What is a camera?

This paper addresses the problem of characterizing a general class of cameras under reasonable, “linear” assumptions. Concretely, we use the formalism and terminology of classical projective geometry to model cameras by two-parameter linear families of straight lines-that is, degenerate reguli (rank-3 families) and non-degenerate linear congruences (rank-4 families). This model captures both the general linear cameras of Yu and McMillan and the linear oblique cameras of Pajdla. From a geometric perspective, it affords a simple classification of all possible camera configurations. From an analytical viewpoint, it also provides a simple and unified methodology for deriving general formulas for projection and inverse projection, triangulation, and binocular and trinocular geometry.

[1]  Robert C. Bolles,et al.  Epipolar-plane image analysis: An approach to determining structure from motion , 1987, International Journal of Computer Vision.

[2]  W. Freeman,et al.  Understanding Camera Trade-Offs through a Bayesian Analysis of Light Field Projections , 2008, ECCV.

[3]  H. Pottmann,et al.  Computational Line Geometry , 2001 .

[4]  Peter F. Sturm,et al.  Multi-view geometry for general camera models , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[5]  Rajiv Gupta,et al.  Linear pushbroom cameras , 1997 .

[6]  D. Hilbert,et al.  Geometry and the Imagination , 1953 .

[7]  Tomás Pajdla.  Stereo with Oblique Cameras , 2004, International Journal of Computer Vision.

[8]  Paul Rademacher,et al.  Multiple-center-of-projection images , 1998, SIGGRAPH.

[9]  Peter F. Sturm,et al.  General Imaging Geometry for Central Catadioptric Cameras , 2008, ECCV.

[10]  Jean Ponce,et al.  On the absolute quadratic complex and its application to autocalibration , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[11]  Leonard McMillan,et al.  General Linear Cameras , 2004, ECCV.

[12]  Daphna Weinshall,et al.  Mosaicing New Views: The Crossed-Slits Projection , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Steven M. Seitz,et al.  The Space of All Stereo Images , 2004, International Journal of Computer Vision.

[14]  Alain Dandurand.  The Rigidity of Compound Spatial Grids , 1984 .

[15]  Daphna Weinshall,et al.  On the epipolar geometry of the Crossed-Slits projection , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.