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<p><b>Abstract</b>—Scale-space filtering is the only known method which provides a hierarchic signal description method by extracting features across a continuum of scales. One of its important characteristics is that it demands the filtering involved does not create generic features as the scale increases. It has been shown in [<ref rid="bibi03094" type="bib">4</ref>], [<ref rid="bibi03095" type="bib">5</ref>], [<ref rid="bibi03096" type="bib">6</ref>] that the Gaussian filter is unique in holding this remarkable property. This is in essence the so-called scaling theorem. In this paper, we propose two scaling theorems for band-limited signals. They are applicable to a broader class of signals and a bigger family of filtering kernels than in [<ref rid="bibi03094" type="bib">4</ref>], [<ref rid="bibi03095" type="bib">5</ref>],[<ref rid="bibi03096" type="bib">6</ref>]. An in-depth discussion of our theorems and the previously published ones is also given.</p>
Scaling theorems, zero crossings, Gaussian kernels, scale space, multiscale analysis, signal descriptions, bandlimited signals, Whittaker-Shannon sampling theorem, quadratic forms.
Vo Anh, Hung Tat Tsui, Ji Yu Shi, "Scaling Theorems for Zero Crossings of Bandlimited Signals", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 18, no. , pp. 309-320, March 1996, doi:10.1109/34.485558
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