Advertisement

Non-convex Relaxation of Optimal Transport for Color Transfer Between Images

  • Julien Rabin
  • Nicolas PapadakisEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

Optimal transport (OT) is a major statistical tool to measure similarity between features or to match and average features. However, OT requires some relaxation and regularization to be robust to outliers. With relaxed methods, as one feature can be matched to several ones, important interpolations between different features arise. This is not an issue for comparison purposes, but it involves strong and unwanted smoothing for transfer applications. We thus introduce a new regularized method based on a non-convex formulation that minimizes transport dispersion by enforcing the one-to-one matching of features. The interest of the approach is demonstrated for color transfer purposes.

Keywords

Optimal transport Relaxation Color transfer 

References

  1. 1.
    Achanta, R., Shaji, A., Smith, K., Lucchi, A., Fua, P., Süsstrunk, S.: SLIC superpixels compared to state-of-the-art superpixel methods. IEEE TPAMI 34(11), 2274–2282 (2012)CrossRefGoogle Scholar
  2. 2.
    Attouch, H., Bolte, J., Svaiter, B.: Convergence of descent methods for semi-algebraic and tame problems. Math. Program. 137(1–2), 91–129 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: NIPS 2013, pp. 2292–2300 (2013)Google Scholar
  4. 4.
    Ferradans, S., Papadakis, N., Peyré, G., Aujol, J.F.: Regularized discrete optimal transport. SIAM J. Imaging Sci. 7(3), 1853–1882 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ferradans, S., Papadakis, N., Rabin, J., Peyré, G., Aujol, J.F.: Blind deblurring using a simplified sharpness index. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds.) SSVM 2013. LNCS, vol. 7893, pp. 86–97. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  6. 6.
    Morovic, J., Sun, P.L.: Accurate 3d image colour histogram transformation. Pattern Recogn. Lett. 24(11), 1725–1735 (2003)CrossRefGoogle Scholar
  7. 7.
    Nikolova, M., Wen, Y.W., Chan, R.H.: Exact histogram specification for digital images using a variational approach. JMIV 46(3), 309–325 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ochs, P., Chen, Y., Brox, T., Pock, T.: ipiano: inertial proximal algorithm for nonconvex optimization. SIAM J. Imaging Sci. 7(2), 1388–1419 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Papadakis, N., Bugeau, A., Caselles, V.: Image editing with spatiograms transfer. IEEE TIP 21(5), 2513–2522 (2012)MathSciNetGoogle Scholar
  10. 10.
    Papadakis, N., Provenzi, E., Caselles, V.: A variational model for histogram transfer of color images. IEEE TIP 20(6), 1682–1695 (2011)MathSciNetGoogle Scholar
  11. 11.
    Pitié, F., Kokaram, A.C., Dahyot, R.: Automated colour grading using colour distribution transfer. CVIU 107, 123–137 (2007)Google Scholar
  12. 12.
    Pouli, T., Reinhard, E.: Progressive color transfer for images of arbitrary dynamic range. Comput. Graph. 35(1), 67–80 (2011)CrossRefGoogle Scholar
  13. 13.
    Rabin, J., Delon, J., Gousseau, Y.: Removing artefacts from color and contrast modifications. IEEE TIP 20(11), 3073–3085 (2011)MathSciNetGoogle Scholar
  14. 14.
    Rabin, J., Peyré, G.: Wasserstein regularization of imaging problem. In: IEEE ICIP 2011, pp. 1541–1544 (2011)Google Scholar
  15. 15.
    Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein barycenter and its application to texture mixing. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 435–446. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  16. 16.
    Rabin, J., Ferradans, S., Papadakis, N.: Adaptive color transfer with relaxed optimal transport. In: IEEE ICIP 2014 (2014)Google Scholar
  17. 17.
    Reinhard, E., Adhikhmin, M., Gooch, B., Shirley, P.: Color transfer between images. IEEE Trans. Comput. Graphics Appl. 21(5), 34–41 (2001)CrossRefGoogle Scholar
  18. 18.
    Su, Z., Zeng, K., Liu, L., Li, B., Luo, X.: Corruptive artifacts suppression for example-based color transfer. IEEE Trans. Multimedia 16(4), 988–999 (2014)CrossRefGoogle Scholar
  19. 19.
    Tai, Y.W., Jia, J., Tang, C.K.: Local color transfer via probabilistic segmentation by expectation-maximization. In: CVPR 2005, pp. 747–754 (2005)Google Scholar
  20. 20.
    Xiao, X., Ma, L.: Color transfer in correlated color space. In: ACM VRCIA 2006, pp. 305–309 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.GREYC, UMR 6072Université de CaenCaenFrance
  2. 2.CNRS, IMB, UMR 5251TalenceFrance

Personalised recommendations