Abstract
Optical flow is the velocity vector field of the projected environmental surfaces when a viewing system moves relative to the environment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, 1950)
K. Nakayama, Biological image motion processing: a survey. Vision. Res. 25, 625–660 (1985)
H.-H. Nagel, On the estimation of optical flow: relations between different approaches and some new results. Artif. Intell. 33(3), 299–324 (1987)
H.-H. Nagel, Image sequence evaluation: 30 years and still going strong, in International Conference on Pattern Recognition, 2000, pp. 1149–1158
J. Barron, D. Fleet, S. Beauchemin, Performance of optical flow techniques. Int. J. Comput. Vision 12(1), 43–77 (1994)
A. Mitiche, Computational Analysis of Visual Motion (Plenum Press, New York, 1994)
A. Mitiche, P. Bouthemy, Computation and analysis of image motion: A synopsis of current problems and methods. Int. J. Comput. Vision 19(1), 29–55 (1996)
C. Stiller, J. Konrad, Estimating motion in image sequences: A tutorial on modeling and computation of 2D motion. IEEE Signal Process. Mag. 16(4), 70–91 (1999)
G. Aubert, P. Kornpbrost, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Springer, New York, 2006)
B. Horn, B. Schunck, Determining optical flow. Artif. Intell. 17, 185–203 (1981)
B.D. Lucas, T. Kanade, An iterative image registration technique with an application to stereo vision, in IJCAI, 1981, pp. 674–679
A. Bruhn, J. Weickert, C. Schnörr, Lucas/kanade meets Horn/Schunck: combining local and global optic flow methods. Int. J. Comput. Vision 61(3), 211–231 (2005)
A. Mitiche, A. Mansouri, On convergence of the Horn and Schunck optical flow estimation method. IEEE Trans. Image Process. 13(6), 848–852 (2004)
C. Koch, J. Luo, C. Mead, J. Hutchinson, Computing motion using resistive networks, in NIPS, 1987, pp. 422–431
J. Hutchinson, C. Koch, J. Luo, C. Mead, Compting motion using analog and binary resistive networks. IEEE Comput. 21(3), 52–63 (1988)
H. Nagel, W. Enkelmann, An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences. IEEE Trans. Pattern Anal. Mach. Intell. 8(5), 565–593 (1986)
H.-H. Nagel, On a constraint equation for the estimation of displacement rates in image sequences. IEEE Trans. Pattern Anal. Mach. Intell. 11(1), 13–30 (1989)
H.-H. Nagel, Extending the ’oriented smoothness constraint’ into the temporal domain and the estimation of derivatives of optical flow, in European Conference on Computer Vision, 1990, pp. 139–148
M. Snyder, On the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction. IEEE Trans. Pattern Anal. Mach. Intell. 13(11), 1105–1114 (November 1991)
A. Mansouri, A. Mitiche, J. Konrad, Selective image diffusion: application to disparity estimation, in International Conference on Image Processing, 1998, pp. 284–288
F. Hampel, E. Ronchetti, P. Rousseeuw, W. Stahel, Robust Statistics: The Approach Based on Influence Functions (Wiley-Interscience, New York, 1986)
M. Black, “Robust incremental optical flow”, in Ph.D. Thesis, Yale University, Research Report YALEU-DCS-RR-923, 1992
M. J. Black, P. Anandan, A framework for the robust estimation of optical flow, in International Conference on Computer Vision, 1993, pp. 231–236
A. Blake, A. Zisserman, Visual Reconstruction (MIT Press, Cambridge, 1987)
E. Memin, P. Perez, Joint estimation-segmentation of optic flow, in European Conference on Computer Vison, 1998, vol. II, pp. 563–578
S. Geman, D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 721–741 (1984)
J. Konrad, E.Dubois, Bayesian estimation of motion vector fields. IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 910–927 (1992)
F. Heitz, P. Bouthemy, Multimodal estimation of discontinuous optical flow using markov random fields. IEEE Trans. Pattern Anal. Mach. Intell. 15(12), 1217–1232 (1993)
J. Zhang, G.G. Hanauer, The application of mean field theory to image motion estimation. IEEE Trans. Image Process. 4(1), 19–33 (1995)
P. Nesi, Variational approach to optical flow estimation managing discontinuities. Image Vision Comput. 11(7), 419–439 (1993)
A. Mitiche, I. Ben Ayed, Variational and Level Set Methods in Image Segmentation (Springer, New York, 2010)
D. Mumford, J. Shah, Boundary detection by using functionals. Comput. Vis. Image Underst. 90, 19–43 (1989)
Y.G. Leclerc, Constructing simple stable descriptions for image partitioning. Int. J. Comput. Vision 3(1), 73–102 (1989)
J. Weickert, A review of nonlinear diffusion filtering, in Scale-Space, 1997, pp. 3–28
L. Blanc-Feraud, M. Barlaud, T. Gaidon, Motion estimation involving discontinuities in a multiresolution scheme. Opt. Eng. 32, 1475–1482 (1993)
M. Proesmans, L.J.V. Gool, E.J. Pauwels, A. Oosterlinck, Determination of optical flow and its discontinuities using non-linear diffusion, in European Conference on Computer Vision, 1994, pp. 295–304
R. Deriche, P. Kornprobst, G. Aubert, Optical-flow estimation while preserving its discontinuities: A variational approach, in Asian Conference on Computer Vision, 1995, pp. 71–80
G. Aubert, R. Deriche, P. Kornprobst, Computing optical flow via variational thechniques. SIAM J. Appl. Math. 60(1), 156–182 (1999)
A. Kumar, A. Tannenbaum, G.J. Balas, Optical flow: a curve evolution approach. IEEE Trans. Image Process. 5(4), 598–610 (1996)
J. Weickert, C. Schnörr, Variational optic flow computation with a spatio-temporal smoothness constraint. J Math. Imaging Vision 14(3), 245–255 (2001)
T. Brox, A. Bruhn, N. Papenberg, J. Weickert, High accuracy optical flow estimation based on a theory for warping, 2004. http://citeseer.ist.psu.edu/brox04high.html.
N. Papenberg, A. Bruhn, T. Brox, S. Didas, J. Weickert, Highly accurate optic flow computation with theoretically justified warping. Int. J. Comput. Vision 67(2), 141–158 (2006)
C. Zach, T. Pock, H. Bischof, A duality based approach for realtime tv-l1 optical flow, in Annual Symposium of the German Association Pattern Recognition, 2007, pp. 214–223
T. Nir, A.M. Bruckstein, R. Kimmel, Over-parameterized variational optical flow. Int. J. Comput. Vision 76(2), 205–216 (2008)
M. Werlberger, W. Trobin, T. Pock, A. Wedel, D. Cremers, H. Bischof, Anisotropic huber-l1 optical flow, in BMVC, 2009
C. Vogel, Computational Methods for Inverse Problems (SIAM, Philadelphia, 2002)
L. I. Rudin, S. Osher, Total variation based image restoration with free local constraints, in ICIP, vol. 1, 1994, pp. 31–35
I. Cohen, Nonlinear variational method for optical flow computation, in SCIA93, 1993, pp. 523–530
P. Perona, J. Malik, Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1981)
G. Bellettini, On the convergence of discrete schemes for the perona-malik equation. Proc. Appl. Math. Mech.7(1), 1023401–1023402 (2007)
W. Enkelmann, Investigation of multigrid algorithms for the estimation of optical flow fields in image sequences. Computer Vision, Graphics, and Image Processing 43(2), 150–177 (August 1988)
D. Terzopoulos, Efficient multiresolution algorithms for computing lightness, shape-from-shading, and optical flow, in AAAI conference, 1984, pp. 314–317
D. Cremers, C. Schnorr, Motion competition: Variational integration of motion segmentation and shape regularization, in DAGM Symposium on, Pattern Recognition, 2002, pp. 472–480
D. Cremers, A multiphase level set framework for motion segmentation, in Scale Space Theories in Computer Vision, ed. by L. Griffin, M. Lillholm (Springer, Isle of Skye, 2003), pp. 599–614
A. Mansouri, J. Konrad, Multiple motion segmentation with level sets. IEEE Trans. Image Process. 12(2), 201–220 (Feb. 2003)
D. Cremers, S. Soatto, Motion competition: A variational approach to piecewise parametric motion segmentation. Int. J. Comput. Vision 62(3), 249–265 (2005)
T. Brox, A. Bruhn, J. Weickert, Variational motion segmentation with level sets, in European Conference on Computer Vision, vol. 1, 2006, pp. 471–483
H. Sekkati, A. Mitiche, Joint optical flow estimation, segmentation, and 3D interpretation with level sets. Comput. Vis. Image Underst. 103(2), 89–100 (2006)
H. Sekkati, A. Mitiche, Concurrent 3D motion segmentation and 3D interpretation of temporal sequences of monocular images. IEEE Trans. Image Process. 15(3), 641–653 (2006)
C. Vazquez, A. Mitiche, R. Laganiere, Joint segmentation and parametric estimation of image motion by curve evolution and level sets. IEEE Trans. Pattern Anal. Mach. Intell. 28(5), 782–793 (2006)
A. Mitiche, H. Sekkati, Optical flow 3D segmentation and interpretation: A variational method with active curve evolution and level sets. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1818–1829 (Nov. 2006)
A. Mitiche, On combining stereopsis and kineopsis for space perception, in IEEE Conference on Artificial Intelligence Applications, 1984, pp. 156–160
A. Mitiche, A computational approach to the fusion of stereopsis and kineopsis, in Motion Understanding: Robot and Human Vision, ed. by W.N. Martin, J.K. Aggarwal (Kluwer Academic Publishers, Boston, 1988), pp. 81–99
S. Negahdaripour, C. Yu, A generalized brightness change model for computing optical flow, in ICCV, 1993, pp. 2–11
M. Mattavelli, A. Nicoulin, Motion estimation relaxing the constancy brightness constraint, in ICIP, vol. 2, 1994, pp. 770–774
R.P. Wildes, M.J. Amabile, A.-M. Lanzillotto, T.-S. Leu, Physically based fluid flow recovery from image sequences, in CVPR, 1997, pp. 969–975
T. Corpetti, É. Mémin, P. Pérez, Dense estimation of fluid flows. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 365–380 (2002)
K. Nakayama, S. Shimojo, Intermediate and higher order aspects of motion processing, in Neural Mechanisms of Visual Perception, ed. by D.M-K. Lam, C.D. Gilbert (Portfolio Publishing Company, The Woodlands, Texas, 1989), pp. 281–296
D. Todorovic, A gem from the past: Pleikart Stumpf’s (1911) anticipation of the aperture problem, reichardt detectors, and perceived motion loss at equiluminance. Perception 25(10), 1235–1242 (1996)
E. Hildreth, The Measurement of Visual Motion (MIT Press, Cambridge, 1983)
J. Kearney, W. Thompson, D. Boley, Optical flow estimation: an error analysis of gradient-based methods with local optimization. IEEE Trans. Pattern Anal. Mach. Intell. 9(2), 229–244 (1987)
K. Wohn, L.S. Davis, P. Thrift, Motion estimation based on multiple local constraints and nonlinear smoothing. Pattern Recogn. 16(6), 563–570 (1983)
V. Markandey, B. Flinchbaugh, Multispectral constraints for optical flow computation, in International Conference on Computer Vision, 1990, pp. 38–41
A. Mitiche, Y.F. Wang, J.K. Aggarwal, Experiments in computing optical flow with the gradient-based, multiconstraint method. Pattern Recogn. 20(2), 173–179 (1987)
O. Tretiak, L. Pastor, Velocity estimation from image sequences with second order differential operators, in International Conference on Pattern Recognition and Image Processing, 1984, pp. 16–19
A. Verri, F. Girosi, V. Torre, Differential techniques for optical flow. J. Opt. Soc. Am. A 7, 912–922 (May 1990)
M. Campani, A. Verri, “Computing optical flow from an overconstrained system of linear algebraic equations, in International Conference on Computer Vision, 1990, pp. 22–26
M. Tistarelli, Computation of coherent optical flow by using multiple constraints, in International Conference on Computer Vision, 1995, pp. 263–268
R. Woodham, Multiple light source optical flow, in International Conference on Computer Vision, 1990, pp. 42–46
S. Baker, I. Matthews, Lucas-kanade 20 years on: a unifying framework. Int. J. Comput. Vision 56(3), 221–255 (2004)
G. Dahlquist, A. Bjork, Numerical Methods (Prentice Hall, Englewood Cliffs, 1974)
P. Ciarlet, Introduction à l’analyse numérique matricielle et à l’optimisation, 5th edn. (Masson, Paris, 1994)
J. Stoer, P. Burlisch, Introduction to Numerical Methods, 2nd edn. (Springer, New York, 1993)
R. Feghali, A. Mitiche, Fast computation of a boundary preserving estimate of optical flow. SME Vision Q. 17(3), 1–4 (2001)
L. Yuan, J. Li, B. Zhu, Y. Qian, A discontinuity-preserving optical flow algorithm, in IEEE International Symposium on Systems and Control in Aerospace and Aeronautics, 2006, pp. 450–455
W. Enkelmann, K. Kories, H.-H. Nagel, G. Zimmermann, An experimental investigation of estimation approaches for optical flow fields, in Motion Understanding: Robot and Human Vision, ed. by W.N. Martin, J.K. Aggarwal, (Chapter 6), (Kluwer Academic Publications, Boston, 1988), pp. 189–226
L. Álvarez, J. Weickert, J. Sánchez, Reliable estimation of dense optical flow fields with large displacements. Int. J. Comput. Vision 39(1), 41–56 (2000)
S. Solimini, J.M. Morel, Variational Methods in Image Segmentation (Springer, New York, 2003)
S. Zhu, A. Yuille, Region competition: Unifying snakes, region growing, and bayes/mdl for multiband image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 118(9), 884–900 (1996)
T. Brox, B. Rosenhahn, D. Cremers, H.-P. Seidel, High accuracy optical flow serves 3- D pose tracking: Exploiting contour and flow based constraints, in European Conference on Computer Vision, 2006, pp. 98–111
C. Zach, T. Pock, H. Bischof, A duality based approach for realtime tv-l1 optical flow, in DAGM, 2007, pp. 214–223
A. Wedel, T. Pock, C. Zach, H. Bischof, D. Cremers, An improved algorithm for tv-l1 optical flow, in Statistical and Geometrical Approaches to Visual Motion Analysis, ed. by D. Cremers, B. Rosenhahn, A. Yuille, F. Schmidt. ser. Lecture Notes in Computer Science, (Springer, Heidelberg, 2009), pp. 23–45
A. Foi, M. Trimeche, V. Katkovnik, K. Egiazarian, Practical poissonian-gaussian noise modeling and fitting for single-image raw-data. IEEE Trans. Image Process. 17(10), 1737–1754 (2008)
J. Bergen, P. Anandan, K. Hanna, R. Hingorani, Hierarchical model-based motion estimation, in European Conference on Computer Vision, 1992, pp. 237–252
É. Mémin, P. Pérez, Dense estimation and object-based segmentation of the optical flow with robust techniques. IEEE Trans. Image Process. 7(5), 703–719 (1998)
P. Burt, E. Adelson, The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31(4), 532–540 (April 1983)
F. Heitz, P. Perez, P. Bouthemy, Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Underst. 59(1), 125–134 (1994)
C. Cassisa, V. Prinet, L. Shao, S. Simoens, C.-L. Liu, Optical flow robust estimation in a hybrid multi-resolution mrf framework, in IEEE Acoustics, Speech, and, Signal Processing, 2008, pp. 793–796
W. Hackbusch, U.Trottenberg (eds.), Multigrid Methods. Lecture Notes in Mathematics, vol. 960, (Springer, New York, 1982)
W.L. Briggs, A Multigrid Tutorial (SIAM, Philadelphia, 1987)
M. Chang, A. Tekalp, M. Sezan, Simultaneous motion estimation and segmentation. IEEE Trans. Image Process. 6(9), 1326–1333 (1997)
D. Cremers, A. Yuille, A generative model based approach to motion segmentation, in German Conference on Pattern Recognition (DAGM), (Magdeburg, Sept 2003), pp. 313–320
D. Cremers, S. Soatto, Variational space-time motion segmentation, in International Conference on Computer Vision, vol 2 (Nice, France, 2003), pp. 886–892
R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985)
J.A. Sethian, Level Set Methods and Fast Marching Methods (Cambridge University Press, Cambridge, 1999)
G. Aubert, M. Barlaud, O. Faugeras, S. Jehan-Besson, Image segmentation using active contours: calculus of variations or shape gradients? SIAM J. Appl. Math. 63(6), 2128–2154 (2003)
H.-K. Zhao, T. Chan, B. Merriman, S. Osher, A variational level set approach to multiphase motion. J. Comput. Phys. 127(1), 179–195 (1996)
N. Paragios, R. Deriche, Coupled geodesic active regions for image segmentation: A level set approach, in Europeean Conference on Computer vision, (Dublin, Ireland, June 2000), pp. 224–240
C. Samson, L. Blanc-Feraud, G. Aubert, J. Zerubia, A level set model for image classification. Int. J. Comput. Vision 40(3), 187–197 (2000)
C. Vazquez, A. Mitiche, I. Ben Ayed, Image segmentation as regularized clustering: A fully global curve evolution method, in International Conference on Image Processing, 2004, pp. 3467–3470
T. Brox, J. Weickert, Level set segmentation with multiple regions. IEEE Trans. Image Process. 15(10), 3213–3218 (2006)
L. Vese, T. Chan, A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vision 50(3), 271–293 (2002)
A. Mansouri, A. Mitiche, C. Vazquez, Multiregion competition: a level set extension of region competition to multiple region partioning. Comput. Vis. Image Underst. 101(3), 137–150 (2006)
I. Ben Ayed, A. Mitiche, Z. Belhadj, Polarimetric image segmentation via maximum likelihood approximation and efficient multiphase level sets. IEEE Trans. Pattern Anal. Mach. Intell. 28(9), 1493–1500 (2006)
I. Ben Ayed, A. Mitiche, A partition constrained minimization scheme for efficient multiphase level set image segmentation, in International Conference on Image Processing, 2006, pp. 1641–1644
I. Ben Ayed, A. Mitiche, A region merging prior for variational level set image segmentation. IEEE Trans. Image Process. 17(12), 2301–2313 (2008)
T. Kadir, M. Brady, Unsupervised non-parametric region segmentation using level sets, in International Conference on Computer Vision, 2003, pp. 1267–1274
A. Tamtaoui, C. Labit, Constrained disparity and motion estimators for 3DTV image sequence coding. Signal Proces.: Image Commun. 4(1), 45–54 (1991)
J. Liu, R. Skerjanc, Stereo and motion correspondence in a sequence of stereo images. Signal Process.: Image Commun. 5(4), 305–318 (October 1993)
Y. Altunbasak, A. Tekalp, G. Bozdagi, Simultaneous motion-disparity estimation and segmentation from stereo, in IEEE International Conference on Image Processing, vol. III, 1994, pp. 73–77
R. Laganière, Analyse stéreocinétique d’une séquence d’images: Estimation des champs de mouvement et de disparité, Ph.D. dissertation, Institut national de la recherche scientifique, INRS-EMT, 1995
I. Patras, N. Alvertos, G. Tziritas, Joint disparity and motion field estimation in stereoscopic image sequences, in IAPR International Conference on Pattern Recognition, vol. I, 1996, pp. 359–363
H. Weiler, A. Mitiche, A. Mansouri, Boundary preserving joint estimation of optical flow and disparity in a sequence of stereoscopic images, in International Conference on Visualization, Imaging, and Image Processing, 2003, pp. 102–106
A. Wedel, T. Brox, T. Vaudrey, C. Rabe, U. Franke, D. Cremers, Stereoscopic scene flow computation for 3D motion understanding. Int. J. Comput. Vision 95(1), 29–51 (2011)
L. Robert, R. Deriche, Dense depth map reconstruction: A minimization and regularization approach which preserves discontinuities, in European Conference on Computer Vision, 1996, pp. I:439–451
O. Faugeras, R. Keriven, Variational principles, surface evolution, PDEs, level set methods, and the stereo problem. IEEE Trans. Image Process. 7(3), 336–344 (1998)
H. Zimmer, A. Bruhn, L. Valgaerts, M. Breuß, J. Weickert, B. Rosenhahn, H.-P. Seidel, PDE-based anisotropic disparity-driven stereo vision, in Vision Modeling and Visualization, 2008, pp. 263–272
C. Wohler, 3D Computer Vision: Efficient Methods and Applications (Springer, Berlin, 2009)
C. Liu, Beyond pixels: Exploring new representations and applications for motion analysis, in Ph.D. Thesis, MIT, May 2009
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Mitiche, A., Aggarwal, J. (2014). Optical Flow Estimation. In: Computer Vision Analysis of Image Motion by Variational Methods. Springer Topics in Signal Processing, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-00711-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-00711-3_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00710-6
Online ISBN: 978-3-319-00711-3
eBook Packages: EngineeringEngineering (R0)