## 3 Results
### Experimental Comparison  
Our proposed method was tested on the New College and City Center datasets with the experimental parameters outlined in Table 3. Initially, ResNet152 was chosen as the main feature-extraction network to assess the impact of features from different convolutional layers on performance in loop detection after compression and transformation. Subsequently, a different compression ratio \(\gamma\) was set for each network layer to observe the influence of varying compression ratios on its feature-representation capability and performance in loop detection. As the features extracted from the shallow layers (conv1, conv2) do not adequately reflect the richness needed, they are not suitable for illustrating the advantages of KL transformation in compressing feature matrices. Therefore, in this experiment, we opted to use deeper layers such as conv3, conv4, and conv5. Due to the residual structure of ResNet152, the skip connections enhance the research value of using deeper convolutional layers. To visually demonstrate the impact of KL transformation on performance in loop closure detection in complex environments, we conducted relevant experiments. Taking ResNet152\({}^{\prime}\)s conv5 as an example, we utilized a Siamese neural network to output the feature matrix of image sequences, performed similarity calculations, and visualized the results. These results were then compared with the Ground Truth, which consists of accurate classification data for loop and non-loop scenes in the New College and City Center datasets, as shown in Figure 17. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Description** \\ \hline Image Size & 224 \(\times\) 224 & Input to ResNet152 \\ Layer & conv3, conv4, conv5 & Convolutional layers of ResNet152 \\ \(\gamma\) & [60\%, 70\%, 80\%, 90\%] & Compression ratio information \\ Image Sequence Length & 10 & Number of images in sequence \\ \(\alpha\) & 0.3 & Similarity detection threshold \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental parameter settings. Figure 17: The Ground Truth for New College and City Center. On the left is the Ground Truth for New College, and on the right is the Ground Truth for City Center. In the image, black regions represent different scenes, while white regions represent the same scene. The similarity-detection threshold is set to \(\alpha=0.3\). In both datasets, the visualized results of loop closure detection are shown in Figure 18. The regions closer to blue in the image indicate lower similarity, while regions closer to red indicate higher similarity. Figure 18a shows the original output of conv5 without KL transformation. It can be observed that due to the presence of redundant information and the abstract information from deep convolutional outputs, the interference factors in the feature matrix are considerable. Although the model can accurately identify loop closures, it also yield many false positives, resulting in an overall low rate of loop closure detection. This result also indicates that the initial choice of compression ratio should be high because lower compression ratios are insufficient to handle this situation. Therefore, in the subsequent experiments, we attempted to set the initial value of \(\gamma\) at 60% and gradually increase it, at intervals of 10%, up to 90%. The impact of different \(\gamma\) values on the original results was observed, as shown in Figure 19.  
In Figure 19, it can be observed that for the New College dataset, after 60% compression, most of the interference information has been removed, and some loops can be accurately detected. However, the similarity in almost all areas still exceeds 60%. When the compression rate reaches 70%, the similarity between non-loop scenes further decreases. When the compression rate reaches 80% and 90%, loop detection can be achieved by setting a lower threshold. The 80% compression rate performs the best, with fewer false positives compared to 90%, while the accuracy is highest for 90%.