Abstract
An analysis of the expected size occupied by a Quadtree is presented. The analysis is based on the general assumption that the storage requirements of internal and external nodes differ. Besides, formulae for the expected number of internal and external nodes at a specific level of the tree are given. Next, the space efficiency of the most popular Quadtree implementations is examined. Finally, the possible usefulness of these analytical tools in other problems is commented.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Burton, F.W., Kollias, V.J., Kollias, J.G.: Expected and worst-case storage requirements for Quadtrees. Pattern Recognition Letters 3 (2) (1985) 131–135
Cheiney, J.P., Tourir, A.: FI-Quadtree: a new data structure for content-oriented retrieval and fuzzy search. Proceedings, 2nd Symposium on Spatial Databases (SSD), Zurich, (1991)
Faloutsos, C.: Analytical results on the Quadtree decomposition of arbitrary rectangles. Pattern Recognition Letters 13 (1) (1992) 31–40
Finkel, R.A., Bentley, J.L.: Quad trees: a data structure for retrieval on composite keys. Acta Informatica 4 (1) (1974) 1–9
Gargantini, I.: An effective way to represent Quadtrees. Communications of the ACM 25 (12) (1982) 905–910
Kawaguchi, E., Endo, T.: On a method of binary picture representation and its application to data compression. IEEE Transactions on Pattern Analysis and Machine Intelligence 2 (1) (1980) 27–35
Mathieu, C., Puech, C., Yahia, H.: Average efficiency of data structures for binary image processing. Information Processing Letters 26 (2) (1987) 89–93
Papoulis, A.: Probabilities, Random Variables and Stochastic Processes. McGraw-Hill, Singapore, (1984)
Samet, H.: The Quadtree and related hierarchical data structures. ACM Computing Surveys 16 (2) (1984) 187–260
Ang, C., Samet, H.: Node distribution in a PR Quadtree. Proceedings, 1st Symposium on Spatial Databases (SSD), Santa Barbara, (1989)
Vassilakopoulos, M., Manolopoulos, Y., Economou, K.: Overlapping Quadtrees for the representation of similar images. To appear in Image and Vision Computing
Vassilakopoulos, M., Manolopoulos, Y.: Efficiency analysis of overlapped Quadtrees. Submitted in GVGIP: Graphical Models and Image Processing
Vassilakopoulos, M., Manolopoulos, Y.: Analytical results on the Quadtree storage-requirements. Internal Report, Div. of Electronics and Computer Engineering, Department of Electrical Engineering, Aristotelian University of Thessaloniki, (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vassilakopoulos, M., Manolopoulos, Y. (1993). Analytical results on the Quadtree storage-requirements. In: Chetverikov, D., Kropatsch, W.G. (eds) Computer Analysis of Images and Patterns. CAIP 1993. Lecture Notes in Computer Science, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57233-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-57233-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57233-6
Online ISBN: 978-3-540-47980-2
eBook Packages: Springer Book Archive