Advertisement

Point probe decision trees for geometric concept classes

  • Esther M. Arkin
  • Michael T. Goodrich
  • Joseph S. B. Mitchell
  • David Mount
  • Christine D. Piatko
  • Steven S. Skiena
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)

Abstract

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.

Keywords

Decision Tree Concept Class Color Classis Simple Polygon Night Vision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Arkin and J. Mitchell. Applications of combinatorics and computational geometry to pattern recognition. Technical report, Cornell University, 1990.Google Scholar
  2. [2]
    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
  3. [3]
    E. Bienenstock, D. Geman, and S. Geman. A relational approach in object recognition. Technical report, Brown University, 1988.Google Scholar
  4. [4]
    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
  5. [5]
    B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. J. ACM, 39:1–54, 1992.CrossRefGoogle Scholar
  6. [6]
    M. Garey. Optimal binary identification procedures. SIAM J. Appl. Math., 23:173–186, 1972.CrossRefGoogle Scholar
  7. [7]
    M. T. Goodrich. A polygonal approach to hidden-line and hidden-surface elimination. CVGIP: Graphical Models and Image Processing, 54:1–12, 1992.CrossRefGoogle Scholar
  8. [8]
    L. Hyafil and R. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5:15–17, 1976.Google Scholar
  9. [9]
    L. Lovász. On the ratio of optimal integral and fractional covers. Discrete Mathematics, 13:383–390, 1975.CrossRefGoogle Scholar
  10. [10]
    V. Mirelli. Computer vision is a highly structured optimization problem. Manuscript, Center for Night Vision and Electro-Optics, Fort Belvoir, VA, 1990.Google Scholar
  11. [11]
    B. Moret. Decision trees and diagrams. Computing Surveys, pages 593–623, 1982.Google Scholar
  12. [12]
    C. H. Papadimitriou. On certain problems in algorithmic vision. Technical report, Computer Science, UCSD, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Esther M. Arkin
    • 1
  • Michael T. Goodrich
    • 2
  • Joseph S. B. Mitchell
    • 1
  • David Mount
    • 3
  • Christine D. Piatko
    • 4
  • Steven S. Skiena
    • 5
  1. 1.Applied MathSUNYStony Brook
  2. 2.Computer ScienceJohns HopkinsBaltimore
  3. 3.Computer Science and UMIACSUniversity of MarylandCollege Park
  4. 4.NISTGaithersburg
  5. 5.Computer ScienceSUNYStony Brook

Personalised recommendations