A Simplified Active Calibration algorithm for Focal Length Estimation

We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point correspondence that relates images taken before and after a degenerate rotation of the camera. The new formulations will be beneficial in robotic and dynamic surveillance environments when the camera needs to be calibrated while it freely moves and zooms. By establishing a correspondence between only two images taken after slightly panning and tilting the camera and a reference image, our proposed Simplified Calibration Method is able to calculate the focal length of the camera. We extensively evaluate the derived formulations on a simulated camera, 3D scenes and real-world images. Our error analysis over simulated and real images indicates that the proposed Simplified Active Calibration formulation estimates the parameters of a camera with low error rates.