Estimation of fractal dimension through morphological decomposition
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...
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2004
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| author | Radhakrishnan, P. Lay Lian, Teo Daya Sagar, B.S. |
| author_facet | Radhakrishnan, P. Lay Lian, Teo Daya Sagar, B.S. |
| author_sort | Radhakrishnan, P. |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | 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 (R-B) and mean diameter ratio (R-L) are computed, employing which another type of fractal dimension is estimated as log R-B/log R-L. 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. (C) 2004 Elsevier Ltd. All rights reserved. |
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| last_indexed | 2025-11-14T18:06:38Z |
| publishDate | 2004 |
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| spelling | mmu-24662011-08-19T05:31:11Z http://shdl.mmu.edu.my/2466/ Estimation of fractal dimension through morphological decomposition Radhakrishnan, P. Lay Lian, Teo Daya Sagar, B.S. QA Mathematics 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 (R-B) and mean diameter ratio (R-L) are computed, employing which another type of fractal dimension is estimated as log R-B/log R-L. 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. (C) 2004 Elsevier Ltd. All rights reserved. 2004-07 Article NonPeerReviewed Radhakrishnan, P. and Lay Lian, Teo and Daya Sagar, B.S. (2004) Estimation of fractal dimension through morphological decomposition. Chaos, Solitons & Fractals, 21 (3). pp. 563-572. ISSN 09600779 http://dx.doi.org/10.1016/j.chaos.2003.12.085 doi:10.1016/j.chaos.2003.12.085 doi:10.1016/j.chaos.2003.12.085 |
| spellingShingle | QA Mathematics Radhakrishnan, P. Lay Lian, Teo Daya Sagar, B.S. Estimation of fractal dimension through morphological decomposition |
| title | Estimation of fractal dimension through morphological decomposition |
| title_full | Estimation of fractal dimension through morphological decomposition |
| title_fullStr | Estimation of fractal dimension through morphological decomposition |
| title_full_unstemmed | Estimation of fractal dimension through morphological decomposition |
| title_short | Estimation of fractal dimension through morphological decomposition |
| title_sort | estimation of fractal dimension through morphological decomposition |
| topic | QA Mathematics |
| url | http://shdl.mmu.edu.my/2466/ http://shdl.mmu.edu.my/2466/ http://shdl.mmu.edu.my/2466/ |