Projective Structure and Motion from Two Views of a Piecewise Planar Scene

In this paper, we address the problem of structure and motion recovery from two views of a scene containing planes, i.e. sets of coplanar points. Most of the existing works do only exploit this constraint in a sub-optimal manner. We propose to parameterize the structure of such scenes with planes and points on planes and derive the MLE (Maximum Likelihood Estimator) using a minimal parameterization based on 2D entities. The result is the estimation of camera motion and 3D structure in projective space, that minimizes reprojection error, while satisfying the piecewise planarity. We propose a quasi-linear estimator that provides reliable initialization values for plane equations. Experimental results show that the reconstruction is of clearly superior quality compared to traditional methods based only on points, even if the scene is not perfectly piecewise planar.

[1]  Bill Triggs.  Optimal Estimation of Matching Constraints , 1998, SMILE.

[2]  Olivier D. Faugeras,et al.  Determining the fundamental matrix with planes: instability and new algorithms , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[3]  Radu Horaud,et al.  Structure and motion from two uncalibrated views using points on planes , 2001, Proceedings Third International Conference on 3-D Digital Imaging and Modeling.

[4]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[5]  William H. Press,et al.  Numerical recipes in C , 2002 .

[6]  Olivier Faugeras,et al.  Motion and Structure from Motion in a piecewise Planar Environment , 1988, Int. J. Pattern Recognit. Artif. Intell..

[7]  Thierry Viéville,et al.  Canonic Representations for the Geometries of Multiple Projective Views , 1994, ECCV.

[8]  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).

[9]  Quang-Tuan Luong.  Matrice fondamentale et autocalibration en vision par ordinateur , 1992 .

[10]  Jean-Philippe Tarel,et al.  A Generic Approach for Planar Patches Stereo Reconstruction , 1995 .

[11]  Thierry Viéville,et al.  Using Singular Displacements for Uncalibrated Monocular Visual Systems , 1996, ECCV.

[12]  S. Bougnoux,et al.  From projective to Euclidean space under any practical situation, a criticism of self-calibration , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

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

[14]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.