This paper describes a noise resistant algorithm for recovering the three-dimensional motion of a rigid object from optical flow. First, it is shown that in the absence of noise three-demensional motion can be obtained exactly by a linear algorithm except in the special case in which the surface of the object is on a general quadratic surface passing through the viewpoint, and the normal vector of the surface at the viewpoint is perpendicular to the translation velocity vector. In the presence of noise, an evaluation function is introduced based on the least squares method. It is shown, however, that the solution which minimizes the evaluation function is not always optimal due to statistical bias. To deal with this problem, a method to eliminate the statistical bias in the evaluation function is proposed for zero mean white noise. Once the statistical bias is eliminated, the solution of the linear algorithm coincides with the correct solution by means of expectation. In this linear algorithm, only the eigenvector corresponding to the zero eigenvalue of a 3
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Norio TAGAWA, Takashi TORIU, Toshio ENDOH, "Un-Biased Linear Algorithm for Recovering Three-Dimensional Motion from optical Flow" in IEICE TRANSACTIONS on Information,
vol. E76-D, no. 10, pp. 1263-1275, October 1993, doi: .
Abstract: This paper describes a noise resistant algorithm for recovering the three-dimensional motion of a rigid object from optical flow. First, it is shown that in the absence of noise three-demensional motion can be obtained exactly by a linear algorithm except in the special case in which the surface of the object is on a general quadratic surface passing through the viewpoint, and the normal vector of the surface at the viewpoint is perpendicular to the translation velocity vector. In the presence of noise, an evaluation function is introduced based on the least squares method. It is shown, however, that the solution which minimizes the evaluation function is not always optimal due to statistical bias. To deal with this problem, a method to eliminate the statistical bias in the evaluation function is proposed for zero mean white noise. Once the statistical bias is eliminated, the solution of the linear algorithm coincides with the correct solution by means of expectation. In this linear algorithm, only the eigenvector corresponding to the zero eigenvalue of a 3
URL: https://global.ieice.org/en_transactions/information/10.1587/e76-d_10_1263/_p
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@ARTICLE{e76-d_10_1263,
author={Norio TAGAWA, Takashi TORIU, Toshio ENDOH, },
journal={IEICE TRANSACTIONS on Information},
title={Un-Biased Linear Algorithm for Recovering Three-Dimensional Motion from optical Flow},
year={1993},
volume={E76-D},
number={10},
pages={1263-1275},
abstract={This paper describes a noise resistant algorithm for recovering the three-dimensional motion of a rigid object from optical flow. First, it is shown that in the absence of noise three-demensional motion can be obtained exactly by a linear algorithm except in the special case in which the surface of the object is on a general quadratic surface passing through the viewpoint, and the normal vector of the surface at the viewpoint is perpendicular to the translation velocity vector. In the presence of noise, an evaluation function is introduced based on the least squares method. It is shown, however, that the solution which minimizes the evaluation function is not always optimal due to statistical bias. To deal with this problem, a method to eliminate the statistical bias in the evaluation function is proposed for zero mean white noise. Once the statistical bias is eliminated, the solution of the linear algorithm coincides with the correct solution by means of expectation. In this linear algorithm, only the eigenvector corresponding to the zero eigenvalue of a 3
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Un-Biased Linear Algorithm for Recovering Three-Dimensional Motion from optical Flow
T2 - IEICE TRANSACTIONS on Information
SP - 1263
EP - 1275
AU - Norio TAGAWA
AU - Takashi TORIU
AU - Toshio ENDOH
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E76-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1993
AB - This paper describes a noise resistant algorithm for recovering the three-dimensional motion of a rigid object from optical flow. First, it is shown that in the absence of noise three-demensional motion can be obtained exactly by a linear algorithm except in the special case in which the surface of the object is on a general quadratic surface passing through the viewpoint, and the normal vector of the surface at the viewpoint is perpendicular to the translation velocity vector. In the presence of noise, an evaluation function is introduced based on the least squares method. It is shown, however, that the solution which minimizes the evaluation function is not always optimal due to statistical bias. To deal with this problem, a method to eliminate the statistical bias in the evaluation function is proposed for zero mean white noise. Once the statistical bias is eliminated, the solution of the linear algorithm coincides with the correct solution by means of expectation. In this linear algorithm, only the eigenvector corresponding to the zero eigenvalue of a 3
ER -