## 3 Experimental Validation
### Comparison Results
#### 3.3.1 XYZRGB Point Cloud Data  
There were 16,384 XYZRGB points in the cloud data, such that the dimensions of the input data were [16384; 6]. The number of points in each image varied between 30,000 and 40,000. The number of points of objects in each scene varied between 400 and 4000. The alpha value for the balanced focus loss function was calculated automatically in each training batch.  
Figure 4 illustrates the mIoU curves obtained using the four methods with 100 epochs. The blue validation curve (baseline training method) reached a maximum value of 91.74% at epoch 37. Note that it reached saturation quickly and fluctuated around 80%. The green curve obtained using the balanced focus loss function reached 96.35% at epoch 62, i.e., 5% higher than the baseline method with less fluctuation. The red curve obtained using hybrid-sampling fluctuated considerably; however, it reached 97.55% accuracy at epoch 60, i.e., 1.2% higher than the balanced focus loss method, and 5.81% higher than the baseline method. Finally, the pink curve obtained using the two-stage framework combining hybrid-sampling with balanced focus loss reached 98.26% accuracy at epoch 97, i.e., 1.91% higher than balanced focus loss, 0.71% higher than hybrid-sampling, and 6.52% higher than the baseline training method.  
Figure 5a-c present the ground truth of a point cloud, the prediction results using the baseline PointNet method, and the prediction results using the proposed two-stage framework when using XYZRGB data. The pink points indicate a single small cuboid. Clearly, the prediction result using the baseline method was incorrect, as the small cuboid was recognized as a pipe, as indicated by the red points. The proposed framework correctly recognized the small cuboid, as indicated by the pink points. This is a clear indication that the proposed two-stage framework outperformed the baseline PointNet training method when using XYZRGB data.  
A further experiment was conducted to evaluate the network in the case of multiple objects. Figure 6a-c compare the ground truth, the baseline training method, and the two-stage framework. In this experiment, the results of the baseline method and the proposed framework were both reasonably good, i.e., most of the point clouds of the objects were detected correctly. Nonetheless, the prediction results obtained using the baseline method in Figure 6b revealed a number of pink points on the point cloud predicted for the wrench. The prediction results obtained using the proposed framework in Figure 6c do not include any points due to noise at the border of the predicted point cloud.  
Figure 4: Comparison of mean intersection over union (mIoU) curves obtained using the four methods to process XYZRGB point cloud data.  
Figure 5: Comparison of ground truth and prediction results obtained when XYZRGB point cloud data was applied to the baseline or proposed training methods. The prediction results from the baseline training method were clearly erroneous: (**a**) ground truth; (**b**) point cloud predicted using conventional training method, showing erroneous prediction where the small cube is predicted as the pipe; (**c**) point cloud predicted using the proposed hybrid training method.