Abstract
In this paper we briefly review a not so well known quadratic, phase invariant image processing operator, the energy operator, and describe its tensor-valued generalization, the energy tensor. We present relations to the real-valued and the complex valued energy operators and discuss properties of the three operators. We then focus on the discrete implementation for estimating the tensor based on Teager’s algorithm and frame theory. The kernels of the real-valued and the tensor-valued operators are formally derived. In a simple experiment we compare the energy tensor to other operators for orientation estimation. The paper is concluded with a short outlook to future work.
This work has been supported by EC Grant IST-2002-002013 MATRIS and by EC Grant IST-2003-004176 COSPAL. However, this paper does not necessarily represent the opinion of the European Community, and the European Community is not responsible for any use which may be made of its contents.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: ISPRS Intercommission Workshop, Interlaken, pp. 149–155 (1987)
Bigün, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: Proceedings of the IEEE First International Conference on Computer Vision, London, Great Britain, pp. 433–438 (1987)
Harris, C.G., Stephens, M.: A combined corner and edge detector. In: 4th Alvey Vision Conference, pp. 147–151 (1988)
Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision. Kluwer Academic Publishers, Dordrecht (1995)
Jähne, B.: Digital Image Processing. Springer, Berlin (2002)
Kovesi, P.: Image features from phase information. Videre: Journal of Computer Vision Research 1 (1999)
Kaiser, J.F.: On a simple algorithm to calculate the ’energy’ of a signal. In: Proc. IEEE Int’l. Conf. Acoust., Speech, Signal Processing, Albuquerque, New Mexico, pp. 381–384 (1990)
Potamianos, A., Maragos, P.: A comparison of the energy operator and the Hilbert transform approach to signal and speech demodulation. Signal Processing 37, 95–120 (1994)
Maragos, P., Bovik, A.C., Quartieri, J.F.: A multi-dimensional energy operator for image processing. In: SPIE Conference on Visual Communications and Image Processing, Boston, MA, pp. 177–186 (1992)
Larkin, K.G., Oldfield, M.A., Bone, D.J.: Demodulation and phase estimation of two-dimensional patterns. Australian patent AU 200110005 A1 (2001)
Felsberg, M., Granlund, G.: POI detection using channel clustering and the 2D energy tensor. In: 26. DAGM Symposium, Mustererkennung, Tübingen (2004)
Felsberg, M., Köthe, U.: Get: The connection between monogenic scale-space and gaussian derivatives. In: Proc. Scale Space Conference (2005)
Bigün, J., Granlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 775–790 (1991)
Bovik, A.C., Maragos, P.: Conditions for positivity of an energy operator. IEEE Transactions on Signal Processing 42, 469–471 (1994)
Weickert, J., Scharr, H.: A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance. Journal of Visual Communication and Image Representation, Special Issue On Partial Differential Equations In Image Processing, Computer Vision, And Computer Graphics, 103–118 (2002)
Knutsson, H., Andersson, M.: Robust N-dimensional orientation estimation using quadrature filters and tensor whitening. In: Proceedings of IEEE International Conference on Acoustics, Speech, & Signal Processing, Adelaide, Australia. IEEE, Los Alamitos (1994)
Burg, K., Haf, H., Wille, F.: Höhere Mathematik für Ingenieure, Band IV Vektoranalysis und Funktionentheorie. Teubner Stuttgart (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Felsberg, M., Jonsson, E. (2005). Energy Tensors: Quadratic, Phase Invariant Image Operators. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds) Pattern Recognition. DAGM 2005. Lecture Notes in Computer Science, vol 3663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550518_61
Download citation
DOI: https://doi.org/10.1007/11550518_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28703-2
Online ISBN: 978-3-540-31942-9
eBook Packages: Computer ScienceComputer Science (R0)