## 4 Results and Discussion  
A summary of the results of pose estimation conducted using our framework is detailed in Table 2. Here, the framework is evaluated based on the precision of point detection and region identification. For the former, potential 3D points corresponding to the detected interest points are reprojected onto the image. The distance between the detected point and the reprojected point is calculated, and the former is accepted as being accurate if this distance is less than 5 pixels. This limits the size of the point detection error in Table 2, since the maximum distance between potential interest points and detected interest points is 5 pixels. By using a low point-ness threshold, the number of points to be evaluated for detection can be increased as much as possible, regardless of their precision. Figure 5: Illustration of the 2D-3D matching process with our voxel-based scene representation system: Voxel regions of inlier 3D points in (**a**) King’s College, (**d**) Old Hospital (**g**) Shop Facade, (**j**) St. Mary’s Church scenes, and (**m**) Heads; Voxel regions detected in (**b**) King’s College, (**e**) Old Hospital (**h**) Shop Facade, (**k**) St. Mary’s Church images, and (**n**) Heads; Interest points in detected voxel regions in (**c**) King’s College, (**f**) Old Hospital (**i**) Shop Facade, (**l**) St. Mary’s Church images, and (**o**) Heads. Similar region detection results were noted for Case 1 and Case 2; with both of these cases, the average of IOU values from all four scenes was 0.92. This result indicates that the detection of voxel regions becomes trivial above a certain size, as these have enough visual features for them to be learned by the neural network. Hence, beyond this threshold, the division of the scene space does not affect region detection. In contrast, it can be noted that interest point detection is better with Case 2 than with Case 1, as there are more inlier 3D points in the former dataset than in the latter. For example, from Table 1, it can be seen that there are 86 inlier voxels in the King's College scene when it is defined as in Case 1, and on average, there are 426 inlier 3D points per voxel. Therefore, in this case, 36,636 inlier 3D points are considered in the training dataset. Conversely, for the same scene, in Case 2, there are 194 inlier voxels and an average of 274 inlier 3D points per voxel. Thus, for this training dataset, there are 52,574 inlier 3D points. This increase in the number of correspondence sets used in SuperPoint's training explains the improved performance noted in Case 2. Similarly, this increased amount of training data improves the technique's camera pose estimation. Table 3 details a comparison of camera pose estimation performances using the two configurations of our technique, and previously developed estimator models, in terms of median translation and rotation errors. The experimental parameters in previous methods have a different setup. For example, PoseNet rescaled the input image so that the smallest dimension was 256 pixels and randomly cropped to the \(224\times 224\) pixels in the training phase. This model was evaluated on a single \(224\times 224\) center crop [3]. In Table 3, the median values of the obtained camera pose results from the test dataset are presented. The localization errors obtained with end-to-end deep learning methods have been larger than with structure-based methods. Our method achieves comparable results to the SfM method to some extent and has near real-time inference times and an appealing simple pipeline. Here, it can be seen that the performance for Case 2 is better than for Case 1, for all four scenes.