**6. Conclusions**

Considering the fact that the petrological properties of coal are complex and widely distributed, in this paper, the microscopic images with heterogeneous natural have been analyzed by the MF-DFA method. We verified the multifractal properties of the microscopic image by the function of *τ*(*q*) and *h*(*q*). In addition, with the multifractal spectrum, we have proposed three important texture descriptors for characterizing image information, such as *α*min, *α*max, and *f*max. It is well known that the texture descriptor of an image should be robust and immune to image quality; thus, the stability experiments have been implemented and the results have verified the anti-noise ability and anti-blur capability of the multifractal descriptors.

A classification model with RBF-SVM classifier has been built to distinguish the 160 microscopic images of inertinite macerals in coal. Our multifractal descriptors have represented the most appealing results in terms of performance metrics of precision, recall, and F-measure, providing excellent performance compared with GLCM-based texture descriptors. The successful implementation of our proposed method in the identification of inertinite materials can assist petrologists to make correct decisions and reduce the influences of subjective factors in practical scenarios, which is particularly beneficial to geologists with less experience. In view of the fact that there are some similarities of structural complicacy and non-linear multi-classification, we will investigate the classification of other maceral groups with a reference to our proposed method in the future. Simultaneously, in order to be more suitable for industrial applications, we will also develop a cross platform software for maceral image recognition and classification in the future work.

**Author Contributions:** Conceptualization, P.W. and M.L.; formal analysis, M.L.; investigation, M.L and S.C.; resources, D.Z.; data curation, D.Z.; writing—original draft preparation, M.L.; writing—review and editing, P.W.; supervision, S.C.; project administration, P.W.; funding acquisition, P.W.

**Funding:** This research was funded by the National Natural Science Foundation of China (number 51574004); Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (number KJ2019A0085); Academic Foundation for Top Talents of the Higher Education Institutions of Anhui Province, China (number 2016041).

**Conflicts of Interest:** The authors declare no conflict of interest.
