Dyadic scale space

Abstract

In this paper, we first approximate the Gaussian function with any scale by the linear finite combination of Gaussian functions with dyadic scale; consequently, the scale space can be constructed much more efficiently: we only perform smoothing at these dyadic scales and the smoothed signals at other scales can be found by calculating linear combinations of these discrete scale signals. We show that the approximation error is so small that our approach can be used in most of the computer vision fields. We analyse the behavior of zero-crossing (ZC) across scales and show that features at any scale can be found efficiently by tracking from the dyadic scales, thus we show that the new representation is necessary and complete. In the case that the derivatives are calculated by a special multiscale filter, we show that all the derivative signals can be treated in the same way.