# Deep Learning-Based Estimation of Muckpile Fragmentation Using Simulated 3D Point Cloud Data
## 5 Verification of Particle Size Distribution Estimation
### Particle Size Distribution Estimation Using Actual Data  
Using the model trained in Section 5.2, the particle size distribution estimation was performed on actual data in the Physical world. For the actual data, three sample data of muckpile fragmentation measured at Curtin University in Kalgoorlie, Australia, were used. The sample data of muckpile fragmentation consisted of particle size distributions measured by sieving at eight levels of [2.36, 4.76, 9.5, 19, 26.5, 37.5, 53, 75] (mm), and as shown in Figure 17, the multi-view images captured by the camera were reconstructed into 3D point clouds using SfM, similar to the Cyber world. An iPhone 6s was used as the camera, and the image resolution was 1080 pixels by 1929 pixels. The reconstructed point clouds were preprocessed by background point removal, downsampling to 50,000 points, and scaling, and then input into the trained model in the Cyber world for estimation.  
Figure 18 shows the results of the particle size distribution estimation for muckpile fragmentation sample 1. Figure 18 represents the cumulative undersize distribution, with the blue line indicating the actual distribution and the yellow line indicating the estimated values. From these results, although the estimation results recognized about 10% of the rocks at [2.36, 53, 75] (mm) which were not included in the actual data, a generally close particle size distribution could be estimated. Next, the results for muckpile fragmentation samples 2 (Figure 19a) and 3 (Figure 19b) are shown in Figure 19. The upper graph represents the cumulative undersize distribution, and the lower graph represents the proportion of each of the eight particle sizes contained in the muckpile fragmentation,  
Figure 16: Performance evaluation of the combined approach using local and global module features.  
Figure 17: The experiment of taking multi-view photos.  
with the blue line indicating the actual values and the yellow line indicating the estimated values. From these results, the cumulative undersize distributions for samples 2 and 3 were significantly different from the actual particle size distributions. However, when the estimated results were compared in terms of the proportions of each particle size, the distribution peaks for samples 2 and 3 matched, and a close overall shape of the distribution could be obtained. However, in muckpile fragmentation like sample 2, which does not contain rocks smaller than 2.36 mm and larger than 26.5 mm, the estimation should be zero, but the estimation was still performed. Factors that may be affecting the estimation results include overlapping ranges when generating groups in the Local module and areas not included in the group.  
Figure 19: Estimation Results of Particle Size Distribution.  
Figure 18: Estimation Results of Particle Size Distribution for Sample 1.  
From these results, it can be said that the particle size distribution estimation network trained and learned in the Cyber world can effectively estimate the particle size distribution of actual muckpile fragmentation.