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An Integrated Model for Evaluating the Amount of Data Required for Reliable Recognition
November 1997 (vol. 19 no. 11)
pp. 1251-1264

Abstract—Many recognition procedures rely on the consistency of a subset of data features with a hypothesis as the sufficient evidence to the presence of the corresponding object. We analyze here the performance of such procedures, using a probabilistic model, and provide expressions for the sufficient size of such data subsets, that, if consistent, guarantee the validity of the hypotheses with arbitrary confidence. We focus on 2D objects and the affine transformation class, and provide, for the first time, an integrated model which takes into account the shape of the objects involved, the accuracy of the data collected, the clutter present in the scene, the class of the transformations involved, the accuracy of the localization, and the confidence we would like to have in our hypotheses. Interestingly, it turns out that most of these factors can be quantified cumulatively by one parameter, denoted "effective similarity," which largely determines the sufficient subset size. The analysis is based on representing the class of instances corresponding to a model object and a group of transformations, as members of a metric space, and quantifying the variation of the instances by a metric cover.

[1] W.E.L. Grimson and D.P. Huttenlocher, eds., special double issue on the Interpretation of 3D Scenes, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 10, Oct. 1991, and vol. 14, no. 2, Feb. 1992.
[2] Geometric Invariance in Computer Vision, J.L. Mundy and A.P. Zisserman, eds. MIT Press, 1992.
[3] 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.
[4] 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.
[5] K.B. Sarachik and W. Grimson, "Gaussian Error Models for Object Recognition," CVPR, pp. 400-406, 1993.
[6] S.J. Maybank, "Probabilistic Analysis of the Application of the Cross Ratio to Model Based Vision," Int'l J. Computer Vision, vol. 16, pp. 5-33, 1993.
[7] M. Lindenbaum, “Bounds on Shape Recognition Performance,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 7, pp. 666-680, July 1995.
[8] S. Ben-David and M. Lindenbaum, "Localization vs. Identification of Semi-Algebraic Sets," Proc. Sixth ACM Conf. Computational Learning Theory, pp. 327-336, 1993.
[9] M. Lindenbaum and S. Ben-David, "Applying vc-Dimension Analysis to Object Recognition," Proc. European Conf. Computer Vision, pp. 239-240, 1994, to appear in J. Machine Intelligence and Vision.
[10] M. Lindenbaum, "On the Amount of Information Required for Object Recognition," CIS Report 9329, Technion, Nov.1993 (revised July 1995). A shorter version appeared in Proc. Int'l Conf. Pattern Recognition, pp. 726-729, 1994.
[11] T.M. Breuel, "Higher-Order Statistics in Visual Object Recognition," Technical Report 93-02, IDIAP, June 1993.
[12] A. Amir and M. Lindenbaum, “Grouping-Based Nonadditive Verification,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 186-192, Feb. 1998.
[13] K.B. Sarachik, "The Effect of Gaussian Error in Object Recognition," Proc. Image Understanding Workshop, pp. 1,269-1,280, 1994.
[14] T. Hagerup and C. Rub, "A Guided Tour of Chernoff Bounds," Information Processing Letters, vol. 33, pp. 305-308, 1989.
[15] W.J. Rucklidge, “Locating Objects Using the Hausdorff Distance,” Proc. Int'l Conf. Computer Vision, pp. 457-464, 1995.
[16] 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. Robotic Research, vol. 8, no. 6, pp. 110-131, 1989.
[17] T.A. Cass, "Polynomial Time Object Recognition in the Presence of Clutter Occlusion, and Uncertainty," Proc. European Conf. Computer Vision, pp. 834-842, 1992.
[18] A. Rudshtein and M. Lindenbaum, "Qualifying the Performance of Feature-Based Recognition," Proc. Int'l Conf. Pattern Recognition, pp. 35-39, 1996.

Index Terms:
Object recognition, localization, pose estimation, similarity measures, noise models, performance analysis.
Citation:
Michael Lindenbaum, "An Integrated Model for Evaluating the Amount of Data Required for Reliable Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 11, pp. 1251-1264, Nov. 1997, doi:10.1109/34.632984
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