## 5 Results and Discussion  
This section describes the experiments conducted to validate the performance, accuracy, and efficiency of the proposed algorithm, as outlined in Section 4. Figure 12: CPU–GPU processing pipeline. The experiments were performed on an electric excavator, as shown in Figure 13. The depth camera was mounted on the excavator's boom link to provide an unobstructed view of the excavation area. The camera used in this experiment was the Intel(r) RealSense(tm) Depth Camera D455 from US. The experimental procedure involved capturing a depth image of the soil surface. The excavator then performed a single digging cycle, and the excavated soil collected in the bucket was weighed to obtain ground truth data. This procedure was repeated twice consecutively. To validate the accuracy of the curve approximation, the raw data points and the approximated curves were plotted to visualize the results of the developed surface reconstruction algorithm. This validation performed before the first digging cycle, after the first digging cycle, and after the second digging cycle. The results for all three datasets are presented in Figure 14.  
Figure 14: Surface reconstruction results. (**a**) Before first digging cycle. (**b**) Before second digging cycle. (**c**) After second digging cycle. Figure 13: Placement of actuators and sensors on electrical excavator. As illustrated in Figure 14, the reconstructed surface smooths out outliers and provides an accurate mathematical representation based on Equations (5) and (11) for the soil surface. In order to compare the proposed method with traditional approaches, the same data is used with the Poisson surface reconstruction. This method generates a 3D surface from a point cloud and the normal vector at each point by solving a Poisson equation. It estimates a scalar field whose divergence matches the input normal field. If normals are not provided, they must be estimated, typically using local surface approximations or principal component analysis, which further increase the computation time. The results are shown in Figure 15.  
One critical drawback of the traditional approaches is the lack of guarantee that the resulting surface is hole-free. The Poisson method fails to maintain the continuity of the soil surface resulting in a hole as shown in Figure 16.  
In addition to the Poisson method, the Crust algorithm also suffers from critical limitations in hole-filling. Although it is designed to reconstruct surfaces from unorganized point clouds, it fails to robustly recover topological consistency in regions with sparse sampling or complex geometry. This often results in incomplete reconstructions with visible holes, as highlighted in Figure 17.  
Figure 16: A hole in surface reconstruction by Poisson method. Figure 17: A hole in surface reconstruction by Crust algorithm. Figure 13.0 Surface reconstruction by Poisson method. (**a**) Before first digging cycle. (**b**) Before second digging cycle. (**c**) After second digging cycle. In addition, the Poisson method and Crust algorithm are more resource intensive. The computation time for the proposed approach, Poisson method, and Crust algorithm is presented in Figure 13.1  
Subsequently, marching cubes models were generated for each of the three datasets based on their corresponding reconstructed surfaces. The soil volumes were calculated at each step. By subtracting the volumes before and after each digging cycle, the volume of removed soil was estimated. Multiplying the estimated volume by the soil density yields the equivalent mass of the excavated soil. These results were compared with the measured weight of the soil collected during the tests and presented in Figure 13.2  
To evaluate the accuracy of surface reconstruction, the raw point cloud generated by the depth camera was compared against the reconstructed surface produced by the proposed method. Additionally, the same raw point cloud was processed using the Poisson method, and the results were compared to assess relative performance.