# In-Depth Analysis of GAF-Net: Comparative Fusion Approaches in Video-Based Person Re-Identification
## 5 Experimental Results
### Results on MARS Dataset
#### 5.2.1 Feature-Level Fusion  
Based on the concatenation defined previously by Equation (7), we introduce a conditional concatenation for MARS to handle cases where gait features are unavailable. For a person's identity (\(i\)), conditional concatenation (\(\mathbf{z}_{c}^{i}\)) is defined as follows:  
\[\mathbf{z}_{c}^{i}= \begin{cases}\phi_{\text{concat}}\left(\mathbf{z}_{\text{ appearance}}^{i},\mathbf{z}_{\text{gait}}^{i}\right)&\text{if gait available}\\ \left[\mathbf{z}_{\text{appearance}}^{i},\mathbf{0}_{d_{\text{gait}}}\right]& \text{otherwise}\end{cases}  \tag{11}\]  
where \(\phi_{\text{concat}}\) is the weighted concatenation function defined in Equation (7), including the weighting factor (\(\lambda\)), and \(d_{\text{gait}}\) is the dimension of the gait feature vector. In our implementation, \(d_{\text{gait}}=128\). This approach allows for flexible integration of both types of features when available, using the \(\lambda\) factor to adjust their relative importance. When gait is not observable, the system can still function by relying only on appearance features, although this may reduce identification accuracy compared to using both types of features. Table 6 presents the results of applying conditional concatenation to the MARS dataset for the two architectures. This approach was used to handle cases where gait information was not available. The results show modest but consistent improvements for the tested models. * OSNet: The OSNet architecture initially achieved an mAP of 81.64% and a rank-1 accuracy of 86.20%. After conditional integration of gait features, we observe a slight improvement in mAP to 81.67% (+0.03%), while rank-1 accuracy showed minimal variation, reaching 86.14% (\(-0.06\%\)). These results suggest that the impact of integrating gait features is marginal for this model on the MARS dataset. * MGH: The MGH model demonstrated more noticeable improvements with conditional concatenation. Its initial mAP of 85.52% increased to 85.56% (+0.04% ), while its rank-1 accuracy improved from 89.40% to 89.51% (+0.11%). Although modest, these improvements are consistent across metrics, indicating a potential benefit of integrating gait features for this model. Conditional concatenation of gait features enhances Re-ID performance on the MARS dataset, with the MGH model showing more notable improvements. Although these gains are smaller than those observed on iLIDS-VID, likely due to dataset differences and the use of the conditional fusion approach, our method consistently improves performance across architectures. This shows its effectiveness even when gait information is intermittently available, adapting to the challenges presented by the MARS dataset. Building upon the PCA concatenation introduced in Equation (8), we propose a conditional version to handle cases where gait features are not available. This approach retains the advantages of PCA in terms of appearance features while adding flexibility to the model. For a person's identity (\(i\)), PCA conditional concatenation (\(\mathbf{z}_{ac}^{i}\)) is defined as follows:  
\[\mathbf{z}_{ac}^{i}= \begin{cases}\phi_{\text{PCA-concat}}\left(\mathbf{z}_{ \text{PCA-appearance}}^{i},\mathbf{z}_{\text{gait}}^{i}\right)&\text{if gait available}\\ \left[\mathbf{z}_{\text{PCA-appearance}}^{i},\mathbf{0}_{d_{\text{gait}}} \right]&\text{otherwise}\end{cases}  \tag{12}\]  
where \(\phi_{\text{PCA-concat}}\) is the weighted concatenation function defined in Equation (8), including the \(\lambda\) factor. \[\phi_{\text{PCA-concat}}\left(\mathbf{z}_{\text{PCA-appearance}}^{i},\mathbf{ z}_{\text{gait}}^{i}\right)=\left[\lambda\cdot\mathbf{z}_{\text{PCA-appearance}}^{i},(1-\lambda)\cdot\mathbf{z}_{\text{ gait}}^{i}\right] \tag{13}\]  
This conditional approach maintains system performance even when gait features are not observable while preserving \(\lambda\) and balancing when they are available.