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Outlier Modeling in Image Matching
March 2003 (vol. 25 no. 3)
pp. 301-315

Abstract—We address the question of how to characterize the outliers that may appear when matching two views of the same scene. The match is performed by comparing the difference of the two views at a pixel level aiming at a better registration of the images. When using digital photographs as input, we notice that an outlier is often a region that has been occluded, an object that suddenly appears in one of the images, or a region that undergoes an unexpected motion. By assuming that the error in pixel intensity generated by the outlier is similar to an error generated by comparing two random regions in the scene, we can build a model for the outliers based on the content of the two views. We illustrate our model by solving a pose estimation problem: the goal is to compute the camera motion between two views. The matching is expressed as a mixture of inliers versus outliers, and defines a function to minimize for improving the pose estimation. Our model has two benefits: First, it delivers a probability for each pixel to belong to the outliers. Second, our tests show that the method is substantially more robust than traditional robust estimators (M -estimators) used in image stitching applications, with only a slightly higher computational complexity.

[1] B.G. Lindsay, “Mixture Models: Theory, Geometry and Applications,” vol. 5, NSF-CBMS Regional Conf. Series in Probability and Statistics, 1995
[2] G. McLachlan and D. Peel, Finite Mixture Models. New York: John Wiley and Sons, 2000.
[3] P. Huber, Robust Statistics. New York: Wiley-Interscience, 1981.
[4] S. Ayer, “Sequential and Competitive Methods for Estimation of Multiple Motions,” PhD thesis, Swiss Fed. Inst. of Technology (EPFL), 1995.
[5] P. Rousseeuw and A. Leory, Robust Regression and Outlier Detection. Wiley Series in Probability and Statistics, 1987.
[6] H.S. Sawhney and S. Ayer, "Compact Representations of Videos Through Dominant and Multiple Motion Estimation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 8, pp. 814-831, 1996.
[7] G. Hager and P. Belhumeur, “Efficient Region Tracking with Parametric Models of Geometry and Illumination,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 10, pp. 1025-1039, Oct. 1998.
[8] J.-I. Park, N. Yagi, K. Enami, K. Aizawa, and M. Hatori, “Estimation of Camera Parameters from Image Sequence for Model-Based Video Coding,” IEEE Trans. Circuit and Systems for Video Technology, vol. 4, no. 3, pp. 288-296, 1994.
[9] V.L. Brailovsky, “An Approach to Outlier Detection Based on Bayesian Probabilistic Model,” Proc. Int'l Conf. Pattern Recognition, pp. 70-74, 1996.
[10] N.S. Netanyahu and I. Weiss, “Analytic Outlier Removal in Line Fitting,” Proc. 12th IAPR Int'l Conf. Computer Vision and Image Processing, vol. 2B, pp. 406-408, 1994.
[11] P. Schroeter, J.-M. Vesin, T. Langenberger, and R. Meuli, “Robust Parameter Estimation of Intensity Distributions for Brain Magnetic Resonance Images,” IEEE Trans. Medical Imaging, vol. 17, no. 2, pp. 172-186, 1998.
[12] P.S. Torr, R. Szeliski, and P. Anandan, “An Integrated Bayesian Approach to Layer Extraction from Image Sequences,” Proc. Int'l Conf. Computer Vision, 1999.
[13] J.M. Mendel, Lessons in Estimation Theory for Signal Processing, Communications, and Control, second ed. New York: Prentice Hall, 1995.
[14] C.F. Olson, “Maximum-Likelihood Template Matching,” Proc. Computer Vision and Pattern Recognition, 2000.
[15] X. Gao and T. Boult, “Statistics of Natural Images and Models,” Proc. Computer Vision and Pattern Recognition, 2000.
[16] D. Hasler, “Perspectives on Panoramic Photography,” PhD thesis, Swiss Fed. Inst. of Technology (EPFL), 2001.
[17] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, second ed. Addison-Wesley 1994.
[18] B. Aiazzi, L. Alparone, and S. Baronti, “Estimation Based on Entropy Matching for Generalized Gaussian pdf Modeling,” IEEE Signal Processing Letters, vol. 6, no. 6, pp. 138-140, 1999.

Index Terms:
Outlier model, outlier rejection, mixture model, robust pose estimation, M -estimators.
David Hasler, Luciano Sbaiz, Sabine Süsstrunk, Martin Vetterli, "Outlier Modeling in Image Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 3, pp. 301-315, March 2003, doi:10.1109/TPAMI.2003.1182094
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