## 2 Methodology
### Model Training and Optimization  
Prior to the relationship-based weight optimization, the YOLOv11 model was trained using our annotated dataset of 641 images with an 80:20 train-validation split. Training was conducted for 100 epochs with an initial learning rate of 0.001, batch size of 16, and input image resolution of 640 \(\times\) 640 pixels. The model was implemented using PyTorch v2.2.0 framework and trained using an NVIDIA RTX 3090 GPU (NVIDIA Corporation, Santa Clara, CA, USA) with 24 GB memory. Data augmentation techniques, including random rotation (\(\pm\)15\({}^{\circ}\)), scaling (0.8-1.2), and color jittering, were applied to enhance model robustness.  
In this study, we conducted a systematic optimization process to determine the optimal weight coefficients (\(\alpha\), \(\beta\), \(\gamma\)) for the three relationship factors (distance, attribute, spatial). This process was designed to quantitatively evaluate and adjust the importance of each relationship factor in the final detection decision.  
Initially, equal weights (\(\alpha=\beta=\gamma=0.33\)) were assigned to each relationship factor to evaluate the reliability of relationship-based detection. This established a baseline under the assumption that all factors contribute equally to the detection process. Subsequently, we explored optimal weight combinations through 10-fold cross-validation. For weight coefficient optimization, we performed a grid search across a total of 120 combinations (\(\alpha\), \(\beta\), \(\gamma\in\{0.10,\,0.15,\,\ldots,1.0\}\)\(\wedge\alpha=\beta+\gamma=1.0\), \(\alpha\), \(\beta\), \(\gamma\geq 0.1\)). For each combination, model performance was measured using accuracy and F1 score as evaluation metrics. Since all test images contained the target object, the image-level precision was fixed at 1.0, and in this case, accuracy is identical to recall. Therefore, this study used accuracy and F1 score as the primary performance metrics. Through this process, the learned optimal coefficients were determined to be \(\alpha=0.50\) (distance relationship), \(\beta=0.20\) (attribute relationship), and \(\gamma=0.30\) (spatial relationship). The highest weight being allocated to the distance relationship (\(D_{R}\)) reflects the physical characteristics of concrete pouring operations. The closer the physical distance between the pouring boom head and concrete, the higher the likelihood that pouring is actually in progress. The spatial relationship (\(S_{R}\)) receiving the second-highest weight demonstrates the importance of the structural constraint that concrete must be positioned below the pouring boom head. The attribute relationship  
Figure 3: Skeletal-based pouring height measurement system.  
(\(\mathbf{A_{R}}\)) received a relatively lower weight but plays a complementary role through visual characteristic distinction.  
Additionally, to set the threshold for final detection decisions, we analyzed the precision-recall curve. We established a candidate threshold range from 0.5 to 0.9 at 5% intervals and measured performance at each point. The optimal threshold was selected at the point where the F1 score reached its maximum along the precision-recall curve. Finally, at a threshold of 0.58, the most balanced performance between precision and recall was demonstrated; thus, this was adopted as the final threshold. This optimization process played a crucial role in ensuring model robustness across various field conditions (lighting changes, viewpoint changes, partial occlusions, etc.). It provided the foundation for stable object detection performance even in situations with high boundary ambiguity. Experimental results showed that the optimized model demonstrated significant performance improvement compared to conventional single-object recognition methods. This validates the effectiveness of the optimal weight coefficients and threshold setting.