The paper proposes a novel approach for planar selfcalibration of radially symmetric cameras. We model these camera images using notions of distortion center and concentric distortion circles around it. The rays corresponding to pixels lying on a single distortion circle form a right circular cone. Each of these cones is associated with two unknowns; optical center and focal length (opening angle). In the central case, we consider all distortion circles to have the same optical center, whereas in the non-central case they have different optical centers lying on the same optical axis. Based on this model we provide a factorization based self-calibration algorithm for planar scenes from dense image matches. Our formulation provides a rich set of constraints to validate the correctness of the distortion center. We also propose possible extensions of this algorithm in terms of non-planar scenes, non-unit aspect ratio and multiview constraints. Experimental results are shown.