# A General Calibration Method for Dual-PTZ Cameras Based on Feedback Parameters
## 1 Introduction  
PTZ (Pan-Tilt-Zoom) cameras, also known as gimbal cameras, can achieve horizontal rotation, pitch rotation, and lens zoom control. They can also provide the current horizontal angle, pitch angle, and zoom value in real time via SDK. PTZ cameras can not only obtain image information from different regions via rotation but they can also obtain spatial images with rich target texture information from different depths, using zoom without sacrificing high resolution in a large range.  
Dual-PTZ cameras simulate the chameleon's vision system, whose left eye and right eye can rotate independently. The left and right cameras can rotate independently to actively track dynamic targets or reconnoiter the surrounding environment via rotationand zoom. They can also point in the same direction and activate stereovision to achieve the 3D-positioning of their targets when locating them. Based on these characteristics, more and more intelligent unmanned systems use PTZ cameras as sensors in their perception modules. They can be used in high-precision 3D reconstruction of large scenes, long-distance reconnaissance, active tracking and target recognition and localization [1; 2; 3; 4; 5].  
Accurate intrinsic and extrinsic parameter calibration results at arbitrary angles and focal lengths are the basis of the aforementioned applications of dual-PTZ cameras. However, in the process of rotating and zooming, the intrinsic and extrinsic parameters change. Furthermore, due to the motion of intelligent unmanned systems, the background of the camera is variable as well. As a result, achieving accurate calibration results for the intrinsic and extrinsic parameters of these cameras in real time has always been a challenge.  
Because the camera's rotation angle and zoom value are based on real-time feedback, we can build a general model for a dual-PTZ camera and calculate its intrinsic and extrinsic parameters directly through its feedback parameters. Previous works have idealized an ideal PTZ camera model using two assumptions: that the horizontal and pitch rotation axes of the camera should coincide with the optical center of the camera and that the horizontal and pitch axes should be orthogonal to each other [6]. However, this idealized model is insufficient for all PTZ cameras because absolutely ideal manufacturing is impossible using real production processes, let alone the fact that some PTZ cameras are specifically designed with the optical center far away from the axis.  
Our main contributions to the literature are as follows:  
1. Establishing a general model for dual-PTZ cameras and differentiating the two different modes of PTZ cameras in a slave relationship between the horizontal rotation and the pitch rotation;
2. Proposing an actual rotation vector and rotation radius vector calibration method based on the proposed model;
3. Deriving the calculation formula of intrinsic and extrinsic parameters at an arbitrary pan degree, tilt degree, and zoom value based on feedback parameters.  
This paper is organized as follows: Section 2 introduces the research progress and related calibration work of dual-PTZ cameras. Section 3 establishes a general model for dual-PTZ cameras. Section 4 presents the fitting method of zoom value and camera's intrinsic parameters. Section 5 deduces the computational formula of the camera's extrinsic parameters based on feedback parameters in variable focal length and posture. Section 6 provides the experimental results. The results calibrated by [PERSON]'s method [7] are taken as the ground truth to validate the accuracy of our proposed method.