This Article 
 Bibliographic References 
 Add to: 
Bounds on Shape Recognition Performance
July 1995 (vol. 17 no. 7)
pp. 666-680

Abstract—The localization and the recognition tasks are analyzed here relying on a probabilistic model, and independently of the recognition method used. Rigorous upper and lower bounds on the probability that a set of measurements is sufficient to localize an object within a certain precision, are derived. The bounds quantify the difficulty of the localization task regarding many of its aspects, including the number of measurements, the uncertainty in their position, the information they reveal, and the “ability of the objects to confuse the recognizer.” Similar results are obtained for the recognition task. The asymptotic difficulty of recognition/localization tasks is characterized by a single parameter, thus making it possible to compare between different tasks. The bounds provide a theoretical benchmark to which experimentally measured performance of localization/recognition methods can be compared.

[1] H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl, "Congruence, Similarity and Symmetries of Geometric Objects," Discrete Computing in Geometry, vol. 3, pp. 237-256, 1988.
[2] E.M. Arkin, L.P. Chew, D.P. Huttenlocher, K. Kedem, and J.S.B. Mitchell, "An Efficiently Computable Metric for Comparing Polygonal Shapes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 209-216, 1991.
[3] H.S. Baird, Model-Based Image Matching Using Location. Cambridge, Mass.: MIT Press, 1985.
[4] G.M. Benedek and A. Itai,“Learnability by fixed distributions,” Proc. of COLT 88, pp. 80-90. Theoretical Computer Science, to appear.
[5] P.J. Besl and R. Jain,“Three-dimensional object recognition,” ACM Computing Surveys, vol. 17, pp. 75-145, Mar. 1985.
[6] A.C. Cass,“Feature matching for object localization in the presence of uncertainty,” Proc. 3rd Int’l Conf. on Comp. Vis.,Osaka, 1991, pp. 360–364.
[7] M. Costa,R.M. Haralick,, and L.G. Shapiro,“Optimal affine-invariant point matching,” Proc. 6th Israeli Conf. on AI, 1989, pp. 35–61.
[8] T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley&Sons, 1991.
[9] R.E. Ellis,“Geometric uncertainties in polyhedral object recognition,” IEEE Tran. Rob. Aut., vol. 7, no. 3, 1991, pp. 361–371.
[10] O.D. Faugeras and M. Hebert,“A 3D recognition and positioning algorithm using geometrical matching between primitive surfaces,” 8th Int’l Joint Conf. Artificial Intell., 1983, pp. 996–1,002.
[11] W.E.L. Grimson,“The combinatorics of local constraints in model-based recognition and localization from sparse data,” J. ACM, vol. 33, no. 4, 1986, pp. 658–686.
[12] W.E.L. Grimson, Object Recognition by Computer. MIT Press, 1990.
[13] W.E.L. Grimson,“The effect of indexing on the complexity of object recognition,” Proc. 3rd Int’l Conf. on Comp. Vis.,Osaka, 1991, pp. 644–651.
[14] W.E.L. Grimson and D.P. Huttenlocher, "On the Sensitivity of the Hough Transform for Object Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 3, pp. 255-274, Mar. 1990.
[15] W.E.L. Grimson and D.P. Huttenlocher,“On the sensitivity of geometric hashing,” Proc. Int’l Conf. Computer Vision, pp. 334-338, 1990.
[16] W.E.L. Grimson and D.P. Huttenlocher, “On the Verification of Hypothesized Matches in Model-Based Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 12, pp. 1201-1213, 1991.
[17] W.E.L Grimson and D.P. Huttenlocher, eds.,special issues on the interpretation of 3D scenes,IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 13, no. 10, 1991, and vol. 14, no. 2, 1992.
[18] W.E.L. Grimson,D.P. Huttenlocher,, and D.W. Jacobs,“A study of affine matching with bounded sensor error,” Proc. European Conf. Computer Vision, pp. 291-306, 1992.
[19] W.E.L. Grimson and T. Lozano-Perez,“Model based recognition and localization from sparse range or tactile data,” Int’l J. Rob. Res., vol. 3, no. 3, 1984, pp. 3–35.
[20] P.G. Gottschalk,J.L. Turney,, and T.N. Mudge,“Efficient recognition of partially visible objects using a logarithmic complexity matching technique,” Int’l J. of Rob. Res., vol. 8, no. 6, 1989, pp. 110–131.
[21] M. Lindenbaum,“Bounds on shape recognition performance,” CIS report 9215, Computer Science Dept., Technion, Haifa, Israel, September 1992.
[22] M. Lindenbaum,“On the amount of data required for reliable recognition,” Int’l Conf. Pattern Recognition,Jerusalem, 1994. See also CIS report 9329, Computer Science Dept., Technion, Haifa, Israel, November 1993.
[23] Y. Lamdan and H.J. Wolfson, “On the Error Analysis of‘Geometric Hashing’,” Proc. IEEE. Conf. Computer Vision and Pattern Recognition, pp. 22-27, 1991.
[24] Y. Moses and S. Ullman,“Limitations of non model-based recognition systems,” AI memo no. 1,301. Cambridge, Mass., AI Lab, MIT, 1991.
[25] J.L. Mundy and A.J. Heller,“The evolution and testing of a model-based object recognition system,” 3rd Int’l Conf. on Computer Vision, 1990, pp. 268–282.

Index Terms:
Recognition, localization, probabilistic models, object similarity, performance evaluation, computer vision.
Michael Lindenbaum, "Bounds on Shape Recognition Performance," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 7, pp. 666-680, July 1995, doi:10.1109/34.391409
Usage of this product signifies your acceptance of the Terms of Use.