  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.
