Analyzing Scenes on a Supporting Plane  The Problem  Suppose we
constrain objects from a known set to stand in certain `upright'
poses on a supporting plane, for instance, chairs and tables on
the floor, or glasses and bottles on a table. The orientation of
such planes is often known, as for a mobile robot in flat
terrain. If the plane orientation is known, the space of object
poses that has to be searched for analyzing such a scene is
reduced to at most 4 dimensions (3 for translation in physical
space, 1 for rotation about an axis) per object. The pose space
is further reduced to 3 dimensions, if the height of the plane
is known, as for a robot's camera system mounted at a certain
height above the ground or table.  In such reduced parameter
spaces, a global search for a scene interpretation may be
feasible. Moreover, the particular nature of stereo data of such
scenes may be exploited by very efficient algorithms that
implement a computational shortcut and a good approximation to a
full maximum-likelihood i