{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T04:12:30Z","timestamp":1785816750924,"version":"3.56.0"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,14]],"date-time":"2022-07-14T00:00:00Z","timestamp":1657756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51479030"],"award-info":[{"award-number":["51479030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e24070977","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:17:10Z","timestamp":1657844230000},"page":"977","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy"],"prefix":"10.3390","volume":"24","author":[{"given":"Wenxuan","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yujun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ji","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"},{"name":"Collaborative Innovation Centre for Advanced Ship and Deep-Sea Exploration, Shanghai Jiaotong University, No. 800 Dongchuan Road, Minhang District, Shanghai 200240, China"},{"name":"State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Naval Architecture and Ocean Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Foreign Languages, Dalian University of Technolog, No. 2 Linggong Road, Ganjingzi District, Dalian 116024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,14]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. 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