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Scale-space segmentation
Scale-space segmentation or multi-scale segmentation is a general framework for signal and image segmentation, based on the computation of image descriptors at multiple scales of smoothing.
==One-dimensional hierarchical signal segmentation==
Witkin's seminal work in scale space〔Witkin, A. P. "Scale-space filtering", Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, Germany,1019--1022, 1983.〕〔A. Witkin, "Scale-space filtering: A new approach to multi-scale description," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), vol. 9, San Diego, CA, Mar. 1984, pp. 150--153.〕 included the notion that a one-dimensional signal could be unambiguously segmented into regions, with one scale parameter controlling the scale of segmentation.
A key observation is that the zero-crossings of the second derivatives (minima and maxima of the first derivative or slope) of multi-scale-smoothed versions of a signal form a nesting tree, which defines hierarchical relations between segments at different scales. Specifically, slope extrema at coarse scales can be traced back to corresponding features at fine scales. When a slope maximum and slope minimum annihilate each other at a larger scale, the three segments that they separated merge into one segment, thus defining the hierarchy of segments.
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