DYADIC SCALE-SPACE

In this paper, we first approximate the Gaussian function with any sca le by the linear finite combination of Gaussian functions with dyadic scale; consequently, the scale space can be constructed much more effi ciently: we only perform smoothing at these dyadic scales and the smoo thed signals at other scales can be found by calculating linear combin ations of these discrete scale signals. We show that the approximation error is so small that our approach can be used in most of the comput er vision fields. We analyse the behavior of zero-crossing (ZC) across scales and show that features at any scale can be found efficiently b y tracking from the dyadic scales, thus we show that the new represent ation is necessary and complete. In the case that the derivatives are calculated by a special multiscale filter, we show that all the deriva tive signals can be treated in the same way. Copyright (C) 1997 Patter n Recognition Society.