Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects
Tsai, Roger Yen-Luen
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https://hdl.handle.net/2142/69229
Description
Title
Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects
Author(s)
Tsai, Roger Yen-Luen
Issue Date
1982
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Abstract
In this thesis, several fundamental breakthroughs have been made on the uniqueness and estimation of 3-D motion parameters of rigid objects, both on theoretical and computational aspects. When the object surface is restricted to be planar, we show that given two image frames, one can determine uniquely eight "pure parameters" which are nonlinear functions of the actual motion parameters. There are two different ways to estimate these pure parameters. The first is the direct method and the second, two-step method. The direct method does not require estimating the point correspondences first, while the two-step method does. Both entail linear equation solving only. Given the pure parameters, it is shown theoretically that there are two distinct solutions for the motion parameters in general. The motion parameters can be estimated by computing the singular value decomposition of a 3 x 3 matrix. The solution would be unique if three distinct frames are given. For the curved surface case, it is shown 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. 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 x 3 matrix containing the essential parameters. No nonlinear equations need be solved.
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