## 3 The Proposed Method
### Matching Calculation Module  
The extracted bone stick features undergo a matching decision computation to determine similarity scores, as illustrated in Figure 8. The architecture comprises a measurement layer and a decision layer. Here, \(\mathrm{h_{fusion1}}\) and \(\mathrm{h_{fusion2}}\) denote the dynamically cross-fused features of two bone sticks. To ensure computational efficiency, this study calculates the difference between the two feature representations, generating a vectorized feature that encapsulates the intrinsic differences between bone sticks. This process is formalized in (23), where D represents the distance metric between the feature representations, and \(\mathrm{h_{fusion1}(x)}\) and \(\mathrm{h_{fusion2}(x)}\) correspond to the deep-layer features of the two bone sticks. By fusing the distance-based measurements, a unified feature representation is synthesized. This resultant vector encodes discriminative differences between the paired bone stick images, which are subsequently projected into a real-valued similarity score ranging from 0 to 1 through a fully connected layer and a sigmoid activation function.  
\[\mathrm{D(x_{1},x_{2})}=\|\mathrm{h_{fusion1}(x)}\!-\!\mathrm{h_{fusion2}(x)}\| \tag{23}\]  
The decision to utilize vector distance for final matching, rather than other similarity measures, is based on several key factors. First, vector distance, particularly in the form of Euclidean or cosine distance, provides a direct and mathematically well-understood metric for quantifying the dissimilarity between feature vectors. These vectors represent multi-dimensional characteristics of bone stick fragments, encapsulating visual, textual, and archeological data. As such, vector distance allows for an intuitive and computationally efficient method to compare the combined feature representations. Furthermore, vector distances are effective at capturing both the magnitude and direction of feature discrepancies, which is crucial when handling multimodal data with varying scales and distributions across features.  
In contrast, other similarity measures such as Jaccard or Pearson correlation may not be as effective in this context because they are more suited to binary or linear comparisons, whereas vector distances inherently accommodate nonlinear relationships and the high-dimensionality of the features. Additionally, vector-based distance metrics, particularly when used in conjunction with a dynamic cross-modal feature fusion approach, allow for better scalability and generalization to unseen data, especially in complex, heterogeneous datasets like the bone stick fragments under study. These advantages make vector distance a more appropriate choice for the matching task in this work.  
The final parameter count for the Dynamic Cross-Modal Feature Fusion (DCFF) module is 20.94 M. To optimize the framework, binary cross-entropy loss is adopted as the objective function, offering an intuitive quantification of similarity while reducing network complexity. Equation (24) defines the binary cross-entropy loss, where N denotes the batch size, and \(\mathrm{y_{i}}\) and \(\mathrm{y_{i}^{\prime}}\) represent the ground-truth labels and predicted similarity scores, respec  
Figure 8: Architecture of the Matching Calculation (MC) module.  
tively. This formulation ensures robust feature alignment and enhances the discriminative power of the model for bone stick verification tasks.  
\[\mathrm{L}(y,\ \hat{y}\ )=-\frac{1}{\mathrm{N}}\sum_{i=1}^{\mathrm{N}}\left(y_{i} \cdot\log(\hat{y}_{i})+(1-y_{i})\cdot\log(1-\hat{y}_{i})\right) \tag{24}\]