From Inpainting to Active Contours

  • François Lauze
  • Mads Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)


We introduce a novel type of region based active contour using image inpainting. Usual region based active contours assume that the image is divided into several semantically meaningful regions and attempt to differentiate them through recovering dynamically statistical optimal parameters for each region. In case when perceptually distinct regions have similar intensity distributions, the methods mentioned above fail. In this work, we formulate the problem as optimizing a ”background disocclusion” criterion, a disocclusion that can be performed by inpainting. We look especially at a family of inpainting formulations that includes the Chan and Shen Total Variation Inpainting (more precisely a regularization of it). In this case, the optimization leads formally to a coupled contour evolution equation, an inpainting equation, as well as a linear PDE depending on the inpainting. The contour evolution is implemented in the framework of level sets. Finally, the proposed method is validated on various examples.


Computer Vision Active Contour Active Contour Model Image Inpainting Shape Derivative 
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  1. 1.
    IEEE Computer Society Press, Boston (June 1995)Google Scholar
  2. 2.
    Aubert, G., Barlaud, M., Jehan-Besson, S., Faugeras, O.: Image segmentation using active contours: Calculus of variations or shape gradients? SIAM Journal of Applied Mathematics 63(6), 2128–2154 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ballester, C., Bertalmio, M., Caselles, V., Sapiro, G., Verdera, J.: Filling-in by joint interpolation of vector fields and gray levels. IEEE Transactions on Image Processing 10(8), 1200–1211 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: Akeley, K. (ed.) Proceedings of the SIGGRAPH, pp. 417–424. ACM Press, ACM SIGGRAPH, Addison Wesley Longman (2000)Google Scholar
  5. 5.
    Bruhn, A., Weickert, J., Feddern, C., Kohlberger, T., Schnörr, C.: Variational Optical Flow Computation in Real Time. IEEE Transactions on Image Processing 14(5), 608–615 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Caselles, V., Catte, F., Coll, T., Dibos, F.: A geometric model for active contours. Numerische Mathematik 66, 1–31 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proceedings of the 5th International Conference on Computer Vision [1], pp. 694–699Google Scholar
  8. 8.
    Chan, T., Shen, J.: Mathematical models for local nontexture inpainting. SIAM journal of appl. Math 62(3), 1019–1043 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chan, T., Vese, L.: Active contours without edges. IEEE Transactions on Image Processing 10(2), 266–277 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    Laurent, D.: Cohen and Isaac Cohen. Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(11), 1131–1147 (1993)CrossRefGoogle Scholar
  11. 11.
    Cremers, D., Schnoerr, C., Weickert, J.: Diffusion-snakes: Combining statistical shape knowledge and image information in a variational framework. In: 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision (2001)Google Scholar
  12. 12.
    Cremers, D., Kohlberger, T., Schnorr, C.: Nonlinear Shape Statistics in Mumford Shah Based Segmentation. In: European Conference on Computer Vision, pp. 93–108 (2002)Google Scholar
  13. 13.
    Evans, L.C.: Partial Differential Equations, Graduate Studies in Mathematics. In: Proceedings of the American Mathematical Society. , vol. 19 (1998)Google Scholar
  14. 14.
    Karlsson, A., Overgaard, N.: Theory for Variational Area-Based Segmentation Using Non-Quadratic Penalty Functions. In: International Conference on Computer Vision and Pattern Recognition. IEEE Comput. Soc, Los Alamitos (2005) (to appear)Google Scholar
  15. 15.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. In: First International Conference on Computer Vision, London, June 1987, pp. 259–268 (1987)Google Scholar
  16. 16.
    Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Proceedings of the 5th International Conference on Computer Vision [1], pp. 810–815Google Scholar
  17. 17.
    Masnou, S., Morel, J.M.: Level lines based disocclusion. In: International Conference on Image Processing, vol. III, pp. 259–263 (1998)Google Scholar
  18. 18.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42, 577–684 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Osher, S., Paragios, N. (eds.): Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  20. 20.
    Paragios, N., Deriche, R.: Geodesic active regions: a new paradigm to deal with frame partition problems in computer vision. Journal of Visual Communication and Image Representation, Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics 13(1/2), 249–268 (2002)Google Scholar
  21. 21.
    Rousson, M., Brox, T., Deriche, R.: Active unsupervised texture segmentation on a diffusion based space. In: International Conference on Computer Vision and Pattern Recognition, Madison, Wisconsin, USA, June 2003, vol. 2, pp. 699–704 (2003)Google Scholar
  22. 22.
    Rousson, M., Paragios, N.: Shape priors for level set representations. In: European Conference on Computer Vision, May 2002, vol. 2, pp. 78–92 (2002)Google Scholar
  23. 23.
    Rybak, I.V.: Monotone and Conservative Difference Schemes for Elliptic Equations with Mixed Derivatives. Mathematical Modelling and Analysis 9(2), 169–178 (2004)zbMATHMathSciNetGoogle Scholar
  24. 24.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Sciences. In: Cambridge Monograph on Applied and Computational Mathematics. Cambridge University Press, Cambridge (1999)Google Scholar
  25. 25.
    Xu, C., Prince, J.L.: Gradient Vector Flow: A New External Force for Snakes. In: International Conference on Computer Vision and Pattern Recognition, p. 66 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • François Lauze
    • 1
  • Mads Nielsen
    • 1
  1. 1.Departement of InnovationThe IT University of CopenhagenDenmark

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