Current methods of fractal analysis rely on capturing approximations of an images’ fractal dimension by distributing iteratively smaller boxes over the image, counting the set of box and fractal, and using linear regression estimators to estimate the slope of the set count line. To minimize the estimation error in those methods, our aim in this study was to derive a generalized fractal feature that operates without iterative box sizes or any linear regression estimators. To do this, we adapted the Minkowski-Bouligand box counting dimension to a generalized form by fixing the box size to the smallest fundamental unit (the individual pixel) and incorporating each pixel's color channels as components of the intensity measurement. The purpose of this study was twofold; to first validate our novel approach, and to then apply that approach to the classification of detailed, organic images of viruses. When validating our method, we a) computed the fractal dimension of known fractal structures to verify accuracy, and b) tested the results of the proposed method against previously published color fractal structures to assess similarity to comparable existing methods. Finally, we performed a case study of twelve virus transmission electron microscope (TEM) images to investigate the effects of fractal features between viruses and across the factors of family (Orthomyxoviridae, Filoviridae, Paramyxoviridae and Coronaviridae) and physical structure (whole cell, capsid and envelope). Our results show that the presented generalized fractal feature is a) accurate when applied to known fractals and b) shows differing trends to comparable existing methods when performed on color fractals, indicating that the proposed method is indeed a single-scale fractal feature. Finally, results of the analysis of TEM virus images suggest that viruses may be uniquely identified using only their computed fractal features.

当前的分形分析方法依靠以下方法来捕获图像的分形维数的近似值：在图像上迭代地分布较小的盒子，对盒子和分形的集合进行计数，并使用线性回归估计量来估计设置的计数线的斜率。为了使这些方法中的估计误差最小化，我们在本研究中的目的是得出一种无需分形盒大小或任何线性回归估计量即可运行的广义分形特征。为此，我们将Box尺寸固定为最小的基本单位（单个像素），并将每个像素的颜色通道合并为强度测量的组成部分。这项研究的目的是双重的。首先验证我们的新颖方法，然后将该方法应用于病毒的详细有机图像分类。在验证我们的方法时，我们a）计算了已知分形结构的分形维数以验证准确性，并且b）针对先前发布的颜色分形结构测试了所提出方法的结果，以评估与可比较的现有方法的相似性。最后，我们对十二个病毒透射电子显微镜（TEM）图像进行了案例研究，以研究病毒之间以及整个家庭因素（正粘病毒科，丝状病毒科，副粘病毒科和冠状病毒科）的分形特征和物理结构（整个细胞，衣壳和信封）。我们的结果表明，所提出的广义分形特征是a）当应用于已知分形时是准确的，并且b）当对颜色分形执行时，与可比的现有方法显示出不同的趋势，表明所提出的方法确实是单尺度分形特征。最后，TEM病毒图像的分析结果表明，仅可以使用计算出的分形特征来唯一识别病毒。