Various derivatives (1st to 4th order) describe different signal characters in scale space: the first derivative represents signal variation which can be used for coding; the second derivative characterizes the size of signal local structure and can be used for adaptive smoothing; the third and fourth order derivatives relate zero-crossing(or other features) contour in scale space to a differential equation which can be used for feature tracking and make quantitative measurements of zero-crossing properties possible. In the case that different derivatives are calculated by a special class of derivative filters, all the derivative signals can be treated in the same way.