An extended class of scale-invariant and recursive scale spacefilters
Pauwels, E.J.
van Gool, L.J.
Fiddelaers, P.
Moons, T.
ESAT-M12, Katholieke Univ., Leuven;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Jul 1995
Volume: 17,
Issue: 7
On page(s): 691-701
ISSN: 0162-8828
References Cited: 26
CODEN: ITPIDJ
INSPEC Accession Number: 5000960
Digital Object Identifier: 10.1109/34.391411
Current Version Published: 2002-08-06
Abstract
Explores how the functional form of scale space filters is
determined by a number of a priori conditions. In particular, if one
assumes scale space filters to be linear, isotropic convolution filters,
then two conditions (viz. recursivity and scale-invariance) suffice to
narrow down the collection of possible filters to a family that
essentially depends on one parameter which determines the qualitative
shape of the filter. Gaussian filters correspond to one particular value
of this shape-parameter. For other values the filters exhibit a more
complicated pattern of excitatory and inhibitory regions. This might
well be relevant to the study of the neurophysiology of biological
visual systems, for recent research shows the existence of extensive
disinhibitory regions outside the periphery of the classical
center-surround receptive field of LGN and retinal ganglion cells (in
cats). Such regions cannot be accounted for by models based on the
second order derivative of the Gaussian. Finally, the authors
investigate how this work ties in with another axiomatic approach of
scale space operators which focuses on the semigroup properties of the
operator family. The authors show that only a discrete subset of filters
gives rise to an evolution which can be characterized by means of a
partial differential equation
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