Projective factorization of planes and cameras in multiple views

This paper proposes a novel method for the projective reconstruction of planes and cameras from multiple images by factorizing a matrix containing all planar homographies between a reference view and all other views. If some planes are not visible in all views an alternative method is presented which solves the problem in two steps: a) all camera centers are recovered simultaneously; b) all planes are reconstructed. The key idea of both methods is to specify one of the planes, which is visible in all views, as the plane at infinity. The methods were applied to synthetic and real data, where VRML models can be created with a small amount of user interaction.

[1]  O. Faugeras,et al.  The Geometry of Multiple Images , 1999 .

[2]  P. Anandan,et al.  About Direct Methods , 1999, Workshop on Vision Algorithms.

[3]  Richard Szeliski,et al.  Geometrically Constrained Structure from Motion: Points on Planes , 1998, SMILE.

[4]  Lihi Zelnik-Manor,et al.  Multi-view subspace constraints on homographies , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

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

[6]  Takeo Kanade,et al.  A unified factorization algorithm for points, line segments and planes with uncertainty models , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[7]  Bill Triggs,et al.  Plane+Parallax, Tensors and Factorization , 2000, ECCV.

[8]  Björn Johansson View synthesis and 3D reconstruction of piecewise planar scenes using intersection lines between the planes , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[9]  C. Rother,et al.  Linear multi view reconstruction and camera recovery , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[10]  Radu Horaud,et al.  Projective Structure and Motion from Two Views of a Piecewise Planar Scene , 2001, ICCV.

[11]  Amnon Shashua,et al.  The Rank 4 Constraint in Multiple (>=3) View Geometry , 1996, ECCV.

[12]  Bill Triggs,et al.  Factorization methods for projective structure and motion , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  A. Bartoli,et al.  Projective structure and motion from two views of a piecewise planar scene , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[14]  Harry Shum,et al.  A linear algorithm for camera self-calibration, motion and structure recovery for multi-planar scenes from two perspective images , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).