## 3 Methods
### YOLOv11 Working Principle
Importantly, 37% of the background pixels were misclassified as either sharp or smooth, with the most significant portion misidentified as sharp. This highlighted a tendency of the model to overpredict object presence, possibly due to the high sensitivity required for detecting small, detailed particles. This trade-off can be optimized through improved background sampling and regularization strategies in future versions. In Figure 13, a collection of label-based statistical visualizations is displayed. The top-left bar plot shows the instance count per class: approximately 1700 instances were labeled as sharp and over 2000 were labeled as smooth. This relatively balanced dataset helps ensure the model receives adequate learning opportunities from both classes. The top-right plot overlays all bounding boxes within the dataset, revealing that most labeled objects are concentrated toward the center of the frame. This pattern is consistent with the experimental setup, where materials flow along the center of the conveyor belt. Figure 11: Confusion matrix showing the raw classification counts for the YOLOv11n-seg model. Figure 12: Normalized confusion matrix for the YOLOv11n-seg shape classification model. Figure 13: Statistical overview of the labeled bounding boxes and shape categories in the training dataset. The bottom row of Figure 13 shows the distribution heatmaps of the bounding box coordinates. The \((x,y)\) location heatmap shows that objects were mostly centered horizontally (\(x\approx 0.5\)) and vertically (\(y\approx 0.5\)), confirming the conveyor alignment assumption. The heatmap of the bounding box \((width,height)\) revealed that most objects were relatively small in size--and they were primarily clustered in the lower width and height regions. This was expected given the fine particle sizes (1-4 mm) being processed in this system. Figure 14 offers a correlogram that was used to evaluate the interdependencies between the bounding box features. The diagonal plots illustrate the marginal distributions for \(x\), \(y\), width, and height, where both \(x\) and \(y\) are firmly centered and both size features are skewed toward smaller values. This confirms that the dataset primarily contains small objects in the image's central region. Additionally, the scatterplots in the lower triangle of the matrix suggest no strong correlation between the object location and size, implying that the model is being trained on a diverse range of object positions and scales without bias. Figure 14: Visualization of the statistical distribution and correlations among the normalized coordinates and dimensions of the bounding boxes used for particle detection on the conveyor belt. The diagonal plots represent the marginal histograms of each variable—x, y, Width, and Height—revealing that most detected objects are centered horizontally (\(x\approx 0.5\)) but spread vertically (y varies uniformly). The lower triangles display 2D histograms that highlight the relationships between features. For instance, width and height show a mild positive correlation, while most bounding boxes tend to be relatively narrow and short, as shown by the concentration of values around lower ranges. These insights help validate dataset balance and guide preprocessing strategies for shape-aware detection models in the BECS system. These visualizations collectively confirm that the YOLOv11n-seg model performs strongly in distinguishing between sharp and smooth materials. The instance balance across classes and the centered spatial distribution of objects reinforce the quality of the training dataset. However, the tendency to confuse the background with sharp objects suggests a potential over-sensitivity that could be addressed by refining negative sampling, enhancing background annotations, or incorporating additional background-focused training samples.