Surface Visibility Probabilities in 3D Cluttered Scenes

  • Michael S. Langer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5302)


Many methods for 3D reconstruction in computer vision rely on probability models, for example, Bayesian reasoning. Here we introduce a probability model of surface visibilities in densely cluttered 3D scenes. The scenes consist of a large number of small surfaces distributed randomly in a 3D view volume. An example is the leaves or branches on a tree. We derive probabilities for surface visibility, instantaneous image velocity under egomotion, and binocular half–occlusions in these scenes. The probabilities depend on parameters such as scene depth, object size, 3D density, observer speed, and binocular baseline. We verify the correctness of our models using computer graphics simulations, and briefly discuss applications of the model to stereo and motion.


Partial Occlusion Surface Visibility Sphere Center Image Speed Visibility Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Belhumeur, P.: A Bayesian approach to binocular stereopsis. International Journal of Computer Vision 19(3), 237–260 (1996)CrossRefGoogle Scholar
  2. 2.
    Bravo, M.J., Farid, H.: A scale invariant measure of clutter. Journal of Vision 8(1), 1–9 (2008)CrossRefGoogle Scholar
  3. 3.
    Egnal, G., Wildes, R.P.: Detecting binocular half-occlusions: Empirical comparisons of five approaches. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(8), 1127–1133 (2002)CrossRefGoogle Scholar
  4. 4.
    Feller, W.: Introduction to Probability Theory and Its Applications. Wiley Series in Probability and Mathematical Statistics, vol. 1 (1968)Google Scholar
  5. 5.
    Garg, K., Nayar, S.K.: Vision and rain. International Journal of Computer Vision 75(1), 3–27 (2007)CrossRefGoogle Scholar
  6. 6.
    Grenander, U., Srivastava, A.: Probability models for clutter in natural images. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(4), 424–429 (2001)CrossRefGoogle Scholar
  7. 7.
    Hall, P.: Introduction to the Theory of Coverage Processes. John Wiley & Sons, Inc., Chichester (1988)zbMATHGoogle Scholar
  8. 8.
    Hegeman, K., Premože, S., Ashikhmin, M., Drettakis, G.: Approximate ambient occlusion for trees. In: I3D 2006: Proceedings of the 2006 symposium on Interactive 3D graphics and games, pp. 87–92. ACM, New York (2006)Google Scholar
  9. 9.
    Ward Larson, G., Shakespeare, R.: Rendering with Radiance: The Art and Science of Lighting Visualization. Morgan Kaufmann, San Francisco (1998)Google Scholar
  10. 10.
    Lee, A.B., Mumford, D., Huang, J.: Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model. International Journal of Computer Vision 41(1/2), 35–59 (2001)CrossRefzbMATHGoogle Scholar
  11. 11.
    Matheron, G.: Random Sets and Integral Geometry. John Wiley and Sons, Chichester (1975)zbMATHGoogle Scholar
  12. 12.
    Mittal, A., Davis, L.S.: A general method for sensor planning in multi-sensor systems: Extension to random occlusion. International Journal of Computer Vision 76(1), 31–52 (2008)CrossRefGoogle Scholar
  13. 13.
    Mutch, K.M., Thompson, W.B.: Analysis of accretion and deletion at boundaries in dynamic scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence 7(2), 133–138 (1985)CrossRefGoogle Scholar
  14. 14.
    Nadler, B., Fibich, G., Lev-Yehudi, S., Cohen-Or, D.: A qualitative and quantitative visibility analysis in urban scenes. Computers and Graphics 23(5), 655–666 (1999)CrossRefGoogle Scholar
  15. 15.
    Narasimhan, S.G., Nayar, S.K.: Vision and the atmosphere. International Journal of Computer Vision 48(3), 233–254 (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    Prusinkiewicz, P.: Modeling of spatial structure and development of plants: a review. Scientia Horticulturae 74, 113–149 (1998)CrossRefGoogle Scholar
  17. 17.
    Grzywacz, N.M., Balboa, R.M., Tyler, C.W.: Occlusions contribute to scaling in natural images. Vision Research 41(7), 955–964 (2001)CrossRefGoogle Scholar
  18. 18.
    Rosenholtz, R., Li, Y., Nakano, L.: Measuring visual clutter. Journal of Vision 7(2), 1–22 (2007)CrossRefGoogle Scholar
  19. 19.
    Roth, S., Black, M.J.: On the spatial statistics of optical flow. International Journal of Computer Vision 74(1), 33–50 (2007)CrossRefGoogle Scholar
  20. 20.
    Ruderman, D.L.: Origins of scaling in natural images. Vision Research 37(23), 3385–3398 (1997)CrossRefGoogle Scholar
  21. 21.
    Ruderman, D.L., Bialek, W.: Statistics of natural images: scaling in the woods. Physical Review Letters 73, 814–817 (1994)CrossRefGoogle Scholar
  22. 22.
    Schechner, Y.Y., Karpel, N.: Clear underwater vision. IEEE Conf. on Computer Vision and Pattern Recognition 1, I–536–I–543 (2004)Google Scholar
  23. 23.
    Serra, J.P.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)zbMATHGoogle Scholar
  24. 24.
    Simoncelli, E.P., Adelson, E.H., Heeger, D.J.: Probability distributions of optical flow. In: Proc Conf. on Computer Vision and Pattern Recognition, Mauii, Hawaii, pp. 310–315. IEEE Computer Society Press, Los Alamitos (1991)Google Scholar
  25. 25.
    Sinoquet, H., Sonohat, G., Phattaralerphong, J., Godin, C.: Foliage randomness and light interception in 3d digitized trees: an analysis of 3d discretization of the canopy. Plant Cell and Environment 29, 1158–1170 (2005)CrossRefGoogle Scholar
  26. 26.
    Szeliski, R., Golland, P.: Stereo matching with transparency and matting. International Journal of Computer Vision 32(1), 45–61 (1999)CrossRefGoogle Scholar
  27. 27.
    van Hateren, J.H.: Theoretical predictions of spatiotemporal receptive fields of fly LMCs, and experimental validation. Journal of Comparative Physiology A 171, 157–170 (1992)CrossRefGoogle Scholar
  28. 28.
    Weiss, Y.: Smoothness in layers: Motion segmentation using nonparametric mixture estimation. In: IEEE Conf. on Computer Vision and Pattern Recognition, pp. 520–526 (1997)Google Scholar
  29. 29.
    Weiss, Y., Fleet, D.J.: Probabilistic Models of the Brain: Perception and Neural Function. In: Velocity likelihoods in biological and machine vision, pp. 77–96. MIT Press, Cambridge (2002)Google Scholar
  30. 30.
    Zacks, S.: Stochastic Visibility in Random Fields. Lecture Notes in Statistics 95. Springer, Heidelberg (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael S. Langer
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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