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Motion and structure from point correspondences: a
robust algorithm for planar case with error estimation
J.
Weng, N. Ahuja and T. Huang
The problem of determining motion and structure for a planar surface and
the error estimation are discussed. Since the motion of a planar patch is a
degenerate case for linear algorithms (algorithms that consist of solving
mainly linear equations and give a closed-form solution) for general
surfaces, the motion of such a planar surface is considered separately. An
algorithm is introduced that gives a closed-form solution to motion
parameters using monocular perspective images of the points on a planar
surface. The algorithm is simpler and more reliable, in the presence of
noise, than existing ones. There are generally two solutions for two image
frames. For three image frames the solution is generally unique. An approach
is proposed to test whether the points are coplanar. The errors in the motion
parameters and surface structure can be estimated for each pair of images.
Specifically, the standard deviation of the errors is calculated in terms of
the variance of the errors in the image coordinates. This approach to
estimating errors is applicable to least-squares, pseudo-inverse and eigenvalue-eigenvector problems.
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