A factorization method for affine structure from line correspondences

A family of structure from motion algorithms called the factorization method has been recently developed from the orthographic projection model to the affine camera model. All these algorithms are limited to handling only point features of the image stream. We propose in this paper an algorithm for the recovery of shape and motion from line correspondences by the factorization method with the affine camera. Instead of one step factorization for points, a multi-step factorization method is developed for lines based on the decomposition of the whole shape and motion into three separate substructures. Each of these substructures can then be linearly solved by factorizing the appropriate measurement matrices. It is also established that affine shape and motion with uncalibrated affine cameras can be achieved with at least seven lines over three views, which extends the previous results of Koenderink and Van Doorn (1989) for points to lines.

[1]  Amnon Shashua,et al.  Algebraic Functions For Recognition , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Thomas S. Huang,et al.  Estimation of rigid body motion using straight line correspondences , 1986, Comput. Vis. Graph. Image Process..

[3]  Richard I. Hartley,et al.  Projective reconstruction from line correspondences , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Andrew Zisserman,et al.  Motion From Point Matches Using Affine Epipolar Geometry , 1994, ECCV.

[5]  S. Ullman,et al.  The interpretation of visual motion , 1977 .

[6]  Daphna Weinshall,et al.  Linear and incremental acquisition of invariant shape models from image sequences , 1993, 1993 (4th) International Conference on Computer Vision.

[7]  O. Faugeras,et al.  About the correspondences of points between N images , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[8]  Thomas S. Huang,et al.  A linear algorithm for motion estimation using straight line correspondences , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[9]  Michel Dhome,et al.  Determination of the Attitude of 3D Objects from a Single Perspective View , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  J J Koenderink,et al.  Affine structure from motion. , 1991, Journal of the Optical Society of America. A, Optics and image science.

[11]  O. Faugeras.  Three-dimensional computer vision: a geometric viewpoint , 1993 .

[12]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[13]  T. Q. Phong,et al.  Optimal estimation of object pose from a single perspective view , 1993, 1993 (4th) International Conference on Computer Vision.

[14]  Takeo Kanade,et al.  A Paraperspective Factorization Method for Shape and Motion Recovery , 1994, ECCV.

[15]  Ian D. Reid,et al.  Recursive Affine Structure and Motion from Image Sequences , 1994, ECCV.

[16]  Peter F. Sturm,et al.  A Factorization Based Algorithm for Multi-Image Projective Structure and Motion , 1996, ECCV.

[17]  Thomas S. Huang,et al.  Finding point correspondences and determining motion of a rigid object from two weak perspective views , 1988, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  B. Triggs.  The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image , 1995 .