## 4 Experimental Results and Discussion  
### Image Segmentation  
The proposed segmentation strategy has been tested on 39 microscopic images taken by Leica DFC 480 digital camera, and the results in terms of accuracy, purity and entropy are given in Table 3. It can be observed that the proposed two-level K-means algorithm achieved significantly higher accuracy (90.82%), higher purity (90.82%) and lower entropy (0.6042) than the other clustering algorithms. In particular, the output result via two-level coarse-to-fine clustering consistently has better segmentation results as compared to the corresponding single-level clustering. For instance, regarding the K-means algorithm, the accuracy of the two-step strategy is 17.59% better than that of applying single-level K-means.  
Furthermore, in this paper, one out of those tested images was selected to visualize the performance of the proposed strategy and the other five kinds of clustering methods. The segmentation results of single-level clustering and two-level clustering are compared with the ground truth segmentations provided by five petrologists for evaluation. It can be seen from Figure 4 that the boundary of the resultant segmentation images by K-means is slightly clearer as compared to Fuzzy c-means (FCM) and K-medoids clustering. The segmented images produced by the two-level clustering are sharper and much closer to the ground truth. Overall, the proposed two-level coarse-to-fine clustering strategy based on K-means has outperformed the other clustering algorithms.  
We also compare the results of image segmentation with the results of the fixed-size window strategy. As can be seen from Figure 5, it is feasible to detect the thin spornites (i.e., a-1) and the granular micrinites (i.e., a-2). We can obtain the shape information for each object of interest. As to the fixed-size window strategy, 41 px \(\times\) 41 px was demonstrated to be the optimal size for maceral identification [3]. However, it is unrealistic to retrieve the shape information in feature extraction. In addition, micrinites distributing through the window may only account for a small amount of the area, and therefore it might be unreliable to train the classification models based on the information provided by the whole window. Similarly, spornites are always thin and they might be misclassified based on the  
Figure 4: Comparison of automated segmentation results with ground truth. From left to right, the images represent original image, ground truth, the segmentation results of single-level Fuzzy c-means (FCM), 2-level FCM, single-level K-medoids, 2-level K-medoids, single-level K-means, and 2-level K-means.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Accuracy (\%)** & **Purity (\%)** & **Entropy** \\ \hline Fuzzy c-means & 69.35 & 86.36 & 0.7291 \\ K-medoids & 68.34 & 89.94 & 0.6805 \\ K-means & 73.21 & 89.43 & 0.6748 \\
2-level Fuzzy c-means & 76.58 & 83.33 & 0.7961 \\
2-level K-medoids & 82.14 & 85.31 & 0.7306 \\
2-level K-means & 90.82 & 90.82 & 0.6042 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Quantitative assessment of automatic segmentation methods.  
fixed-size window strategy. Our method is also very effective in extracting macroal composition with a large area (i.e., a-3), which is helpful to improve classification accuracy. Although the proposed strategy achieved satisfying performance in identifying the objects of interest (i.e., macroal groups), the differences in term of gray scale values between macroal components are too subtle to differentiate them. More discriminative features are required.