On significant maxima detection: a fine-to-coarse algorithm

We suggest two efficient algorithms for the detection of ‘perceptual significance’ among the local maxima of a 1-d signal. For an input function f(x) and an integer n, the first algorithm finds the n most significant maxima of f(x). The second algorithm finds all significant maxima of f(x), irrespective of their number. We represent an input signalf(x) as aG-graphG(f(x)), the vertices of which represent the ‘lumps’ of the graph of f(x). G(f(x)) is gradually reduced via a ‘small leaf ’ trimming procedure, resulting in a sequence of graphs that give a hierarchy of representations of f(x) such that the leaves of ‘deeper’ graphs correspond to more significant maxima of f(x). Based on this hierarchy, we introduce a measure of ‘perceptual significance’ among the maxima of f(x). Experimental results are presented.