## 2 Methodology
### Relationship-Based Weight Analysis
When defining the visual attributes of the pouring boom and concrete as \(\mathbf{F_{Boom}}\) and \(\mathbf{F_{Concrete}}\), respectively, the similarity between the two vectors is calculated as follows. Here, \(\mathbf{A_{R}}\) is the attribute association value, which is the similarity value before normalization. \(\mathbf{Sim(F_{Boom},F_{Concrete})}\) represents the similarity between the feature vectors of the two objects, based on cosine similarity. \[\mathbf{A_{R}}=\mathbf{1}-\mathbf{Sim(F_{Boom},F_{Concrete})} \tag{4}\]  
As shown in Equation (5), cosine similarity is the value obtained by dividing the dot product of two vectors by the magnitude of each vector, ranging from \(-1\) to 1. Similarity closer to 1 indicates that the two vectors are similar, while values closer to \(-1\) indicate opposite directions. Therefore, the \(\mathbf{A_{R}}\) value, which is the similarity subtracted from 1, represents how visually distinguishable the two objects are, with higher values indicating better visual distinction between the two objects. Here \(\mathbf{F_{1}}\)= \(\mathbf{F_{Boom}}\) is the visual attribute (feature vector) of the pouring boom (Boom) including color and texture, and \(\mathbf{F_{2}}\)= \(\mathbf{F_{Concrete}}\) is the visual attribute (feature vector) of the detected concrete (Concrete) including color and texture. The feature vector \(\mathbf{F_{1}},\mathbf{F_{2}}\) of each object is generated through a Convolutional Neural Network-based (CNN) feature extractor using the image patch of the object from the YOLOv11 detection result. Specifically, we extract feature maps with dimensions N \(\times\) N \(\times\) 512 from the penultimate layer (\"neck\") of the YOLOv11 backbone. To convert these feature maps into 512-dimensional feature vectors, we apply Global Average Pooling (GAP) operation across the spatial dimensions. This operation computes the average value for each of the 512 channels, effectively reducing the spatial dimensions while preserving the essential feature information for each object. We then apply L2 normalization (\(\|\mathbf{F}\|_{2}=1\)) to each vector before similarity computation. These feature vectors numerically represent the visual characteristics of objects in multi-dimensional space and are used to evaluate attribute relationships between objects by analyzing the similarity between the two vectors. \[\mathbf{Sim(F_{1},F_{2})}=\frac{\mathbf{F_{1}}\cdot\mathbf{F_{2}}}{\|\mathbf{F_{1}}\|\|\mathbf{F _{2}}\|} \tag{5}\]Since \(A_{R}\) can have varying ranges depending on the dataset, it is normalized to \(A_{norm}\) as defined in Equation (6) and used for the weight calculation. The normalization process applies min-max normalization and is expressed as follows. Here, \(A_{norm}\) is the normalized attribute association value, and \(A_{min}\) and \(A_{max}\) are the minimum and maximum attribute association values within the dataset. This transforms the attribute association value to a consistent scale within the 0-1 range. To address potential out-of-range values in real-world applications, we implement a clamping procedure that constrains \(A_{norm}\) values to the [0, 1] interval. If the computed \(A_{norm}\) exceeds 1, it is set to 1; if it falls below 0, it is set to 0. Additionally, for optimal performance in different deployment scenarios, the \(A_{min}\) and \(A_{max}\) values can be recalibrated based on site-specific data or robust normalization techniques can be employed to handle outliers. Values closer to 1 indicate that the visual characteristics between the pouring boom and the detected concrete object are clearly distinguishable. The normalized attribute association value is used as a factor reflecting the relationship with the pouring boom in the weight calculation process. This enables more accurate object detection and pouring height analysis.