A Geometric Interpretation of Weak-Perspective Motion

We present a geometric interpretation of the problem of motion recovery from three weak-perspective images. Our interpretation is based on reducing the problem of estimating the motion to a problem of finding triangles on a sphere whose angles are known. Using this geometric interpretation, a simple method to completely recover the motion parameters using three images is developed. The results of running the algorithm on real images are presented. In addition, we describe which of the various motion parameters can be recovered already from two images.

[1]  T. Kanade,et al.  A multi-body factorization method for motion analysis , 1995, ICCV 1995.

[2]  Ronen Basri,et al.  Recognition by Linear Combinations of Models , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

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

[4]  R. Basri Paraperspective Aane , 1994 .

[5]  C. W. Gear,et al.  Feature grouping in moving objects , 1994, Proceedings of 1994 IEEE Workshop on Motion of Non-rigid and Articulated Objects.

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

[7]  Yiannis Aloimonos,et al.  Perspective approximations , 1990, Image Vis. Comput..

[8]  L L Kontsevich,et al.  Pairwise comparison technique: a simple solution for depth reconstruction. , 1993, Journal of the Optical Society of America. A, Optics and image science.

[9]  Thomas S. Huang,et al.  Motion and structure from orthographic projections , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[10]  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.

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

[12]  Narendra Ahuja,et al.  Motion and Structure Factorization and Segmentation of Long Multiple Motion Image Sequences , 1992, ECCV.

[13]  Jan J. Koenderink,et al.  Solid shape , 1990 .

[14]  Toshiyuki Sakai,et al.  Obtaining Surface Orientation from Texels under Perspective Projection , 1981, IJCAI.