OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation

Pascal Zille, Thomas Corpetti

Abstract

This paper is concerned with the multi-resolution issue used in many computer vision applications. Such approaches are very popular to optimize a cost function that, in most of the situations, has been linearized for mathematical facility reasons. In general, a multi-resolution setup consists in a redefinition of the problem at a different resolution level where the mathematical assumptions (usually linearity) hold. Following a coarseto- fine strategy, a usual process consists in 1) optimizing the large scales and 2) use this result as an initial condition for the estimation at finer scales. Such process is repeated until the plain image resolution. One of the main drawbacks of such downscaling approach is its incapacity to correct the eventual errors that have been made at larger scales. These latter are indeed propagated along the scales and disturb the final result. In this paper, we suggest a new formulation of the multi-resolution setup where we exploit some smoothing techniques issued from optimal control theory and in particular variational data assimilation. The time is here artificial and is related to the various scales we are dealing with. Following a consistent mathematical framework, we define an original downscaling/upscaling technique to perform the multi-resolution. We validate this approach by defining a simple optical flow estimation technique based on Lucas-Kanade. Experimental results on synthetic data demonstrate the efficiency of this new methodology.

References

  1. Alvarez, L., Weickert, J., and Sánchez, J. (2000). Reliable estimation of dense optical flow fields with large displacements. International Journal of Computer Vision, 39(1):41-56.
  2. Baatz, M. and Schaape, A. (2000). Multiresolution Segmentation: an optimization approach for high quality multi-scale image segmentation. In Strobl, J., editor, Angewandte Geographische Informationsverarbeitung XII. Beiträge zum AGIT-Symposium Salzburg 2000, Karlsruhe, Herbert Wichmann Verlag, pages 12-23.
  3. Bajcsy, R. and Kovacic, S. (1989). Multiresolution elastic matching. Computer Vision, Graphics, and Image Processing, 46(1):1 - 21.
  4. Baker, S. and Matthews, I. (2004). Lucas-Kanade 20 Years On: A Unifying Framework. International Journal of Computer Vision, 56(3):221-255.
  5. Baker, S., Scharstein, D., Lewis, J., Roth, S., Black, M., and Szeliski, R. (2007). A Database and Evaluation Methodology for Optical Flow. In Int. Conf. on Comp. Vis., ICCV 2007.
  6. Baker, S., Scharstein, D., Lewis, J. P., Roth, S., Black, M. J., and Szeliski, R. (2010). A Database and Evaluation Methodology for Optical Flow. International Journal of Computer Vision, 92(1):1-31.
  7. Barron, J., Fleet, D., Beauchemin, S., and Burkitt, T. (1994). Performance Of Optical Flow Techniques. International Journal of Computer Vision, 12(1):43-77.
  8. Bennett, A. (1992). Inverse Methods in Physical Oceanography. Cambridge University Press.
  9. Brox, T., Bruhn, A., Papenberg, N., and Weickert, J. (2004). High accuracy optical flow estimation based on a theory for warping. pages 25-36. Springer.
  10. Burt, P. (1988). Smart sensing within a pyramid vision machine. Proceedings of the IEEE, 76(8):1006 - 1015.
  11. Corpetti, T., Héas, P., Mémin, E., and Papadakis, N. (2009). Pressure image assimilation for atmospheric motion estimation. Tellus Series A: Dynamic Meteorology and Oceanography, 61(1):160-178.
  12. Corpetti, T. and Mémin, E. (2012). Stochastic uncertainty models for the luminance consistency assumption. IEEE Trans. on Image Processing, to appear.
  13. Corpetti, T., Mémin, E., and Pérez, P. (2002). Dense Estimation of Fluid Flows. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(3):365-380.
  14. Delanay, A. and Bresler, Y. (1998). Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography. IEEE Trans. Image Processing, 7(2):204-221.
  15. Cane, B., Novins, K., Mason, D., and Mills, S. (1998). Recovering motion fields: an analysis of eight optical flow algorithms. In Proc. British Mach. Vis. Conf., Southampton.
  16. Geman, D. and Reynolds, G. (1992). Constrained Restoration and The Recovery Of Discontinuities. IEEE Trans. Pattern Anal. Machine Intell., 14(3):367-383.
  17. Horn, B. and Schunck, B. (1981). Determining optical flow. Artificial Intelligence, 17(1-3):185-203.
  18. Huber, P. (1981). Robust Statistics. John Wiley & Sons.
  19. Le Dimet, F.-X. and Talagrand, O. (1986). Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus, pages 97- 110.
  20. Lions, J.-L. (1971). Optimal control of systems governed by PDEs. Springer-Verlag.
  21. Lucas, B. and Kanade, T. (1981). An iterative image registration technique with an application to stereo vision. International joint conference on artificial, 130:121- 130.
  22. Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:674-693.
  23. Mitiche, A. and Bouthemy, P. (1996). Computation of image motion: a synopsis of current problems and methods. Int. Journ. of Comp. Vis., 19(1):29-55.
  24. Ojala, T., Pietikainen, M., and Maenpaa, T. (2002). Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24:971-987.
  25. Talagrand, O. (1997). Assimilation of observations, an introduction. J. Meteor. Soc. Jap., 75:191-209.
  26. Talagrand, O. and Courtier, P. (1987). Variational assimilation of meteorological observations with the adjoint vorticity equation. {I}: Theory. J. of Roy. Meteo. soc., 113:1311-1328.
  27. Vidard, P., Blayo, E., Le Dimet, F.-X., and Piacentini, A. (2000). 4D Variational Data Analysis with Imperfect Model. Flow, Turbulence and Combustion, 65(3- 4):489-504.
  28. Yuan, J., Schnoerr, C., and Mémin, E. (2007). Discrete orthogonal decomposition and variational fluid flow estimation. Journ. of Mathematical Imaging and Vision, 28(1):67-80.
Download


Paper Citation


in Harvard Style

Zille P. and Corpetti T. (2012). OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012) ISBN 978-989-8565-04-4, pages 134-143. DOI: 10.5220/0003841401340143


in Bibtex Style

@conference{visapp12,
author={Pascal Zille and Thomas Corpetti},
title={OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)},
year={2012},
pages={134-143},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003841401340143},
isbn={978-989-8565-04-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)
TI - OPTIMAL CONTROL THEORY FOR MULTI-RESOLUTION PROBLEMS IN COMPUTER VISION - Application to Optical-flow Estimation
SN - 978-989-8565-04-4
AU - Zille P.
AU - Corpetti T.
PY - 2012
SP - 134
EP - 143
DO - 10.5220/0003841401340143