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On the Spatial Statistics of Optical Flow
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Training Products of Experts by Minimizing Contrastive Divergence
Hinton, G. E. (2002) · Neural Computation · doi:10.1162/089976602760128018 · Cited by 4,879 · cited 2×
“To speed up the learning process, we use the contrastive divergence algorithm [15], which approximates maximum likelihood learning, but only relies on a fixed, small number of Markov chain iterations in the sampling phase.”
MethodOn the spatial statistics of optical flow
Roth, S., & Black, M. J. (2005) · Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 · doi:10.1109/iccv.2005.180 · Cited by 95
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- Alvarez, L., Weickert, J., and Sánchez, J. 2000. Reliable estimation of dense optical flow fields with large displacements. Int. J. Comput. Vision, 39(1):41–56. · DOI · Paper page
- Barbu, A. and Yuille, A. 2004. Motion estimation by Swendsen-Wang cuts. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), vol. 1, pp. 754–761.
- Barron, J.L., Fleet, D.J., and Beauchemin, S.S. 1994. Performance of optical flow techniques. Int. J. Comput. Vision, 12(1):43–77. · DOI · Paper page
- Ben-Ari, R. and Sochen, N. 2006. A general framework and new alignment criterion for dense optical flow. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), vol. 1, pp. 529–536.
- Betsch, B.Y., Einhäuser, W., Körding, K.P., and König, P. 2004. The world from a cat’s perspective—Statistics of natural videos. Biological Cybernetics, 90(1):41–50. · DOI
- Black, M.J. and Anandan, P. 1991. Robust dynamic motion estimation over time. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), pp. 296–302.
- Black, M.J. and Anandan, P. 1996. The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields. Comput. Vis. Image Und., 63(1):75–104. · DOI · Paper page
- Bruhn, A., Weickert, J., and Schnörr, C. 2005. Lucas/Kanade meets Horn/Schunck: Combining local and global optic flow methods. Int. J. Comput. Vision, 61(3):211–231. · DOI · Paper page
- Calow, D., Krüger, N., Wörgötter, F., and Lappe, M. 2004. Statistics of optic flow for self-motion through natural scenes. In Dynamic Perception, Ilg, U., Bülthoff, H. and Mallot, H. (eds.), pp. 133–138.
- Cremers, D. and Soatto, S. 2005. Motion competition: A variational approach to piecewise parametric motion segmentation. Int. J. Comput. Vision, 62(3):249–265. · DOI · Paper page
- Davis, T.A. 2004.A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software, 30(2):165–195. · DOI · Paper page
- Fablet, R. and Bouthemy, P. 2001. Non parametric motion recognition using temporal multiscale Gibbs models. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), vol. 1, pp. 501–508.
- Fermüller, C., Shulman, D., and Aloimonos, Y. 2001. The statistics of optical flow. Comput. Vis. Image Und., 82(1):1–32. · DOI
- Fleet, D.J., Black, M.J., Yacoob, Y., and Jepson, A.D. 2000. Design and use of linear models for image motion analysis. Int. J. Comput. Vision, 36(3):171–193. · DOI
- Fleet, D.J., Black, M.J., and Nestares, O. 2002. Bayesian inference of visual motion boundaries. In Exploring Artificial Intelligence in the New Millennium, G. Lakemeyer and B. Nebel (eds.), Morgan Kaufmann Publisher, pp. 139–174.
- Grenander, U. and Srivastava, A. 2001. Probability models for clutter in natural images. IEEE Trans. Pattern Anal. Mach. Intell., 23(4):424–429. · DOI
- Heitz, F. and Bouthemy, P. 1993. Multimodal estimation of discontinuous optical flow using Markov random fields. IEEE Trans. Pattern Anal. Mach. Intell., 15(12):1217–1232. · DOI · Paper page
- Hinton, G.E. 1999. Products of experts. In Int. Conf. on Art. Neur. Netw. (ICANN), vol. 1, pp. 1–6.
- Horn, B.K.P. and Schunck, B.G. 1981. Determining optical flow. Artificial Intelligence, 17(1–3):185–203. · DOI · Paper page
- Huang, J., Lee, A.B., and Mumford, D. 2000. Statistics of range images. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), vol. 1, pp. 1324ff.
- Huang, J. 2000. Statistics of Natural Images and Models. PhD thesis, Brown University.
- Irani, M. 1999. Multi-frame optical flow estimation using subspace constraints. In IEEE Int. Conf. on Comp. Vis. (ICCV), vol. 1, pp. 626–633. · DOI
- Kailath, T. 1967. The divergence and Bhattacharyya distance measures in signal selection.IEEE Transactions on Communication Technology, COM-15(1):52–60. · DOI · Paper page
- Konrad, J. and Dubois, E. 1988. Multigrid Bayesian estimation of image motion fields using stochastic relaxation. In IEEE Int. Conf. on Comp. Vis. (ICCV), pp. 354–362.
- Krajsek, K. and Mester, R. 2006. On the equivalence of variational and statistical differential motion estimation. In Southwest Symposium on Image Analysis and Interpretation, Denver, Colorado, pp. 11–15.
- Lee, A.B., Mumford, D., and Huang, J. 2001. Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model. Int. J. Comput. Vision, 41(1–2):35–59. · DOI · Paper page
- Lewen, G.D., Bialek, W., and de Ruyter van Steveninck, R.R. 2001. Neural coding of naturalistic motion stimuli. Network: Comp. Neural, 12(3):317–329. · DOI
- Lu, H. and Yuille, A.L. 2006. Ideal observers for detecting motion: Correspondence noise. In Adv. in Neur. Inf. Proc. Sys. (NIPS), vol. 18, pp. 827–834.
- Lucas, B.D. and Kanade, T. 1981. An iterative image registration technique with an application to stereo vision. In Int. J. Conf. on Art. Intel. (IJCAI), pp. 674–679.
- Marroquin, J., Mitter, S., and Poggio, T. 1987. Probabilistic solutions of ill-posed problems in computational vision. J. Am. Stat. Assoc., 82(397):76–89. · DOI
- Martin, D., Fowlkes, C., Tal, D., and Malik, J. 2001. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In IEEE Int. Conf. on Comp. Vis. (ICCV), vol. 2, pp. 416–423.
- Mémin, É. and Pérez, P. 2002. Hierarchical estimation and segmentation of dense motion fields. Int. J. Comput. Vision, 46(2):129–155. · DOI
- Murray, D.W. and Buxton, B.F. 1987. Scene segmentation from visual motion using global optimization. IEEE Trans. Pattern Anal. Mach. Intell., 9(2):220–228. · DOI · Paper page
- Olshausen, B.A. and Field, D.J. 1996. Natural image statistics and efficient coding. Network: Comp. Neural, 7(2):333–339. · doi:10.1088/0954-898x/7/2/014 · Paper page
- Papenberg, N., Bruhn, A., Brox, T., Didas, S., and Weickert, J. 2006. Highly accurate optic flow computation with theoretically justified warping. Int. J. Comput. Vision, 67(2):141–158. · DOI · Paper page
- Proesmans, M., Van Gool, L.J., Pauwels, E.J., and Oosterlinck, A. 1994. Determination of optical flow and its discontinuities using non-linear diffusion. In Eur. Conf. on Comp. Vis. (ECCV), J.-O. Eklundh (ed.), vol. 801 of Lect. Notes in Comp. Sci., pp. 295–304. · DOI · Paper page
- Ross, M.G. and Kaelbling, L.P. 2005. Learning static object segmentation from motion segmentation. In Nat. Conf. on Art. Int. (AAAI), Menlo Park, California, AAAI Press, pp. 956–961.
- Roth, S. and Black, M.J. 2005a. Fields of experts: A framework for learning image priors. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), vol. 2, pp. 860–867.
- Ruderman, D.L. 1994. The statistics of natural images. Network: Comp. Neural, 5(4):517–548. · DOI · Paper page
- Scharr, H. 2004. Optimal filters for extended optical flow. In First International Workshop on Complex Motion, vol. 3417 of Lect. Notes in Comp. Sci., Springer.
- Scharr, H. and Spies, H. 2005. Accurate optical flow in noisy image sequences using flow adapted anisotropic diffusion. Signal Processing: Image Communication, 20(6):537–553. · DOI
- Simoncelli, E.P., Adelson, E.H., and Heeger, D.J. 1991. Probability distributions of optical flow. In IEEE Conf. on Comp. Vis. and Pat. Recog. (CVPR), pp. 310–315.
- Srivastava, A., Lee, A.B., Simoncelli, E.P., and Zhu, S.-C. 2003. On advances in statistical modeling of natural images. J. Math. Imaging Vision, 18(1):17–33. · DOI · Paper page
- Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., and Rother, C. 2006. A comparative study of energy minimization methods for Markov random fields. In Eur. Conf. on Comp. Vis. (ECCV), A. Leonardis, H. Bischof, and A. Prinz (eds.), vol. 3952 of Lect. Notes in Comp. Sci., pp. 16–29. · DOI · Paper page
- Teh, Y.W., Welling, M., Osindero, S., and Hinton, G.E. 2003. Energy-based models for sparse overcomplete representations. J. Mach. Learn. Res., 4(Dec.):1235–1260. · DOI
- Torralba, A. 2003. Contextual priming for object detection. Int. J. Comput. Vision, 53(2):169–191. · DOI · Paper page
- Torralba, A. and Oliva, A. 2003. Statistics of natural image categories. Network: Comp. Neural, 14(2):391–412. · doi:10.1088/0954-898x/14/3/302 · Paper page
- van Harteren, J.H. and Ruderman, D.L. 1998. Independent component analysis of natural image sequences yields spatio-temporal filters similar to simple cells in primary visual cortex. J. Roy. Stat. Soc. B, 265(1412):2315–2320.
- Weickert, J. and Schnörr, C. 2001. Variational optic flow computation with a spatio-temporal smoothness constraint. J. Math. Imaging Vision, 14(3):245–255. · DOI · Paper page
- Weiss, Y. and Adelson, E.H. 1998. Slow and smooth: A Bayesian theory for the combination of local motion signals in human vision. Technical Report AI Memo 1624, MIT AI Lab, Cambridge, Massachusetts.
- Zhu, S.C. and Mumford, D. 1997. Prior learning and Gibbs reaction-diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 19(11):1236–1250. · DOI · Paper page
- Zhu, S.C., Wu, Y., and Mumford, D. 1998. Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling. Int. J. Comput. Vision, 27(2):107–126. · DOI · Paper page
Cited by
PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume
Sun, D., Yang, X., Liu, M.-Y., & Kautz, J. (2018) · 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2018.00931 · Cited by 2,648
A Database and Evaluation Methodology for Optical Flow
Baker, S., Scharstein, D., Lewis, J. P., Roth, S., Black, M. J., & Szeliski, R. (2011) · International Journal of Computer Vision · doi:10.1007/s11263-010-0390-2 · Cited by 2,205
“Rather than manually making these decision and tuning parameters, learning algorithms have been used to choose the data and prior terms and optimize their parameters by maximizing performance on a set of training data (Roth and Black 2007; Sun et al. 2008; Li and Huttenlocher 2008).”
BackgroundMethodSelf-citationA Naturalistic Open Source Movie for Optical Flow Evaluation
Butler, D. J., Wulff, J., Stanley, G. B., & Black, M. J. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-33783-3_44 · Cited by 1,842
Self-citationRoth, S., & Black, M. J. (2009) · International Journal of Computer Vision · doi:10.1007/s11263-008-0197-6 · Cited by 847
Self-citationSuper SloMo: High Quality Estimation of Multiple Intermediate Frames for Video Interpolation
Jiang, H., Sun, D., Jampani, V., Yang, M.-H., Learned-Miller, E., & Kautz, J. (2018) · 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2018.00938 · Cited by 829
Metadata
- Authors
- Roth, S., & Black, M. J.
- Venue
- International Journal of Computer Vision
- Published
- 2007-01-09
- Volume
- 74
- Issue
- 1
- Pages
- 33-50
- ISSN
- 0920-5691 (ISSN-L)
- 1573-1405
- OpenAlex
- W2019661178
- Cited by
- 168
- References
- 2
- FWCI
- 19.64
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- www.springer.com/tdm (vor)
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