Camera Calibration from Coplanar Circles

The estimation of camera intrinsic parameters plays a crucial role in all computer vision tasks for which the underlying model that drives the image formation process has to be known. As a consequence, a deluge set of different approaches has been proposed in literature over the last decades. Most of those lean on the observation of a known object (i.e. a calibration target) from different point of views, providing the necessary data to estimate the model through different optimization approaches. In this work, we exploit the projective properties of conics to estimate the focal length and optical center of a pinhole camera just by observing a set of coplanar circles, where neither the radius nor the reciprocal position of each circle has to be known a-priori. This make such method particularly interesting whenever the usage of a calibration target is not a feasible option. Our contribution is twofold. First, we propose a reliable method to locate coplanar circles from images by means of a non-cooperative evolutionary game. Second, we refine the estimation of camera parameters with a non-linear function minimization through a simple yet effective gradient descent. Performance of the proposed approach is assessed through an experimental section consisting on both quantitative and qualitative tests.