Camera linear self-calibration method based on the Kruppa equation

The Kruppa equation-based camera self-calibration methods using nonlinear optimization are easily stuck in some local minimum. A new method is presented for the linearization of the Kruppa equation under two special cases where the camera rotation axis is either parallel or perpendicular to the translation direction. For the parallel case, the unknown scale in equation is represented using the singular value decomposition (SVD)-based factorization result of the fundamental matrix. As for the perpendicular case, the unknown scale is represented by one of the two non-zero eigenvalues of a specific matrix, and the method to choose between the two non-zero eigenvalues is given using the rank constraint. This method simplifies the utilization of the SVD-based Kruppa equation and avoid considering all possible combinations. Simulation results validate the correctness of the proposed method.