Pattern vs. surrounding 3D pattern for fisheye camera calibration

For a fisheye camera with wider FOV (field of view) than hemisphere, a 2D plane pattern cannot cover the whole FOV. Intuitively, a surrounding 3D pattern covering the whole FOV of a fisheye camera may acquire a better parameters estimation of the fisheye camera than a 2D plant pattern. However, it seems there is no result available concerning quantitative evaluation on this expectation until now. In this paper we give a case study result on the comparison between 2D pattern and surrounding 3D pattern for fisheye camera calibration. Control points are extracted from circles painted on the calibration patterns. A better estimate of projection curve of fisheye camera and smaller standard deviations of the back-projection of the control points on the fisheye image are obtained in our simulation experiments.