16 December 1992 Local estimation of visual signal translation using modulated wavelet transforms
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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 fo(x), and another sample ft(x) taken momentarily afterwards; compute the translation parameter (tau) which provides a best-fit for the transformation model, T(tau ) : fo(x) yields ft(x) equals fo(x + (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.
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Roy A. Eagleson, Roy A. Eagleson, } "Local estimation of visual signal translation using modulated wavelet transforms", Proc. SPIE 1766, Neural and Stochastic Methods in Image and Signal Processing, (16 December 1992); doi: 10.1117/12.130824; https://doi.org/10.1117/12.130824

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