Abstract
We present an approach to parallel variational optical flow computation on standard hardware by domain decomposition. Using an arbitrary partition of the image plane into rectangular subdomains, the global solution to the variational approach is obtained by iteratively combining local solutions which can be efficiently computed in parallel by separate multi-grid iterations for each subdomain. The approach is particularly suited for implementations on PC-clusters because inter-process communication between subdomains (i.e. processors) is minimized by restricting the exchange of data to a lower-dimensional interface. By applying a dedicated interface preconditioner, the necessary number of iterations between subdomains to achieve a fixed error is bounded independently of the number of subdomains. Our approach provides a major step towards real-time 2D image processing using off-the-shelf PC-hardware and facilitates the efficient application of variational approaches to large-scale image processing problems.
Chapter PDF
Similar content being viewed by others
Keywords
- Motion Estimation
- Domain Decomposition
- Message Passing Interface
- Multigrid Method
- Domain Decomposition Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Anandan, P.: A computational framework and an algorithm for the measurement of visual motion. Int. J. of Comp. Vision 2, 283–310 (1989)
Aubin, J.P.: Approximation of Elliptic Boundary-Value Problems. Wiley&Sons, New York (1972)
Beauchemin, J.L., Barron, S.S.: The computation of optical flow. ACM Computing Surveys 27, 433–467 (1995)
Black, M.J., Anandan, P.: The robust estimation of multiple motions: Parametric and piecewise–smooth flow fields. Comp. Vis. Image Underst.: CVIU 63(1), 75–104 (1996)
Bouthemy, P., Francois, E.: Motion segmentation and qualitative dynamic scene analysis from an image sequence. Int. J. of Comp. Vision 10(2), 157–182 (1993)
Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 31(138), 333–390 (1977)
Bruhn, A., Weickert, J., Feddern, C., Kohlberger, T., Schnörr, C.: Real-time optic flow computation with variational methods. In: Petkov, N., Westenberg, M.A. (eds.) CAIP 2003. LNCS, vol. 2756, pp. 222–229. Springer, Heidelberg (2003)
Bruhn, A., Weickert, J., Feddern, C., Kohlberger, T., Schnörr, C.: Variational optic flow computation in real-time. Technical Report 89/2003, Dpt. of Mathematics, Saarland University, Germany (June 2003)
Chan, T.F., Mathew, T.P.: Domain decomposition algorithms. Acta Numerica, 61–143 (1994)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland Publ. Comp., Amsterdam (1978)
Corpetti, T., Mémin, E., Pérez, P.: Dense estimation of fluid flows. IEEE Trans. Patt. Anal. Mach. Intell. 24(3), 365–380 (2002)
Dryja, M., Widlund, O.B.: Schwarz methods of neumann-neumann type for three dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48, 121–155 (1995)
Enkelmann, W.: Investigation of multigrid algorithms for the estimation of optical flow fields in image sequences. Comp. Vis. Graph. Imag. Proc. 43, 150–177 (1987)
Fleury, M., Clark, A.F., Downton, A.C.: Evaluating optical-flow algorithms on a parallel machine. Image and Vision Comp 19(3), 131–143 (2001)
Ghosal, S., Vanĕk, P.: A fast scalable algorithm for discontinuous optical flow estimation. IEEE Trans. Patt. Anal. Mach. Intell. 18(2), 181–194 (1996)
Hackbusch, W.: Multigrid Methods and Applications. Springer, Heidelberg (1985)
Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Springer, Heidelberg (1993)
Heitz, F., Perez, P., Bouthemy, P.: Multiscale minimization of global energy functions in some visual recovery problems. Comp. Vis. Image Underst.: CVIU 59(1), 125–134 (1994)
Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artif. Intell. 17, 185–203 (1981)
Hwang, S.H., Lee, S.U.: A hierarchical optical flow estimation algorithm based on the interlevel motion smoothness constraint. Patt. Recog. 26(6), 939–952 (1993)
Konrad, J., Dubois, E.: Bayesian estimation of motion vector fields. IEEE Trans. Patt. Anal. Mach. Intell. 14(9), 910–927 (1992)
Mandel, J.: Balancing domain decomposition. Comm. Numer. Meth. Eng. 9, 233–241 (1993)
Mémin, E., Pérez, P.: Optical flow estimation and object–based segmentation with robust techniques. IEEE Trans. on Image Proc. 7(5), 703–719 (1998)
Mémin, E., Pérez, P.: Hierarchical estimation and segmentation of dense motion fields. Int. J. of Comp. Vision 46(2), 129–155 (2002)
Mitiche, A., Bouthemy, P.: Computation and analysis of image motion: A synopsis of current problems and methods. Int. J. of Comp. Vision 19(1), 29–55 (1996)
Nagel, H.H.: On the estimation of optical flow: Relations between different approaches and some new results. Artif. Intell. 33, 299–324 (1987)
Nagel, H.H., Enkelmann, W.: An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences. IEEE Trans. Patt. Anal. Mach. Intell. 8(5), 565–593 (1986)
Nesi, P.: Variational approach to optical flow estimation managing discontinuities. Image and Vis. Comp. 11(7), 419–439 (1993)
Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford Univ. Press, Oxford (1999)
Smith, B., Bjorstad, P., Gropp, W.: Domain Decomposition: Parallel Multilevel Methods for the Solution of Elliptic Partial Differential Equations. Cambridge University Press, Cambridge (1996)
Valentinotti, F., Dicaro, G., Crespi, B.: Real-time parallel computation of disparity and optical flow using phase difference. Machine Vision and Appl. 9(3), 87–96 (1996)
Weickert, J., Schnörr, C.: A theoretical framework for convex regularizers in pde–based computation of image motion. Int. J. Computer Vision 45(3), 245–264 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kohlberger, T., Schnörr, C., Bruhn, A., Weickert, J. (2004). Parallel Variational Motion Estimation by Domain Decomposition and Cluster Computing. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24673-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-24673-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21981-1
Online ISBN: 978-3-540-24673-2
eBook Packages: Springer Book Archive