Scaling theorems for zero crossings of bandlimited signals
Vo Anh
Ji Yu Shi
Hung Tat Tsui
Sch. of Math., Queensland Univ., Brisbane, Qld. ;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Mar 1996
Volume: 18,
Issue: 3
On page(s): 309-320
ISSN: 0162-8828
References Cited: 21
CODEN: ITPIDJ
INSPEC Accession Number: 5234465
Digital Object Identifier: 10.1109/34.485558
Current Version Published: 2002-08-06
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 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
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