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 “probe” 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 (“decision trees”) 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.
KeywordsDecision Tree Concept Class Color Classis Simple Polygon Night Vision
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- E. Arkin and J. Mitchell. Applications of combinatorics and computational geometry to pattern recognition. Technical report, Cornell University, 1990.Google Scholar
- E.M. Arkin, H. Meijer, J.S.B. Mitchell, D. Rappaport, and S.S. Skiena. Decision trees for geometric models. Proc. Ninth ACM Symp. on Comput. Geometry, 1993.Google Scholar
- E. Bienenstock, D. Geman, and S. Geman. A relational approach in object recognition. Technical report, Brown University, 1988.Google Scholar
- E. Bienenstock, D. Geman, S. Geman, and D.E. McClure. Phase II: Development of laser radar ATR algorithms. Contract No. DAAL02-89-C-0081, CECOM Center for Night Vision and Electro-Optics, 1990.Google Scholar
- L. Hyafil and R. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5:15–17, 1976.Google Scholar
- V. Mirelli. Computer vision is a highly structured optimization problem. Manuscript, Center for Night Vision and Electro-Optics, Fort Belvoir, VA, 1990.Google Scholar
- B. Moret. Decision trees and diagrams. Computing Surveys, pages 593–623, 1982.Google Scholar
- C. H. Papadimitriou. On certain problems in algorithmic vision. Technical report, Computer Science, UCSD, 1991.Google Scholar