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Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy

The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate...

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Autores principales: Jiang, Wenxuan, Liu, Yujun, Wang, Ji, Li, Rui, Liu, Xiao, Zhang, Jian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9324739/
https://www.ncbi.nlm.nih.gov/pubmed/35885199
http://dx.doi.org/10.3390/e24070977
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author Jiang, Wenxuan
Liu, Yujun
Wang, Ji
Li, Rui
Liu, Xiao
Zhang, Jian
author_facet Jiang, Wenxuan
Liu, Yujun
Wang, Ji
Li, Rui
Liu, Xiao
Zhang, Jian
author_sort Jiang, Wenxuan
collection PubMed
description The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate parameter choices, limiting the calculation accuracy. Many studies have been conducted to increase the algorithm’s computational accuracy by improving the calculating parameters of the differential box-counting method. The grid size is a crucial parameter for the DBC method. Generally, there are two typical ways for selecting the grid size in relevant studies: consecutive integer and divisors of image size. However, both methods for grid size selection are problematic. The consecutive integer method cannot partition the image entirely and will result in the undercounting of boxes; the divisors of image size can partition the image completely. However, this method uses fewer grid sizes to compute fractal dimensions and has a relatively huge distance error (DE). To address the shortcomings of the above-mentioned two approaches, this research presents an improved grid size selection strategy. The improved method enhances computational accuracy by computing the discarded image edge areas in the consecutive integer method, allowing the original image information to be used as thoroughly as the divisor strategy. Based on fractional Brownian motion (FBM), Brodatz, and Aerials image sets, the accuracy of the three grid size selection techniques (consecutive integer method, divisors of image size method, and the improved algorithm) to compute the fractal dimension is then compared. The results reveal that, compared to the two prior techniques, the revised algorithm described in this study minimizes the distance error and increases the accuracy of the fractal dimension computation.
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spelling pubmed-93247392022-07-27 Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy Jiang, Wenxuan Liu, Yujun Wang, Ji Li, Rui Liu, Xiao Zhang, Jian Entropy (Basel) Article The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate parameter choices, limiting the calculation accuracy. Many studies have been conducted to increase the algorithm’s computational accuracy by improving the calculating parameters of the differential box-counting method. The grid size is a crucial parameter for the DBC method. Generally, there are two typical ways for selecting the grid size in relevant studies: consecutive integer and divisors of image size. However, both methods for grid size selection are problematic. The consecutive integer method cannot partition the image entirely and will result in the undercounting of boxes; the divisors of image size can partition the image completely. However, this method uses fewer grid sizes to compute fractal dimensions and has a relatively huge distance error (DE). To address the shortcomings of the above-mentioned two approaches, this research presents an improved grid size selection strategy. The improved method enhances computational accuracy by computing the discarded image edge areas in the consecutive integer method, allowing the original image information to be used as thoroughly as the divisor strategy. Based on fractional Brownian motion (FBM), Brodatz, and Aerials image sets, the accuracy of the three grid size selection techniques (consecutive integer method, divisors of image size method, and the improved algorithm) to compute the fractal dimension is then compared. The results reveal that, compared to the two prior techniques, the revised algorithm described in this study minimizes the distance error and increases the accuracy of the fractal dimension computation. MDPI 2022-07-14 /pmc/articles/PMC9324739/ /pubmed/35885199 http://dx.doi.org/10.3390/e24070977 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Jiang, Wenxuan
Liu, Yujun
Wang, Ji
Li, Rui
Liu, Xiao
Zhang, Jian
Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title_full Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title_fullStr Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title_full_unstemmed Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title_short Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy
title_sort problems of the grid size selection in differential box-counting (dbc) methods and an improvement strategy
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9324739/
https://www.ncbi.nlm.nih.gov/pubmed/35885199
http://dx.doi.org/10.3390/e24070977
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