@Article{stewart:ijcv96,
author = {C.V.\ Stewart and R.\ Flatland and K.\ Bubna},
title = {Geometric constraints and stereo disparity
computation},
journal = ijcv,
year = 1996,
volume = 20,
number = 3,
pages = {143--168},
abstract = {Most stereo techniques compute disparity assuming
that it varies slowly along surfaces. We quantify
and justify this assumption, using weak assumptions
about surface orientation distributions in the world
to derive the density of disparity surface orientations.
The small disparity change assumption is justified by
the orientation density's heavy bias toward disparity
surfaces that are nearly parallel to the image plane.
In addition, the bias strengthens with smaller baselines,
larger focal lengths, and as surfaces move farther from
the cameras. To analyze current stereo techniques, we
derive three densities from the first density, those
of the disparity gradient magnitude, the directional
derivative of disparity, and the difference in disparity
between neighboring surface points. The latter may be
used in Bayesian algorithms computing dense disparity
fields. The directional derivative density and the
disparity difference density both show that feature-based
algorithms should strongly favor small disparity changes,
contrary to several well-known algorithms. Finally, we
use our original surface orientation density and the
gradient magnitude density to derive two new
"surfaces-from-stereo" techniques, techniques combining
feature-based matching and surface reconstruction. The
first uses the densities to severely restrict the search
range for the optimum fit. The second incorporates the
surface orientation density into the optimization criteria,
producing a Bayesian formulation. Both algorithms are
shown to be efficient and effective.}
}