visible to left

1
Surface visibility probabilities in 3D cluttered
scenes Michael Langer Center for Intelligent
Machines School of Computer Science, McGill
University, Montreal, Canada
4. Moving monocular observer (or static binocular
observer)
1. Motivation
3D reconstruction methods require a prior on
surface geometry. A typical prior is that
surfaces are piecewise smooth/continuous.
However, many natural scenes do not obey this
assumption e.g. plants, trees, forest. We will
need alternative priors for such scenes, in
order to more effectively perform 3D
reconstruction.
observer
2. Model

• Surfaces all have identical geometry spheres
  of radius R (or squares of width R)
• Surface centers are distributed uniformly and
  independently, with density h (Poisson)

Result Position (and existence) of maximum at
an intermediate speed (or disparity) depends on
perspective and occlusion effects.
occlusions
perspective
3. Static monocular observer
5. Binocular observer (probability of half
occlusions)
Simulation/Experiment 2 x 10 scenes rendered
with RADIANCE, and held constant.
Depth buffer gives histograms of binned depths.
Theory For a volume V, Poisson model gives
not visible to left (half occlusion)
not visible to left (half occlusion)
visible to left
visible to left
L
depth Z
depth Z
R
Result It is easy to show i.e.
same as monocular case, and falloff rate is
slower for larger R. Hence, binocular half
occlusions are less frequent for larger objects
(with fixed monocular visibility p(Z)).
Conditional visibility (Bayes)
Results Good fit (no surprise), but larger
standard errors for scenes found for scenes with
larger/fewer objects.