Recovering projected centers of circle-pairs with common tangents

This paper describes a closed-form algorithm of recovering the projected centers of a parallel circle-pair from one image. By using the common tangents of a circle-pair as the key helper for solving the problem, we have developed an algorithm that only uses real, visible and concrete geometrical features for describing itself and for representing the intermediate results. This makes the jobs of checking the behavior or verifying the intermediate and the final results easy. This characteristic greatly improves the reliability of our algorithm when applied to noisy images. We have checked the behavior of our algorithm in various camera settings and the influence of image noise using simulated images and real images, and compared ours with the algorithm that uses two concentric circles and the algorithm that uses three circles.