Journal of Mathematical Imaging and Vision

, Volume 52, Issue 1, pp 108–123 | Cite as

The Role of Diffusion in Figure Hunt Games

  • Julia DieboldEmail author
  • Sibel Tari
  • Daniel Cremers


We consider the task of tracing out target figures hidden in teeming figure pictures known as figure hunt games. Figure hunt games are a popular genre of visual puzzles; a timeless classic for children, artists and cognitive scientists. We argue and experimentally demonstrate that diffusion is a key to algorithmically search for a target figure in a binary line drawing. Particularly suited to the considered task, we propose a diffuse representation which diffuses the image while retaining the contour information.


Screened Poisson PDE and variants Level sets Non-linear diffusion Figure hunt games Teeming figure pictures Applications of variational and PDE methods 



We thank three anonymous reviewers for their constructive feedback. We also acknowledge the financial support from the Alexander von Humboldt Foundation and Tubitak through Grant 112E208.


  1. 1.
    Ambrosio, L., Tortorelli, V.M.: Approximation of functional depending on jumps by elliptic functional via t-convergence. Commun. Pure Appl. Math. 43(8), 999–1036 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Aslan, C., Tari., S.: An axis-based representation for recognition. In: IEEE International Conference on Computer Vision (ICCV), vol. 2, pp. 1339–1346 (2005)Google Scholar
  3. 3.
    Aubert, G., Aujol, J.F.: Poisson skeleton revisited: a new mathematical perspective. J. Math. Imaging Vision (JMIV) 48(1), 149–159 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Ballard, D.H.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recognit. 13(2), 111–122 (1981)CrossRefzbMATHGoogle Scholar
  5. 5.
    Barrow, H.G., Tenenbaum, J.M., Bolles, R.C., Wolf, H.C.: Parametric correspondence and chamfer matching: two new techniques for image matching. In: International Joint Conference on Artificial Intelligence (IJCAI), vol. 2, pp. 659–663. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (1977)Google Scholar
  6. 6.
    Bergbauer, J., Tari, S.: Wimmelbild analysis with approximate curvature coding distance images. In: Scale Space and Variational Methods in Computer Vision (SSVM), pp. 489–500. Springer, Berlin (2013)Google Scholar
  7. 7.
    Blake, A., Zisserman, A.: Visual Reconstruction, vol. 2. MIT press, Cambridge (1987)Google Scholar
  8. 8.
    Chu, H.K., Hsu, W.H., Mitra, N.J., Cohen-Or, D., Wong, T.T., Lee, T.Y.: Camouflage images. ACM Trans. Gr. 29(4), 51 (2010)Google Scholar
  9. 9.
    Fornasier, M., Toniolo, D.: Fast, robust and efficient 2D pattern recognition for re-assembling fragmented images. Pattern Recognit. 38(11), 2074–2087 (2005)CrossRefGoogle Scholar
  10. 10.
    Gottschaldt, K.: Über den Einfluss der Erfahrung auf die Wahrnehmung von Figuren. Psychol. Forsch. 8(1), 261–317 (1926)Google Scholar
  11. 11.
    Gurumoorthy, K.S., Rangarajan, A.: A Schrödinger equation for the fast computation of approximate Euclidean distance functions. In: Scale Space and Variational Methods in Computer Vision (SSVM), pp. 100–111. Springer, Berlin (2009)Google Scholar
  12. 12.
    Keles, H., Ozkar, M., Tari, S.: Weighted shapes for embedding perceived wholes. Environ. Plan. 39, 360–375 (2012)CrossRefGoogle Scholar
  13. 13.
    Ma, T., Yang, X., Latecki, L.J.: Boosting chamfer matching by learning chamfer distance normalization. In: European Conference on Computer Vision (ECCV), pp. 450–463. Springer, Berlin (2010)Google Scholar
  14. 14.
    Mainberger, M., Schmaltz, C., Berg, M., Weickert, J., Backes, M.: Diffusion-based image compression in steganography. In: International Symposium on Advances in Visual Computing (ISVC), pp. 219–228. Springer, Berlin (2012)Google Scholar
  15. 15.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, Berlin (2003)zbMATHGoogle Scholar
  17. 17.
    Paragios, N.: A variational approach for the segmentation of the left ventricle in cardiac image analysis. Int. J. Comput. Vis. (IJCV) 50(3), 345–362 (2002)CrossRefzbMATHGoogle Scholar
  18. 18.
    Tari, S., Genctav, M.: From a modified Ambrosio-Tortorelli to a randomized part hierarchy tree. In: Scale Space and Variational Methods in Computer Vision (SSVM), pp. 267–278. Springer, Berlin (2012)Google Scholar
  19. 19.
    Tari, S., Genctav, M.: From a non-local Ambrosio-Tortorelli phase field to a randomized part hierarchy tree. J. Math. Imaging Vis. (JMIV) 49(1), 69–86 (2014)CrossRefzbMATHGoogle Scholar
  20. 20.
    Tari, S., Shah, J., Pien, H.: Extraction of shape skeletons from grayscale images. Comput. Vis. Image Underst. 66(2), 133–146 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Technische Universität MünchenMunichGermany
  2. 2.Middle East Technical UniversityAnkaraTurkey

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