A Variational Method for the Optimization of Tone Mapping Operators

  • Praveen Cyriac
  • Thomas Batard
  • Marcelo Bertalmío
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8333)


Given any metric that compares images of different dynamic range, we propose a method to reduce their distance with respect to this metric. The key idea is to consider the metric as a non local operator. Then, we transform the problem of distance reduction into a non local variational problem. In this context, the low dynamic range image having the smallest distance with a given high dynamic range is the minimum of a suitable energy, and can be reached through a gradient descent algorithm. Dealing with an appropriate metric, we present an application to Tone Mapping Operator (TMO) optimization. We apply our gradient descent algorithm, where the initial conditions are Tone Mapped (TM) images. Experiments show that our algorithm does reduce the distance of the TM images with the high dynamic range source images, meaning that our method improves the corresponding TMOs.


Tone mapping Dynamic range independent metric Contrast distortion Variational methods 


  1. 1.
    Adams, J.E., Deever, A.T., Morales, E.O., Pillman, B.H.: Perceptually based Image Processing Algorithm Design. Perceptual Digital Imaging: Methods and Applications 6, 123 (2012)Google Scholar
  2. 2.
    Ashikhmin, M.: A Tone Mapping Algorithm for High Contrast Images. In: Proc. Eurographics Workshop Rendering, pp. 1–11 (2002)Google Scholar
  3. 3.
    Aydin, T.O., Mantiuk, R., Myszkowski, K., Seidel, H.-P.: Dynamic Range Independent Image Quality Assessment. In: Proc. ACM SIGGRAPH, pp. 1–10 (2008)Google Scholar
  4. 4.
    Daly, S.: The Visible Differences Predictor: An Algorithm for the Assessment of Image Fidelity. In: Watson, A.B. (ed.) Digital Images and Human Vision, pp. 179–206. MIT Press (1993)Google Scholar
  5. 5.
    Drago, F., Myszkowski, K., Annen, T., Chiba, N.: Adaptive Logarithmic Mapping for Displaying High Contrast Scenes. Computer Graphics Forum 22(3), 419–426 (2003)CrossRefGoogle Scholar
  6. 6.
    Durand, F., Dorsey, J.: Fast Bilateral Filtering for the Display of High Dynamic Range Images. In: Proc. ACM SIGGRAPH, pp. 257–266 (2002)Google Scholar
  7. 7.
  8. 8.
    Fattal, R., Lischinski, D., Werman, M.: Gradient Domain High Dynamic Range Compression. In: Proc. ACM SIGGRAPH, pp. 249–256 (2002)Google Scholar
  9. 9.
    Ferradans, S., Bertalmío, M., Provenzi, E., Caselles, V.: An Analysis of Visual Adaptation and Contrast Perception for Tone Mapping. IEEE Trans. on Pattern Analysis and Machine Intelligence 33(10), 2002–2012 (2011)CrossRefGoogle Scholar
  10. 10.
    Jobson, D., Rahman, Z., Woodell, G.: A Multiscale Retinex for Bridging the Gap between Color Images and the Human Observation of Scenes. IEEE Trans. Image Processing 6(7), 965–976 (1997)CrossRefGoogle Scholar
  11. 11.
    Krawczyk, G., Myszkowski, K., Seidel, H.-P.: Lightness Perception in Tone Reproduction for High Dynamic Range Images. Computer Graphics Forum 24(3), 635–645 (2005)CrossRefGoogle Scholar
  12. 12.
    Kuang, J., Johnson, G.M., Fairchild, M.: iCAM06: A Refined Image Appearance Model for HDR Image Rendering. J. Visual Comm. and Image Representation 18, 406–414 (2007)CrossRefGoogle Scholar
  13. 13.
    Mantiuk, R., Daly, S., Myszkowski, K., Seidel, H.-P.: Predicting Visible Differences in High Dynamic Range Images - Model and its Calibration. In: Human Vision and Electronic Imaging X. SPIE Proceedings Serie, vol. 5666, pp. 204–214 (2005)Google Scholar
  14. 14.
    Mantiuk, R., Myszkowski, K., Seidel, H.-P.: A Perceptual Framework for Contrast Processing of High Dynamic Range Images. ACM Trans. Applied Perception 3(3), 286–308 (2006)CrossRefGoogle Scholar
  15. 15.
    Mantiuk, R., Daly, S., Kerofsky, L.: Display Adaptative Tone Mapping. In: Proc. ACM SIGGRAPH, vol. 68 (2008)Google Scholar
  16. 16.
    Mantiuk, R., Kim, K.J., Rempel, A.G., Heidrich, W.: HDR-VDP-2: A Calibrated Visual Metric for Visibility and Quality Predictions in all Luminance Conditions. In: Proc. ACM SIGGRAPH, vol. 40 (2011)Google Scholar
  17. 17.
  18. 18.
    Pattanaik, S., Tumblin, J., Yee, H., Greenberg, D.: Time-Dependent Visual Adaptation for Fast Realistic Image Display. In: Proc. ACM SIGGRAPH, pp. 47–54 (2000)Google Scholar
  19. 19.
    Reinhard, E., Ward, G., Pattanaik, S., Debevec, P.: High Dynamic Range Imaging, Acquisition, Display, and Image-Based Lighting. Morgan Kaufmann (2005)Google Scholar
  20. 20.
    Reinhard, E., Devlin, K.: Dynamic Range Reduction Inspired by Photoreceptor Physiology. IEEE Trans. Visualization and Computer Graphics 11(1), 13–24 (2005)CrossRefGoogle Scholar
  21. 21.
    Shen, J.: On the Foundations of Vision Modeling, I. Weber’s law and Weberized TV (Total Variation) Restoration. Phys. D 175, 241–251 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Smith, K., Krawczyk, G., Myszkowski, K., Seidel, H.-P.: Beyond Tone Mapping: Enhanced Depiction of Tone Mapped HDR Images. Computer Graphics Forum 25(3), 427–438 (2006)CrossRefGoogle Scholar
  23. 23.
    Tumblin, J., Turk, G.: Lcis: A Boundary Hierarchy for Detail-Preserving Contrast Reduction. In: Proc. ACM SIGGRAPH, pp. 83–90 (1999)Google Scholar
  24. 24.
    Wang, Z., Bovik, A.C.: A Universal Image Quality Index. IEEE Signal Processing Letters 9(3), 81–84 (2002)CrossRefGoogle Scholar
  25. 25.
    Ward, G., Rushmeier, H., Piatko, C.: A Visibility Matching Tone Reproduction Operator for High Dynamic Range Scenes. IEEE Trans. Visualization and Computer Graphics 3(4), 291–306 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Praveen Cyriac
    • 1
  • Thomas Batard
    • 1
  • Marcelo Bertalmío
    • 1
  1. 1.Department on Information and Communication TechnologiesUniversitat Pompeu FabraBarcelonaSpain

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