Calibration of quad-camera measurement systems using a one-dimensional calibration object for three-dimensional point reconstruction

A quad-camera visual measurement system must have a calibration accuracy that is equivalent to its reconstruction accuracy. We investigate the effects of quad-camera calibration methods and propose a method based on a one-dimensional (1-D) object. First, the essential matrices are calculated and combined with the RANSAC method to obtain the image coordinate of the 1-D calibration object. Then, the initial values of the four camera matrices are retrieved from the essential matrices to scale. Subsequently, the Euclidean distance between the calibration points of the 1-D calibration object is used to retrieve the scale factor. Furthermore, an uncertainty analysis of three-dimensional (3-D) point reconstruction is conducted, and based on this, an iterative linear calibration method is introduced to refine the initial calibration results. Finally, a set of calibration objective functions are established by analyzing the measurement process. A synthetic optimizing algorithm is adopted to obtain the high-precision calibration results of the quad-camera measurement system. Experiments are conducted to analyze the calibration accuracy and robustness of the proposed method in the presence of noise. The results indicate that the proposed method can increase the 3-D measurement accuracy and robustness.