Projective rectification without epipolar geometry

We present a novel algorithm performing projective rectification which does not require explicit computation of the epipolar geometry and specifically of the fundamental matrix. Instead of finding the epipoles and computing two homographies mapping the epipoles to infinity, as done in recent work on projective rectification, we exploit the fact that the fundamental matrix of a pair of rectified images has a particular, known form. This allows us to set up a minimization that yields the rectifying, homographies directly from image correspondences. Experimental results show that our method works quite robustly even in the presence of noise, and with inaccurate point correspondences. The code of our implementation will be made available at the author's web site.

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

[2]  Tim J. Dennis,et al.  Epipolar line estimation and rectification for stereo image pairs , 1996, IEEE Trans. Image Process..

[3]  S. P. Mudur,et al.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[4]  Richard I. Hartley,et al.  In Defense of the Eight-Point Algorithm , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  S. B. Kang,et al.  An Active Multibaseline Stereo System with Real-Time Image Acquisition , 1994 .

[6]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[7]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[8]  Richard Szeliski,et al.  Hierarchical spline-based image registration , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[9]  Steven M. Seitz,et al.  View morphing , 1996, SIGGRAPH.

[10]  C. A. HART,et al.  Manual of Photogrammetry , 1947, Nature.

[11]  Emanuele Trucco,et al.  Rectification with unconstrained stereo geometry , 1997, BMVC.

[12]  Nicholas Ayache,et al.  Artificial vision for mobile robots - stereo vision and multisensory perception , 1991 .

[13]  M. Hebert,et al.  Applications of Non-Metric Vision to some Visually Guided Robotics Tasks , 1995 .

[14]  Charles Hansen,et al.  Rectification of images for binocular and trinocular stereovision , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[15]  George Wolberg,et al.  Digital image warping , 1990 .