Abstract
Properties of Pyramidal Representations. The categorization of different components generalizes the classical concept of image pyramids and provides a powerful tool for efficient image analysis. Three aspects of image pyramids are distinguished: their structure, the contents of their cells and the processes that operate on them. The properties of these three aspects of a pyramidal system are discussed and illustrated by examples. The general theory covers the most recent results, e.g. structure preserving irregular pyramids, sigmoid pyramids, the concept of equivalent interpretation, and the fuzzy curve pyramid.
This work was supported by the Austrian National Fonds zur Förderung der wissenschaftlichen Forschung under grant S 7002.
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
Ackermann, F., Hahn, M.: Image pyramids for digital photogrammetry. In: Digital photogrammetric systems (Ebner, H., et al., eds.), pp. 43–58. Karlsruhe: Wichmann 1991.
Aloimonos, Y., ed.: Active Perception. Hillsdale, New Jersey: Lawrence Erlbaum 1993.
Bischof, H.: Pyramidal Neural Networks. PhD thesis, Technische Universität Wien, 1993.
Bischof, H., Kropatsch, W. G.: The fuzzy curve pyramid. In: 12th IAPR International Conference on Pattern Recognition Vol. 1 (Peleg, S., Ullman, S., Yeshurun, Y., eds.), pp. 505–509. Washington, Brussels, Tokyo: IEEE Comp. Soc., 1994.
Bister, M., Cornelis, J., Rosenfeld, A.: A critical view of pyramid segmentation algorithms. Pattern Rec. Lett. 11, 605–617 (1990).
Blanford, R. P., Tanimoto, S. L.: Bright spot detection in pyramids. Comput. Vision Graphics Image Proc. 43, 133–149 (1988).
Burt, P. J., Adelson, E. H.: The Laplacian pyramid as a compact image code. IEEE Trans. Comm. COM-31, 532–540 (1983).
Burt, P. J., Hong, T.-H., Rosenfeld, A.: Segmentation and estimation of image region properties through cooperative hierarchical computation. IEEE Trans. Systems Man Cybernetics SMC-11, 802–809 (1981).
Jolion, J.-M., Montanvert, A.: The adaptive pyramid, a framework for 2D image analysis. Comput. Vision Graphics Image Proc. Image Underst. 55, 339–348 (1992).
Kropatsch, W. G.: Curve representations in multiple resolutions. Pattern Rec. Lett. 6, 179–184 (1987).
Kropatsch, W. G.: Preserving contours in dual pyramids. Proc. 9th International Conference on Pattern Recognition, pp. 563–565, Rome, Italy, November 1988. IEEE Comp. Soc.
Kropatsch, W. G.: Rezeptive Felder in Bildpyramiden. In: Mustererkennung 1988 (Bunke, H., Kubler, O., Stucki, P., eds.), pp. 333–339. Berlin, Heidelberg, New York, Tokyo: Springer 1988 (Informatik Fachberichte Vol. 180).
Kropatsch, W. G.: Image pyramids and curves—an overview. Technical Report PRIP-TR-2, Institute f. Automation 183/2, Dept. for Pattern Recognition and Image Processing, TU Wien, Austria, 1991.
Kropatsch, W. G.: Building irregular pyramids by dual graph contraction. Technical Report PRIP-TR-35, Institute f. Automation 183/2, Dept. for Pattern Recognition and Image Processing, TU Wien, Austria, 1994.
Kropatsch, W. G., Montanvert, A.: Irregular versus regular pyramid structures. In: Geometrical problems of image processing (Eckhardt, U., Hübler, A., Nagel, W., Werner, G., eds.), pp. 11–22. Berlin: Akademie Verlag 1991.
Kropatsch, W. G., Neuhauser, M. A., Leitgeb, I. J.: Iterated function systems—A direct discrete approach with pyramids. In: Pattern recognition 1992, pp. 108–118. OCG-Schriftenreihe, Band 62. Österr. Arbeitsgemeinschaft für Mustererkennung. München: R. Oldenburg 1992.
Kropatsch, W. G., Reither, C., Willersinn, D., Wlaschitz, G.: The dual irregular pyramid. In: Proceedings CAIP’93, Budapest, pp. 31–40, 1993.
Leonardis, A.: Image analysis using parametric models: model-recovery and model-selection paradigm. PhD thesis, University of Ljubljana, Department of Computer and Information Science, Faculty of Electrical Engineering and Computer Science, 1993.
Leonardis, A.: A robust approach to estimation of parametric models. In: Theoretical foundations of computer vision (Kropatsch, W., Klette, R., Solina, F., eds.), pp. 113–130. Wien, New York: Springer 1996 (Computing Suppl. 11).
Meer, P.: Stochastic image pyramids. Comput. Vision Graphics Image Proc. 45, 269–294 (1989).
Meer, P., Jiang, S.-N., Baugher, E. S., Rosenfeld, A.: Robustness of image pyramids under structural perturbations. Comput. Vision Graphics Image Proc. 44, 307–331 (1988).
Montanvert, A., Meer, P., Rosenfeld, A.: Irregular tesselation based image analysis. In: Proc. 10th International Conference on Pattern Recognition, pages 474–479, Atlantic City, New Jersey, USA, June 1990. IEEE Comp. Soc. Vol. I.
Nacken, P. F.: Image analysis methods based on hierarchies of graphs and multi-scale mathematical morphology. PhD thesis, Universiteit van Amsterdam, The Netherlands, June 1994.
Rosenfeld, A.: Quadtrees and pyramids: hierarchical representation of images. Technical Report TR-1171, University of Maryland, Computer Science Center, May 1982.
Rosenfeld, A., Kak, A. C.: Digital picture processing, 2nd ed., Vol. 1 and 2. New York: Academic Press 1982.
Willersinn, D.: Parallel graph contraction for dual irregular pyramids. Technical Report PRIP-TR-28 Institute f. Automation 183/2, Dept. for Pattern Recognition and Image Processing, TU Wien, Austria, 1994.
Willersinn, D., Kropatsch, W. G.: Dual graph contraction for irregular pyramids. In: 12th IAPR International Conference on Pattern Recognition, Vol. III (Peleg, S., Ullman, S., Yeshurun, Y., eds.), pp. 251–256. Washington, Brussels, Tokyo: IEEE Comp. Soc., 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Wien
About this paper
Cite this paper
Kropatsch, W.G. (1996). Properties of Pyramidal Representations. In: Kropatsch, W., Klette, R., Solina, F., Albrecht, R. (eds) Theoretical Foundations of Computer Vision. Computing Supplement, vol 11. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6586-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6586-7_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82730-7
Online ISBN: 978-3-7091-6586-7
eBook Packages: Springer Book Archive