Image Inpainting by Cooling and Heating

  • David Gustavsson
  • Kim S. Pedersen
  • Mads Nielsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)


We discuss a method suitable for inpainting both large scale geometric structures and stochastic texture components. We use the well-known FRAME model for inpainting. We introduce a temperature term in the learnt FRAME Gibbs distribution. By using a fast cooling scheme a MAP-like solution is found that can reconstruct the geometric structure. In a second step a heating scheme is used that reconstruct the stochastic texture. Both steps in the reconstruction process are necessary, and contribute in two very different ways to the appearance of the reconstruction.


Inpainting FRAME ICM MAP Simulated Annealing 


  1. 1.
    Chan, T.F., Shen, J.: Variational image inpainting. Communications on Pure and Applied Mathematics 58 (2005)Google Scholar
  2. 2.
    Efros, A.A., Freeman, W.T.: Image quilting for texture synthesis and transfer. In: Proceedings of SIGGRAPH ’01, Los Angeles, California, USA (August 2001)Google Scholar
  3. 3.
    Efros, A.A., Leung, T.K.: Texture synthesis by non-parametric sampling. In: IEEE International Conference on Computer Vision, Corfu, Greece, September 1999, pp. 1033–1038. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  4. 4.
    Bonet, J.S.D.: Multiresolution sampling procedure for analysis and synthesis of texture images. In: Computer Graphics, ACM SIGGRAPH, pp. 361–368 (1997)Google Scholar
  5. 5.
    Bertalmio, M., Vese, L., Sapiro, G., Osher, S.: Simultaneous structure and texture image inpainting. IEEE Transcations On Image Processing 12(8), 882–889 (2003)CrossRefGoogle Scholar
  6. 6.
    Gustavsson, D., Pedersen, K.S., Nielsen, M.: Geometric and texture inpainting by gibbs-sampling. In: SSBA07 (2007)Google Scholar
  7. 7.
    Zhu, S.C., Wu, Y.N., Mumford, D.: Filters, random fields and maximum entropy (frame): To a unified theory for texture modeling. International Journal of Computer Vision 27(2), 107–126 (1998)CrossRefGoogle Scholar
  8. 8.
    Zhu, S.C., Wu, Y.N., Mumford, D.: Minimax entropy principle and its application to texture modelling. Neural Computation 9(8), 1627–1660 (1997)CrossRefGoogle Scholar
  9. 9.
    Geman, S., Geman, D.: Stochastic relaxation, gibbs distribution, and the bayesian restoration of images. IEEE Transaction PAMI 6, 721–741 (1984)zbMATHGoogle Scholar
  10. 10.
    Winkler, G.: Image Analysis, Random Fields, and Markov Chain Monte Carlo Methods. Stochastic Modelling and Applied Probability, vol. 27. Springer, Heidelberg (2006)Google Scholar
  11. 11.
    Bigun, J.: Vision with Direction - A Systematic Introduction to Image Processing and Computer Vision. Springer, Heidelberg (2006)Google Scholar
  12. 12.
    Jain, A.K., Farrokhnia, F.: Unsupervised texture segmentation using gabor filters. Pattern Recogn. 24(12), 1167–1186 (1991)CrossRefGoogle Scholar
  13. 13.
    ter Haar Romeny, B.M.: Front-End Vision and Multi-Scale Image Analysis: Multi-Scale Computer Vision Theory and Applications, written in Mathematica. Computional Imaging and Vision, vol. 27. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  14. 14.
    Liu, J.S.: Monte Carlo Strategies in Scientific Computing. Springer Series in Statistics. Springer, Heidelberg (2004)Google Scholar
  15. 15.
    Zhu, S.C., Mumford, D.: Prior learning and gibbs reaction-diffusion. IEEE Transaction on Pattern Analysis and Machine Intelligence 19(11), 1236–1250 (1997)CrossRefGoogle Scholar
  16. 16.
    Zhu, S.C., Mumford, D.: Grade: Gibbs reaction and diffusion equation - a framework for pattern synthesis, denoising, image enhancement, and clutter removal. IEEE Trans. PAMI 19(11), 1627–1660 (1997)Google Scholar
  17. 17.
    Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures. American Mathematical Society (AMS), Boston (2001)zbMATHGoogle Scholar
  18. 18.
    Aujol, J.F., Gilboa, G., Chan, T., Osher, S.: Structure-texture image decomposition — modeling, algorithms, and parameter selection. International Journal of Computer Vision 67(1), 111–136 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • David Gustavsson
    • 1
  • Kim S. Pedersen
    • 2
  • Mads Nielsen
    • 2
  1. 1.IT University of Copenhagen, Rued Langgaards Vej 7, DK-2300 Copenhagen SDenmark
  2. 2.DIKU, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen ØDenmark

Personalised recommendations