International Journal of Computer Vision

, Volume 7, Issue 3, pp 195–210 | Cite as

The cost of choosing the wrong model in object recognition by constrained search

  • W. Eric
  • L. Grimson
Article
Received:
Revised:

Abstract

Many current recognition systems use variations on constrained tree search to locate objects in cluttered environments. If the system is simply finding instances of an object known to be in the scene, then previous formal analysis has shown that the expected amount of search is quadratic in the number of model and data features when all the data is known to come from a single object, but is exponential when spurious data is included. If one can group the data into subsets likely to have come from a single object, then terminating the search once a “good enough” interpretation is found reduces the expected search to cubic. Without successful grouping, terminated search is still exponential. These results apply to finding instances of a known object in the data. What happens when the object is not present? In this article, we turn to the problem of selecting models from a library, and examine the combinatorial cost of determining that an incorrectly chosen candidate object is not present in the data. We show that the expected search is again exponential, implying that naive approaches to library indexing are likely to carry an expensive overhead, since an exponential amount of work is needed to weed out each incorrect model. The analytic results are shown to be in agreement with empirical data for cluttered object recognition.

Keywords

Computer Vision Computer Image Object Recognition Recognition System Tree Search 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ayache, N., and Faugeras, O.D. 1986. HYPER: A new approach for the recognition and positioning of two-dimensional objects. IEEE Trans. Patt. Anal. Mach. Intell. 8(1): 44–54.Google Scholar
  2. Ballard, D.H. 1981. Generalizing the Hough transform to detect arbitrary patterns. Pattern Recognition 13(2): 111–122.Google Scholar
  3. Bolles, R.C., and Cain, R.A. 1982. Recognizing and locating partially visible objects: The local feature focus method. Intern. J. Robotics Res. 1(3): 57–82.Google Scholar
  4. Cass, T.A. 1988. A robust parallel implementation of 2D model-based recognition. IEEE Conf. Comput. Vision, Patt. Recog., Ann Arbor, MI, pp. 879–884.Google Scholar
  5. Cyganski, D., and Orr, J.A. 1985. Applications of tensor theory to object recognition and orientation determination. IEEE Trans. Patt. Anal. Mach. Intell. 7(6): 662–673.Google Scholar
  6. Davis, L.S. 1982. Hierarchical generalized Hough transforms and line-segment based generalized Hough transforms. Pattern Recognition. 15: pp. 277.Google Scholar
  7. Flynn, P.J., and Jain, A.K. 1991. BONSAI: 3D object recognition using constrained search. IEEE Trans. Patt. Anal. Mach. Intell. 13(10):1066–1075.Google Scholar
  8. Freuder, E.C., 1978. Synthesizing constraint expressions. Comm. ACM 21(11): 958–966.Google Scholar
  9. Freuder, E.C. 1982. A sufficient condition for backtrack-free search. J. Assoc. Comput. Mach. 29(1):24–32Google Scholar
  10. Gaschnig, J. 1979. Performance measurement and analysis of certain search algorithms. Ph.D. thesis, Carnegie-Mellon University, Computer Science.Google Scholar
  11. Gleason, G., and Agin, G.J. 1979. A modular vision system for sensorcontrolled manipulation and inspection. Proc. 9th Intern. Symp. Indust. Robots, pp. 57–70.Google Scholar
  12. Graham, R.L., Knuth, D.E., and Patashnik, O. 1989. Concrete Mathematics, Addison-Wesley: Reading, MA.Google Scholar
  13. Grimson, W.E.L. 1989. On the recognition of curved objects. IEEE Trans. Patt. Anal. Mach. Intell. 11(6): 632–643.Google Scholar
  14. Grimson, W.E.L. 1990a. The combinatorics of object recognition in cluttered environments using constrained search. Artificial Intelligence, 44(1–2): 121–166.Google Scholar
  15. Grimson, W.E.L. 1990b. The effect of indexing on the complexity of object recognition. Proc. 3rd Intern. Conf. Comput. Vision, Osaka, Japan, pp. 644–651.Google Scholar
  16. Grimson, W.E.L. 1991. The combinatorics of heuristic search termination for object recognition in cluttered environments. IEEE Trans. Patt. Anal. Mach. Intell. 13(9):920–935.Google Scholar
  17. Grimson, W.E.L., and Huttenlocher, D.P. 1988. On the sensitivity of the Hough transform for object recognition. Proc. 2nd Intern. Conf. Comput. Vision, Tarpon Springs, FL., pp. 700–706.Google Scholar
  18. Grimson, W.E.L., and Huttenlocher, D.P. 1989. On choosing thresholds for terminating search in object recognition. Memo 1110, M.I.T. Artificial Intelligence Laboratory (also to appear in IEEE Trans. Patt. Anal. Mach. Intell. 1991). 13(12):1201–1213.Google Scholar
  19. Grimson, W.E.L., and Lozano-Pérez, T. 1984. Model-based recognition and localization from sparse range or tactile data. Intern. J. Robotics Res., 3(3): 3–35.Google Scholar
  20. Grimson, W.E.L., and Lozano-Pérez, T. 1987. Localizing overlapping parts by searching the interpretation tree. IEEE Trans. Patt. Anal. Mach. Intell. 9(4): 469–482.Google Scholar
  21. Haralick, R.M., and Elliot, G.L. 1980. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14: 263–313.Google Scholar
  22. Haralick, R.M., and Shapiro, L.G. 1979. The consistent labeling problem: Part 1: IEEE Trans. Patt. Anal. Machine Intell., 1(4), pp. 173–184.Google Scholar
  23. Hough, P.V.C. 1962. Methods and means for recognizing complex patterns. U.S. Patent 3069654.Google Scholar
  24. Hu, M.K. 1962. Visual pattern recognition by moment invariants. IRE Trans. Inform. Theory 8: 179–187.Google Scholar
  25. Huttenlocher, D.P. and Ullman, S. 1987. Object recognition using alignment. Proc. 1st Intern. Conf. Comput. Vision, London, pp. 102–111.Google Scholar
  26. Illingworth, J., and Kittler, J. 1988. A survey of the Hough transform. Comput. Vision, Graphics, Image Proc. 44: 87–116.Google Scholar
  27. Knapman, J. 1987. 3D model identification from stereo data. Proc. 1st Intern. Conf. Comput. Vision, London, pp. 547–551.Google Scholar
  28. Lamdan, Y., Schwartz, J.T., and Wolfson, H.J. 1988. Object recognition by affine invariant matching. Proc. IEEE Conf. Comput. Vision. Patt. Recog., pp. 335–344.Google Scholar
  29. Lowe, D.G. 1985. Perceptual Organization and Visual Recognition. Kluwer Academic Publishers: Boston.Google Scholar
  30. Mackworth, A.K. 1977. Consistency in networks of constraints. Artificial Intelligence 8: 99–118.Google Scholar
  31. Mackworth, A.K., and Freuder, E.C. 1985. The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artificial Intelligence 25: 65–74.Google Scholar
  32. Murray, D.W., and Cook, D.B. 1988. Using the orientation of fragmentary 3D edge segments for polyhedral object recognition. Intern J. Comput. Vision. 2(2): 153–169.Google Scholar
  33. Nudel, B. 1983. Consistent-labeling problems and their algorithms: Expected-complexities and theory-based heuristics. Artificial Intelligence 21: 135–178.Google Scholar
  34. Silberberg, T.M., Harwood, D.A., and Davis, L.S. 1986. Object recognition using oriented model points. Comput. Vision. Graphics. Image Proc. 35: 47–71.Google Scholar
  35. Stockman, G., Kopstein, S., and Benett, S. 1982. Matching images to models for registration and object detection via clustering. IEEE Trans. Patt. Anal. Mach. Intell. 3(3): 229–241.Google Scholar
  36. Teague, M.R. 1980. Image analysis via the general theory of moments. J. Optical Soc. Amer. 70: 920–930.Google Scholar
  37. Thompson, D.W., and Mundy, J.L. 1987. Three-dimensional model matching from an unconstrained viewpoint. IEEE Intern. Conf. Robotics Autom., Raleigh, NC, pp. 28–220.Google Scholar
  38. Wang, Y.F., Magee, M.J., and Aggarwal, J.K. 1984. Matching three-dimensional objects using silhouettes. IEEE Trans. Patt. Anal. and Mach. Intell. 6(4): 513–518.Google Scholar
  39. Zahn, C.T. and Roskies, R.Z. 1972. Fourier descriptors for plane closed curves. IEEE Trans. Comput. 21(3): 269–281.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • W. Eric
    • 1
  • L. Grimson
    • 1
  1. 1.MIT Artificial Intelligence LaboratoryCambridge

Personalised recommendations