Abstract
We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Adrian. Particle imaging techniques for experimental fluid mechanics. Annal Rev. Fluid Mech., 23:261–304, 1991.
A. Amini. A scalar function formulation for optical flow. In Proc. Europ. Conf. Computer Vision, pages 125–131, 1994.
L. Bannehr, R. Rohn, and G. Warnecke. A functionnal analytic method to derive displacement vector fields from satellite image sequences. Int. Journ. of Remote Sensing, 17(2):383–392, 1996.
T. Corpetti, E. Mémin, and P. Pérez. Dense estimation of fluid flows. IEEE Trans. Pattern Anal. Machine Intell., 24(3):365–380, 2002.
T. Corpetti, E. Mémin, and P. Pérez. Dense motion analysis in fluid imagery. In European Conference on Computer Vision, ECCV’02, pages 676–691, 2002.
S. Das Peddada and R. McDevitt. Least average residual algorithm (LARA) for tracking the motion of arctic sea ice. IEEE trans. on Geoscience and Remote sensing, 34(4):915–926, 1996.
J.M. Fitzpatrick and C.A. Pederson. A method for calculating fluid flow in time dependant density images. Electronic Imaging, 1:347–352, 1988.
W. Hackbusch. Theorie und Numerik elliptischer Differentialgleichungen. B.G. Teubner, Stuttgart, 1986.
B. Horn and B. Schunck. Determining optical flow. Artificial Intelligence, 17:185–203, 1981.
D. J. Fleet J. L. Barron and S. S. Beauchemin. Perfomance of optical flow techniques. Int. J. Computer Vision, 1994.
R. Larsen, K. Conradsen, and B.K. Ersboll. Estimation of dense image flow fields in fluids. IEEE trans. on Geoscience and Remote sensing, 36(1):256–264, 1998.
S.P. McKenna and W.R. McGillis. Performance of digital image velocimetry processing techniques. Experiments in Fluids, 32:106–115, 2002.
A. Ottenbacher, M. Tomasini, K. Holmlund, and J. Schmetz. Low-level cloud motion winds from Meteosat high-resolution visible imagery. Weather and Forecasting, 12(1):175–184, 1997.
C. Schnörr. Segmentation of visual motion by minimizing convex non-quadratic functionals. In 12th Int. Conf. on Pattern Recognition, Jerusalem, Israel, Oct 9–13 1994.
C. Schnörr, R. Sprengel, and B. Neumann. A variational approach to the design of early vision algorithms. Computing Suppl., 11:149–165, 1996.
J. Shukla and R. Saha. Computation of non-divergent streamfunction and irrotational velocity potential from the observed winds. Monthly weather review, 102:419–425, 1974.
J. Simpson and J. Gobat. Robust velocity estimates, stream functions, and simulated Lagrangian drifters from sequential spacecraft data. IEEE trans. on Geosciences and Remote sensing, 32(3):479–492, 1994.
S.M. Song and R.M. Leahy. Computation of 3D velocity fields from 3D cine and CT images of human heart. IEEE trans. on medical imaging, 10(3):295–306, 1991.
D. Suter. Motion estimation and vector splines. In Proc. Conf. Comp. Vision Pattern Rec., 1994.
J. Weickert and C. Schnörr. A theoretical framework for convex regularizers in pde-based computation of image motion. Int. J. Computer Vision, 45(3):245–264, 2001.
L. Zhou, C. Kambhamettu, and D. Goldgof. Fluid structure and motion analysis from multi-spectrum 2D cloud images sequences. In Proc. Conf. Comp. Vision Pattern Rec., volume 2, pages 744–751, Hilton Head Island, South Carolina, USA, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kohlberger, T., Mémin, É., Schnörr, C. (2003). Variational Dense Motion Estimation Using the Helmholtz Decomposition. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_30
Download citation
DOI: https://doi.org/10.1007/3-540-44935-3_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40368-5
Online ISBN: 978-3-540-44935-5
eBook Packages: Springer Book Archive