# A Fast and Simple Method for Absolute Orientation Estimation Using a Single Vanishing Point
###### Abstract  
Absolute orientation estimation is one of the key steps in computer vision, and \(n\) 2D-3D point correspondences can be used to obtain the absolute orientation, which is known as the perspective-n-point problem (PnP). The lowest number of point correspondences is three if there is no other information, and the corresponding algorithm is called the P3P solver. In practice, the real scene may consist of some geometric information, e.g., the vanishing point. When scenes contain parallel lines, they intersect at vanishing points. Hence, to reduce the number of point correspondences and increase the computational speed, we proposed a fast and simple method for absolute orientation estimation using a single vanishing point. First, the inertial measurement unit (IMU) was used to obtain the rotation of  
estimate the orientation or position independently, and hence the number of point correspondences cannot be decreased. When the number of 2D-3D point correspondences is three, up to four solutions can be given through the non-linear algorithm, and the corresponding methods are called P3P solvers [26; 27; 28; 29]. When more 2D-3D point correspondences are given, some intrinsic camera parameters can be simultaneously estimated, i.e., using P4 Pf solvers [30; 31] and P5 Pfr solvers [32]. When the number of 2D-3D point correspondences of known positions is not fewer than six, the camera orientation and position can be estimated linearly, and the corresponding solvers are called DLTs (direct linear transforms) [33; 34; 35; 36]. In practice, however, it is difficult to obtain 3D points with known positions. Some algorithms have been proposed to reduce the number of 3D points with known positions or orientations [37; 38; 39], but they still need two or more 3D points. In some scenes, 3D lines exist (e.g., ceilings and floors indoor, or the walls of buildings) and thus many PnL solvers have been proposed [40; 41; 42; 43] that can use this information. Similar to the 3D points in the PnP problem, 3D lines with known absolute positions are also difficult to obtain. This restriction prevents the application of PnL solvers from scenarios where not enough 3D lines with known absolute positions are provided. However, when scenes contain parallel lines, they intersect at a vanishing point in images, and some algorithms [44; 45; 46; 47] use this information to estimate the camera pose because many parallel lines, e.g., ceilings and floors indoors, may exist in certain scenarios. [PERSON] proposed a method to use two vanishing points to estimate the camera pose [48]. However, this method has a disadvantage as it supposes that the parallel lines of the first set are perpendicular to those of the second, and the intersection of the two sets is the origin of the world frame. When more vanishing points or other constraints are given, the disadvantage can be overcome and more parameters of the camera can be estimated [49]. More vanishing points can estimate more parameters and improve the accuracy. However, many scenarios may only have one or two vanishing points and thus the origin of the world frame could be arbitrary, which limits the corresponding methods from being employed. In this paper, we proposed a fast and simple method for absolute orientation estimation using a single vanishing point to overcome these disadvantages descried above. Our proposed method uses IMU to provide the roll angle, and then estimates the camera orientation using only one vanishing point. Moreover, the positions of the parallel 3D lines of this vanishing point are not essential, only the direction vector. Our proposed method can separate the camera orientation from the position, and hence the orientation can be estimated independently because the six dof are not coupled in our method. This increases the computational speed. The angular accuracy of the roll angle in low cost IMUs [39; 50] is about 0.02\({}^{\circ}\), and hence using the roll information cannot decrease the accuracy of our proposed method.