A fast and simple method to calibrate scale factor using telephoto lens

In this paper, we present a simple method to extract the scale factor, a parameter that has to be determined during the calibration of a camera. Our method is built on the basic idea due to Penna (1991), and it effectively deals with situations where Penna´s method would produce inaccurate results. The proposed technique images a sphere orthographically, as a circle on the image plane, and estimates the scale factor from the observed shape (in the digitized image) of that circle. Our motivation to project the sphere orthographically as against perspectively as was done by Penna, is that it does not impose the constraint that the center of the sphere be on the optical axis of the camera. There is an additional advantage in that, the estimation of the scale factor becomes independent of the radial distortion introduced by the lens, which is an additional cause of concern when the circle is obtained by perspective projection