Concentric-circle-based camera calibration

In recent years, camera calibration and three-dimensional (3D) reconstruction have attracted more and more attentions in the vision community and found wide applications in many vision-based robotics. This article discusses about a new technique for camera calibration based on concentric circles, whose positions and sizes can be arbitrary. Here, the key problem is how to efficiently estimate the projections of the circle centre from the images. The solution for this problem is formulated into a first-order polynomial eigenvalue problem (PEP) by considering the pole-polar relationship in the image. Then the camera can be calibrated with the images of circular points or the vanishing points. Accordingly, two algorithms are suggested. Finally, both numerical simulation and real data experiments have been carried out to validate the algorithms.