# A Method for the Calibration of a LiDAR and Fisheye Camera System
## 3 Results
### Real Environment
Figure 11: Images of the real environment experiment where the difference between a pinhole image and a fisheye-distorted image is shown. not very different from the minimization method in the second row, but the MPE from the proposed method is a bit higher, which means that the reprojection error is higher. The time required to calculate the transformation is much lower than for the minimization method, which is a plus for the proposed method. Once again, as is evident in Table 2, the minimization method provides better results in terms of reprojection error, while the proposed method achieves a very close result in a small fraction of the time. The detection of the corners of the rectangular polygons in the image is not completely perfect and depends on the quality of both the image and the point cloud sensors and the quality of the fisheye lens calibration. This makes it harder to obtain a reprojection error as low as in the simulation. It is also noticeable that the transformation parameters obtained are not very different between the two methods, so the quality of the calibration is not very different between them. Even the rotation parameters are very close to each other. Figure 12 presents qualitative results. In this figure, the point cloud is shown after being reprojected onto the fisheye image. The points are reprojected onto the image after translating and rotating them with the transformation obtained from the proposed method so that they are in the same reference system as the image. The point cloud is colored based on the distance from the camera, so the points closer to the camera are shown in red and the points further away are shown in blue. The reprojection of the point cloud onto the image is visually correct and enables good fusion of the information from both sensors with a large field of view thanks to the fisheye lens. It is also noticeable that, even though the mean reprojection error is around 1.8 pixels in the equirectangular image, the LiDAR points are correctly reprojected onto the image without much distortion because the MPE (mean pixel error) is measured in the equirectangular image, which is a projection of the fisheye image with a higher resolution, to be compared with the simulation results. Figure 12: Point cloud projected onto the fisheye image after calculating the transformation between both systems with the minimization method. The color of the points is based on the distance from the camera, so the points closer to the camera are shown in blue and the points further away are shown in red. The projection of the LiDAR points onto the image is not perfect but accurate enough for the fusion of the information from both sensors. It can be seen in Figure 13 that the points are correctly reprojected onto the image, but some points obtained by the LiDAR sensor are placed over surfaces that they do not belong to. This occurs because the reference system of the LiDAR points is changed for the projection, so, from the perspective of the camera reference system, there will be further points obtained by the LiDAR that will stay behind other closer points sharing the same surfaces.