Camera Calibration Using Rotation Symmetric Patterns

Computer vision measurement technique is an important technique means to achieve industrial manufacture automation and intelligence. Camera calibration is the primary part of the computer vision measurement technique, since the accuracy of the calibration has a vital influence for the precision of the whole measurement system. Therefore, an easy and accurate method for calibration is of great significance to improve the performance of the measurement system.Traditional camera calibration methods mainly do the calibration job by solving linear equations that arise from correspondence of feature points between the reference object and the observed images. The major weaknesses of those methods can be summed up in two aspects.(1) It is required to extract image features, which leads to a dilemma that in practice it is difficult to accurately extract features in observed images in the presence of noise. This makes the traditional methods limited in practical application.(2) Its manipulation is complicated. Traditional methods usually require multiple images and to be done multiple times, and sometimes human intervention is necessary, which makes it difficult for traditional methods to realize automation. In particular, traditional methods are not suitable for calibrating a camera in dynamic real-time occasions.Taking the shortcoming of the traditional methods into account, we propose an easy and flexible camera calibration method which only requires the camera to observe a planar rotation symmetric pattern from an oblique view. The main principle is that a rotation symmetric image can be converted to a translated symmetric one by frieze-expansion transformation, and the degree of translation symmetry of one image can be measured by the rank of its gray-level matrix. Based on that principle, we first establish the forward model between the camera parameters and the symmetry of the template image, and then solve the inverse problem by low-rank optimization algorithm to obtain the intrinsic and extrinsic parameters. This method doesn’t need to detect and extract feature points, thus it’s easy to operate and suitable for dynamic real-time occasions. Specifically, we propose two concrete solutions according to the above model:The first solution is that we directly establish the forward model between the camera parameters and the symmetry of the pattern image. The physical meaning of the solution parameters is clear and the solution can be calculated fast. However, the intrinsic and extrinsic parameters have a different dimension, which leads to the numerical instability of the solution. So this solution is suitable for situations in which we need to measure extrinsic parameters of a camera whose intrinsic parameters are known.The second solution is that we establish the forward model between the homography and the symmetry of the pattern image, and then we parse the homography with vanishing point principle to obtain the camera parameters. This solution avoids the numerical instability of the first solution. However, it is complex and slow to calculate. So this solution is suitable for situations in which we have a lower demand in real-time and need to calculate simultaneously the intrinsic and extrinsic parameters of a camera.The calibration procedure of the two solutions gets rid of the human intervention. Hence, the proposed method is particularly useful for those people who are not familiar with computer vision. Extensive simulation and experimental results with real images demonstrate that the proposed method is accurate, robust and practical.