Single-image camera calibration with model-free distortion correction

Camera calibration is a process of paramount importance in computer vision applications that require accurate quantitative measurements. The popular method developed by Zhang relies on the use of a large number of images of a planar grid of fiducial points captured in multiple poses. Although flexible and easy to implement, Zhang's method has some limitations. The simultaneous optimization of the entire parameter set, including the coefficients of a predefined distortion model, may result in poor distortion correction at the image boundaries or in miscalculation of the intrinsic parameters, even with a reasonably small reprojection error. Indeed, applications involving image stitching (e.g. multi-camera systems) require accurate mapping of distortion up to the outermost regions of the image. Moreover, intrinsic parameters affect the accuracy of camera pose estimation, which is fundamental for applications such as vision servoing in robot navigation and automated assembly. This paper proposes a method for estimating the complete set of calibration parameters from a single image of a planar speckle pattern covering the entire sensor. The correspondence between image points and physical points on the calibration target is obtained using Digital Image Correlation. The effective focal length and the extrinsic parameters are calculated separately after a prior evaluation of the principal point. At the end of the procedure, a dense and uniform model-free distortion map is obtained over the entire image. Synthetic data with different noise levels were used to test the feasibility of the proposed method and to compare its metrological performance with Zhang's method. Real-world tests demonstrate the potential of the developed method to reveal aspects of the image formation that are hidden by averaging over multiple images.