差分盒计数（DBC）方法中的网格大小选择问题及改进策略,Entropy

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差分盒计数（DBC）方法中的网格大小选择问题及改进策略
Entropy ( IF 2.1 ) Pub Date : 2022-07-14 , DOI: 10.3390/e24070977
Wenxuan Jiang ₁ , Yujun Liu ₁ , Ji Wang _{1,

2,

3} , Rui Li ₁ , Xiao Liu ₁ , Jian Zhang ₄

Affiliation

差分盒计数 (DBC) 方法可用于确定灰度图像的分形维数。它易于学习和实施，并已被广泛使用。但是，这种方法存在几个问题，例如由于参数选择不当导致框数过多或过少，从而限制了计算精度。已经进行了许多研究以通过改进差分盒计数方法的计算参数来提高算法的计算精度。网格大小是 DBC 方法的关键参数。通常，相关研究中选择网格大小的典型方法有两种：连续整数和图像大小的除数。然而，这两种网格大小选择的方法都是有问题的。连续整数法不能对图像进行完整的分割，会导致box的计数不足；图像大小的除数可以完全分割图像。然而，这种方法使用较少的网格大小来计算分形维数，并且具有相对较大的距离误差（DE）。针对上述两种方法的不足，本研究提出了一种改进的网格尺寸选择策略。改进后的方法通过在连续整数方法中计算丢弃的图像边缘区域来提高计算精度，使原始图像信息与除数策略一样彻底地使用。基于分数布朗运动 (FBM)、Brodatz 和 Aerials 图像集，三种网格尺寸选择技术（连续整数法、图像尺寸除数法、然后比较计算分形维数的改进算法。结果表明，与两种现有技术相比，本研究中描述的修正算法最大限度地减少了距离误差并提高了分形维数计算的准确性。

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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 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.

更新日期：2022-07-18

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