The objective of this paper is to introduce a fourth-order cost functi
on of the displaced frame difference (DFD) capable of estimating motio
n even for small regions or blocks. Using higher than second-order sta
tistics is appropriate in case the image sequence is severely corrupte
d by additive Gaussian noise. Some results are presented and compared
to those obtained from the mean kurtosis and the mean square error of
the DFD.