Supplementary study on camera calibration based on triangle

The similarity invariants of a triangle are introduced in this paper firstly, and the constraints between the camera intrinsic parameters and its similarity invariants are discussed under simplified camera model when a triangle performs a special motion. 2N images of the triangle can produce 2(N-1) quadratic equations about the intrinsic parameters of the camera while the triangle does parallel motion or rotates around a fixed point with 180 degrees. Using these constraint equations, we obtain the constraints based on special triangle , which can be used to determine the intrinsic parameters linearly. Simulated experiments are carried out in the end to analyze the robustness of the results, and from the experiments the RMS error of each parameter in intrinsic matrix of the camera increases almost linearly with the noise level and it is in allowable range.