## 2 Methodology
### Relationship-Based Weight Analysis  
This study proposes a relationship-based weighting module that quantitatively analyzes the association between the pouring boom and concrete objects. The goal is to improve detection accuracy in construction environments where visually similar elements frequently coexist. The analysis is conducted within the ROI defined in the previous step. The association is computed based on three relationship factors--distance, attribute, and spatial positioning--to determine whether each detected concrete object is actively involved in the pouring operation. Initially, to quantitatively analyze the distance-based association value derived from the distance relationship, this study includes the process of calculating and normalizing distance-based association values. As shown in Equation (2), \(\mathbf{D_{R}}\) is the distance-based association value calculated from the distance relationship between the two objects. It represents the physical proximity between the pouring boom and the detected concrete object, where closer distances indicate higher association. The distance association value is calculated based on the difference between the bottom boundary (\(\mathbf{y_{max}}\)) of the detected pouring boom bounding box and the top boundary (\(\mathbf{y_{min}}\)) of the detected concrete bounding box. Here, \(\mathbf{D_{R}}\) is the distance association value before normalization, representing the vertical distance difference between the two objects. \(y_{Boom,max}\) is the bottom boundary of the pouring boom bounding box, and \(y_{Concrete,min}\) is the top boundary of the detected concrete bounding box. \[\mathbf{D_{R}}=\left|\mathbf{y_{Boom,max}}-\mathbf{y_{Concrete,min}}\right| \tag{2}\]  
The smaller this value, the closer the pouring boom and concrete object are positioned, indicating higher association, while increasing distance difference indicates lower associ  
Figure 2: Region of interest and distance-relationship illustration: (**a**) ROI defined directly beneath the detected boom; and (**b**) distance relationship \(\mathbf{D_{R}}\) visualised between the boom and the pouring concrete. ation. However, since detected distance values can have a wide range depending on the data, there is a need to normalize them for use within a consistent range. As defined in Equation (3), this study calculates \(\mathbf{D_{norm}}\) by normalizing the distance association value and uses it for the weight calculation process. The normalization process is defined as follows:  
\[\mathbf{D_{norm}}=\mathbf{1}-\frac{\mathbf{D_{R}}}{\mathbf{D_{max}}} \tag{3}\]  
Through Equation (3), a value of \(\mathbf{D_{norm}}\) close to 1 corresponds to very close objects (\(\mathbf{D_{R}}\approx 0\)), whereas a value approaching 0 denotes little association as \(\mathbf{D_{R}}\) approaches \(\mathbf{D_{max}}\). Here, \(\mathbf{D_{max}}\) is set as the maximum detectable distance within the ROI, and relative distance values are normalized based on this. The normalized distance association value is used in the weight calculation process for object detection, enhancing final detection confidence by reflecting the physical relationship with the pouring boom. Through this, the proposed design overcomes the limitations of individual object-based detection methods and enables detection that considers relationships between objects. Building upon the distance relationships, the attribute association value \(\mathbf{A_{R}}\) is defined by Equation (4), analyzing the visual distinctiveness between the pouring boom and the detected concrete object, and the normalized value \(\mathbf{A_{norm}}\) is used ultimately. The attribute association value is calculated based on cosine similarity, serving as an indicator that evaluates how distinctly the visual characteristics (feature vectors) of the two objects are differentiated. It is designed to have higher values when the two objects are visually clearly distinguishable.