Abstract
The structure of hypersurfaces corresponding to different spatio-temporal patterns is considered, and in particular representations based on geometrical invariants, such as the Riemann and Einstein tensors and the scalar curvature are analyzed. The spatio-temporal patterns result from translations, Lie-group transformations, accelerated and discontinuous motions and modulations. Novel methods are obtained for the computation of motion parameters and the optical flow. Moreover, results obtained for accelerated and discontinuous motions are useful for the detection of motion boundaries.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ballard, D., Brown, C.: Computer Vision. Prentice Hall, Englewood Cliffs (1982)
Barth, E.: Bewegung als intrinsische Geometric von Bildfolgen. In: Forster, W., Buhmann, J.M., Faber, A., Faber, P. (eds.) Mustererkennung 1999, Bonn, pp. 301–308. Springer, Berlin (1999)
Barth, E.: The minors of the structure tensor. In: Sommer, G. (ed.) Mustererkennung 2000, Kiel. Springer, Berlin (2000) (in print)
Barth, E.: Spatio-temporal curvature and the visual coding of motion. In: Neural Computation, Proceedings of the International ICSC Congress, Berlin (2000)
Barth, E., Watson, A.B.: Nonlinear spatio-temporal model based on the geometry of the visual input. Invest. Ophthalm. Vis. Sci., 39-4 (Suppl.):S-2110 (1998)
Jahne, B., HauBecker, H., GeiBler, P. (eds.): Handbook of Computer Vision and Applications. HauBecker and Spies, vol. 2, ch. 13. Academic Press, Boston (1999)
Liou, S.-P., Jain, R.C.: Motion detection in spatio-temporal space. Computer Vision, Graphics and Image Processing 45, 227–250 (1989)
Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, New York (1986)
Schutz, B.: Geometrical methods of mathematical physics. Cambridge University Press, Cambridge (1980)
Schutz, B.: A first course in general relativity. Cambridge University Press, Cambridge (1985)
Tretiak, O., Pastor, L.: Velocity estimation from image sequences with second order differential operators. In: Proc. 7th Int. Conf. Pattern Recognition, Montreal, Canada, pp. 16–19. IEEE Computer Society Press, Los Alamitos (1984)
Wolfram, S.: Mathematica: a system for doing mathematics by computer, 2nd edn. Addison- Wesley Publishing Co., Redwood City (1991)
Zetzsche, C., Barth, E.: Direct detection of flow discontinuities by 3D curvature operators. Pattern Recognition Letters 12, 771–779 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barth, E., Ferraro, M. (2000). On the Geometric Structure of Spatio-temporal Patterns. In: Sommer, G., Zeevi, Y.Y. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 2000. Lecture Notes in Computer Science, vol 1888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722492_8
Download citation
DOI: https://doi.org/10.1007/10722492_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41013-3
Online ISBN: 978-3-540-45260-7
eBook Packages: Springer Book Archive