Skip to main content
Log in

Network snakes: graph-based object delineation with active contour models

  • Original Paper
  • Published:
Machine Vision and Applications Aims and scope Submit manuscript

Abstract

In this paper, a graph-based method of active contour models called network snakes is presented and investigated. Active contour models are a well-known method in computer vision, bridging the gap between low-level feature extraction or segmentation and high-level geometric representation of objects. But the original concept is limited to single closed object boundaries. Network snakes are the method enabling a free optimization of arbitrary graphs representing the geometric position of networks and boundaries between adjacent objects. The main impacts of network snakes are the combination of the image energy representing objects in the real world, the internal energy incorporating shape characteristics, and the topology representing the structure of the scene. The introduction and exploitation of the topology in a comprehensive energy functional turn out to be a powerful technique to cope with complex questions of object delineation from imagery. Network snakes are analyzed and evaluated with both synthetic and real data to point out the role of the required initialization, the benefit of the introduced topology and the transferability. Exemplary investigated real applications are the delineation of field boundaries from remotely sensed imagery, the refinement of road networks from airborne SAR images and bio-medical tasks delineating adjacent biological cells in microscopic images. Concluding remarks are given at the end to discuss potential future research.

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.

Similar content being viewed by others

References

  1. Blake A., Isard M.: Active Contours. Springer, Berlin (1998)

    Book  Google Scholar 

  2. Bresson X., Esedoglu S., Vandergheynst P., Thiran J.P., Osher S.: Fast Global Minimization of the Active Contour/Snake Model. J. Math. Imaging Vis. 28(2), 151–167 (2007)

    Article  MathSciNet  Google Scholar 

  3. Butenuth, M.: Segmentation of imagery using network snakes. Photogrammetrie Fernerkundung Geoinformation 1/2007, pp. 7–16 (2007)

  4. Butenuth, M., Heipke, C.: Network snakes-supported extraction of field boundaries from imagery. In: Kropatsch, W., Sablatnig, R., Hanbury, A. (eds.) Pattern Recognition, Lecture Notes in Computer Science, vol. 3663, pp. 417–424. Springer, Berlin (2005)

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Chan T.F., Vese L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)

    Article  MATH  Google Scholar 

  7. Cohen L.D., Cohen I.: Finite element methods for active contour models and balloons for 2D and 3D images. IEEE Trans. Pattern Anal. Mach. Intell. 15(11), 1131–1147 (1993)

    Article  Google Scholar 

  8. Delagnes P., Benois J., Barba D.: Active contours approach to object tracking in image sequences with complex background. Pattern Recognit. Lett. 16(2), 171–178 (1995)

    Article  Google Scholar 

  9. Delingette H., Montagnat J.: Shape and topology constraints on parametric active contours. Comput. Vis. Image Underst. 83(2), 140–171 (2001)

    Article  MATH  Google Scholar 

  10. Dickinson, S.J., Jasiobedzki, P., Olofsson, G., Christensen, H.I.: Qualitative tracking of 3-D objects using active contour networks. In: Proceedings of Computer Vision and Pattern Recognition, pp. 812–817 (1994)

  11. Fua, P.: Parametric models are versatile: the case of model based optimization. In: International Archives of Photogrammetry and Remote Sensing III/2, pp. 828–833 (1995)

  12. Fua P., Grün A., Haihong L.: Optimization-based approaches to feature extraction from aerial images. In: Dermanis, A., Grün, A., Sanso, F. (eds) Geomatic Methods for the Analysis of Data in the Earth Sciences, pp. 190–228. Springer, Berlin (1999)

    Google Scholar 

  13. Grün A., Li H.: Semi-automatic linear feature extraction by dynamic programming and LSB-snakes. Photogramm. Eng. Remote Sens. 63(8), 985–995 (1997)

    Google Scholar 

  14. Han X., Xu C., Prince J.L.: A topology preserving level set method for geometric deformable models. IEEE Trans. Pattern Anal. Mach. Intell. 25(6), 755–768 (2003)

    Article  Google Scholar 

  15. Jasiobedzki, P.: Adaptive adjacency graphs. In: Vemuri, B.C. (ed.) Geometric Methods in Computer Vision II, pp. 294–303 (1993)

  16. Kanizsa G.: Subjective Contours. Sci. Am. 234(4), 48–52 (1976)

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Lachaud J., Montanvert A.: Deformable meshes with automated topology changes for coarse-to-fine three-dimensional surface extraction. Med. Image Anal. 3(2), 187–207 (1999)

    Article  Google Scholar 

  19. Laptev I., Mayer H., Lindeberg T., Steger A., Baumgartner A.: Automatic extraction of roads from aerial images based on scale space and snakes. Mach. Vis. Appl. 12(1), 23–31 (2000)

    Article  Google Scholar 

  20. Leitner, F., Cinquin, P.: Complex topology 3-D objects segmentation. In: Larson, R.M., Nasr, H.N. (eds.) Model-Based Vision Development and Tools. SPIE 1609, pp. 16–26 (1992)

  21. Leroy, B., Herlin, I.L., Cohen, L.D.: Multi-resolution algorithms for active contour models. In: Proceedings of International Conference on Analysis and Optimization of Systems, pp. 58–65 (1996)

  22. Malladi R.: Geometric Methods in Bio-Medical Image Processing. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  23. 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 

  24. McInerney T., Terzopoulos D.: Deformable models in medical image analysis: a survey. Med. Image Anal. 1(2), 91–108 (1996)

    Article  Google Scholar 

  25. McInerney, T., Terzopoulos, D.: Topologically adaptable snakes. In: Proceedings of International Conference on Computer Vision, pp. 840–845 (1995)

  26. Merriman B., Bence J.K., Osher S.J.: Motion of multiple junctions: a level set approach. J. Comput. Phys. 112(2), 334–363 (1994)

    Article  MathSciNet  Google Scholar 

  27. Osher S., Paragios N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, Berlin (2003)

    MATH  Google Scholar 

  28. Paragios N., Deriche R.: Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans. Pattern Anal. Mach. Intell. 22(3), 266–280 (2000)

    Article  Google Scholar 

  29. Paragios N., Deriche R.: Geodesic active regions: a new framework to deal with frame partition problems in computer vision. J. Vis. Commun. Image Represent. 13(1), 249–268 (2002)

    Article  Google Scholar 

  30. Peteri, R., Celle, J., Ranchin, T.: Detection and extraction of road networks from high resolution satellite images. In: Proceedings of International Conference on Image Processing, pp. 301–304 (2003)

  31. Ray N., Acton S.T., Altes T., De Lange E.E., Brookeman J.: Merging parametric active contours within homogeneous image regions for MRI-based lung segmentation. IEEE Trans. Med. Imaging 22(2), 189–199 (2003)

    Article  Google Scholar 

  32. Singh A., Goldgof D.B., Terzopoulos D.: Deformable Models in Medical Image Analysis. IEEE Computer Society Press, Los Alamitos (1998)

    Google Scholar 

  33. Smith K.A., Solis F.J., Chopp D.L.: A projection method for motion of triple junctions by level sets. Interfaces Free Bound. 4(3), 263–276 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Sundaramoorthi G., Yezzi A.: Global regularizing flows with topology preservation for active contours and polygons. IEEE Trans. Image Process. 16(3), 803–812 (2007)

    Article  MathSciNet  Google Scholar 

  35. Suri J.S., Setarehdan S.K., Singh S.: Advanced Algorithmic Approaches to Medical Image Segmentation: State-of-the-Art Applications in Cardiology, Neurology, Mammography and Pathology. Springer, Berlin (2002)

    Google Scholar 

  36. Unal G., Yezzi A., Krim H.: Information-theoretic active polygons for unsupervised texture segmentation. Int. J. Comput. Vis. 62(3), 199–220 (2005)

    Article  Google Scholar 

  37. 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)

    Article  MATH  Google Scholar 

  38. Williams D.J., Shah M.: A fast algorithm for active contours and curvature estimation. CVGIP: Image Underst. 55(1), 14–26 (1992)

    Article  MATH  Google Scholar 

  39. Wolf B., Heipke C.: Automatic extraction and delineation of single trees from remote sensing data. Mach. Vis. Appl. 18(5), 317–330 (2007)

    Article  Google Scholar 

  40. Xu, C., Prince, J.L.: Gradient vector flow: a new external force for snakes. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 66–71 (1997)

  41. Xu C., Prince J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. Image Process. 7(3), 359–369 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yezzi, A., Tsai, A., Willsky, A.: A statistical approach to snakes for bimodal and trimodal imagery. In: Proceedings of International Conference on Computer Vision, pp. 898–903 (1999)

  43. Zhang, B., Zimmer, C., Olivo-Marin, J.: Tracking fluorescent cells with coupled geometric active contours. In: Proceedings of International Symposium on Biomedical Imaging: Nano to Macro, pp. 476–479 (2004)

  44. Zhao H., Chan T., Merriman B., Osher S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127(1), 179–195 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zhu, S.C., Lee, T.S., Yuille, A.L.: Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. In: Proceedings of International Conference on Computer Vision, pp. 416–425 (1995)

  46. Zhu S.C., Yuille A.L.: Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 18(9), 884–900 (1996)

    Article  Google Scholar 

  47. Zimmer C., Olivo-Marin J.: Coupled parametric active contours. IEEE Trans. Pattern Anal. Mach. Intell. 27(11), 1838–1842 (2005)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthias Butenuth.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Butenuth, M., Heipke, C. Network snakes: graph-based object delineation with active contour models. Machine Vision and Applications 23, 91–109 (2012). https://doi.org/10.1007/s00138-010-0294-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00138-010-0294-8

Keywords

Navigation