# A Method for the Calibration of a LiDAR and Fisheye Camera System
## 1 Introduction
### State of the Art
#### 1.1.1 Targetless Calibration  
Targetless methods do not require a specific calibration object but use the natural features of the environment (corners or edges) to establish the relationship between the camera and LiDAR systems. These methods are more flexible than target-based methods but may be less accurate in some situations. All these methods have been developed for pinhole cameras, so they are not directly applicable to fisheye cameras [9; 10; 11].  
The targetless calibration methods for LiDAR-camera systems can be classified into three main categories: motion-based, deep-learning-based, and traditional (image- and LiDAR feature-based) [5].  
Motion-Based  
These approaches take advantage of the motion of the camera-LiDAR system to estimate the transformation between the two systems. Optimization algorithms are used to estimate the transformation that best explains the observations in both systems. For instance, in [PERSON] et al. [9], a method based on ICP (Iterative Closest Point) is used to estimate the motion in the LiDAR reference system by using RANSAC (RANdom SAmple Consensus) [12] and the five-point algorithm. Also, in [PERSON] et al. [13], the camera motion between two frames is estimated, making use of descriptors obtained with the AKAZE algorithm [14] calculated from the point cloud.  
These methods employ deep neural networks to learn the correspondences between image features and LiDAR point clouds. There are some methods that employ deep learning for LiDAR-camera calibration [10; 15; 16; 17]. Deep learning has proven to be effective in calibrating LiDAR-camera systems, especially in complex and challenging environments.  
Traditional  
These approaches extract relevant pieces of information from images and point clouds, such as features of the environment (corners, edges, and flat surfaces) and intrinsic features of the camera and LiDAR (grayscale and reflectance, respectively), and establish correspondences between them. Then, they use optimization algorithms, such as RANSAC or ICP, to estimate the transformation that best aligns the corresponding features. These methods usually rely on automatic point feature detection algorithms, which are much more widespread for imagery than for LiDAR, so some proposed methods base their innovation on the development of feature detectors for point clouds.  
Some of these methods use grayscale imaging and point cloud reflectivity [18]; others combine the extraction of Canny edges [19] for imaging and the computation of edges at discontinuities in depth for LiDAR [20; 21]; and others [22; 23] use lines detected in both the camera and the LiDAR.  
Two of the most recent methods for the calibration of LiDAR-camera systems are presented in [11; 24]. While the first is based on image segmentation supported by Segment Anything [25], the second uses keypoints in both the images and a LiDAR intensity image.  
These methods are less sensitive to variations in the appearance and geometry of the environment than motion-based methods but can be more sensitive to noise and ambiguities in feature correspondences.