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Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces

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2 Author(s)
Tsai, R.Y. ; Coordinated Science Laboratory and the Department of Electrical Engineering, University of Illinois, Urbana, IL 61801; IBM T. J. Watson Research Center, Yorktown Heights, NY 10598. ; Huang, Thomas S.

Two main results are established in this paper. First, we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces. The seven points should not be traversed by two planes with one plane containing the origin, nor by a cone containing the origin. Second, a set of ``essential parameters'' are introduced which uniquely determine the motion parameters up to a scale factor for the translations, and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points. The actual motion parameters can subsequently be determined by computing the singular value decomposition (SVD) of a 3×3 matrix containing the essential parameters.

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-6 ,  Issue: 1 )

Date of Publication:

Jan. 1984

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