Classic mosaic is one of the oldest and most durable art forms. There has been a growing interest in simulating classic mosaics from digital images recently. To be visually pleasing, a mosaic should satisfy the following constraints: tiles should be non-overlapping, tiles should align to the perceptually important edges in the underlying digital image, and orientation of the neighbouring tiles should vary smoothly across the mosaic. Most of the existing approaches operate in two steps: first they generate tile orientation field and then pack the tiles according to this field. However, previous methods perform these two steps based on heuristics or local optimisation which, in some cases, is not guaranteed to converge. Some other major disadvantages of previous approaches are: (i) either substantial user interaction or hard decision making such as edge detection is required before mosaicing starts (ii) the number of tiles per mosaic must be fixed beforehand, which may cause either undesired overlap or gap space between the tiles. In this work, we propose a novel approach by formulating the mosaic simulating problem in a global energy optimisation framework. Our algorithm also follows the two-step approach, but each step is performed with global optimisation. For the first step, we observe that the tile orientation constraints can be naturally formulated in an energy function that can be optimised with the α-expansion algorithm. For the second step of tightly packing the tiles, we develop a novel graph cuts based algorithm. Our approach does not require user interaction, explicit edge detection, or fixing the number of tiles, while producing results that are visually pleasing.


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  1. 1.
    Hausner, A.: Simulating decorative mosaics. In: Proceedings of SIGGRAPH 2001, pp. 573–580 (2001)Google Scholar
  2. 2.
    Elber, G., Wolberg, G.: Rendering traditional mosaics. The Visual Computer 19, 67–78 (2003)CrossRefGoogle Scholar
  3. 3.
    Blasi, G.D., Gallo, G.: Artificial mosaics. The Visual Computer 21, 373–383 (2005)CrossRefGoogle Scholar
  4. 4.
    Battiato, S., Blasi, G.D., Farinella, G.M., Gallo, G.: A novel technique for opus vermiculatum mosaic rendering. In: Proceedings of ACM/WSCG 2006, pp. 3247–3259 (2004)Google Scholar
  5. 5.
    Schlechtweg, S., Germer, T., Strothotte, T.: Renderbots-multi-agent systems for direct image generation. Computer Graphics Forum 24(2), 137–148 (2005)CrossRefGoogle Scholar
  6. 6.
    PhotoShop: Adobe photoshop (2006)Google Scholar
  7. 7.
    Boykov, Y., Veksler, O., Zabih, R.: Efficient approximate energy minimization via graph cuts. IEEE transactions on PAMI 21(12), 1222–1239 (2001)Google Scholar
  8. 8.
    Kwatra, V., Schodl, A., Essa, I., Turk, G., Bobick, A.: Graphcut textures: Image and video synthesis using graph cuts. ACM Transactions on Graphics, SIGGRAPH 2003 22(3), 277–286 (2003)Google Scholar
  9. 9.
    Agarwala, A., Dontcheva, M., Agrawala, M., Drucker, S., Colburn, A., Curless, B., Salesin, D., Cohen, M.: Interactive digital photomontage. ACM Transaction on Graphics (Proceedings of SIGGRAPH 2004) 23(3), 294–302 (2004)CrossRefGoogle Scholar
  10. 10.
    Eden, A., Uyttendaele, M., Szeliski, R.: Seamless image stitching of scenes with large motions and exposure differences. In: Proceedings of 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 2498–2505 (2006)Google Scholar
  11. 11.
    Kolmogorov, V., Zabih, R.: Computing visual correspondence with occlusion via graph cuts. In: Proceedings of IEEE International Conference on Computer Vision, pp. 508–515 (2001)Google Scholar
  12. 12.
    Kim, J., Kolmogorov, V., Zabih, R.: Visual correspondence using energy minimization and mutual information. In: Proceedings of IEEE International Conference on Computer Vision, vol. 2, pp. 1033–1040 (2003)Google Scholar
  13. 13.
    Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M.: Comparative study of energy minimization methods for markov random fields. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 16–29. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Intelligence(PAMI) 24, 137–148 (2004)Google Scholar
  15. 15.
    Viola, P., Jones, M.: Rapid object detection using a boosted cascade of simple features. In: Proceedings of the IEEE CVPR 2001, vol. 1, pp. 511–518 (2001)Google Scholar
  16. 16.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 147–159 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yu Liu
    • 1
  • Olga Veksler
    • 1
  • Olivier Juan
    • 1
  1. 1.Department of Computer Science, University of Western Ontario, London, Ontario, N6A 5B7Canada

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