*5.3. Experimental Results*

Based on the classification model, each RBF-SVM classifier is trained with the training samples to get specific values of parameters *c* and *γ*, as summarized in Table 3. For the testing samples, the previous evaluation performance of classifying inertinite macerals using multifractal descriptors is reported in Table 4. For each maceral, the classification result has achieved satisfactory performance in terms of precision, recall, and F-measure. We notice that the precision performances of oxyfusinite, secretinite, and funginite are slightly lower than those of the best performances of about 0.1304, 0.9520, and 0.1000, which may be due to their fractal similarity corresponding to the distribution of multifractal spectra, as shown in Figure 3. Remarkably, the result for macrinite presents the most

appealing performance with three full marks. This may be attributed to the fact that the MF-DFA method can effectively eliminate the local trends of non-stationary images and detect their multifractal features more accurately. These data from the evaluation matrices indicate that our multifractal features are effective in representing texture information of microscopic images of inertinite macerals.

**Table 3.** Objects and parameters of different classifiers. (**a**) Pyrofusinite; (**b**) oxyfusinite; (**c**) semifusinite; (**d**) secretinite; (**e**) funginite; (**f**) macrinitee; (**g**) inertodetrinite; (**h**) micirinite.


As a comparison, the performance evaluation of the classification of GLCM-based descriptors is reported in Table 5. It is not surprising to find that the GLCM-based descriptors always lead to unsatisfactory performance when compared to multifractal descriptors. This may be explained by the fact that the statistical features based on GLCM are not applicable for describing texture images with complex and heterogeneous naturals. Especially for the maceral of inertodetrinite, the three evaluation values are as low as 0.667, 0.5000, and 0.667, nearly half of the corresponding evaluation values of our method, which are far from satisfying our classification purpose. Overall, we give the average performance evaluation in Figure 12. The macro-precision of the GLCM-based descriptors can be improved by means of the proposed multifractal descriptors up to 7.99%. This holds in both micro-recall and macro-F with improvements of 10.00% and 9.02%, respectively. These data present report the effectiveness and feasibleness of our proposed method.

**Figure 12.** Average performance evaluation of different texture descriptors.


**Table 4.** Performance of inertinite macerals' classification with multifractal descriptors.

**Table 5.** Performance of inertinite macerals' classification with GLCM-based descriptors.

