## 4 Verification and Evaluation of the Method on Target Particle Statistics Based on Digital Images  
### Simple Case for Recognizing Circle Particles Partially Obstructed  
In order to verify the correctness of the program written and to analyze the differences in identifying obstructed particles, as well as the pattern of determining the number of particles, including obstructed particles, a simple test was conducted by laying 38 black Go pieces with an average diameter of about 23 mm on a white paper. Among them, there were six pairs of Go pieces on the white paper with varying degrees of mutual occlusion between them, as shown in Figure 5a. The results of binarization and morphological processing of the image are shown in Figure 5b,c, respectively. Based on Figure 5c, the average area of the Go pieces can be obtained as \(P_{\mathrm{m}}=116{,}618\) pixels, and the variance \(\delta=1667\). The results obtained by fitting an equal diameter circle are shown in Figure 5d.  
In order to evaluate the application effect of the k-means method, the results of analyzing the sixth pair of overlapping particle graphs using this method are given, as shown in Figure 6; that is, the graph of SSE convergence result with the increase in iteration times. It can be seen that all results converge rapidly after about 10 iterations. The figure also shows the position movement diagram of the two cluster center points when the set value of the number of go sub-pixel points is 23,000, as shown by the \"\(\times\)\" point under the white arrow in the blue-background binary diagram in the figure.  
Figure 5: DIP processes of the mode 1–3 test.  
The number of particles obtained from the fitting result of the medium-diameter circle in Figure 5d is 38, and the minimum value of the relationship between the number of obstructed pixels _Dao_ and \(P_{i}\) mentioned earlier was used as the judgment condition to determine the number of particles. In order to discuss the reasonableness of the judgment condition, the relationship between _Dao_ and Pi within the range of \(P_{1}=[P_{\text{m}}-a\delta,P_{\text{m}}+a\delta]\) is shown in Figure 6. The execution results show that there is a minimum point in the relationship between the number of obstructed particle pixels and the input single-particle pixel number \(P_{1}\). The number of particles corresponding to this minimum point is used to match the actual number of Go pieces, as shown in Figure 7.  
Figure 6: Convergence of SSE with iterations.  
Figure 7: The change in particle number counted and _Dao_ with the set value of the single-particle pixel number.  
In addition, careful comparison shows that the overlapping area in the simulated image of the same diameter circle is very close to the actual obstructed area, as shown in Figure 6. The obstructed Go piece and other unobstructed Go pieces are curved upwards on white paper, and the pixel area obtained from the shooting is close. Therefore, the actual obstructed area can be calculated as the distance between the centers of the obstructed Go pieces, as shown in Figure 5a,b.  
In summary, using the minimum value of the _Dao_-\(P_{i}\) relationship as the criterion to determine the number of particles is reasonable.