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Toshio ENDOH, Takashi TORIU, Norio TAGAWA, "A Superior Estimator to the Maximum Likelihood Estimator on 3-D Motion Estimation from Noisy Optical Flow" in IEICE TRANSACTIONS on Information,
vol. E77-D, no. 11, pp. 1240-1246, November 1994, doi: .
Abstract: We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.
URL: https://global.ieice.org/en_transactions/information/10.1587/e77-d_11_1240/_p
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@ARTICLE{e77-d_11_1240,
author={Toshio ENDOH, Takashi TORIU, Norio TAGAWA, },
journal={IEICE TRANSACTIONS on Information},
title={A Superior Estimator to the Maximum Likelihood Estimator on 3-D Motion Estimation from Noisy Optical Flow},
year={1994},
volume={E77-D},
number={11},
pages={1240-1246},
abstract={We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.},
keywords={},
doi={},
ISSN={},
month={November},}
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TY - JOUR
TI - A Superior Estimator to the Maximum Likelihood Estimator on 3-D Motion Estimation from Noisy Optical Flow
T2 - IEICE TRANSACTIONS on Information
SP - 1240
EP - 1246
AU - Toshio ENDOH
AU - Takashi TORIU
AU - Norio TAGAWA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E77-D
IS - 11
JA - IEICE TRANSACTIONS on Information
Y1 - November 1994
AB - We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.
ER -