Scale space filtering

An initial description ought to be as compact as possible, and its elements should correspond as closely as possible to meaningful objects or events in the signal-forming process. Frequently, local extrema in the signal and its derivatives-- and intervals bounded by extrema--are particularly appropriate descriptive primitives: although local and closely tied to the signal data, these events often have direct semantic interpretations, e.g. as edges in images. A description that characterizes a signal by its extrema and those of its first few derivatives is a qualitative description of exactly the kind we were taught to use in elementary calculus to "sketch" a function. A great deal of effort has been expended to obtain this kind of primitive qualitative description (for overviews of this literature, see [1,2,3].) and the problem has proved extremely difficult. The problem of scale has emerged consistently as a fundamental source of difficulty, because the events we perceive and find meaningful vary enormously in size and extent. The problem is not so much to eliminate fine-scale noise, as to separate events at different scales arising from distinct physical processes.[4]