## 1 Introduction
In the paper, we adopt another way to express the indicator of the Hurst exponent--the class of the Hurst exponent--instead of the value of the Hurst exponent. In fact, however, a class of the Hurst exponent can be viewed as an equivalent estimate with a fixed interval, say, 0.1. To understand the tolerable spacing between two Hurst exponents, two resolutions--11 and 21 classes or Hurst exponents with equal intervals--will be considered. For each resolution, we first estimate Hurst exponents of 2D FBM images via the efficient MLE. Next, we use the estimated Hurst exponents as the only feature to train and further classify them through machine learning models. Finally, a classification report will be provided--hence, its resolution will be implied. Based on the same data or images as machine learning models, we use the original images--not the estimated Hurst exponents--to train deep learning models and then classify them. Finally, a classification report will also be provided. The paper is composed of two main purposes. The first aim is to see whether deep learning models on the FBM images have any possibilities to surpass the traditional way--that is, machine-learning models are run on the only feature of the estimated Hurst exponents of 2D FBM images. If successful, the second aim is to apply theses promising deep learning models to recognize the classes of images--or equivalently estimate Hurst exponents of images. Among artificial intelligence methods, machine learning analyzes data through algorithms, understand the content of the data, and then applies the learned knowledge to determine other data and make appropriate decisions. Deep learning is a branch of machine learning. It uses the concept of \"layers\" to construct learning models that can automatically learn and then make intelligent decisions. Although deep learning belongs to machine learning, their functions are different. Deep learning can perform artificial intelligence functions that approximate the logic of human thinking as closely as possible; however, machine learning still needs human intervention and guidance. In the deep learning model, the algorithm can determine whether or not the prediction result is accurate. If the algorithm returns inaccurate predictions, its developer will step in and retrain the proposed model [23]. For better results, deep learning requires a large amount of data. Fortunately, with the advancement of modern computer technology, the acquisition and collection of data at present are more efficient than in the past. However, if the amount of data is not enough, the performance of deep learning, in general, will not be very good. Relatively, machine learning requires more resources than deep learning. For example, before performing machine learning, we need to extract some useful features from the original data and then use these features to train models. Besides, in the past, deep learning models were run under central processing units (CPUs), and hence they take a very long time to train. As the technology of graphics processing units (GPUs) gets mature, deep learning models have become more efficient. Hence, GPUs have gradually become the mainstream of artificial intelligence [24]. In the paper, we will apply four machine-learning methods and four deep-learning models to compare and explore the classification of 2D FBM images. For machine learning [25; 26], we use logistic regression (LR) for classification--simply called LR, support vector machines (SVMs), K-nearest neighbors (KNNs), and decision tree (DT). For deep learning [27; 28; 29], we will design a simple deep learning model and choose three pretrained models--AlexNet, GoogleNet, and Xception to evaluate their performances. In the paper, Section 2 describes the materials and methods related to our study. Section 3 performs our experiments and works on the discussion. Applications through deep learning models for medical images are provided in Section 4. Finally, Section 5 concludes the paper with some facts and future works.