International Journal of Computer Vision

, Volume 69, Issue 1, pp 27–42 | Cite as

Higher Order Active Contours

  • Marie Rochery
  • Ian H. Jermyn
  • Josiane Zerubia


We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies. While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals, and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families of contours that share complex geometric properties, without making reference to any particular shape, and they require no pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Networks are a shape family of great importance in a number of applications, including remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures, and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising experimental results are shown on real images.


active contour shape prior geometric higher-order polynomial quadratic road network remote sensing 


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  1. Adalsteinsson, D. and Sethian, J. A. 1999. The fast construction of extension velocities in level set methods. J. Comp. Phys., 148:2–22MathSciNetCrossRefGoogle Scholar
  2. Barzohar, M. and Cooper, D. 1996.Automatic finding of main roads in aerial images by using geometric-stochastic models and estimation. IEEE Trans. Patt. Anal. Mach. Intell., 18(7):707–721CrossRefGoogle Scholar
  3. Bossavit, A. 2002.Applied differential geometry: A compendium,
  4. Caselles, V., Catte, F., Coll, T., and Dibos, F. 1993.A geometric model for active contours. Numerische Mathematik, 66:1–31MathSciNetCrossRefGoogle Scholar
  5. Caselles, V., Kimmel, R., and Sapiro, G. 1997.Geodesic active contours. Int’l J. Comp. Vis., 22(1):61–79CrossRefGoogle Scholar
  6. Chan, T. F. and Vese, L. A. 2001.Active contours without edges. IEEE Trans. Im. Proc., 10-2:266–277CrossRefGoogle Scholar
  7. Chen, Y., Thiruvenkadam, S., Tagare, H. D., Huang, F., Wilson, D., and Geiser, E. 2001.On the incorporation of shape priors into geometric active contours. Proc. IEEE Workshop VLSM, pp. 145–152Google Scholar
  8. Cohen, L. D. 1991.On active contours and balloons. CVGIP: Image Understanding, 53:211–218zbMATHCrossRefGoogle Scholar
  9. Cremers, D., Schnorr, C., and Weickert, J. 2001.Diffusion-snakes: combining statistical shape knowledge and image information in a variational framework. Proc. IEEE Workshop VLSM, pp. 137–144Google Scholar
  10. Fischler, M. A., Tenenbaum, J. M., and Wolf, H. C. 1981.Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique. Comp. Graph. and Im. Proc., 15:201–223CrossRefGoogle Scholar
  11. Foulonneau, A., Charbonnier, P., and Heitz, F. 2003.Geometric shape priors for region-based active contours. Proc. IEEE ICIP., 3:413– 416Google Scholar
  12. Fua, P. and Leclerc, Y. G. 1990.Model driven edge detection. Mach. Vis. and Appl., 3:45–56CrossRefGoogle Scholar
  13. Geman, D. and Jedynak, B. 1996.An active testing model for tracking roads in satellite images. IEEE Trans. Patt. Anal. Mach. Intell., 18:1–14CrossRefGoogle Scholar
  14. Jehan-Besson, S., Barlaud, M., and Aubert, G. 2003. DREAM2S: Deformable regions driven by an Eulerian accurate minimization method for image and video segmentation. Int’l J. Comp. Vis., 53:45–70CrossRefGoogle Scholar
  15. Jermyn, I. H. and Ishikawa, H. 2001.Globally optimal regions and boundaries as minimum ratio cycles. IEEE Trans. Patt. Anal. Mach. Intell. (Special Section on Graph Algorithms and Computer Vision), 23(10):1075–1088Google Scholar
  16. Kass, M., Witkin, A., and Terzopoulos, D. 1988.Snakes: Active contour models. Int’l J. Comp. Vis., pp. 321–331Google Scholar
  17. Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., and Yezzi, A. 1995.Gradient flows and geometric active contour models. Proc. ICCV, pp. 810–815.Google Scholar
  18. Kimmel, R. and Bruckstein, A. M. 2003.On regularized laplacian zero crossings and other optimal (ed.), integrators. Int’l J. Comp. Vis., 53(3):225–243.CrossRefGoogle Scholar
  19. Lacoste, C., Descombes, X., and Zerubia, J. 2002.A comparative study of point processes for line network extraction in remote sensing.Research Report 4516, INRIA, France.Google Scholar
  20. Laptev, I., Lindeberg, T., Eckstein, W., Steger, C., and Baumgartner, A. 2000.Automatic extraction of roads from aerial images based on scale space and snakes. Mach. Vis. and Appl., 12:23–31CrossRefGoogle Scholar
  21. Leventon, M. E., Grimson, W. E. L., and Faugeras, O. 2000.Statistical shape influence in geodesic active contours. Proc. IEEE CVPR, 1:316–322Google Scholar
  22. Malladi, R., Sethian, J. A., and Vemuri, B. C. 1995.Shape modeling with front propagation: A level set approach. IEEE Trans. Patt. Anal. Mach. Intell., 17:158–175CrossRefGoogle Scholar
  23. Merlet, N. and Zerubia, J. 1996.New prospects in line detection by dynamic programming. IEEE Trans. Patt. Anal. Mach. Intell., 18(4):426–431CrossRefGoogle Scholar
  24. Neuenschwander, W. M., Fua, P., Iverson, L., Székely, G., and Kubler, O. 1997.Ziplock snakes. Int’l J. Comp. Vis., 25(3):191–201CrossRefGoogle Scholar
  25. Osher, S. and Sethian, J. A. 1988.Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys., 79:12–49MathSciNetCrossRefGoogle Scholar
  26. Paragios, N. and Deriche, R. 2002.Geodesic active regions: A new framework to deal with frame partition problems in computer vision. Journal of Visual Communication and Image Representation, 13:249–268CrossRefGoogle Scholar
  27. Paragios, N. and Rousson, M. 2002.Shape priors for level set representations. Proc. ECCV, pp. 78–92Google Scholar
  28. Pavlidis, T. 1982. Algorithms for Graphics and Image Processing, chapter 7.Computer Science Press, Inc.Google Scholar
  29. Rochery, M., Jermyn, I. H. and Zerubia, J. 2003.Higher order active contours and their application to the detection of line networks in satellite imagery.In Proc. IEEE Workshop VLSM, at ICCV, Nice, France.Google Scholar
  30. Sethian, J. A. 1996. Fast marching methods. SIAM Rev., 41-2:199–235MathSciNetCrossRefGoogle Scholar
  31. Sethian, J. A. 1999. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Geometry Fluid Mechanics, Computer Vision and Materials Science.Cambridge University Press.Google Scholar
  32. Siddiqi, K., Kimia, B. B., and Shu, C-W. 1997.Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution. Graphical Models and Image Processing, 59:278–301CrossRefGoogle Scholar
  33. Steiner, A., Kimmel, R., and Bruckstein, A. M. 1998.Shape enhancement and exaggeration. Graphical Models and Image Processing, 60(2):1112–1124CrossRefGoogle Scholar
  34. Stoica, R., Descombes, X., and Zerubia, J. 2004.A Gibbs point process for road extraction from remotely sensed images. Int’l J. Comp. Vis., 57(2):121–136CrossRefGoogle Scholar
  35. Sussman, M. and Fatemi, E. 1997.An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM J. Sci. Comp., 20(4):1165–1191MathSciNetCrossRefGoogle Scholar
  36. Sussman, M., Smereka, P., and Osher, S. 1994.A level set approach for computing solutions to incompressible 2-phase flow. J. Comp. Phys., 114:146–159CrossRefGoogle Scholar
  37. Tupin, F., Maitre, H., Mangin, J-F., Nicolas, J-M., and Pechersky, E. 1998.Detection of linear features in SAR images: Application to road network extraction. IEEE Trans. Geoscience and Remote Sensing, 36(2):434–453CrossRefGoogle Scholar
  38. Vasilevskiy, A. and Siddiqi, K. 2002.Flux maximizing geometric flows. IEEE Trans. Patt. Anal. Mach. Intell., 24(12):1565–1578CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Marie Rochery
    • 1
  • Ian H. Jermyn
    • 1
  • Josiane Zerubia
    • 1
  1. 1.Ariana (joint research group INRIA/I3S)INRIAFrance

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