Scale-space filtering: A new approach to multi-scale description

TLDR

Scale-space filtering provides a qualitative signal description that resolves the scale‑selection problem by capturing extrema across all scales. The method expands the signal with Gaussian convolution over a continuum of sizes, collapses the resulting scale‑space image into a tree that preserves qualitative structure at every scale, and refines this tree with a stability criterion to highlight events that persist across large changes in scale.

Abstract

The extrema in a signal and its first few derivatives provide a useful general purpose qualitative description for many kinds of signals. A fundamental problem in computing such descriptions is scale: a derivative must be taken over some neighborhood, but there is seldom a principled basis for choosing its size. Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way. The signal is first expanded by convolution with gaussian masks over a continuum of sizes. This "scale-space" image is then collapsed, using its qualitative structure, into a tree providing a concise but complete qualitative description covering all scales of observation. The description is further refined by applying a stability criterion, to identify events that persist of large changes in scale.