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Some Properties of the E Matrix in Two-View Motion Estimation
December 1989 (vol. 11 no. 12)
pp. 1310-1312
ASCII Text
x 
 
T.S. Huang, O.D. Faugeras, "Some Properties of the E Matrix in Two-View Motion Estimation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1310-1312, December, 1989.
 
 
BibTex
x
 
@article{ 10.1109/34.41368,
author = {T.S. Huang and O.D. Faugeras},
title = {Some Properties of the E Matrix in Two-View Motion Estimation},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {11},
number = {12},
issn = {0162-8828},
year = {1989},
pages = {1310-1312},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.41368},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Some Properties of the E Matrix in Two-View Motion Estimation
IS - 12
SN - 0162-8828
SP1310
EP1312
EPD - 1310-1312
A1 - T.S. Huang,
A1 - O.D. Faugeras,
PY - 1989
KW - picture processing; pattern recognition; 3D motion determination; structure determination; two-view motion estimation; eight-point linear algorithm; E matrix; skew-symmetrical matrix; translation components; rotation matrix; necessary and sufficient condition; matrix algebra; pattern recognition; picture processing
VL - 11
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

In the eight-point linear algorithm for determining 3D motion/structure from two perspective views using point correspondences, the E matrix plays a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. The authors show that a necessary and sufficient condition for a 3*3 matrix to be so decomposable is that one of its singular values is zero and the other two are equal. Several other forms of this property are presented. Some applications are briefly described.

[1] H. C. Longuet-Higgins, "A computer program for reconstructing a scene from two projections,"Nature, vol. 392, pp. 133-135, 1981.
[2] R. Y. Tsai and T. S. Huang, "Uniqueness and estimation of 3-D motion parameters of rigid bodies with curved surfaces,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 13-27, Jan. 1984.
[3] O. D. Faugeras, F. Lustman, and G. Toscani, "Motion and structure from motion from point and line matches," inProc. 1st ICCV, London, England, June 1987.
[4] J. Weng, T. S. Huang, and N. Ahuja, "Error analysis of motion parameters determination from image sequences," inProc. 1st ICCV, London, England, June 1987.
[5] C. Braccini, private communication to O. D. Faugeras, Feb. 1987.
[6] H. C. Longuet-Higgins, private communication to T. S. Huang, Jan. 29, 1987.
[7] T. S. Huang and Y. S. Shim, "Linear algorithm for motion estimation: How to handle degenerate cases," Coord. Sci. Lab., Univ. Illinois, Urbana, Tech. Note ISP-102, Nov. 30, 1986.
[8] H. C. Longuet-Higgins, private communication to T. S. Huang, Mar. 23, 1987.
[9] A. Netravali, T. S. Huang, R. Holt, and A. S. Krishnakumar, "Algebraic methods in 3-D motion estimation from two-view point correspondences,"Int. J. Imaging Syst. Technol., to be published.
[10] C. Braccini, G. Gambardella, A. Grattarola, and S. Zappatore, "Motion estimation of rigid bodies: Effects of the rigidity constraints," inProc. EUSIPCO-86, The Hague, The Netherlands, Sept. 1986.

Index Terms:
picture processing; pattern recognition; 3D motion determination; structure determination; two-view motion estimation; eight-point linear algorithm; E matrix; skew-symmetrical matrix; translation components; rotation matrix; necessary and sufficient condition; matrix algebra; pattern recognition; picture processing
Citation:
T.S. Huang, O.D. Faugeras, "Some Properties of the E Matrix in Two-View Motion Estimation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1310-1312, Dec. 1989, doi:10.1109/34.41368
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