A calibration method for non-overlapping cameras based on mirrored phase target

A novel calibration method for non-overlapping cameras is proposed in this paper. A LCD screen is used as a phase target to display two groups of orthogonal phase-shifted sinusoidal patterns during the calibration process. Through a mirror reflection, the phase target is captured by the cameras respectively. The relations between each camera and the phase target can be obtained according the proposed algorithm. Then the relation between the cameras can be calculated by treating the phase target as an intermediate value. The proposed method is more flexible than conventional mirror-based approach, because it do not require the common identification points and is robust to out-of-focus images. Both simulation work and experimental results show the proposed calibration method has a good result in calibrating a non-overlapping cameras system. Introduction Multiple cameras are applied in visual measurement [1, 2], scene surveillance [3, 4], and mobile robotics [5, 6] in case of single camera could not satisfy the functional requirement. Due to the design restrictions and cost savings, the field of view (FOV) of the cameras are unable to be guaranteed overlapped. In these cases, the camera parameter and the relative positions of the cameras should be calibrated for a system consisted of non-overlapping cameras. Recently, several types of calibration approaches are researched to calibrate the non-overlapping cameras. One type of the approaches introduces extra calibration tools to assist the calibration process. Pagel et al. [5] developed an approach for calibrating non-overlapping cameras with hand-eye calibration (HEC) technique. Guan et al. [7] researched an approach to obtain the internal and external parameters of non-overlapping camera fig based on HEC. Lamprecht et al. [8] calibrated a non-overlapping cameras system on a vehicle online. However these approaches are sensitive to the localization accuracy of the calibration tools and are failure when the cameras are unable to move. Other approaches were researched based on a target which moves in the cameras’ FOV. Ali et al. [9] proposed an approach for simultaneously recovering the trajectory of a target and the external calibration parameters of non-overlapping cameras. However this type of approaches cannot meet the accuracy demand of visual measurement. Researchers studied to extend the target size to cover the FOV of cameras simultaneously. Liu et al. [10] proposed an approach to calibrate the extrinsic parameters of multiple vision sensors based on 1D target. Dong et al. [11] combined a multiple cameras system using arbitrarily distributed encoded targets on a wall. However this type of approaches is limited by the target size and cannot calibrate cameras with 180 degree angle. The mirror-based calibration approaches [12, 13] applied a planar mirror to generate an overlapping view between cameras and calibrate cameras based on a 2D calibration target. This type of approaches improves the flexibility in the design of calibration target size, avoids the error introduced by positioning tools and does not require the cameras’ movement during calibration process. However it is less convenient to implement because cameras have to find the same identification points though the mirror reflection. Moreover, the common points cannot be extracted successfully when the target is not in the depth of field (DOF) of the cameras. This paper presents a novel calibration method based on mirrored phase target for non-overlapping cameras. Though the mirror reflection, the relation between each camera and the phase target can be obtained. Then the relation between the cameras can be calculated by treating the phase target as an intermediate value. Since the phase target is consisted of sinusoidal fringe patterns, the proposed method is robust to out-of-focus. Principle The illustration of the proposed method is illustrated in Fig. 1. A LCD screen is used to display two groups of orthogonal phase-shifting sinusoidal patterns. Through the reflection of flat mirrors, the patterns are captured by the cameras. After phase-shifting and phase unwrapped algorithm [13] applied, two orthogonal absolute phase maps can be obtained. The calculated phase maps are used as targets during the calibration process. Fig. 1. The illustration of the proposed method For a pixel m of camera 1, the corresponding physical position '( , ) w w M x y in the mirrored LCD coordinate system can be uniquely located based on its absolute phase value ( , ) x y   according to Eq. (1). ( / 2 ) ( / 2 ) w p x w p y x n p y n p              . (1) where p is the size of LCD pixel pitch and p n is the number of LCD pixels per fringe period. Camera parameter 1 A and the relation   ' ' R t between mirrored screen and the camera coordinate system can be obtained based on the pinhole model by moving mirror 1 to at least 3 arbitrary positions:   1 ' ' ' sm A R t M    . (2) The relation   1 1 R t between the camera and the real screen can be calculated with the least-squares solution by at least three mirror reflections according to Eq. (3).