A single-scale fractal feature for classification of color images: A virus case study

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.