Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T13:18:02.424Z Has data issue: false hasContentIssue false
  • English
  • Français

Wavelets and Optical Flow Motion Estimation

Published online by Cambridge University Press:  28 May 2015

P. Dérian ,
P. Héas ,
C. Herzet  and
E. Mémin
P. Dérian*
Affiliation:
Departments of Physics and Geosciences, California State University Chico, Chico, CA 95929-0555, USA
P. Héas*
Affiliation:
INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes CEDEX, France
C. Herzet*
Affiliation:
INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes CEDEX, France
E. Mémin*
Affiliation:
INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes CEDEX, France
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Get access

Abstract

This article describes the implementation of a simple wavelet-based optical-flow motion estimator dedicated to continuous motions such as fluid flows. The wavelet representation of the unknown velocity field is considered. This scale-space representation, associated to a simple gradient-based optimization algorithm, sets up a well-defined multiresolution framework for the optical flow estimation. Moreover, a very simple closure mechanism, approaching locally the solution by high-order polynomials is provided by truncating the wavelet basis at fine scales. Accuracy and efficiency of the proposed method is evaluated on image sequences of turbulent fluid flows.

Keywords

68T4565T6076F99Waveletsoptical flowmotion estimationlarge displacementsfluid flows
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 116 - 137
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bernard, C., Wavelets and Ill Posed Problems: Optic Flow and Scattered Data Interpolation, PhD thesis, École Polytechnique, 1999.Google Scholar
[2] Black, M. and Anandan, P., The robust estimation of multiple motions: parametric and piecewise-smooth flow fields, Computer Vision and Image Understanding, 63(1) (1996), pp. 75–104.Google Scholar
[3] Brox, T., Bruhn, A., Papenberg, N. and Weickert, J., High accuracy optical flow estimation based on a theory for warping, Computer Vision-ECCV 2004, pages 25–36, 2004.Google Scholar
[4] Chen, L., Liao, H. and Lin, J., Wavelet-based optical flow estimation, Circuits and Systems for Video Technology, IEEE Transactions on, 12(1) (2002), pp. 1–12.Google Scholar
[5] Corpetti, T., E. Mémin and Pérez, P., Dense estimation of fluid flows, Pattern Anal Mach Intel, 24(3) (2002), pp. 365–380.Google Scholar
[6] Dérian, P., Héas, P., Herzet, C. and Mémin, E., Wavelets to reconstruct turbulence multifractals from experimental image sequences, In 7th Int. Symp. on Turbulence and Shear Flow Phenomena, TSFP-7, Ottawa, Canada, July 2011.Google Scholar
[7] Héas, P., Mémin, E., Heitz, D. and Mininni, P., Power laws and inverse motion modelling: application to turbulence measurements from satellite images, Tellus A, 64 (10962), 2012.Google Scholar
[8] Heitz, D., Carlier, J. and Arroyo, G., Final report on the evaluation of the tasks of the work-package 2, FLUID project deliverable 5.4, Technical report, INRIA-Cemagref, 2007.Google Scholar
[9] Horn, B. and Schunck, B., Determining optical flow, Artificial Intelligence, 17 (1981), pp. 185–203.Google Scholar
[10] Kadri Harouna, S., Dérian, P., Héas, P. and Memin, E., Divergence-free wavelets and high order regularization. Accepted for publication in IJCV, 2012Google Scholar
[11] Lucas, B. and Kanade, T., An iterative image registration technique with an application to stereovision, In Int. Joint Conf. on Artificial Intel. (IJCAI), pages 674–679, 1981.Google Scholar
[12] Mallat, S., A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, 2008.Google Scholar
[13] Nocedal, J. and Wright, S. J., Numerical Optimization, Springer Series in Operations Research, Springer-Verlag, New York, NY, 1999.Google Scholar
[14] Tai, X. and Xu, J., Global and uniform convergence of subspace correction methods for some convex optimization problems, Math. Comput., 71(237) (2002), pp. 105–124.Google Scholar
[15] Wu, Y., Kanade, T., Li, C. and Cohn, J., Image registration using wavelet-based motion model, Int. J. Computer Vision, 38(2) (2000), pp. 129–152.Google Scholar
[16] Yuan, J., Schnörr, C. and Memin, E., Discrete orthogonal decomposition and variational fluid flow estimation, J. Math. Imaging Vison, 28 (2007), pp. 67–80.Google Scholar
[17] Yuan, J., Schnörr, C. and Steidl, G., Simultaneous higher-order optical flow estimation and decomposition, SIAM J. Sci. Computing, 29(6) (2007), pp. 2283–2304.Google Scholar