Abstract
Before the notion of motion is generalized to arbitrary images, we first give a brief introduction to motion analysis for videos. We will review how motion is estimated when the underlying motion is slow and smooth, especially the Horn–Schunck (Artif Intell 17:185–203, 1981) formulation with robust functions. We show step-by-step how to optimize the optical flow objective function using iteratively reweighted least squares (IRLS), which is equivalent to conventional Euler–Lagrange variational approach but more succinct to derive. Then we will briefly discuss how motion is estimated when the slow and smooth assumption becomes invalid, especially how large displacement motion is estimated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Baker, S., Matthews, I.: Lucas-kanade 20 years on: a unifying framework. Int. J. Comput. Vis. 56(3), 221–255 (2004)
Baker, S., Scharstein, D., Lewis, J.P., Roth, S., Black, M.J., Szeliski, R.: A database and evaluation methodology for optical flow. Int. J. Comput. Vis. 92, 1–31 (2010)
Barnes, C., Shechtman, E., Finkelstein, A., Goldman, D.B.: PatchMatch: a randomized correspondence algorithm for structural image editing. ACM Trans. Graph. (Proc. SIGGRAPH) 28(3) (2009)
Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. Int. J. Comput. Vis. 12, 43–77 (1994)
Bay, H., Tuytelaars, T., Gool, L.V.: SURF: speeded up robust features. In: European Conference on Computer Vision (ECCV) (2006)
Black, M.J., Anandan, P.: The robust estimation of multiple motions: parametric and piecewise-smooth flow fields. Comput. Vis. Image Underst. 63(1), 75–104 (1996)
Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)
Brox, T., Malik, J.: Large displacement optical flow: descriptor matching in variational motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 500–513 (2011)
Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: European Conference on Computer Vision (ECCV), pp. 25–36 (2004)
Bruhn, A., Weickert, J., Schnörr, C.: Lucas/Kanade meets Horn/Schunk: combining local and global opti flow methods. Int. J. Comput. Vis. 61(3), 211–231 (2005)
Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2005)
Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artif. Intell. 17, 185–203 (1981)
Levin, A., Weiss, Y.: User assisted separation of reflections from a single image using a sparsity prior. IEEE Trans. Pattern Anal. Mach. Intell. 1(9), 72–91 (2007)
Liu, C.: Beyond pixels: exploring new representations and applications for motion analysis. Ph.D. thesis, Massachusetts Institute of Technology (2009)
Liu, C., Freeman, W.T., Adelson, E.H., Weiss, Y.: Human-assisted motion annotation. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2008)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)
Sand, P., Teller, S.: Particle video: long-range motion estimation using point trajectories. Int. J. Comput. Vis. 1(80), 72–91 (2008)
Strang, G.: Introduction to Applied Mathematics. Wellesley-Cambridge Press, Wellesley (1986)
Sun, D., Roth, S., Black, M.J.: Secrets of optical flow estimation and their principles. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2010)
Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, Berlin (2010)
Xu, L., Jia, J., Matsushita, Y.: Motion detail preserving optical flow estimation. IEEE Trans. Pattern Anal. Mach. Intell. 34(9), 1744–1575 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Liu, C. (2016). Introduction to Dense Optical Flow. In: Hassner, T., Liu, C. (eds) Dense Image Correspondences for Computer Vision. Springer, Cham. https://doi.org/10.1007/978-3-319-23048-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-23048-1_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23047-4
Online ISBN: 978-3-319-23048-1
eBook Packages: EngineeringEngineering (R0)