Abstract
In [4], the following pyramid construction problem was proposed: Given nonnegative valued functions ρ and μ in d variables, we consider the optimal pyramid maximizing the total parametric gain of ρ against μ. The pyramid can be considered as the optimal unimodal approximation of ρ relative to μ, and can be applied to hierarchical data segmentation. In this paper, we give efficient algorithms for a couple of two-dimensional pyramid construction problems.
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
Asano, T., Chen, D., Katoh, N., Tokuyama, T.: Efficient Algorithms for Optimization-Based Image Segmentation. International Journal of Computational Geometry and Applications 11, 145–166 (2001)
Bloch, I.: Spatial Relationship between Objects and Fuzzy Objects using Mathematical Morphology. In: Geometry, Morphology and Computational Imaging, 11th Dagsthul Workshop on Theoretical Foundations of Computer Vision (April 2002)
Chen, D., Chun, Z., Katoh, N., Tokuyama, T.: Layered Data Segmentation for Numeric Data Mining (in preparation)
Chun, Z., Katoh, N., Tokuyama, T.: How to reform a terrain into a pyramid (preprint)
Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Mining Optimized Association Rules for Numeric Attributes. Journal of Computer and System Sciences 58, 1–12 (1999)
Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Data Mining with Optimized Two-Dimensional Association Rules. ACM Transaction of Database Systems 26, 179–213 (2001)
Morimoto, Y., Ishii, H., Morishita, S.: Construction of Regression Trees with Range and Region Splitting. In: The 23rd VLDB Conference, pp. 166-175 (1997)
Morimoto, Y., Fukuda, T., Morishita, S., Tokuyama, T.: Implementation and Evaluation of Decision Trees with Range and Region Splitting. Constraints, 402–427 (1997)
Preparata, F.P., Shamos, M.I.: Computational Geometry – An Introduction, 2nd edn. Springer, Heidelberg (1988)
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
Chun, J., Sadakane, K., Tokuyama, T. (2003). Efficient Algorithms for Constructing a Pyramid from a Terrain. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-44400-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
Online ISBN: 978-3-540-44400-8
eBook Packages: Springer Book Archive