Camera Calibration from Symmetry

This paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution. Camera calibration is the process of determining the intrinsic or internal parameters (i.e. aspect ratio, focal length and principal point) of a camera, and is important for both motion estimation and metric reconstruction of 3D models. In this paper, a novel and simple calibration technique has been introduced which is based on the symmetry of images of surfaces of revolution. Traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern (such as a calibration grid). The use of surfaces of revolution, which are commonly found in daily life (e.g. bowls and vases), makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects. In this paper, it is shown that 2 images of surface of revolution will provide enough information for determining the aspect ratio, focal length and principal point of a camera. An analytical error model is developed, providing variances and confidence intervals of the parameters estimated. The techniques presented in this paper have been implemented and tested with both synthetic and real data. Experiment results show that the camera calibration method presented here is both practical and accurate.

[1]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[2]  Andrew Zisserman,et al.  Combining scene and auto-calibration constraints , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[3]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[4]  Roger Y. Tsai,et al.  A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses , 1987, IEEE J. Robotics Autom..

[5]  David A. Forsyth,et al.  Class-based grouping in perspective images , 1995, Proceedings of IEEE International Conference on Computer Vision.

[6]  Joseph L. Mundy,et al.  Repeated Structures: Image Correspondence Constraints and 3D Structure Recovery , 1993, Applications of Invariance in Computer Vision.

[7]  Roger Y. Tsai,et al.  Techniques for calibration of the scale factor and image center for high accuracy 3D machine vision metrology , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[8]  Roger Y. Tsai,et al.  Techniques for Calibration of the Scale Factor and Image Center for High Accuracy 3-D Machine Vision Metrology , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Kenichi Kanatani,et al.  Statistical optimization for geometric computation - theory and practice , 1996, Machine intelligence and pattern recognition.

[10]  Andrew Zisserman,et al.  Recognizing general curved objects efficiently , 1992 .

[11]  Roberto Cipolla,et al.  Camera Calibration from Vanishing Points in Image of Architectural Scenes , 1999, BMVC.

[12]  J. Mundy,et al.  Recognition of plane projective symmetry , 1997, Proceedings of 40th Midwest Symposium on Circuits and Systems. Dedicated to the Memory of Professor Mac Van Valkenburg.

[13]  Andrew Zisserman,et al.  Quadric reconstruction from dual-space geometry , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[14]  O. Faugeras.  Three-dimensional computer vision: a geometric viewpoint , 1993 .