## 4 Evaluation and Analysis
### Experimental Results
#### 4.3.2 Evaluation of Feature Extraction Component  
To evaluate the performance of the feature extraction module, we present an ablation study comparing MetricNet with the closely related patch-matching-based method like [35]. The approach [35] directly divides each input image into four patches for further deep feature extraction. In this experiment, we named this ablation version as MetricNet_direct. The experimental results on the Nordland dataset are shown in Figure 9. The frames of winter1 (Figure 9a) and summer1 (Figure 9b) are collected at the same place, while winter2 in Figure 9c is captured from a different location. The similarity matrices of winter1 and summer1 calculated by MetricNet_direct and MetricNet are shown in Figure 9d and Figure 9f, respectively. The similarity matrices of winter2 and summer1 calculated by MetricNet_direct and MetricNet are shown in Figure 9e and Figure 9g, respectively. It can be seen that our feature refinement in the Channel Weighting Module significantly improves the performance of MetricNet. It can help the proposed method construct a more robust similarity matrix for subsequent similarity score calculation. This superior similarity matrix naturally provides a more stable classification basis for the similarity measurement. Although both MetricNet_direct and MetricNet achieve promising performance, MetricNet enlarges the difference between positive and negative pairs. When encountering positive pairs, the diagonal values of MetricNet are much larger than the off-diagonal ones. For the negative pairs, the values of the similarity matrix tend to be more random. We can conclude that the MetricNet algorithm has the ability to make the difference between positive and negative more prominent, making the inputs easier to distinguish. To demonstrate this conclusion more clearly, we compare the differences between the mean of diagonal and off-diagonal values (calculated by Equation (9)) in the positive-pair and negative-pair similarity matrices. The differences \(d\) generated by MetricNet and MetricNet_direct can be defined as \(d_{1}\) and \(d_{2}\), respectively. We plot the probability density distribution of \(\Delta=d_{1}-d_{2}\) for positive and negative pairs on each dataset. As shown in Figure 10, the horizontal axis represents the similarity difference of \(\Delta\), and the vertical axis represents the corresponding probability density. The corresponding probability density function can be expressed as:  
\[f(\Delta)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{-\frac{(\Delta-\mu)^{2}}{2\sigma^ {2}}} \tag{21}\]  
where \(\mu\) and \(\sigma\) denote the mean and standard deviation of \(\Delta\), respectively. The area under the curve represents the probability of \(\Delta\). When \(\Delta>0\), we fill the area under the curve with orange, otherwise with medium violet red. As shown in Figure 10, testing on the positive pairs from three datasets, the similarity differences obtained by  
Figure 10: The probability density distribution of \(\Delta\), where \(\Delta=d_{1}-d_{2}\) (\(d_{1}\) and \(d_{2}\) are the differences \(d\) in Equation (9) calculated by MetricNet and MetricNet_direct, respectively). Figure 9: The similarity matrixes obtained by MetricNet_direct and MetricNet. (**d**) Similarity matrix of winter1 and summer1 obtained by MetricNet_direct. (**e**) Similarity matrix of winter2 and summer1 obtained by MetricNet. (**g**) Similarity matrix of winter2 and summer1 obtained by MetricNet. MetricNet are mostly more significant than those obtained by MetricNet_direct. It means that MetricNet's weighted similarity matrix can make the image descriptors more distinguishable. Besides, as for the negative pairs, MetricNet tends to generate the similarity matrix with more random diagonal and off-diagonal values, where the difference between these elements is evidently smaller.