## 4 Evaluation and Analysis
### Experimental Results
#### 4.3.3 Evaluation of Similarity Measurement Component  
In this section, another ablation study is conducted to evaluate the proposed similarity measurement component. We utilized three conventional distance metrics, i.e., cosine, Euclidean, and average similarity (AVE-SIMI) distance, to replace the adaptive weighted similarity matrix in MetricNet. In this experiment, the cosine and Euclidean distances are computed directly to obtain the similarity matrix based on the complete image features without dividing them into patches. As for the version with AVE-SIMI, all the similarity matrix elements are directly averaged for the final measurement. The PR curves tested on three datasets (i.e., Gardens Point, Nordland, and St. Lucia datasets) are shown in Figure 11. It can be observed that both MetricNet and the ablation models can provide promising precision at low recall rates. However, MetricNet performs better when the recall rate is high. It can be concluded that MetricNet can correctly detect more true loops than other versions, which reveals the effectiveness of the proposed similarity measurement. We conclude that this is mainly because the similarity between images is reflected in the absolute distance and direction between the feature descriptors, and the lack of spatial information in the features is compensated by the construction of the similarity matrix based on adaptive weighting in MetricNet. Figure 12 shows their maximum recall rate at the precision of 100%. Testing on all the datasets, MetricNet obtains the highest recall rate at 100% precision, and the method based on Euclidean distance gets the worst performance. The experimental results reveal that MetricNet can yield fewer false loop detections. The mean average precision of MetricNet and the ablation methods is shown in Table 4 and Figure 13. It can be seen that the proposed method achieves the best mAP performance on all three datasets, which indicates the considerable reliability of MetricNet in handling scenes with significant appearance variations. The above comparisons emphasize the meaningfulness of optimizing the similarity measurement of LCD networks. After comparing the Euclidean and cosine-based methods, it can be found that the full utilization of the image information to construct a similarity matrix will partially solve the lack of sufficient global spatial cues from the feature extrac  
Figure 11: The PR-curves of different distance measurement on (**a**) Gardens Point, (**b**) Nordland, and (c) St. Lucia datasets. The images in these two datasets are not collected sequentially, and they are usually used for image retrieval rather than localization tasks. Therefore, the sequence-based LCD algorithms cannot work in this condition. Since it is unfair to adopt state-of-the-art algorithms specifically designed for viewpoint variations, we compare the proposed method with related works, such as CBE [13], SGH [14], ITQ [12], LPM [18], UBEF [15], and SMVF-CVT [19], as shown in Table 5.  
Note that all the binary encoding-based algorithms (i.e., CBE, SGH, ITQ, and UBEF) utilize CNN-based image descriptors as features. SMVF-CVT simultaneously uses multi-view features, such as CNN, VLAD+, and TEDA. We also include another ablation model, MetricNet_3x3 (i.e., the version with the same backbone as MetricNet but have the feature maps divided into 3 \(\times\) 3 patches), to handle this more challenging situation. MetricNet_3x3 has a smaller particle size when processing feature maps for similarity matrix construction. Despite the viewpoint variations of the Oxford5K and Paris6K datasets being significantly dramatic, the proposed methods still achieve reliable performance compared to the other algorithms. The results of SMVF-CVT demonstrate that utilizing multi-view fusion features can help improve image matching performance, which is designed for instance-level image retrieval. It can also be seen that MetricNet_3x3 is more effective in dealing with the testing datasets having significant viewpoint variations.