Structure and motion from uncalibrated catadioptric views

In this paper we present a new algorithm for structure from motion from point correspondences in images taken from uncalibrated catadioptric cameras with parabolic mirrors. We assume that the unknown intrinsic parameters are three: the combined focal length of the mirror and lens and the intersection of the optical axis with the image. We introduce a new representation for images of points and lines in catadioptric images which we call the circle space. This circle space includes imaginary circles, one of which is the image of the absolute conic. We formulate the epipolar constraint in this space and establish a new 4/spl times/4 catadioptric fundamental matrix. We show that the image of the absolute conic belongs to the kernel of this matrix. This enables us to prove that Euclidean reconstruction is feasible from two views with constant parameters and from three views with varying parameters. In both cases, it is one less than the number of views necessary with perspective cameras.

[1]  Shree K. Nayar,et al.  Ego-motion and omnidirectional cameras , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[2]  Peter F. Sturm,et al.  Critical motion sequences for the self-calibration of cameras and stereo systems with variable focal length , 1999, Image Vis. Comput..

[3]  Yasushi Yagi,et al.  Real-time omnidirectional image sensor (COPIS) for vision-guided navigation , 1994, IEEE Trans. Robotics Autom..

[4]  P. Sturm.  A method for 3D reconstruction of piecewise planar objects from single panoramic images , 2000, Proceedings IEEE Workshop on Omnidirectional Vision (Cat. No.PR00704).

[5]  Alfred M. Bruckstein,et al.  Omniview cameras with curved surface mirrors , 2000, Proceedings IEEE Workshop on Omnidirectional Vision (Cat. No.PR00704).

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

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

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

[10]  Shree K. Nayar,et al.  Catadioptric omnidirectional camera , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[11]  Olivier D. Faugeras,et al.  The geometry of multiple images - the laws that govern the formation of multiple images of a scene and some of their applications , 2001 .

[12]  Seth J. Teller,et al.  Automatic recovery of relative camera rotations for urban scenes , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[13]  D. Pedoe,et al.  Geometry, a comprehensive course , 1988 .

[14]  Anders Heyden,et al.  Euclidean reconstruction from image sequences with varying and unknown focal length and principal point , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[16]  Reinhard Koch,et al.  Self-Calibration and Metric Reconstruction Inspite of Varying and Unknown Intrinsic Camera Parameters , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[17]  J. Davenport.  Editor , 1960 .

[18]  Camillo J. Taylor.  Video Plus , 2000 .

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

[20]  H. Ishiguro,et al.  Panoramic Vision , 2001, Monographs in Computer Science.