Local estimation of visual signal translation using modulated wavelet transforms

摘要

Abstract: In computational perception, `visual motion analysis' is most commonly identified with the problem of measuring the infinitesimal rate of translation at various local spatial neighborhoods in a time-varying signal. Many problems associated with measuring these motion vectors can be addressed by considering the following simplified one-dimensional case. Given two samples, an original function f$-o$/(x), and another sample f$-t$/(x) taken momentarily afterwards; compute the translation parameter $tau which provides a best-fit for the transformation model, T$-$tau$/ : f$-o$/(x) $YLD f$-t$/(x) $EQ f$-o$/(x $PLU $tau@) over some finite local region. The `goodness' of this fit requires evaluation by a suitable performance metric since measurement uncertainty and added noise will corrupt the solution of $tau@. This error can be reduced if the measurement is supported by a wider spatial region. However, the `pure translation' model is usually only valid within some small local neighborhood. These two competing constraints inherently compromise the measurement process. In this paper, a new technique is developed for estimating this translation parameter using a localized (`wavelet') representation, and it provides a measure of the uncertainty of the resulting estimate. In addition, a trade-off is identified between the local neighborhood width and the uncertainty of the translation estimate. It is similar to the well-known Heisenberg uncertainty principle: The product of the variances of the uncertainty of position and translation is bounded below by a finite constant. !9