## 3 Sensor Calibration  
During the scanning process, the depth information from each sensor can be retrieved in real-time. However, the 3D depth information depends on the coordinate system of the sensor. Therefore, it is essential to define a method for representing depth information in a single coordinate system via sensor calibration. For ease of calibration, the line lasers and a flat calibration object were used, as shown in Figure 2.  
Generally, low-cost, mass-produced LiDAR sensors have a bandwidth of 905 nm. The scanning area with the infrared (IR) filter removed captures the laser lines [16]. Hence, when the line laser and LiDAR scan areas are matched, the area to be scanned by LiDAR can also be determined from the stereo camera image, as shown in Figure 3.  
With \(T\) defined as the Euclidean transformation relation between two coordinate systems, the transformation matrix, \(T\), is represented by a single (\(3\times 3\)) rotation transformation matrix, \(R\), and a (\(3\times 1\)) translation transformation vector, \(t\). When the 3D matching points obtained from the stereo camera and the LiDAR sensor are expressed as \(\text{Q}_{\text{i}}\) and \(\text{P}_{\text{i}}\), respectively, and three matching points theoretically exist, the transformation matrix, \(\text{T}_{(\text{L}\rightarrow\text{C})}\), between the two coordinate systems can be obtained as follows:  
\[Q_{n}=T_{L\rightarrow\text{C}}P_{n} \tag{1}\]  
If there are more than three matching points, the transformation matrix between the two points in time can be obtained using the singular value decomposition (SVD) or the Levenberg-Marquardt (LM) algorithm to minimize the error [17], as shown in Equation (2):  
\[\varepsilon=\sum_{n}||\ Q_{n}-T_{L\rightarrow\text{C}}P_{n}||. \tag{2}\]  
In order to facilitate calibration, the LiDAR sensors were positioned so that they sensed the calibration board, and the center point of the line was detected by each LiDAR  
Figure 3: Example of data acquisition process using a calibration plate. (**a**) Depth information obtained from LiDAR; (**b**) Image information obtained from stereo camera.  
Figure 2: Calibration tool to calibrate the sensor. (**a**) calibration object; (**b**) line laser.  
sensor and camera as a match point, as shown in Figure 4. The distance information of the calibration board scanned by the LiDAR sensor was segmented as a distance value for detection, and the stereo camera used the images to detect the calibration board. Based on the random sample consensus algorithm (RANSAC), the detected lines were fitted more precisely, and the center point was determined [18].  
After placing the calibration board at various positions and obtaining the transformation matrices using Equation (2), an accurate projection of the data obtained from the LiDAR sensor onto the position of the line laser was available, as shown in Figure 5. The accuracy of calibration becomes greater with the increasing number of match points, but this study confirmed that six were sufficient. Figure 6 shows the results when inter-device calibration was performed and when it was not.  
With the calibrated device in the outdoors scan experiment, it is possible to obtain three-dimensional depth information expressed in one coordinate system. In this study, the reference coordinate system of the device was defined as the stereo camera's coordinate system.  
Figure 4: Example of detecting the center point from the depth information acquired by LIDAR and stereo. (**a**) A center point of the line in LIDAR data; (**b**) A center point of the line in the camera data.  
Figure 5: The result of calibrating the LIDAR and stereo camera using the center points. (**a**) 3D point cloud obtained from the stereo camera; (**b**) The result of superimposing the information scanned from the LIDAR on the stereo 3D point cloud.