Some Properties of the E Matrix in Two-View Motion Estimation

T. S. Huang; O. D. Faugeras

doi:10.1109/34.41368

Some Properties of the E Matrix in Two-View Motion Estimation

T. S. Huang, O. D. Faugeras

Research output: Contribution to journal › Article › peer-review

Abstract

In the eight-point linear algorithm for determining 3-D motion/structure from two perspective views using point correspondences, the E matrix occupies a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. In this correspondence, we show that a necessary and sufficient condition for a 3 x 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 also presented. Finally, some applications are briefly described.

Original language	English (US)
Pages (from-to)	1310-1312
Number of pages	3
Journal	IEEE transactions on pattern analysis and machine intelligence
Volume	11
Issue number	12
DOIs	https://doi.org/10.1109/34.41368
State	Published - Dec 1989
Externally published	Yes

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/34.41368

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abstract = "In the eight-point linear algorithm for determining 3-D motion/structure from two perspective views using point correspondences, the E matrix occupies a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. In this correspondence, we show that a necessary and sufficient condition for a 3 x 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 also presented. Finally, some applications are briefly described.",

author = "Huang, {T. S.} and Faugeras, {O. D.}",

note = "Funding Information: Manuscript received April 25, 1988; revised March 31, 1989. Recommended for acceptance by W. B. Thompson. This work was supported by the National Science Foundation under Grant IRI-8605400. T. S. Huang is with the Coordinated Science Laboratory, University of Illinois, Urbana, IL 61801. 0. D. Faugeras is with the INRIA Sophia-Antipolis, F-06565 Val-bonne, France. IEEE Log Number 8929960.",

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N2 - In the eight-point linear algorithm for determining 3-D motion/structure from two perspective views using point correspondences, the E matrix occupies a central role. The E matrix is defined as a skew-symmetrical matrix (containing the translation components) postmultiplied by a rotation matrix. In this correspondence, we show that a necessary and sufficient condition for a 3 x 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 also presented. Finally, some applications are briefly described.

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Some Properties of the E Matrix in Two-View Motion Estimation

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