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Chaos, Solitons & Fractals
Volume 21, Issue 3, July 2004, Pages 563-572
 
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doi:10.1016/j.chaos.2003.12.085    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Elsevier Ltd. All rights reserved.

Estimation of fractal dimension through morphological decomposition

P. Radhakrishnan a, Teo Lay Lian b and B. S. Daya Sagar Corresponding Author Contact Information, E-mail The Corresponding Author, b

a Faculty of Information Science and Technology, Melaka Campus, Multimedia University, Jalan Ayer Keroh Lama, 75450, Melaka, Malaysia b Faculty of Engineering and Technology, Melaka Campus, Multimedia University, Jalan Ayer Keroh Lama, 75450, Melaka, Malaysia

Accepted 4 December 2003. 
Available online 11 February 2004.

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Abstract

Set theory based morphological transformations have been employed to decompose a binary fractal by means of discrete structuring elements such as square, rhombus and octagon. This decomposition provides an alternative approach to estimate fractal dimensions. The fractal dimensions estimated through this morphological decomposition procedure by employing different structuring elements are considerably similar. A color-coding scheme is adapted to identify the several sizes of decomposed non-overlapping disks (DNDs) that could be fit into a fractal. This exercise facilitates to test the number–radius relationship from which the fractal dimension has been estimated for a Koch Quadric, which yield the significantly similar values of 1.67 ± 0.05 by three structuring elements. In addition to this dimension, by considering the number of DNDs of various orders (radii) and the mean diameter of disks (MDDs) of corresponding order, two topological quantities namely number ratio (RB) and mean diameter ratio (RL) are computed, employing which another type of fractal dimension is estimated as Image . These results are in accord with the fractal dimensions computed through number–radius relationship, and connectivity network of the Koch Quadric that is reported elsewhere.

Article Outline

1. Introduction
2. Morphological transformations
3. Morphological decomposition: fractal dimension
3.1. Dimension based on two topological quantities
4. Results and conclusion
Acknowledgements
References








 
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