Can We Consider Central Catadioptric Cameras and Fisheye Cameras within a Unified Imaging Model

There are two kinds of omnidirectional cameras often used in computer vision: central catadioptric cameras and fisheye cameras. Previous literatures use different imaging models to describe them separately. A unified imaging model is however presented in this paper. The unified model in this paper can be considered as an extension of the unified imaging model for central catadioptric cameras proposed by Geyer and Daniilidis. We show that our unified model can cover some existing models for fisheye cameras and fit well for many actual fisheye cameras used in previous literatures. Under our unified model, central catadioptric cameras and fisheye cameras can be classified by the model’s characteristic parameter, and a fisheye image can be transformed into a central catadioptric one, vice versa. An important merit of our new unified model is that existing calibration methods for central catadioptric cameras can be directly applied to fisheye cameras. Furthermore, the metric calibration from single fisheye image only using projections of lines becomes possible via our unified model but the existing methods for fisheye cameras in the literatures till now are all non-metric under the same conditions. Experimental results of calibration from some central catadioptric and fisheye images confirm the validity and usefulness of our new unified model.

[1]  Sing Bing Kang,et al.  Radial Distortion Snakes , 2001, MVA.

[2]  Tomás Svoboda,et al.  Epipolar Geometry of Panoramic Cameras , 1998, ECCV.

[3]  Shree K. Nayar,et al.  Stereo with mirrors , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[4]  Andrew W. Fitzgibbon,et al.  Direct Least Square Fitting of Ellipses , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Zhengyou Zhang,et al.  Parameter estimation techniques: a tutorial with application to conic fitting , 1997, Image Vis. Comput..

[6]  Jake K. Aggarwal,et al.  Intrinsic parameter calibration procedure for a (high-distortion) fish-eye lens camera with distortion model and accuracy estimation , 1996, Pattern Recognit..

[7]  Shree K. Nayar,et al.  A theory of catadioptric image formation , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[8]  Bernd Neumann,et al.  Computer Vision — ECCV’98 , 1998, Lecture Notes in Computer Science.

[9]  Kenro Miyamoto,et al.  Fish Eye Lens , 1964 .

[10]  Kostas Daniilidis,et al.  Catadioptric camera calibration , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[11]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[12]  Christopher M. Bishop,et al.  Non-linear Bayesian Image Modelling , 2000, ECCV.

[13]  Mads Nielsen,et al.  Computer Vision — ECCV 2002 , 2002, Lecture Notes in Computer Science.

[14]  Mongi A. Abidi,et al.  Efficient techniques for wide-angle stereo vision using surface projection models , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[15]  Kostas Daniilidis,et al.  Paracatadioptric Camera Calibration , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Andrew W. Fitzgibbon,et al.  Direct least squares fitting of ellipses , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[17]  Kenneth Turkowski,et al.  Creating image-based VR using a self-calibrating fisheye lens , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Helder Araújo,et al.  Geometric Properties of Central Catadioptric Line Images , 2002, ECCV.

[19]  Christian Bräuer-Burchardt,et al.  A new algorithm to correct fish-eye- and strong wide-angle-lens-distortion from single images , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[20]  Olivier D. Faugeras,et al.  Automatic calibration and removal of distortion from scenes of structured environments , 1995, Optics & Photonics.

[21]  Shree K. Nayar,et al.  Non-metric calibration of wide-angle lenses and polycameras , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[22]  Anup Basu,et al.  Alternative models for fish-eye lenses , 1995, Pattern Recognit. Lett..

[23]  Xianghua Ying,et al.  Catadioptric camera calibration using geometric invariants , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[24]  Kostas Daniilidis,et al.  A Unifying Theory for Central Panoramic Systems and Practical Applications , 2000, ECCV.

[25]  Andrew W. Fitzgibbon,et al.  Simultaneous linear estimation of multiple view geometry and lens distortion , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[26]  Tomás Pajdla,et al.  Estimation of omnidirectional camera model from epipolar geometry , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..