This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Motion Estimation Using Statistical Learning Theory
April 2004 (vol. 26 no. 4)
pp. 466-478

Abstract—This paper describes a novel application of Statistical Learning Theory (SLT) to single motion estimation and tracking. The problem of motion estimation can be related to statistical model selection, where the goal is to select one (correct) motion model from several possible motion models, given finite noisy samples. SLT, also known as Vapnik-Chervonenkis (VC), theory provides analytic generalization bounds for model selection, which have been used successfully for practical model selection. This paper describes a successful application of an SLT-based model selection approach to the challenging problem of estimating optimal motion models from small data sets of image measurements (flow). We present results of experiments on both synthetic and real image sequences for motion interpolation and extrapolation; these results demonstrate the feasibility and strength of our approach. Our experimental results show that for motion estimation applications, SLT-based model selection compares favorably against alternative model selection methods, such as the Akaike's fpe, Schwartz' criterion (sc), Generalized Cross-Validation (gcv), and Shibata's Model Selector (sms). The paper also shows how to address the aperture problem using SLT-based model selection for penalized linear (ridge regression) formulation.

[1] H. Akaike, Statistical Predictor Information Ann. Inst. of Statistical Math., vol. 22, pp. 203-217, 1970.
[2] Y. Aloimonos and Z. Duric, Estimating Heading Direction Using Normal Flow Int'l J. Computer Vision, vol. 13, pp. 33-56, 1994.
[3] A.R. Barron, Universal Approximation Bounds for Superpositions of a Sigmoidal Function IEEE Trans. Information Theory, vol. 39, no. 3, pp. 930-945, Mar. 1993.
[4] M.J. Black and P. Anandan, The Robust Estimation of Multiple Motions: Parametric and Piecewise-Smooth Flow Fields Computer Vision and Image Understanding, vol. 63, pp. 75-104, 1996.
[5] M.J. Black, Y. Yacoob, and S.X. Ju, Recognizing Human Motion Using Parametrized Models of Optical Flow Motion-Based Recognition, S. Mubarak and R. Jain, eds., pp. 245-269, Kluwer, 1997.
[6] M.J. Black, D.J. Fleet, and Y. Yacoob, Robustly Estimating Changes in Image Appearance Computer Vision and Image Understanding, vol. 78, pp. 8-31, 2000.
[7] K. Bubna and C.V. Stewart, Model Selection and Surface Merging in Reconstruction Algorithms Proc. Conf. Computer Vision and Pattern Recognition, pp. 895-902, 1998.
[8] K. Bubna and C.V. Stewart, Model Selection Techniques and Merging Rules for Range Data Segmentation Algorithms Computer Vision and Image Understanding, vol. 80, pp. 215-245, 2000.
[9] V. Cherkassky and F. Mulier, Learning from Data. Wiley, 1998.
[10] V. Cherkassky, X. Shao, F. Mulier, and V. Vapnik, Model Selection for Regression Using VC-Generalization Bounds IEEE Trans. Neural Networks, vol. 10, pp. 1075-1089, 1999.
[11] P. Craven and G. Wahba, Smoothing Noisy Data with Spline Functions Numerische Math., vol. 31, pp. 377-403, 1979.
[12] Z. Duric, F. Li, Y. Sun, and H. Wechsler, Using Normal Flow for Detection and Tracking of Limbs in Color Images Proc. Int'l Conf. Pattern Recognition, 2002.
[13] J.H. Friedman, An Overview of Predictive Learning and Function Approximation From Statistics to Neural Networks: Theory and Pattern Recognition Applications, V. Cherkassky, J.H. Friedman, and H. Wechsler, eds., NATO ASI Series F, vol. 136, Springer, 1994.
[14] F. Girosi, Regularization Theory, Radial Basis Functions and Networks From Statistics to Neural Networks: Theory and Pattern Recognition Applications, V. Cherkassky, J.H. Friedman, and H. Wechsler, eds., NATO ASI Series F, v. 136, Springer, 1994.
[15] G.H. Golub and C.F. Van Loan, Matrix Computation, third ed. John Hopkins Univ. Press, 1996.
[16] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel, Robust Statistics: An Approach Based on Influence Functions. Wiley, 1986.
[17] P.J. Huber, Robust Statistics. Wiley, 1981.
[18] W. Lee, P. Bartlett, and R. Williamson, Efficient Agnostic Learning in Neural Networks with Bounded Fan-In IEEE Trans. Information Theory, vol. 42, pp. 2118-2132, 1996.
[19] P. Meer, D. Mintz, and A. Rosenfeld, Robust Regression Methods for Computer Vision: A Review Int'l J. Computer Vision, vol. 6, pp. 59-70, 1991.
[20] P. Meer, C.V. Stewart, and D.E. Tyler, Robust Computer Vision: An Interdisciplinary Challenge Computer Vision and Image Understanding, vol. 78, pp. 1-7, 2000.
[21] T.M. Moeslund and E. Granum, A Survey of Computer Vision-Based Human Motion Capture Computer Vision and Image Understanding, vol. 81, pp. 231-268, 2001.
[22] S. Nayar and T. Poggio, Early Visual Learning, S. Nayar and T. Poggio, eds., Oxford Univ. Press, 1996.
[23] T. Poggio and C.R. Shelton, Machine Learning, Machine Vision, and the Brain AI Magazine, vol. 20, no. 3, pp. 37-55, 1999.
[24] B.D. Ripley, Pattern Recognition and Neural Networks. Cambridge Univ. Press, 1996.
[25] P.H.S. Torr, An Assessment of Information Criteria for Model Selection Proc. Conf. Computer Vision and Pattern Recognition, pp. 47-53, 1997.
[26] R. Shibata, An Optimal Selection of Regression Variables Biometrika, vol. 68, pp. 45-54, 1981.
[27] G. Schwartz, Estimating the Dimension of a Model Ann. Statistics, vol. 6, pp. 461-464, 1978.
[28] E. Trucco and A. Verri, Introductory Techniques for 3D Computer Vision. Prentice Hall, 1998.
[29] V.N. Vapnik, Statistical Learning Theory. Wiley, 1998.
[30] V.N. Vapnik, The Nature of Statistical Learning Theory, second ed. Springer Verlag, 1999.

Index Terms:
Aperture problem, complexity control, condition number, image flow, model selection, motion estimation, robust learning, statistical learning theory, tracking, visual motion.
Citation:
Harry Wechsler, Zoran Duric, Fayin Li, Vladimir Cherkassky, "Motion Estimation Using Statistical Learning Theory," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 4, pp. 466-478, April 2004, doi:10.1109/TPAMI.2004.1265862
Usage of this product signifies your acceptance of the Terms of Use.