OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 11 — Oct. 31, 2012

Visibility in three-dimensional cluttered scenes

Michael S. Langer and Fahim Mannan  »View Author Affiliations

JOSA A, Vol. 29, Issue 9, pp. 1794-1807 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1096 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Three-dimensional (3D) cluttered scenes consist of a large number of small surfaces distributed randomly in a 3D view volume. The canonical example is the foliage of a tree or bush. 3D cluttered scenes are challenging for vision tasks such as object recognition and depth perception because most surfaces or objects are only partly visible. This paper examines the probabilities of surface visibility in 3D cluttered scenes. We model how the probabilities of visible gaps, depth discontinuities, and binocular and half-occluded points depend on scene parameters such as the size and density of the surfaces that make up the clutter, as well as on depth and inverse depth. Inverse depth is of particular interest since both binocular disparity and motion parallax depend directly on it. The probability models are verified using data from synthetic 3D cluttered scenes, which are generated using computer graphics.

© 2012 Optical Society of America

OCIS Codes
(150.6910) Machine vision : Three-dimensional sensing
(330.1400) Vision, color, and visual optics : Vision - binocular and stereopsis

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: January 3, 2012
Revised Manuscript: May 11, 2012
Manuscript Accepted: June 29, 2012
Published: August 8, 2012

Virtual Issues
Vol. 7, Iss. 11 Virtual Journal for Biomedical Optics

Michael S. Langer and Fahim Mannan, "Visibility in three-dimensional cluttered scenes," J. Opt. Soc. Am. A 29, 1794-1807 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. Rosenholtz, Y. Li, and L. Nakano, “Measuring visual clutter,” J. Vision 7, 1–22 (2007). [CrossRef]
  2. J. M. Wolfe, “Guided search 2.0: a revised model of visual search,” Psychon. Bull. Rev. 1, 202–238 (1994).
  3. M. A. Changizi and S. Shimojo, “X-ray vision and the evolution of forward-facing eyes,” J. Theor. Biol. 254, 756–767 (2008). [CrossRef]
  4. T. E. Avery and H. E. Burkhart, Forest Measurements, 5th ed. (McGraw-Hill, 2002).
  5. P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants (Springer-Verlag, 1990).
  6. P. Prusinkiewicz, “Modeling of spatial structure and development of plants: a review,” Scientia Horticulturae 74, 113–149 (1998). [CrossRef]
  7. T. Nilson, “A theoretical analysis of the frequency of gaps in plant stands,” Agric. Meteor. 8, 25–38 (1971).
  8. P. R. van Gardingen, G. E. Jackson, S. Hernandez-Daumas, G. Russell, and L. Sharp, “Leaf area index estimates obtained for clumped canopies using hemispherical photography,” Agric. Forest Meteor. 94, 243–257 (1999).
  9. J. M. Chen and J. Cihlar, “Plant canopy gap-size analysis theory for improving optical measurements of leaf-area index,” Appl. Opt. 34, 6211–6222 (1995). [CrossRef]
  10. H. Sinoquet, G. Sonohat, J. Phattaralerphong, and C. Godin, “Foliage randomness and light interception in 3-d digitized trees: an analysis from multiscale discretization of the canopy,” Plant Cell Environ. 28, 1158–1170 (2005). [CrossRef]
  11. D. L. Ruderman and W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994). [CrossRef]
  12. G. Matheron, Random Sets and Integral Geometry (Wiley, 1975).
  13. J. P. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).
  14. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987). [CrossRef]
  15. D. L. Ruderman, “Origins of scaling in natural images,” Vis. Res. 37, 3385–3398 (1997). [CrossRef]
  16. R. M. Balboa, C. W. Tyler, and N. M. Grzywacz, “Occlusions contribute to scaling in natural images,” Vis. Res. 41, 955–964 (2001). [CrossRef]
  17. J. Huang, A. Lee, and D. Mumford, “Statistics of range images,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 324–331.
  18. A. Lee, D. Mumford, and J. Huang, “Occlusion models for natural images: a statistical study of a scale-invariant dead leaves model,” Int. J. Comput. Vis. 41, 35–59 (2001). [CrossRef]
  19. Z. Yang and D. Purves, “Image/source statistics of surfaces in natural scenes,” Network Comput. Neural Syst. 14, 371–390 (2003). [CrossRef]
  20. B. Potetz and T. S. Lee, “Statistical correlations between two-dimensional images and three-dimensional structures in natural scenes,” J. Opt. Soc. Am. A 20, 1292–1303 (2003). [CrossRef]
  21. D. Calow and M. Lappe, “Local statistics of retinal optic flow for self-motion through natural sceneries,” Network Comput. Neural Syst. 18, 343–374 (2007). [CrossRef]
  22. S. Roth and M. J. Black, “On the spatial statistics of optical flow,” Int. J. Comput. Vis. 74, 33–50 (2007). [CrossRef]
  23. P. B. Hibbard, “A statistical model of binocular disparity,” Vis. Cogn. 15, 149–165 (2007).
  24. Y. Liu, A. Bovik, and L. Cormack, “Disparity statistics in natural scenes,” J. Vision 8(2):17, 1–22 (2008). [CrossRef]
  25. J. Harris and L. Wilcox, “The role of monocularly visible regions in the perception of three-dimensional scenes,” Vis. Res. 49, 2666–2685 (2009). [CrossRef]
  26. J. Forte, J. W. Peirce, and P. Lennie, “Binocular integration of partially occluded surfaces,” Vis. Res. 42, 1225–1235(2002). [CrossRef]
  27. P. Belhumeur, “A Bayesian approach to binocular stereopsis,” Int. J. Comput. Vis. 19, 237–260 (1996). [CrossRef]
  28. S. Kang, R. Szeliski, and J. Chai, “Handling occlusions in dense multi-view stereo,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. I:103–110.
  29. G. Egnal and R. Wildes, “Detecting binocular half-occlusions: Empirical comparisons of five approaches,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1127–1133 (2002). [CrossRef]
  30. V. Kolmogorov and R. Zabih, “Computing visual correspondence with occlusions via graph cuts,” in Proceedings of 8th IEEE International Conference on Computer Vision (IEEE, 2001), pp. II:508–515.
  31. Y. Wei and L. Quan, “Asymmetrical occlusion handling using graph cut for multi-view stereo,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, Vol. 2 (IEEE, 2005), pp. 902–909.
  32. V. Vaish, M. Levoy, R. Szeliski, C. L. Zitnick, and S. B. Kang, “Reconstructing occluded surfaces using synthetic apertures: stereo, focus and robust measures,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 2331–2338.
  33. A. Mittal and L. Davis, “A general method for sensor planning in multi-sensor systems: extension to random occlusion,” Int. J. Comput. Vis. 76, 31–52 (2007). [CrossRef]
  34. P. Hall, Introduction to the Theory of Coverage Processes(Wiley, 1988).
  35. S. Zacks, Stochastic Visibility in Random Fields, Lecture Notes in Statistics 95 (Springer-Verlag, 1994).
  36. B. Nadler, G. Fibich, S. Lev-Yehudi, and D. Cohen-Or, “A qualitative and quantitative visibility analysis in urban scenes,” Comput. Graphics 23, 655–666 (1999).
  37. J. H. van Hateren, “Theoretical predictions of spatiotemporal receptive fields of fly LMCs, and experimental validation,” J. Comp. Physiol. A 171, 157–170 (1992).
  38. M. Langer, “Surface visibility probabilities in 3d cluttered scenes,” in Proceedings of 10th European Conference on Computer Vision (Springer-Verlag, 2008), pp. I:401–412.
  39. H. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,” Proc. R. Soc. B 208, 385–397 (1980). [CrossRef]
  40. G. W. Larson and R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization (Morgan Kaufmann, 1998).
  41. R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov, A. Agarwala, M. Tappen, and C. Rother, “A comparative study of energy minimization methods for Markov random fields with smoothness-based priors,” IEEE Trans. Pattern Anal. Machine Intell. 30, 1068–1080 (2008). [CrossRef]
  42. “The blender greenhouse,” http://yorik.uncreated.net/greenhouse.html .
  43. “Ngplant—open source plant modeling suite,” http://ngplant.sourceforge.net/ .
  44. G. Kanizsa, Organization in Vision: Essays on Gestalt Perception (Praeger, 1979).
  45. M. Hansard, “Binocular projection of a random scene,” in Proceedings of British Machine Vision Conference (Springer-Verlag, 2012), to be published.
  46. D. C. Knill, “Surface orientation from texture: Ideal observers, generic observers and the information content of texture cues,” Vis. Res. 38, 1655–1682 (1998). [CrossRef]
  47. R. van Ee and B. Anderson, “Motion direction, speed, and orientation in binocular matching,” Nature 410, 690–694 (2001). [CrossRef]
  48. L. Zhang and S. M. Seitz, “Estimating optimal parameters for MRF stereo from a single image pair,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 331–342 (2007).
  49. K. Engel, M. Hadwiger, J. M. Kniss, and D. W. C. Rezk-Salama, Real-Time Volume Graphics (AK Peters, 2006).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited