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Some Properties of the E Matrix in Two-View Motion Estimation
December 1989 (vol. 11 no. 12)
pp. 1310-1312

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.

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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
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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