## 5 Experimental Results  
In this section, various experiments were performed to verify the performance of the proposed algorithm. We used the _Nordland dataset_[21; 22], which comprises images of all seasons from four journeys on a 728 km train route across Norway, and the _KAIST dataset_[23], which includes six sequences in various illumination conditions: day, night, sunset, and sunrise. They are challenging datasets widely used for long-term place recognition because images between sequences show drastic appearance changes. In each sequence, 1600 images were used for training, and 6400 images were used as a test. All the images were resized to \(224\times 224\) pixels. The output shape of the encoding part in our model is shown in Table 1. To effectively compress the data, several layers of convolutional and fully connected layers were used. Then, the output from the sampling layer is the latent feature \(z\), and this feature is divided into \(\mathbf{z}_{p}\) with 96 nodes and \(\mathbf{z}_{c}\) with 32 nodes. The decoding part includes a part that reconstructs the input image \(\mathbf{x}\) from the \(\mathbf{z}_{p}\) and \(\mathbf{z}_{c}\) similar to a typical VAE, and a part that generates a context vector \(\mathbf{c}\) from the \(\mathbf{z}_{c}\). Since the dataset has four seasons, the context vector \(\mathbf{c}\) is defined as a four-dimensional one-hot encoding vector. The first experiment is a visualization test to confirm if the model has been trained to make \(\mathbf{z}_{p}\) and \(\mathbf{z}_{c}\) independent as intended. Let \({}^{u}\mathbf{x}\) and \({}^{v}\mathbf{x}\) be images obtained from different environments \(u\) and \(v\), respectively. Then, we can extract the latent features \({}^{u}\mathbf{z}=\{{}^{u}\mathbf{z}_{p},{}^{u}\mathbf{z}_{c}\}\) and \({}^{v}\mathbf{z}=\{{}^{v}\mathbf{z}_{p},{}^{v}\mathbf{z}_{c}\}\) from each image respectively using the encoder of the trained model. Since the reconstructed image from the decoder is mainly affected by the condition-sensitive feature \(\mathbf{z}_{c}\), not the condition-invariant feature \(\mathbf{z}_{p}\), we can expect the reconstructed image from the combined feature \(\{{}^{u}\mathbf{z}_{p},{}^{v}\mathbf{z}_{c}\}\) will be \(\mathbf{x}_{p}\). The results of combining \(\mathbf{z}_{p}\) and \(\mathbf{z}_{c}\) extracted from each sequence image are shown in Figures 6 and 7. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Layer** & **Input Size** & **Output Size** \\ \hline conv1 & \(224\times 224\times 3\) & \(112\times 112\times 32\) \\ conv2 & \(112\times 112\times 32\) & \(56\times 56\times 64\) \\ conv3 & \(56\times 56\times 64\) & \(28\times 28\times 64\) \\ conv4 & \(28\times 28\times 64\) & \(14\times 14\times 128\) \\ conv5 & \(14\times 14\times 128\) & \(7\  
As can be seen from the reconstructed image results in Figure 6, there is no significant change in the \(\mathbf{z}_{p}\) change, whereas different season images are created in \(\mathbf{z}_{c}\) change. Similarly, there is no significant difference in the change of \(\mathbf{z}_{p}\), but it can be seen that images at different times are created according to the change of \(\mathbf{z}_{c}\) in Figure 7. We can conclude that the environmental information is compressed in \(\mathbf{z}_{c}\) since the reconstructed image is changed by the influence of the \(\mathbf{z}_{c}\) rather than \(\mathbf{z}_{p}\). As the \(\mathbf{z}_{c}\) plays a significant role in reconstructing the image, similar images would be generated if the same \(\mathbf{z}_{c}\) is used to reconstruct the image. In other words, if we define \({}^{o}\mathbf{z}_{c}\) as a constant vector, \(\{^{u}\mathbf{z}_{p},{}^{o}\mathbf{z}_{c}\}\) and \(\{^{v}\mathbf{z}_{p},{}^{o}\mathbf{z}_{c}\}\) will reconstruct condition-invariant images \({}^{o}\mathbf{x}\) since the image is mainly affected by the condition-sensitive feature \({}^{o}\mathbf{z}_{c}\). The results of the condition-invariant image are shown in Figures 8 and 9. Figure 6: The independence visualization result of the Nordland dataset.