Iterative multistep explicit camera calibration

Perspective camera calibration has been in the last decades a research subject for a large group of researchers and as a result several camera calibration methodologies can be found in the literature. However, only a small number of those methods base their approaches on the use of monoplane calibration points. We developed one of those methodologies using monoplane calibration points to perform an explicit three-dimensional (3-D) camera calibration. This methodology is based on an iterative approach. To avoid the singularities obtained with the calibration equations when monoplane calibration points are used, this method computes the calibration parameters in a multistep procedure and requires a first-guess solution for the intrinsic parameters. These intrinsic parameters are updated and their accuracy increased during the iterative procedure. All computations required are linear and in addition to the extrinsic parameters (Rotation and Translation) the proposed method also computes the first coefficient of the radial distortion (k(1)) and the skew angle. A first-guess value for the focal length of the lens is required but its value is iteratively updated using the Gauss lens model. This methodology also includes the uncertainty horizontal image scale factor (S-x) on the set of calibration parameters to be computed, which makes this approach independent of the accuracy of the horizontal scale factor. The proposed methodology has the advantage that it can be used with monoplane calibration data with no restrictions for the pose geometry of the camera. In this approach the pose estimation problem is treated separately, computing the pose orientation of the camera in a first step and using this information to compute the pose location. A model for the expected stability of the camera look angles (camera's orientation) from noisy image data and its stability analysis as a function of the pose geometry of the camera is presented. Camera pose view strategies for accurate camera orientation computation can be extracted from the pose view stability analysis. Several experimental and simulated analyzes were performed and are presented on this paper. Tests were performed using synthetic and real calibration data considering different camera pose geometries. The accuracy of the computed parameters was analised with real and synthetic data, and their stability in the presence of random gaussian noise was analised with synthetic data. Finally, a comparative analysis between this new method and the Radial Alignment Constraint method proposed by R. Tsai is presented.