A Superior Estimator to the Maximum Likelihood Estimator on 3-D Motion Estimation from Noisy Optical Flow

Toshio ENDOH  Takashi TORIU  Norio TAGAWA  

IEICE TRANSACTIONS on Information and Systems   Vol.E77-D   No.11   pp.1240-1246
Publication Date: 1994/11/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Computer Vision)
computer vision,  motion analysis,  optical flow,  maximum likelihood estimation,  covariance matrix,  

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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.