The Role of Diffusion in Figure Hunt Games


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.

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  1. 1.

    The integer constraints on \(t_r\), \(t_c\) can also be omitted with the drawback of higher computational costs. However, our experiments showed a sufficient accuracy when restricting the translation to integers.


  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)

    Article  MATH  MathSciNet  Google 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)

  3. 3.

    Aubert, G., Aujol, J.F.: Poisson skeleton revisited: a new mathematical perspective. J. Math. Imaging Vision (JMIV) 48(1), 149–159 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  4. 4.

    Ballard, D.H.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recognit. 13(2), 111–122 (1981)

    Article  MATH  Google 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)

  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)

  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)

  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)

    Article  Google Scholar 

  10. 10.

    Gottschaldt, K.: Über den Einfluss der Erfahrung auf die Wahrnehmung von Figuren. Psychol. Forsch. 8(1), 261–317 (1926)

  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)

  12. 12.

    Keles, H., Ozkar, M., Tari, S.: Weighted shapes for embedding perceived wholes. Environ. Plan. 39, 360–375 (2012)

    Article  Google 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)

  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)

  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)

    Article  MATH  MathSciNet  Google Scholar 

  16. 16.

    Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, Berlin (2003)

    MATH  Google 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)

    Article  MATH  Google 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)

  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)

    Article  MATH  Google 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)

    Article  Google Scholar 

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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.

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Correspondence to Julia Diebold.

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Diebold, J., Tari, S. & Cremers, D. The Role of Diffusion in Figure Hunt Games. J Math Imaging Vis 52, 108–123 (2015).

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