This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Geometric Interpretation of Weak-Perspective Motion
March 1999 (vol. 21 no. 3)
pp. 252-257

Abstract—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] Y. Aloimonos, "Perspective Approximations," Image and Vision Computing, vol. 8, no. 3, pp. 179-192, Aug. 1990.
[2] R. Basri, "Paraperspective = Affine," Int'l J. of Computer Vision, vol. 19, no. 2, pp. 169-179, Aug. 1996.
[3] J. Costeira and T. Kanade, "A Multi-Body Factorization Method for Motion Analysis," Int'l Conf. Computer Vision, pp. 1,071-1,076,Cambridge, Mass., June 1995.
[4] C. Debrunner and N. Ahuja, "Motion and Structure Factorization and Segmentation of Long Multiple Motion Image Sequences," Proc. European Conf. Computer Vision, 1992, pp. 217-221.
[5] M.A. Fischler and R.C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Graphics and Image Processing, vol. 24, no. 6, pp. 381–395, June 1981.
[6] W.C. Gear, "Feature Grouping in Moving Objects," IEEE Workshop on Non-Rigid and Articulate Motion, 1994.
[7] T.S. Huang and C.H. Lee, "Motion and Structure From Orthographic Projections," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 536-540, 1989.
[8] J. Koënderink, Solid Shape. Cambridge, Mass.: MIT Press, 1991.
[9] L.L. Kontsevich, "Pairwise Comparison Technique: A Simple Solution for Depth Reconstruction," J. Optical Soc. of Am., vol. 10, no. 6, pp. 1,129-1,135, June 1993.
[10] C-H. Lee and T.S. Huang, "Finding Point Correspondences and Determining Motion of a Rigid Object from Two Weak Perspective Views," Comp. Vis. Graph. and Image Processing, vol. 52, no. 3, pp. 309-327, Mar. 1990.
[11] Y. Ohta and K. Maenobu, and T. Sakai, "Obtaining Surface Orientation From Texels Under Perspective Projection," Proc. Int'l Joint Conf. Artificial Intelligence, 1981, pp. 746-751.
[12] C. Poelman and T. Kanade, A Paraperspective Factorization Method for Shape and Motion Recovery IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 3, pp. 206-219, Mar. 1997.
[13] L.S. Shaprio, A. Zisserman, and M. Brady, "3D Motion Recovery Via Affine Epipolar Geometry," Int'l J. Computer Vision, vol. 16, pp. 147-182, 1995.
[14] C. Tomasi and T. Kanade, "Shape and Motion From Image Streams Under Orthography: A Factorization Method," Int'l J. Computer Vision, vol. 9, no. 2, pp. 137-154, 1992.
[15] S. Ullman, The Interpretation of Visual Motion.Cambridge, Mass.: M.I.T. Press, 1979.
[16] S. Ullman and R. Basri, "Recognition by Linear Combinations of Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 992-1006, 1991.

Index Terms:
Weak-perspective projection, structure from motion.
Citation:
Ilan Shimshoni, Ronen Basri, Ehud Rivlin, "A Geometric Interpretation of Weak-Perspective Motion," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 252-257, March 1999, doi:10.1109/34.754615
Usage of this product signifies your acceptance of the Terms of Use.