Camera Calibration and Direct Reconstruction from Plane with Brackets

Camera calibration and 3D reconstruction are important issues in computer vision. Two applications of bracket algebra in these two issues are presented in this work. Firstly, a camera calibration method is proposed, which is from only distance ratios of object points. Thanks to the effective computations of brackets, this method does not need to set up any world coordinate system and thus can use the geometric information of irregular objects conveniently. Secondly, we represent the reconstruction solution of plane structure directly from four known control points and give some new and useful error analysis results. The solution based on brackets is concise and short, and the error analysis results can act as a theoretical guidance in practice. Simulations and experiments on real images validate our proposed camera calibration method, direct reconstruction solution and error analysis results.

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