An Analytic Solution of a Linear Camera Self-Calibration

We propose an analytic solution for the self-calibration of five-parameter linear camera from three pairs of views of a scene, of four-parameter linear camera from two pairs of views and of two-parameter linear camera from one pairs of views based on Kruppa equations, respectively. The approach does not need any initial value, and can calculate accurate solution. The analysis was performed first by writing a suitable set of equations under introducing unknown scale factors from Kruppa's equations. Then, by an elimination scheme and symbolic computation, only one unknown scale factor was retained, so the equation set was reduced to a 30th order univariate polynomial equation for five-parameter or four-parameter camera, and a 3rd order univariate polynomial equation for two-parameter camera. After scale factors were attained, the camera intrinsic parameters were computed by a linear method. A numerical example was reported that confirms the theoretical results by "Mathematica" software