# Ore Rock Fragmentation Calculation Based on Multi-Modal Fusion of Point Clouds and Images
## 4 Experiments
### Experiments and Analysis
#### 4.2.2 Quantitative Experiments  
Figure 12 shows the statistical results of the equivalent diameter, elliptical long diameter, and elliptical short diameter calculation errors of ORFCM on all 30 sets of test samples.  
Figure 11: Segmentation results of the ore rock point clouds: (**a**) Ground truth; (**b**) Proposed method.  
Figure 10: Segmentation results of the ore rock images: (**a**) Ground truth; (**b**) Proposed method.  
It can be found that the calculation error of the equivalent diameter was the smallest among the three evaluation indicators, with an average error value of 0.66 cm on all test samples; the second was the elliptical short diameter, which had an average error value of 1.06 cm on all test samples; finally, the elliptical long diameter had an average error value of 1.42 cm on all test samples. Experiments demonstrate that the multimodal fusion method for calculating rock fragmentation proposed in this article had relatively small computational errors in all three evaluation indicators and could effectively meet the practical needs of intelligent mining electric shovels for calculating rock fragmentation.  
Furthermore, we selected three samples to present the experimental results in more detail by using the equivalent diameter and the elliptical long diameter as the metrics. The computed results for the size of rock blocks in Sample I are presented in Figure 13.  
Figure 12: Mean error of ORFM on the test samples.  
Figure 13: Ore rock fragmentation calculation of sample I: (a) Statistical histogram of equivalent diameter of ore rock blocks; (b) Statistical histogram of elliptical long diameter of ore rock blocks.  
Figure 13a shows the histogram of the equivalent diameters for all rock blocks in Sample I. It can be observed that the difference between the equivalent diameters of rock blocks and the ideal values was minimal, with an average error of 0.7 cm for all rock blocks. Figure 13b displays the histogram of the major axes for all rock blocks in Sample I. Upon close examination of the data, it is evident that the disparity between the major axes of rock blocks and the ideal values was negligible, with an average discrepancy of only 1.7 cm for all rock blocks.  
Figure 14 presents the computed results of rock block size for Sample II. Figure 14a displays the histogram of the equivalent diameters for all rock blocks in Sample II. The obtained equivalent diameters of ore rock blocks exhibited minimal disparity with the ideal values, with an average error of 0.8 cm for all rock blocks. The statistical histogram of the major axes for all rock blocks in Sample II is shown in Figure 14b, indicating a slight variation in the elliptical major axis of the rock blocks compared with the ideal values. The average error in the elliptical major axis of all rock blocks is 1.7 cm.  
Figure 14: Ore rock fragmentation calculation of sample II: (**a**) Statistical histogram of equivalent diameter of ore rock blocks; (**b**) Statistical histogram of elliptical long diameter of ore rock blocks.  
From Table 1, we can see that our method performed best in terms of the mean errors of \(D_{E}\), \(D_{L}\), and \(D_{S}\). Among all the comparison methods, Ref. [21] performed the worst, mainly due to the low resolution of point clouds obtained by LiDAR, which made it difficult to accurately calculate the block size of fine-grained ore rocks. Compared with our method, Refs. [3; 6] did not perform as well in solving the problem of image under-segmentation caused by blurry edges as our method.