Probabilities of binocular half occlusions in 3D cluttered scenes

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Probabilities of binocular half occlusions in
3D cluttered scenes

• Michael Langer
• School of Computer Science
• McGill University

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Occlusions
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Half Occlusions
monocular left monocular right
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Half Occlusions
monocular left monocular right
da Vinci Stereopsis Nakayama Shimojo,
Vision Research 1990
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Natural 3D Cluttered Scene
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Synthetic 3D cluttered scenes
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Two Questions

• Monocular How are visible surfaces distributed
  over depth?
• Binocular What percentage of visible surfaces
  at each depth are half occluded (binocular) ?

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Assumptions of Model
observer
density h
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Monocular Visibility
Take surface point at depth Z. Is it visible?
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Monocular Visibility
A point at depth Z is visible if and only if no
sphere center lies within a distance R from the
line of sight.
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Poisson model
V
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Poisson model
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Probability of monocular visibility
depth Z
depth Z
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Two Main Questions

• How are visible surfaces distributed over depth
  ?
• What percentage of points at each depth are half
  occluded ?

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Probability of binocular visibility
L
R
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Probability of binocular visibility
L
V
R
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Conditional probability of binocular visibility
Given that a point at depth Z is visible to the
right eye, what is the probability that it is
also visible to the left eye ?
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Conditional probability of visibility
left occluded
left visible
right visible at depth Z
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Conditional probability of visibility
left occluded
left visible
right visible at depth Z
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Conclusion

• The conditional probability that a surface point
  is visible to one eye, given that it is visible
  to the other eye, is an (approximately)
  exponentially decreasing function of depth.
• The decay rate depends on the size and density of
  the surfaces present.

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For more details, see paper

• Surface visibility probabilities in 3D cluttered
  scenes
• M.S. Langer
• 10th European Conference on Computer Vision
  (ECCV)
• Marseilles FR, Oct. 2008

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Computational Theory (Bayes)

• binocular vs. monocular
• half occluded

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Poisson model