Single-Image Calibration of Off-Axis Catadioptric Cameras Using Lines

We present a novel calibration method for off-axis catadioptric cameras, i.e. standard perspective cameras placed in a generic position w.r.t. an axial-symmetric mirror of unknown shape. The proposed method estimates the intrinsic parameters of the natural perspective camera, the 3D shape of the mirror and its pose w.r.t. the camera. The peculiarity of our approach is that, unlike several other calibration methods, we do not require any cross section of the mirror to be visible in the image. Instead, we require that the catadioptric image contains at least the image of one generic space line. We then derive some constraints that, combined with the harmonic homology relating the apparent contours of the mirror, allow us to calibrate the off-axis camera. We provide experimental results both on synthetic and camera images that prove the validity of the technique.

[1]  James E. pLebensohn.  Geometry and the Imagination , 1952 .

[2]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Yasushi Yagi,et al.  Omnidirectional imaging with hyperboloidal projection , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[4]  Kenichi Kanatani,et al.  Geometric computation for machine vision , 1993 .

[5]  Seth J. Teller,et al.  Determining the Lines Through Four Lines , 1999, J. Graphics, GPU, & Game Tools.

[6]  Zhanyi Hu,et al.  Planar conic based camera calibration , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[7]  Sing Bing Kang,et al.  Catadioptric self-calibration , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[8]  Daniel G. Aliaga.  Accurate catadioptric calibration for real-time pose estimation in room-size environments , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

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

[10]  Ryad Benosman,et al.  Calibration of panoramic catadioptric sensors made easier , 2002, Proceedings of the IEEE Workshop on Omnidirectional Vision 2002. Held in conjunction with ECCV'02.

[11]  Shree K. Nayar,et al.  A Theory of Single-Viewpoint Catadioptric Image Formation , 1999, International Journal of Computer Vision.

[12]  Qian Chen,et al.  Camera Calibration with Two Arbitrary Coplanar Circles , 2004, ECCV.

[13]  Xianghua Ying,et al.  Linear Catadioptric Camera Calibration from Sphere Images , 2005 .

[14]  Alberto Del Bimbo,et al.  Metric 3D reconstruction and texture acquisition of surfaces of revolution from a single uncalibrated view , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Hongbin Zha,et al.  Simultaneously calibrating catadioptric camera and detecting line features using Hough transform , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Masahiko Yachida,et al.  Calibration Method for Misaligned Catadioptric Camera , 2006, IEICE Trans. Inf. Syst..

[17]  Vincenzo Caglioti,et al.  "How many planar viewing surfaces are there in noncentral catadioptric cameras?" Towards singe-image localization of space lines , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[18]  Douglas Lanman,et al.  Reconstructing a 3D Line from a Single Catadioptric Image , 2006, Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06).

[19]  Vincenzo Caglioti,et al.  Methods for space line localization from single catadioptric images: new proposals and comparisons , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[20]  Vincenzo Caglioti,et al.  Determining Radius and Position of a Sphere from a Single Catadioptric Image , 2008, J. Intell. Robotic Syst..