The 3D Line Motion Matrix and Alignment of Line Reconstructions

We study the problem of aligning two 3D line reconstructions expressed in Plucker line coordinates. We introduce the 6/spl times/6 3D line motion matrix that acts on Plucker coordinates in projective, affine or Euclidean space. We characterize its algebraic properties and its relation to the usual 4/spl times/4 point motion matrix, and propose various methods for estimating 3D motion from line correspondences, based on image-related and 3D cost functions. We assess the quality of the different estimation methods using simulated data and real images.

[1]  Olivier D. Faugeras,et al.  From projective to Euclidean reconstruction , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[2]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

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

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

[5]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using orthonormal matrices , 1988 .

[6]  Fadi Dornaika,et al.  Visually guided object grasping , 1998, IEEE Trans. Robotics Autom..

[7]  Olivier D. Faugeras,et al.  The critical sets of lines for camera displacement estimation: A mixed Euclidean-projective and constructive approach , 1993, 1993 (4th) International Conference on Computer Vision.

[8]  Olivier D. Faugeras,et al.  Tracking and grouping 3D line segments , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[9]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Philip E. Gill,et al.  Practical optimization , 1981 .

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

[12]  Thierry Viéville,et al.  Canonical Representations for the Geometries of Multiple Projective Views , 1996, Comput. Vis. Image Underst..

[13]  Olivier D. Faugeras,et al.  Determination of Camera Location from 2-D to 3-D Line and Point Correspondences , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Thomas Buchanan,et al.  Critical Sets for 3D Reconstruction Using Lines , 1992, ECCV.

[15]  Olivier D. Faugeras,et al.  On the geometry and algebra of the point and line correspondences between N images , 1995, Proceedings of IEEE International Conference on Computer Vision.

[16]  Radu Horaud,et al.  Finding the Collineation between Two Projective Reconstructions , 1999, Comput. Vis. Image Underst..

[17]  Radu Horaud,et al.  Motion-Egomotion Discrimination and Motion Segmentation from Image-Pair Streams , 2000, Comput. Vis. Image Underst..

[18]  Olivier D. Faugeras,et al.  Determination of camera location from 2D to 3D line and point correspondences , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[19]  Cordelia Schmid,et al.  Automatic line matching across views , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[20]  Gregory D. Hager,et al.  X Vision: A Portable Substrate for Real-Time Vision Applications , 1998, Comput. Vis. Image Underst..

[21]  David J. Kriegman,et al.  Structure and Motion from Line Segments in Multiple Images , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Andrew Zisserman,et al.  Metric rectification for perspective images of planes , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[23]  Radu Horaud,et al.  Stereo Calibration from Rigid Motions , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Olivier D. Faugeras,et al.  Determining motion from 3D line segment matches: a comparative study , 1991, Image Vis. Comput..

[25]  Zhengyou Zhang.  Estimating Motion and Structure from Correspondences of Line Segments between Two Perspective Images , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Radu Horaud,et al.  Visual Servoing from Lines , 2002, Int. J. Robotics Res..