K.: A discrete operator calculus for finite difference approximations. Comput. Methods Appl. Mech. Eng. 187(3–4), 365–383 (2000)

    Article  MATH  Google Scholar 

  27. Sukumar, N., Bolander, J.E.: Numerical computation of discrete differential operators on non-uniform grids. Comput. Model. Eng. Sci. x(x), 1–15 (2003)

  28. Kroon, D.J.: Segmentation of the Mandibular Canal in Cone-Beam CT Data. PhD thesis, Signals & Systems group, EEMCS Faculty, University of Twente, ISBN 978-90-365-3280-8, Netherlands (2011)

  29. Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors thank Dr. Béchir Abdelmoula of the Ibn Zohr Center of Radiology of Tunis for providing the CT medical image data.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Houda Bakir.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bakir, H., Charfi, M. & Zrida, J. Automatic active contour segmentation approach via vector field convolution. SIViP 10, 9–18 (2016). https://doi.org/10.1007/s11760-014-0695-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-014-0695-7

Keywords

Navigation