COMPARING LINEAR AND CONVEX RELAXATIONS FOR STEREO AND MOTION

Thomas Schoenemann

Abstract

We provide an analysis of several linear programming relaxations for the problems of stereo disparity estimation and motion estimation. The problems are cast as integer linear programs and their relaxations are solved approximately either by block coordinate descent (TRW-S and MPLP) or by smoothing and convex optimization techniques. We include a comparison to graph cuts. Indeed, the best energies are obtained by combining move-based algorithms and relaxation techniques. Our work includes a (slightly novel) tight relaxation for the typical motion regularity term, where we apply a lifting technique and discuss two ways to solve the arising task. We also give techniques to derive reliable lower bounds, an issue that is not obvious for primal relaxation methods, and apply the technique of (Desmet et al., 1992) to a-priori exclude some of the labels. Moreover we investigate techniques to solve linear and convex programming problems via accelerated first order schemes which are becoming more and more widespread in computer vision.

References

  1. Bertsekas, D. (1999). Nonlinear Programming, 2nd edition. Athena Scientific.
  2. Bhusnurmath, A. and Taylor, C. J. (2008). Solving stereo matching problems using interior point methods. In Fourth International Symposium on 3D Data Processing, Visualization and Transmission, 3DPVT.
  3. Bruhn, A. (2006). Variational optic flow computation: Accurate modelling and efficient numerics. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany.
  4. Dantzig, G. and Thapa, M. (1997). Linear Programming 1: Introduction. Springer Series in Operations Research. Springer.
  5. Desmet, J., Maeyer, M. D., Hazes, B., and Lasters, I. (1992). The dead-end elimination theorem and its use in protein side-chain positioning. Nature, 356:539- 542.
  6. Felzenszwalb, P. and Huttenlocher, D. (2006). Efficient belief propagation for early vision. International Journal on Computer Vision (IJCV), 70(1).
  7. Globerson, A. and Jaakkola, T. (2007). Fixing max-product: Convergent message passing algorithms for MAP relaxations. In Conference on Neural Information Processing Systems (NIPS), Vancouver, Canada.
  8. Glocker, B., Komodakis, N., Tziritas, G., Navab, N., and Paragios, N. (2008). Dense image registration through MRFs and efficient linear programming. Medical Image Analysis, 12:731-741.
  9. Goldlü cke, B. and Cremers, D. (2010). Convex relaxation for multilabel problems with product label spaces. In European Conference on Computer Vision (ECCV), Iraklion, Greece.
  10. Goldstein, T., Bresson, X., and Osher, S. (2009). Global minimization of Markov random fields with applications to optical flow. Technical Report 09-77, UCLA CAM report.
  11. Horn, B. and Schunck, B. (1981). Determining optical flow. Artificial Intelligence, 17:185-203.
  12. Ishikawa, H. (2003). Exact optimization for Markov Random Fields with convex priors. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 25(10):1333-1336.
  13. Klaus, A., Sormann, M., and Karner, K. (2006). Segmentbased stereo matching using adaptive cost aggregation and dynamic programming. In International Conference on Pattern Recognition (ICPR), Hong Kong, China.
  14. Kleinberg, J. and Tardos, E. (1999). Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov Random Fields. In Symposium on Foundations of Computer Science.
  15. Kolmogorov, V. (2006). Convergent tree-reweighted message passing for energy minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 28(10):1568-1583.
  16. Lellmann, J., Becker, F., and Schnö rr, C. (2009). Convex optimization for multi-class image labeling by simplex-constrained total variation. In IEEE International Conference on Computer Vision (ICCV), Kyoto, Japan.
  17. Meltzer, T., Yanover, C., and Weiss, Y. (2005). Globally optimal solutions for energy minimization in stereo vision using reweighted belief propagation. In IEEE International Conference on Computer Vision (ICCV), Beijing, China.
  18. Memin, E. and Perez, P. (1998). Dense estimation and object-based segmentation of the optical flow with robust techniques. IEEE Transactions on Image Processing (TIP), 7(5):703-719.
  19. Michelot, C. (1986). A finite algorithm for finding the projection of a point onto the canonical simplex of Rn. Journal on Optimization Theory and Applications, 50(1).
  20. Nesterov, Y. (2004). Introductory lectures on convex optimization. Applied Optimization. Kluwer Academic Publishers.
  21. Nesterov, Y. (2005). Smooth minimization of non-smooth functions. Mathematical Programming, 103(1):127- 152.
  22. Papenberg, N., Bruhn, A., Brox, T., Didas, S., and Weickert, J. (2006). Highly accurate optic flow computation with theoretically justified warping. International Journal on Computer Vision (IJCV), 67(2):141-158.
  23. Pock, T., Schoenemann, T., Cremers, D., and Bischof, H. (2008). A convex formulation for continuous multilabel problems. In European Conference on Computer Vision (ECCV), Marseille, France.
  24. Scharstein, D. and Szeliski, R. (2002). A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal on Computer Vision (IJCV), 47(1-3):7-42.
  25. Shekhovtsov, A., Kovtun, I., and Hlavác?, V. (2008). Efficient MRF deformation model for non-rigid image matching. Computer Vision and Image Understanding, 112(1):91-99.
  26. Sontag, D., Globerson, A., and Jaakkola, T. (2010). Introduction to dual decomposition for inference. In Optimization for Machine Learning. MIT Press.
  27. Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., and Rother, C. (2008). A comparative study of energy minimization methods for Markov random fields with smoothness-based priors. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 30(6):1068-1080.
  28. Trobin, W., Pock, T., Cremers, D., and Bischof, H. (2008). An unbiased second-order prior for high-accuracy motion estimation. In Pattern Recognition (Proc. DAGM), Munich, Germany.
  29. Wainwright, M., Jaakkola, T., and Willsky, A. (2005). MAP estimation via agreement on (hyper-)trees: Messagepassing and linear programming approaches. IEEE Tansactions on Information Theory, 51(11):3697- 3717.
  30. Woodford, O., Torr, P., Reid, I., and Fitzgibbon, A. (2008). Global stereo reconstruction under second order smoothness priors. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), Anchorage, Alaska.
  31. Yang, Q., Wang, L., Yang, R., Stewénius, H., and Nistér, D. (2009). Stereo matching with color-weighted correlation, hierarchical belief propagation and occlusion handling. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 31(3):492-504.
  32. Zach, C., Gallup, D., Frahm, J.-M., and Niethammer, M. (2008). Fast global labeling for real-time stereo using multiple plane sweeps. In Vision, Modeling and Visualization Workshop (VMV), Konstanz, Germany.
  33. Zach, C., Pock, T., and Bischof, H. (2007). A duality based approach for realtime TV-L1 optical flow. In Pattern Recognition (Proc. DAGM), Heidelberg, Germany.
Download


Paper Citation


in Harvard Style

Schoenemann T. (2012). COMPARING LINEAR AND CONVEX RELAXATIONS FOR STEREO AND MOTION . In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM, ISBN 978-989-8425-99-7, pages 5-14. DOI: 10.5220/0003710400050014


in Bibtex Style

@conference{icpram12,
author={Thomas Schoenemann},
title={COMPARING LINEAR AND CONVEX RELAXATIONS FOR STEREO AND MOTION},
booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},
year={2012},
pages={5-14},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003710400050014},
isbn={978-989-8425-99-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,
TI - COMPARING LINEAR AND CONVEX RELAXATIONS FOR STEREO AND MOTION
SN - 978-989-8425-99-7
AU - Schoenemann T.
PY - 2012
SP - 5
EP - 14
DO - 10.5220/0003710400050014