Local estimation of visual signal translation using modulated wavelet transforms

Roy A. Eagleson

doi:10.1117/12.130824

16 December 1992 Local estimation of visual signal translation using modulated wavelet transforms

Roy A. Eagleson

Proceedings Volume 1766, Neural and Stochastic Methods in Image and Signal Processing; (1992) https://doi.org/10.1117/12.130824
Event: San Diego '92, 1992, San Diego, CA, United States

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) yields f_t(x) equals f_o(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.

Citation Download Citation

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); https://doi.org/10.1117/12.130824

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KEYWORDS

Signal processing

Image processing

Modulation

Stochastic processes

Visualization

Wavelets

Wavelet transforms

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