Scaling theorems for zero crossings of bandlimited signals

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 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 Babaud et al. (1986), Yuille et al. (1986) and Wu-Xie (1990). An in-depth discussion of our theorems and the previously published ones is also given.