Inclinometer Assembly Error Calibration and Horizontal Image Correction in Photoelectric Measurement Systems
Inclinometer assembly error is one of the key factors affecting the measurement accuracy of photoelectric measurement systems. In order to solve the problem of the lack of complete attitude information in the measurement system, this paper proposes a new inclinometer assembly error calibration and horizontal image correction method utilizing plumb lines in the scenario. Based on the principle that the plumb line in the scenario should be a vertical line on the image plane when the camera is
... ed horizontally in the photoelectric system, the direction cosine matrix between the geodetic coordinate system and the inclinometer coordinate system is calculated firstly by three-dimensional coordinate transformation. Then, the homography matrix required for horizontal image correction is obtained, along with the constraint equation satisfying the inclinometer-camera system requirements. Finally, the assembly error of the inclinometer is calibrated by the optimization function. Experimental results show that the inclinometer assembly error can be calibrated only by using the inclination angle information in conjunction with plumb lines in the scenario. Perturbation simulation and practical experiments using MATLAB indicate the feasibility of the proposed method. The inclined image can be horizontally corrected by the homography matrix obtained during the calculation of the inclinometer assembly error, as well. Sensors 2018, 18, 248 2 of 20 information, the assembly error of the inertial sensor or inclinometer  and other system interference factors should be considered and calibrated first, and then combined into the calculation to obtain the desired system precision [15, 19] . On the one hand, the inclinometer is a measuring implement used for small-angle measurement  . It can be fixed in photoelectric measurement systems to obtain attitude changes relative to the system's horizontal plane  . The real position of the object to be measured in the three-dimensional space coordinate system can be calculated by modeling the variables obtained from the inclinometer and combining them with image processing methods [10, 22] . However, the inclinometer can only measure the angle between the assembly plane and the horizontal plane, and cannot acquire complete system attitude information. Thus, in order to perform assembly error calibration, inertial sensors are often needed for assistance. Nevertheless, the drawback is that the cumulative errors of the inertial sensor itself will affect the accuracy of the system's assembly error calibration  . Additionally, the cost of high-precision inertial sensors or gyroscopes is very high, and they are not convenient for system integration. On the other hand, with regard to the field of photography  and image processing in computer vision, in order to meet some demands while taking photos-for example, taking panoramic  or distant-view pictures-the camera needs to remain a fixed degree. Additionally, when using functions based on multiple exposures or bracketed exposures for shooting, the pictures will not overlap if the levels are not the same for two exposures, creating ghosting images. Furthermore, sometimes, objects in the image are inclined due to shaking of the camera, or other factors while capturing. For example, some buildings are not perpendicular to the ground, edges of the door and wall are not perpendicular to the floor, etc. These images will not look correct if horizontal correction is not performed. Therefore, it is necessary to pay attention to the level of the camera. Through the use of an inclinometer in the photoelectric system, the image can be horizontally corrected, and the design of the picture can be optimized. In this paper, a new method for inclinometer assembly error calibration and horizontal image correction is proposed based on plumb lines in the scenario. During the calibration, only images with plumb lines captured by the camera and inclination data from the inclinometer are needed. This paper firstly analyzes the expression of the inclinometer assembly error in photoelectric measurement systems, and then establishes the optimization function of the inclinometer assembly error according to the principle that "the plumb lines of edges of constructions in the real world should become vertical lines on the image plane after horizontal correction by the inclinometer". Finally, the image is horizontally corrected to verify the accuracy of the calibration result, and calibration errors are discussed through simulation and practical experiments. The structure of this paper is as follows. Section 2 provides the related work on applications of the camera and the inclinometer, as well as the contributions made by the proposed method. Section 3 explains inclinometer assembly error in photoelectric measurement systems. Section 4 introduces the proposed calibration and horizontal image correction method based on plumb lines. Section 5 shows the experimental results and analyzes the system errors. Section 6 is the conclusion. Related Work and Motivation Much progress has been witnessed in recent years in inertial and inclinometer calibration, and their applications in various areas. Merckel , et al. described a method for finding the pose of an object from a single image using an inclinometer attached to the camera to reduce the number of unknown parameters during the exact pose calculation, and efficiently compute the pose by using a classical iterative optimization method. Chang  , et al. introduced a four-parameter mathematical computing model for the state parameters of the inclinometer, and analyzed various calculation models for the state parameters of the inclinometer.