# The Classification of Inertinite Macerals in Coal Based on the Multifractal Spectrum Method  
[PERSON]  
1 School of Electrical and Information Engineering, Anhui University of Technology,  
Ma'anshan 243002, China; [EMAIL_ADDRESS] (M.L.); [EMAIL_ADDRESS] (S.C.)  
[PERSON]  
1 School of Electrical and Information Engineering, Anhui University of Technology,  
Ma'anshan 243002, China; [EMAIL_ADDRESS] (M.L.); [EMAIL_ADDRESS] (S.C.)  
[PERSON]  
1 School of Electrical and Information Engineering, Anhui University of Technology,  
Ma'anshan 243002, China; [EMAIL_ADDRESS] (M.L.); [EMAIL_ADDRESS] (S.C.)  
[PERSON]  
3 Anhui Key Laboratory of Clean Conversion and Utilization, Anhui University of Technology,  
Ma'anshan 243002, China; ag  
in coal. Some related references have been published. To name a few, the authors of [9] completed the detection of approximately circular particles in the microscopic image of coal by the contour features, and the authors of [10] proposed a method to extract the outline of the maceral area by using structural elements. The texture features of local binary patterns (LBP) and the gray level co-occurrence matrix (GLCM) were combined to identify three major groups in coal macroals [11]. Grey scale, GLCM, Tamura, contourlet transform, and supervised locality preserving projections methods were employed by the authors in the previous work [12; 13; 14; 15] to describe features of macroals. However, because the complex construction of macroals and similar morphological features among some different macroals exist, these techniques may not characterize them perfectly, especially for the features of texture.  
In recent years, the fractal theory, first coined in [16], has been rapidly developed as a powerful analytical tool, which can reflect the heterogeneity and irregularities of a physical surface. There are several published techniques for characterizing the surface irregularity of coal with the mono-fractal method [17; 18; 19; 20; 21]. Nevertheless, it can not provide a comprehensive and accurate description of the details of image changes at different scales owing to the single scale of fractal dimensions. Coal's surface is known to be non-stationary and heterogeneous as a consequence of the long-term and multi-stage effects of geological processes. Some local trends in texture and dramatic changes in gray value are universal in microscopic images of macroals. Fortunately, a method named multifractal detrended fluctuation analysis (MF-DFA) can quickly eliminate local trends [22], making itself more suitable for describing the texture characteristics of the microscopic images of macroals. Given the superiority in solving non-stationary problems, the MF-DFA method has applications in quite a few fields [23; 24; 25; 26]. Nevertheless, it was the first attempt that the approach was applied for the purpose of the classification of macroals in coal.  
The major goal of our work was to find an artificial intelligence method to distinguish eight groups of inertinite macroals with few but stable and effective texture features. We analyzed and verified the multifractal properties of inertinite macroals by the method of MF-DFA. Additionally, multifractal descriptors of microscopic images were proposed based on the multifractal spectrum. In order to demonstrate the effectiveness of the multifractal descriptors, a comparison experiment of stability was implemented. Finally, we built an automatic classification model with support vector machine (SVM) to identify the inertinite macroals.