Precise calibration of linear camera equipped with cylindrical lenses using a radial basis function-based mapping technique.

The linear camera equipped with cylindrical lenses has prominent advantages in high-precision coordinate measurement and dynamic position-tracking. However, the serious distortion of the cylindrical lenses limits the application of this camera. To overcome this obstacle, a precise two-step calibration method is developed. In the first step, a radial basis function-based (RBF-based) mapping technique is employed to recover the projection mapping of the imaging system by interpolating the correspondence between incident rays and image points. For an object point in 3D space, the plane passing through the object point in camera coordinate frame can be calculated accurately by this technique. The second step is the calibration of extrinsic parameters, which realizes the coordinate transformation from the camera coordinate frame to world coordinate frame. The proposed method has three aspects of advantage. Firstly, this method (black box calibration) is still effective even if the distortion is high and asymmetric. Secondly, the coupling between extrinsic parameters and other parameters, which is normally occurred and may lead to the failure of calibration, is avoided because this method simplifies the pinhole model and only extrinsic parameters are concerned in the simplified model. Thirdly, the nonlinear optimization, which is widely used to refine camera parameters, is better conditioned since fewer parameters are needed and more accurate initial iteration value is estimated. Both simulative and real experiments have been carried out and good results have been obtained.