Point probe decision trees for geometric concept classes

A fundamental problem in model-based computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a ldquoproberdquo to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies (ldquodecision treesrdquo) for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal.These results grew out of discussions that began in a series of workshops on Geometric Probing in Computer Vision, sponsored by the Center for Night Vision and Electro-Optics, Fort Belvoir, Virginia, and monitored by the U.S. Army Research Office. The views, opinions, and/or findings contained in this report are those of the authors and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation.