Extrinsic parameters and focal length calibration using rotation-symmetric patterns

The authors present a camera calibration method for estimating the extrinsic parameters and focal length of a camera using only a single image of a planar rotation-symmetric pattern. The frontal parallel image of the pattern can preserve the rotation-symmetric pattern, causing the corresponding frieze-expansion (FE) pattern to be expressed as a low-rank matrix, which does not exist when the image is captured from an oblique view. The proposed method derives the forward formulation between the FE of the image observed from an oblique view and the low-rank, FE pattern of the frontal parallel image. An optimisation problem arises when rank minimisation techniques are introduced; by solving this problem, one can obtain the camera parameters relative to the front view. Simultaneously, the rotation-symmetric texture is recovered as a by-product. This new method takes advantage of the raw intensity values of the observed image itself, bypassing the need to extract any low-level features and simplifying human intervention. Experimental results demonstrate the validity of the proposed method.