A Linear Metric Reconstruction by Complex Eigen-Decomposition
Summary :
This paper proposes a linear algorithm for metric reconstruction from projective reconstruction. Metric reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The algorithm is applied to three different sets of real data and the results show a feasibility of the algorithm. Additionally, our comparison of results of the linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.
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- IEICE TRANSACTIONS on Information Vol.E84-D No.12 pp.1626-1632
- Publication Date
- 2001/12/01
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- Special Section PAPER (Special Issue on Machine Vision Applications)
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Yongduek SEO, Ki-Sang HONG, "A Linear Metric Reconstruction by Complex Eigen-Decomposition" in IEICE TRANSACTIONS on Information,
vol. E84-D, no. 12, pp. 1626-1632, December 2001, doi: .
Abstract: This paper proposes a linear algorithm for metric reconstruction from projective reconstruction. Metric reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The algorithm is applied to three different sets of real data and the results show a feasibility of the algorithm. Additionally, our comparison of results of the linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.
URL: https://global.ieice.org/en_transactions/information/10.1587/e84-d_12_1626/_p
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@ARTICLE{e84-d_12_1626,
author={Yongduek SEO, Ki-Sang HONG, },
journal={IEICE TRANSACTIONS on Information},
title={A Linear Metric Reconstruction by Complex Eigen-Decomposition},
year={2001},
volume={E84-D},
number={12},
pages={1626-1632},
abstract={This paper proposes a linear algorithm for metric reconstruction from projective reconstruction. Metric reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The algorithm is applied to three different sets of real data and the results show a feasibility of the algorithm. Additionally, our comparison of results of the linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.},
keywords={},
doi={},
ISSN={},
month={December},}
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TY - JOUR
TI - A Linear Metric Reconstruction by Complex Eigen-Decomposition
T2 - IEICE TRANSACTIONS on Information
SP - 1626
EP - 1632
AU - Yongduek SEO
AU - Ki-Sang HONG
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E84-D
IS - 12
JA - IEICE TRANSACTIONS on Information
Y1 - December 2001
AB - This paper proposes a linear algorithm for metric reconstruction from projective reconstruction. Metric reconstruction problem is equivalent to estimating the projective transformation matrix that converts projective reconstruction to Euclidean reconstruction. We build a quadratic form from dual absolute conic projection equation with respect to the elements of the transformation matrix. The matrix of quadratic form of rank 2 is then eigen-decomposed to produce a linear estimate. The algorithm is applied to three different sets of real data and the results show a feasibility of the algorithm. Additionally, our comparison of results of the linear algorithm to results of bundle adjustment, applied to sets of synthetic image data having Gaussian image noise, shows reasonable error ranges.
ER -
English
