# Registration of Urban Aerial Image and LiDAR Based on Line Vectors
## 3 Results  
### Testing Methods  
Three datasets of corresponding lines from the synthetic, ISPRS test project, and real image are adopted for experiments. The synthetic image is adopted to verify the correctness of the proposed algorithm, and the ISPRS test project image and real image are adopted to verify the practicability of the proposed algorithm. Conventional registration and the proposed registration method based on line vectors are performed in each type of image. The initial set of unknowns in conventional registration is \(X_{L}=Y_{L}=Z_{L}=\omega=\phi=\kappa=0\), while the LVR gives data of \(q_{1}=1\), \(q_{2}=q_{3}=q_{4}=q_{01}=q_{02}=q_{03}\)\(=q_{04}=0\), equivalent to the initial set in conventional registration. A description of each dataset is described below.  
(1) Synthetic images: The generation method of synthetic data is as follows: firstly a parameter distortion model (PDM) is used in the camera calibration with radial distortion and decentering distortion included. Then the accurate camera inner orientation parameters (IOPs) and the EOPs of each image are obtained. Substituting the ground control points, camera parameters, and the EOPs of the image into the collinear equation, the coordinates of corresponding points can then be calculated. Finally, the IOPs and the corresponding points in the image and LiDAR data coordinate framework are used as the given data to solve the EOPs, since there may be some random errors in the measurement of point coordinates in practical applications. To simulate the actual situation, we using the Gaussian random function to produce Gaussian errors with zero-mean and 1.0 pixel standard deviation based on simulated data, assign these data in the \(x\)-axis and \(y\)-axis of 18 endpoints of image lines, wherein random errors on the \(x\)-axis and \(y\)-axis are required to be, respectively, generated to ensure their independence. The IOPs of the synthetic image have a principal point of \(x_{0}=0\), \(y_{0}=0\) and a principal distance of \(f=28\) mm. The image format was 1024 \(\times\) 1280 with a pixel size of 0.008 mm.  
(2) ISPRS test project data: A group of data is a subset of the ISPRS test project on Urban Classification and 3D Building Reconstruction. Everyone can download it from the ISPRS website. The study area is located in Vaihingen City. Aerial images are shot by a digital mapping camera (DMC), wherein the focal length of DMC is 120 mm, the charge-coupled device (CCD) pixel size is 12 \(\upmu\)m ground resolution of images and the frame of image is 7680 \(\times\) 13,824. LiDAR point clouds are collected by the Leica ALS50 subminiature LiDAR with a density of the point clouds of 6.7 point/m\({}^{2}\).  
(3) Real aerial imagery and airborne LiDAR data: The study area is located at the University of Calgary. Aerial imagery is shot by Phase One, wherein the focal length of DMC is 60.6785 mm, the CCD pixel is 6 \(\upmu\)m ground resolution of images and the frame of image is 6732 \(\times\) 8984. The density of the point clouds is 3.5 point/m\({}^{2}\).  
For each dataset, a single image is selected for registration with the LiDAR data. The image lines and LiDAR lines were manually measured. A set of nine evenly-distributed control lines were manually selected for each dataset, while others were used as check lines. Figure 4 shows the distributed control lines for the ISPRS test project, and the real image, respectively. Yellow lines are used to represent control lines and green lines are used to represent check lines.  
Figure 4: Distribution of (**a**) simulated and (**b**) ISPRS test project.