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Bayesian Estimation of Motion Vector Fields
September 1992 (vol. 14 no. 9)
pp. 910-927

A stochastic approach to the estimation of 2D motion vector fields from time-varying images is presented. The formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vector-binary Markov random fields. Two estimation criteria are studied. In the maximum a posteriori probability (MAP) estimation, the a posteriori probability of motion given data is maximized, whereas in the minimum expected cost (MEC) estimation, the expectation of a certain cost function is minimized. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs sampler. Two versions are developed: one for a discrete state space and the other for a continuous state space. The MAP estimation is incorporated into a hierarchical environment to deal efficiently with large displacements.

[1] P. Anandan, "Measuring visual motion from image sequences," Ph.D. thesis, Univ. of Mass., May 1987.
[2] M. Bertero, T. A. Poggio, and V. Torre, "Ill-posed problems in early vision,"Proc. IEEE, vol. 76, pp. 869-889, Aug. 1988.
[3] J. Besag, "Spatial interaction and the statistical analysis of lattice systems,"J. Roy. Stat. Soc., vol. B 36, pp. 192-236, 1974.
[4] J. Besag, "On the statistical analysis of dirty pictures,"J. Roy. Stat. Soc., vol. B 48, pp. 259-279, 1986.
[5] P. Bouthemy and P. Lalande, "Motion detection in an image sequence using Gibbs distributions," inProc. IEEE Int. Conf. Acoust. Speech Signal Processing, May 1989, pp. 1651-1654.
[6] P. Burt, "Fast filter transforms for image processing,"Comput. Vision Graphics Image Processing, vol. 16, pp. 20-51, 1981.
[7] H. Derin and H. Elliott, "Modeling and segmentation of noisy and textured images using Gibbs random fields,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 39-55, Jan. 1987.
[8] E. Dubois, "The sampling and reconstruction of time-varying imagery with application in video systems,"Proc. IEEE, vol. 73, pp. 502-522, Apr. 1985.
[9] W. Enkelmann, "Investigations of multigrid algorithms for the estimation of optical flow fields in image sequences,"Comput. Vision Graphics Image Processing, vol. 43, pp. 150-177, 1988.
[10] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
[11] M. A. Gennert and S. Negahdaripour, "Relaxing the brightness constancy assumption in computing optical flow," Artificial Intell. Lab., Mass. Inst. Technol., MIT AI Memo 975, June 1987.
[12] F. Glazer, "Hierarchical motion detection," Ph.D. thesis, Univ. of Mass., Feb. 1987.
[13] M. Hassner and J. Sklansky, "The use of Markov random fields as models for texture" inImage Modeling(E. A. Rosenfeld, Ed.). New York: Academic, 1981, pp. 185-198.
[14] F. Heitz and P. Bouthemy, "Motion estimation and segmentation using a global Bayesian approach," inProc. IEEE Int. Conf. Acoust. Speech Signal Processing, 1990, pp. 2305-2308.
[15] F. Heitz and P. Bouthemy, "Multimodal motion estimation and segmentation using Markov random fields," inProc. IEEE Int. Conf. Patt. Recogn., June 1990, pp. 378-383.
[16] E. Hildreth, "Computation underlying the measurement of visual motion,"Artificial Intell., vol. 23, pp. 309-354, 1984.
[17] B. P. Horn and B. Schunck, "Determining optical flow,"Artificial Intell., vol. 17, pp. 185-203, 1981.
[18] J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks,"Comput., vol. 21, pp. 52-63, Mar. 1988.
[19] R. G. Keys, "Cubic convolution interpolation for digital image processing,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 1153-1160, 1981.
[20] S. Kirkpatrick, C. Gelatt, Jr., and M. Vecchi, "Optimization by simulated annealing,"Sci., vol. 220, pp. 671-680, May 1983.
[21] J. Konrad and E. Dubois, "Estimation of image motion fields: Bayesian formulation and stochastic solution," inProc. IEEE Int. Conf. Acoust. Speech Signal Processing, Apr. 1988, pp. 1072-1075.
[22] J. Konrad and E. Dubois, "Multigrid Bayesian estimation of image motion fields using stochastic relaxation," inProc. IEEE Int. Conf. Comput. Vision, Dec. 1988, pp. 354-362.
[23] J. Konrad and E. Dubois, "Motion-compensated interpolation for TV frame-rate conversion," Tech. Rep. 26, INRS-Télécommunications, Oct. 1988.
[24] J. Konrad and E. Dubois, "Bayesian estimation of motion fields from image sequences," Ph.D. thesis, Dept. of Elect. Eng., McGill Univ., Montreal, June 1989.
[25] J. Konrad and E. Dubois, "Bayesian estimation of discontinuous motion in images using simulated annealing," inProc. Conf. Vision Interface VI'89June 1989, pp. 51-60.
[26] J. Konrad and E. Dubois, "Comparison of stochastic and deterministic solution methods in Bayesian estimation of 2-D motion,"Image Vision Comput., vol. 9, pp. 215-228, Aug. 1991.
[27] J. Marroquin, "Probablistic solution of inverse problems," Ph.D. thesis, Mass. Inst. Technol., Cambridge, Sept. 1985.
[28] D. Martinez, "Model-based motion estimation and its application to restoration and interpolation of motion pictures," Ph.D. thesis, Mass. Inst. Technol., Cambridge, Aug. 1986.
[29] N. Metropolis, A. Rosenbluth, M. Rosenbluth, H. Teller, and E. Teller, "Equation of state calculations by fast computing machines,"J. Chem. Phys., vol. 21, pp. 1087-1092, June 1953.
[30] D. W. Murray and B. F. Buxton, "Scene segmentation from visual motion using global optimization,"IEEE Trans. Patt. Analy. Machine Intell., vol. PAMI-9, pp. 161-180, 1987.
[31] H.-H. Nagel and W. Enkelmann, "An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 5, pp. 565-593, Sept. 1986.
[32] S. Ross,Applied Probability Models with Optimization Applications. San Francisco: Holden-Day, 1970.
[33] B. Schunck, "Motion segmentation and estimation," Ph.D. thesis, Mass. Inst. Technol., Cambridge, May 1983.
[34] O. Tretiak and L. Pastor, "Velocity estimation from image sequences with second order differential operators," inProc. IEEE Int. Conf. Patt. Recogn., July 1984, pp. 16-19.
[35] J. Woods, "Two-dimensional discrete Markov random fields,"IEEE Trans. Inform. Theory,vol. IT-18, pp. 232-240, 1972.

Index Terms:
Bayesian estimation; minimum expected cost estimation; picture processing; 2D motion vector fields; time-varying images; deterministic structural model; vector Markov random fields; piecewise smooth model; maximum a posteriori probability; stochastic relaxation; Gibbs sampler; state space; Bayes methods; estimation theory; Markov processes; picture processing; probability; state-space methods
J. Konrad, E. Dubois, "Bayesian Estimation of Motion Vector Fields," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 9, pp. 910-927, Sept. 1992, doi:10.1109/34.161350
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