Abstract
We address the problem of maximum a posteriori (MAP) estimation of optical flow with a geometric prior from gray-value images. We estimate simultaneously the optical flow and the corresponding surface – the structural optical flow (SOF) – subject to three types of constraints: intensity constancy, geometric, and smoothness constraints. Our smoothness constraints restrict the unknowns to locally coincide with a set of finitely parameterized admissible functions. The geometric constraints locally enforce consistency between the optical flow and the corresponding surface. Our theory amounts to a discrete generalization of regularization defined in terms of partial derivatives. The point-wise regularizers are efficiently implemented with linear run-time complexity in the number of discretization points. We demonstrate the applicability of our method by example computations of SOF from photographs of human faces.
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References
McCane, B., Novins, K., Crannitch, D., Galvin, B.: On Benchmarking Optical Flow. Computer Vision and Image Understanding 84(1) (2001)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2000)
Horn, B.K., Schunck, B.G.: Determining optical flow. Technical report, Massachusetts Institute of Technology, Cambridge, MA, USA (1980)
Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High Accuracy Optical Flow Estimation Based on a Theory for Warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)
Bruhn, A., Weickert, J., Schnörr, C.: Lucas/kanade meets horn/schunck: combining local and global optic flow methods. Int. J. Comput. Vision 61, 211–231 (2005)
Zach, C., Pock, T., Bischof, H.: A Duality Based Approach for Realtime TV-L1 Optical Flow. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 214–223. Springer, Heidelberg (2007)
Lucas, B.D., Kanade, T.: An Iterative Image Registration Technique with an Application to Stereo Vision. In: IJCA 1981, vol. 81, pp. 674–679 (1981)
Kanatani, K.: Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science Inc., New York (1996)
Li, S.Z.: Markov random field modeling in image analysis. Springer-Verlag New York, Inc., Secaucus (2001)
Nir, T., Bruckstein, A.M., Kimmel, R.: Over-parameterized variational optical flow. Int. J. Comput. Vision 76, 205–216 (2008)
Lamovsky, D.V., Lasaruk, A.: Calibration and Reconstruction Algorithms for a Handheld 3D Laser Scanner. In: Blanc-Talon, J., Kleihorst, R., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2011. LNCS, vol. 6915, pp. 635–646. Springer, Heidelberg (2011)
Corrochano, E.B., Förstner, W.: Uncertainty and projective geometry. In: Handbook of Geometric Computing, pp. 493–534. Springer, Heidelberg (2005)
Hoeffken, M., Oberhoff, D., Kolesnik, M.: Temporal Prediction and Spatial Regularization in Differential Optical Flow. In: Blanc-Talon, J., Kleihorst, R., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2011. LNCS, vol. 6915, pp. 576–585. Springer, Heidelberg (2011)
Cheney, E.: Introduction to approximation theory. AMS Chelsea Publishing Series. AMS Chelsea Pub. (1982)
Björck, Å.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia (1996)
Salvi, J., Matabosch, C., Fofi, D., Forest, J.: A review of recent range image registration methods with accuracy evaluation. Image Vision Comput. 25, 578–596 (2007)
Wackernagel, H.: Multivariate Geostatistics: An Introduction With Applications. Springer (2003)
Liu, C., Freeman, W.T., Szeliski, R., Kang, S.B.: Noise estimation from a single image. IEEE Computer Vision and Pattern Recognition 1, 901–908 (2006)
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Lasaruk, A. (2012). Approximate Regularization for Structural Optical Flow Estimation. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P., Zemčík, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2012. Lecture Notes in Computer Science, vol 7517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33140-4_30
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DOI: https://doi.org/10.1007/978-3-642-33140-4_30
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