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Scaling Theorems for Zero Crossings of Bandlimited Signals
March 1996 (vol. 18 no. 3)
pp. 309-320

Abstract—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 [4], [5], [6] 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 [4], [5],[6]. An in-depth discussion of our theorems and the previously published ones is also given.

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Index Terms:
Scaling theorems, zero crossings, Gaussian kernels, scale space, multiscale analysis, signal descriptions, bandlimited signals, Whittaker-Shannon sampling theorem, quadratic forms.
Vo Anh, Ji Yu Shi, Hung Tat Tsui, "Scaling Theorems for Zero Crossings of Bandlimited Signals," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 309-320, March 1996, doi:10.1109/34.485558
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