This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
3-D Pose from 3 Points Using Weak-Perspective
August 1994 (vol. 16 no. 8)
pp. 802-808

This correspondence discusses computing the pose of a model from three matching point pairs under weak-perspective projection. A new approach to the problem that is motivated geometrically is described. Like previous methods, the method here involves solving a biquadratic equation, but here the biquadratic's solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which leads to a simple expression for the image position of any unmatched model point.

[1] T.D. Alter, "Robust and Efficient 3-D Recognition by Alignment," MIT Artificial Intell. Lab. TR 1410, 1992.
[2] M. Costa, R. M. Haralick, and L. G. Shapiro, "Optimal affine-invariant point matching," inProc. Sixth Israeli Conf. on Artificial Intell., 1990, pp. 35-61.
[3] D. Cyganski, and J. Orr, "Object recognition and orientation determination by tensor methods,"Advances in Computer Vision and Image Processing, vol. 3, T. Huang, Ed. Greenwich, CT: Jai Press, 1988.
[4] M. A. Fischler and R. C. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,"Commun. ACM, vol. 24, no. 6, pp. 381-395, 1981.
[5] Graustein, W. C.,Introduction to Higher Geometry. New York: Macmillan {\.\.}, 1930.
[6] W. E. L. Grimson, D. P. Huttenlocher, and T. D. Alter, "Recognizing 3-D Objects from 2-D Images: An Error Analysis," inProc. IEEE Conf. Comput. Vision Pattern Recognit., 1992.
[7] B. K. P. Horn, "Closed-form solution of absolute orientation using unit quaternions,"J. Opt. Soc. Am., vol. 4, no. 4, Apr. 1987.
[8] D.P. Huttenlocher and S. Ullman, "Object recognition using alignment," inProc. First Int. Conf. Comput. Vision, June 1987, pp. 102-111.
[9] D. P. Huttenlocher and S. Ullman, "Recognizing solid objects by alignment with an image,"J. Comput. Vision, vol. 5, no. 2, pp. 195-212, 1990.
[10] D. W. Jacobs, "Optimal matching of planar models in 3-D scenes," inProc. IEEE Conf. Comput. Vision Pattern Recognit., 1991, pp. 269-274.
[11] T. Kanade and J. R. Kender, "Mapping image properties into shape constraints: skew symmetry, affine-transformable patterns, and the shape-from-texture paradigm,"Human and Machine Vision, Beck, Hope, and Rosenfeld, Eds. New York: Academic Press, 1983.
[12] Y. Lamdan, J. T. Schwartz, and H. J. Wolfson, "Object recognition by affine invariant matching," inProc. CVPR 88, 1988.
[13] Y. Lamdan and H. Wolfson, "On the Error Analysis of Geometric Hashing,"Proc. Computer Vision 91 and Pattern Recognition Conf., Computer Society Press, Los Alamitos, Calif., Order No. 2148, 1991, pp. 22-27.
[14] S. Linnainmaa, D. Harwood, and L. S. Davis, "Pose determination of a three-dimensional object using triangle pairs,"IEEE Trans. Pattern Anal. Machine Intell., vol. 10, no. 5, pp. 634-647, Sept. 1988.
[15] I. Rigoutsos and R. Hummel, "Robust similarity invariant matching in the presence of noise," inEighth Israeli Conf. Artificial Intell. Comput. Vision, Tel Aviv, 1991.
[16] L. G. Roberts, "Machine perception of three-dimensional solids,"Optical and Electro-Optical Information Processing, J. T. Tippettet al., Eds. Cambridge, MA: MIT Press, 1965.
[17] D. Thompson and J. Mundy, "Three dimensional model matching from an unconstrained viewpoint,"Proc. Int. Conf. Robotics Automation, 1987, pp. 208-220.
[18] S. Ullman, and R. Basri, "Recognition by linear combinations of models,"IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 10, pp. 992-1006, Oct. 1991.

Index Terms:
image recognition; image sequences; geometry; 3-D pose; weak-perspective; matching point pairs; biquadratic equation; image position; unmatched model point
Citation:
T.D. Alter, "3-D Pose from 3 Points Using Weak-Perspective," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 802-808, Aug. 1994, doi:10.1109/34.308475
Usage of this product signifies your acceptance of the Terms of Use.