# Registration of Urban Aerial Image and LiDAR Based on Line Vectors
## 1 Introduction  
LiDAR is characterized by high elevation accuracy, strong autonomy, and well-operated automatization [1], which could directly obtain the three-dimensional information of ground features. The discreteness in LiDAR data makes it difficult to directly obtain semantic information (e.g., texture and structure) of ground features [2]. Aerial images are abundant in spectral information and texture information of ground features, therefore, the surface accuracy is much higher. However, there are potential risks in three-dimensional points with sufficient density acquired by auto-matching superimposed images. LiDAR data and aerial images are highly complementary [2], so the combination of these two sources of data could simultaneously obtain three-dimensional, semantic, and texture information from spatial targets. This has important significance for feature extraction [3], three-dimensional reconstruction of buildings [4; 5; 6], and manufacturing of true orthophotos [7]. Various reference frames in airborne LiDAR data and imagery, along with systematic errors inside of the LiDAR system and aerial photography system, cause spatial position deviations between the LiDAR data and the image, which may greatly affect the accuracy of the data results. Both of them, before being integrated for application, should be included in a unified coordinate system to achieve their spatially-accurate registration, namely the registration of LiDAR data and aerial images [8]. The commonly-used features in registration mainly include point features and the line features. Compared with point features, linear features have the potential to be reliably, accurately, andautomatically extracted from images [9]. In addition, linear features are abundant and can be easily obtained in urban areas without the requirement for the line segment endpoint corresponding to the same point, allowing the linear features to be partially occluded [10; 11; 12; 13; 14; 15]. In registration based on linear features, [PERSON] et al. proposed to directly incorporate LiDAR lines representing a sequence of intermediate points along the line features as controls in bundle adjustment [16; 17]. [PERSON] et al. proposed to establish coplanar equations of bundle adjustments by the coplanar constraints of linear features and collinear constraints of tie points [18]. However, this requires appropriate initial exterior orientation parameters (EOPs) to obtain approximate locations when projecting three-dimensional (3D) line segments in the LiDAR data coordinate framework to the image coordinate framework. These methods solve the position parameters and direction parameters separately when solving EOPs due to which coupling error exists. To overcome the probable error accumulation in the process of asynchronous calculation of transformation parameters, dual quaternions are used to describe the spatial rotation and to ensure the simultaneous calculation of registration parameters. However, the registration model of this method is a spatial similarity transformation, whose registration primitive is a feature point [19; 20]. Almost all of the aforementioned methods use the collinearity equation or coplanarity condition as a mathematical foundation for registration and regard line direction as a control or linear features as known variables in the solution, whose adjustment form is identical to the point registration method. In fact, any line in the space is solely determined by its own position and direction [21; 22]. If merely using the direction information for registration, the geometry constraint of registration model is not strong enough. On the basis of the existing methods with linear features, registration of an urban aerial image and LiDAR based on line vectors that aggregate line direction and line position is proposed in this paper. The remainder of this paper is organized as follows: The principle of line vectors is first introduced. Then, the mathematical model of the registration method based on line vectors is discussed in detail.