## 2 Proposed Method
### Interest Point Detection and Description  
In this study, we defined our training dataset to include the inlier 3D points and the inlier voxel regions. To train the detector and descriptor network to identify interest points (inlier 3D points and their 2D reprojections), correspondence between image pairs is also required. Hence, in our architecture, the image pairs to be included in the training dataset are determined based on two conditions. First, we define a threshold for the minimum number of points of correspondence required for training (set to 80 in experiments). Then, we identify image pairs with the minimum number of interest points and define a fraction (set to 40% in experiments) to be used for the selection of image pairs. To be included in the training dataset, the ratio of the number of points of correspondence to the number of interest points should be above this fraction. With this procedure, our training dataset can include image pairs with a large baseline, unlike with previous techniques, which were restricted to using pairs of consecutive monocular images [4]. Hence, with this training architecture, the deep learning models can consider the effects of changes in camera viewpoints and illumination, as illustrated in Figure 3. Furthermore, the size of the training image set is also increased, because the number of combinations of image pairs with sufficient correspondence is much larger than the number of test images. Interest points in the input image are detected as reprojections of the inlier 3D points from extracted voxel regions. The description information for these points is also required to complete the matching procedure. Here, we employ the SuperPoint model as the detector and descriptor network for the interest points, as it produces pixel-level interest point locations accompanied by L2-normalized descriptors. To address the possibility of missing interest points, SuperPoint applies homographic adaptations during training [20], for which it requires interest points before training, as homography is a good model for the transformation that occurs when the same 3D point is seen from different viewpoints. This homographic adaptation is most effective with planar scenes or scenes, such as panoramas, where most elements are far away from the camera. However, in general, there are several different planes in outdoor scenes, and the location of the camera when capturing the target scene cannot always be dictated. With our training architecture, interest points and their 2D correspondence set are provided in image pairs. Since these interest points are distributed on the main plane of a voxel, geometric variations across images can be considered by homographic transformation. Hence, the computationally intensive pre-training steps in the original SuperPoint model can be avoided, since the interest points in the voxel in one image and their correspondence points in another image have homographic relation. An illustration of the two networks used for voxel region detection and interest point detection/description is shown in Figure 4. Here, interest points are identified using the voxel regions detected in the input image. To decrease the number of candidate interest points used in descriptor matching, we examine their positions first, and then, compare their description information, ensuring that only interest points in the detected voxel are evaluated in this process. In this study, we obtained description vectors for 3D inlier points across multiple images, and used the average of these vectors as representative description information. Here, the descriptor used by SuperPoint has 256 dimensions. To complete the localization, the description information of an interest point in a query image is compared with the representative description of 3D points, with the nearest neighbor search used as the metric for point matching.