# A General Calibration Method for Dual-PTZ Cameras Based on Feedback Parameters
## 2 Related Works  
More and more research is devoted to the calibration of PTZ cameras. To calibrate intrinsic parameters, [PERSON] et al. collected a large number of pre-calibrated intrinsic parameters with different dispersed zoom values as datasets [3], and they obtained these parameters using a lookup table based on the camera's current zoom values while in use. However, this method is time-consuming, and only a few discrete focal length values can be obtained. [PERSON] et al. discussed the calibration of intrinsic parameters and the radial distortion captured by the image automatically, and they validated their approaches by calibrating two different cameras [8]. [PERSON] [6] and [PERSON] established different fitting models between focal length and zoom scales for different cameras, and [PERSON] also modeled the lens distortion coefficient as a function of the zoom scale [9]. For lens distortion, [PERSON] conducted a thorough study of the mathematical model between lens distortion and focal length [10]. [PERSON] used a distortion matrix to describe the distortions of different parts of the lens under non-axisymmetric conditions [11].  
For the calibration of extrinsic parameters, [PERSON], based on the aforementioned two assumptions in Section 1, deduced the rotation matrix relative to the original position according to the rotation angle [6; 12]. In this model, the rotation will not produce a translation vector. Some researchers have considered the offset between the rotation axis and the optical center for single cameras and dual cameras, and they have introduced more complete models for the motion of the camera to avoid the problem above [13; 14; 15; 16]. [PERSON] et al. [17] proposed a calibration method based on [PERSON]'s approach, using an augmented checkerboard composed of eight small checkerboards. This calibration is formulated as an optimization problem to be solved with an improved particle swarm optimization (PSO) method.  
Some of the above calibration methods for intrinsic and extrinsic parameters are meant to extract a series of image feature points or use a special calibration board to obtain the parameters, for example, in Refs. [8; 9; 10; 17]; these methods are suitable for situations where the camera position is fixed relative to the background, so they are not applicable when mounting the camera on a mobile intelligent unmanned system. Refs. [6; 9; 10; 12] discussed the relationship between intrinsic and extrinsic parameters and feedback parameters based on different models. Moreover, Ref. [9] aimed at the problem that feedback parameters reported by PTZ cameras become inaccurate after many hours of operation, and propose a method with 10 images to achieve accurate calibration results, which solved the problem of feedback precision.  
However, the works above rarely propose a general calibration method under a nonidealized model to systematically determine both the intrinsic and extrinsic parameters of dual-PTZ cameras; the majority of the works are only for single PTZ cameras. In this article, we study how to use real-time feedback parameters (pan angle, tilt angle, zoom value) to calculate the intrinsic and extrinsic parameters of dual-PTZ cameras based on our proposed general model.