This Article 
 Bibliographic References 
 Add to: 
IMPSAC: Synthesis of Importance Sampling and Random Sample Consensus
March 2003 (vol. 25 no. 3)
pp. 354-364

Abstract—This paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. The method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation. The method operates on a pyramid from coarse to fine resolution, thus raising the problem of how to propagate information from one level to another in a statistically consistent way. The distribution of the parameters at each resolution is encoded nonparametrically as a set of particles. At the coarsest level, a RANSAC-MCMC estimator is used to initialize this set of particles, the posterior can then be approximated as a mixture of Gaussians fitted to these particles. The distribution at a coarser level influences the distribution at a finer level using the technique of sampling-importance-resampling (SIR) and MCMC, which allows for asymptotically correct approximations of the posterior distribution. The estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles, which can be further improved by MCMC. It is shown that the method is superior to previous single resolution RANSAC-style feature matchers.

[1] N. Ayache, Artificial Vision for Mobile Robots. MIT Press, 1991.
[2] P. Beardsley, A. Zisserman, and D.W. Murray, “Navigation Using Affine Structure and Motion,” Signal Processing, pp. 85-96, 1994.
[3] P.A. Beardsley, P. Torr, and A.P. Zisserman, “3D Model Acquisition from Extended Image Sequences,” Proc. Fourth European Conf. Computer Vision, B.F. Buxton and R. Cipolla, eds., Apr. 1996.
[4] J.R. Bergen, P. Anandan, K.J. Hanna, and R. Hingorani, “Hiercharchical Model-Based Motion Estimation,” Proc. European Conf. Computer Vision, pp. 237-252, 1992.
[5] J.M. Bernardo and A.F.M. Smith, Bayesian Theory. New York: Wiley, 1994.
[6] T. Cham and R. Cipolla, “A Statistical Framework for Long-Range Feature Matching in Uncalibrated Image Mosaicing,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 442-447, 1998.
[7] F. Dellaert, S.M. Seitz, C.E. Thorpe, and S. Thrun, “Structure From Motion without Correspondence,” pp. 557-564, 2000.
[8] N.M. Dempster, A.P. Laird, and D.B. Rubin, “Maximum Likelihood From Incomplete Data via the EM Algorithm,” J. Royal Statistics Soc. B, vol. 39, pp. 185-197, 1977.
[9] O. Faugeras, "What can be seen in three dimensions with an uncalibrated stereo rig?" Second European Conf. Computer Vision, pp. 563-578, 1992.
[10] M.A. Fischler and R.C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Graphics and Image Processing, vol. 24, no. 6, pp. 381–395, June 1981.
[11] A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian Data Analysis. Chapman and Hall, 1995.
[12] Markov Chain Monte Carlo in Practice. W. Gilks, S. Richardson, D. Spiegelhalter, eds., London: Chapman and Hall, 1996.
[13] C. Harris and M. Stephens, “A Combined Corner and Edge Detector,” Proc. Alvey Conf., pp. 189-192, 1987.
[14] C.J. Harris, “Determination of Ego-Motion From Matched Points,” pp. 189-192, 1987.
[15] R. Hartley, “Estimation of Relative Camera Positions for Uncalibrated Cameras,” Proc. European Conf. Computer Vision, G. Sandini, ed., vol. 588, pp. 579-587, May 1992.
[16] W.K. Hastings, “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, vol. 57, pp. 97-109, 1970.
[17] M. Irani and P. Anandan, “Parallax Geometry of Pairs of Points for 3D Scene Analysis,” Proc. European Conf. Computer Vision, A, pp. 17-30, Apr. 1996.
[18] M. Isard and A. Blake, “Condensation-Conditional Density Propagation for Visual Tracking,” Int'l J. Computer Vision, vol. 29, pp. 5-28, 1998.
[19] D.G. Lowe, “Object Recognition from Local Scale-Invariant Features,” Proc. Seventh Int'l. Conf. Computer Vision, pp. 1150-1157, Sept. 1999.
[20] J. Matas, O. Chum, M. Urban, and T. Pajdl, “Robust Wide Baseline Stereo from Maximally Stable Extremal Regions,” Proc. British Machine Vision Conf., pp. 384-393, 2002.
[21] G.I. McLachlan and K. Basford, Mixture Models: Inference and Applications to Clustering. New York: Marcel Dekker, 1988.
[22] P.F. McLauchlan and D.W. Murray, “A Unifying Framework for Structure from Motion Recovery from Image Sequences,” Proc. Int'l Conf. Computer Vision, pp. 314-320, 1995.
[23] N. Metropolis and S. Ulam, “The Monte Carlo Method,” J. Am. Statistical Assoc., vol. 44, pp. 335-341, 1949.
[24] K. Mikolajczyk and C. Schmid, “An Affine Invariant Interest Point Detector,” Proc. Int'l Conf. Computer Vision, vol. 1, pp. 128-142, 2001.
[25] D. Myatt, J.M. Bishop, R. Craddock, S. Nasuto, and P.H.S. Torr, “NAPSAC: High Noise, High Dimensional Robust Estimation—It's in the Bag,” Proc. British Machine Vision Conf., pp. 458-467, 2002.
[26] R.M. Neal, “Probabilistic Inference Using Monte Carlo Markov Chains,” Technical Report CRG-TR-93-1, Univ. of Toronto, 1993.
[27] P. Pritchett and A. Zisserman, Wide Baseline Stereo Matching IEEE Proc. Int'l Conf., pp. 754-760, Jan. 1998.
[28] L.H. Quam, “Hierarchical Warp Stereo,” Proc. Image Understanding Workshop, L.S. Baumann, ed., pp. 149-155, Oct. 1984.
[29] B.D. Ripley, Stochastic Simulation. 1987.
[30] F. Schaffalitzky and A. Zisserman, “Viewpoint Invariant Texture Matching and Wide Baseline Stereo,” Proc. Eighth Int'l Conf. Computer Vision, 2001.
[31] C. Schmid and A. Zisserman, “Automatic Line Matching Across Views,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 666-671, 1997.
[32] C.V. Stewart, “Bias in Robust Regression Caused by Discontinuities and Multiple Structures,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 816-833, Aug. 1997.
[33] H. Tao, H. Sawhney, and R. Kumar, A Global Matching Framework for Stereo Computation Proc. Int'l Conf. Computer Vision, pp. 532-539, 2001.
[34] D.M. Titterington, A.F.M. Smith, and U.E. Makov, Statistical Analysis of Finite Mixture Distributions. John Wiley&Sons, 1985.
[35] C. Tomasi and T. Kanade, "Shape and Motion From Image Streams Under Orthography: A Factorization Method," Int'l J. Computer Vision, vol. 9, no. 2, pp. 137-154, 1992.
[36] P.H.S. Torr, “Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting,” Technical Report msr-tr-2002-29, Microsoft Research, 2002. to appear in Int'l J. Computer Vision.
[37] P.H.S. Torr, P.A. Beardsley, and D.W. Murray, “Robust Vision,” Proc. Fifth British Machine Vision Conf., J. Illingworth, ed., pp. 145-155, 1994.
[38] P.H.S. Torr and C. Davidson, “IMPSAC: A Synthesis of Importance Sampling and Random Sample Consensus to Effect Multi-Scale Image Matching for Small and Wide Baselines,” Proc. European Conf. Computer Vision, vol. 1, pp. 819-833, 2000.
[39] P.H.S. Torr and D.W. Murray, “Outlier Detection and Motion Segmentation,” Sensor Fusion VI, P.S. Schenker, ed., pp. 432-443, 1993.
[40] P. Torr and D. Murray, “The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix,” Int'l J. Computer Vision, vol. 3, no. 24, pp. 271-300, 1997.
[41] P.H.S. Torr and A. Zisserman, “Robust Parameterization and Computation of the Trifocal Tensor,” Image and Vision Computing, vol. 15, pp. 591-607, 1997.
[42] P.H.S. Torr and A. Zisserman, “Robust Computation and Parametrization of Multiple View Relations,” Proc. Int'l Conf. Computer Vision, Narosa Publishing House, U. Desai, ed., pp. 727-732, 1998.
[43] P.H.S. Torr and A. Zisserman, “MLESAC: A New Robust Estimator with Application to Estimating Image Geometry,” Computer Vision and Image Understanding, vol. 78, no. 1, pp. 138-156, 2000.
[44] P.H.S. Torr, A.W. Fitzgibbon, and A. Zisserman, The Problem of Degeneracy in Structure and Motion Recovery from Uncalibrated Image Sequences Int'l J. Computer Vision, vol. 32, no. 1, pp. 27-44, Aug. 1999.
[45] T. Tuytelaars and L. Van Gool, “Wide Baseline Stereo Matching Based on Local, Affinely Invariant Regions,” Proc. British Machine Vision Conf., pp. 412-422, 2000.
[46] Y. Weiss and E.H. Adelson, “Slow and Smooth: A Bayesian Theory for the Combination of Local Motion Signals in Human Vision,” Technical Report MIT AI Memo 1624 (CBCL Paper 158), MIT, 1998.
[47] E. Weisstein, Maths Encyclopedia, http:/, 2002.
[48] C. Zeller, “Projective, Affine, and Euclidean Calibration in Compute Vision and the Application of Three Dimensional Perception,” PhD thesis, RobotVis Group, INRIA Sophia-Antipolis, 1996.
[49] Z. Zhang, R. Deriche, O. Faugeras, and Q.T. Luong, “A Rubust Technique for Matching Two Uncalibrated Images through the Recovery of the Unknown Epipolar Geometry,” Artificial Intelligence J., vol. 78, pp. 87-119, 1995.
[50] Z. Zhang and O. Faugeras, 3D Dynamic Scene Analysis. Springer Verlag, 1992.

Index Terms:
Bayesian methods, structure from motion, stereoscopic vision, importance sampling.
Philip H.S. Torr, Colin Davidson, "IMPSAC: Synthesis of Importance Sampling and Random Sample Consensus," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 3, pp. 354-364, March 2003, doi:10.1109/TPAMI.2003.1182098
Usage of this product signifies your acceptance of the Terms of Use.