Single-view calibration of a catadioptric camera based on a theodolite model

The catadioptric panoramic imaging system may provide 360° panoramic imaging by employing the convex surface of a quadric surface with rotational symmetry as the reflector, which effectively compensates for the disadvantages of the narrow field of view in typical camera systems. First, this paper proposes a theodolite-based catadioptric camera image model based on the rotational symmetry of a catadioptric camera mirror, which simplifies the 2D modeling problem to a 1D problem. Simultaneously, the equivalence of the theodolite imaging model and the standard spherical imaging model also is demonstrated in this work. Second, this paper presents a method to calibrate the theodolite model parameters using only a single view and explains the calculation of model parameter initialization and iterative optimization steps in detail. Then, this paper demonstrates how to calibrate the theodolite model parameters using only a single view, as well as how to calculate the model parameter initialization and iterative optimization steps. Finally, simulation experiments and actual experiments have confirmed the correctness and stability of the method. The experimental results show that the average and standard deviation of the back-projection error are, respectively, 0.1983125 pixels and 0.0006153 pixels, in this model. We believe the theodolite model suggested in this paper offers a viable approach to catadioptric camera image modeling.