@InProceedings{bonmassar1994:geometric,
author = {Bonmassar, Giorgio and Schwartz, Eric L.},
title = {Geometric invariance in space-variant vision
systems: the exponential chirp transform},
editor = {Shmuel Peleg and Shimon Ullman},
booktitle = {Proceedings of the 12th IAPR International
Conference on Pattern Recognition},
pages = {204--207},
year = 1994,
volume = 3,
month = {9-13 Oct.},
datestr = 199410,
organization = {Int. Association for Pattern Recognition, IEEE
Comput. Soc., Inf. Process. Assoc. Israel},
publisher = {IEEE Comput. Soc. Press},
http =
{http://ieeexplore.ieee.org/servlet/opac?punumber=4429},
url =
{http://ieeexplore.ieee.org/xpls/abs_all.jsp?&arNumber=577160},
ISBN = 0818662654,
OCLC = 4986186,
abstract = {Outlines a method to derive geometric invariance
kernels which may be applied to a space-variant
sensor architecture. The basic idea as to transform
a kernel with desired symmetry properties (e.g. the
Fourier kernel) in the domain to the range of the
transform. By combining this transformed kernel with
the Jacobian of the transformation, the authors
obtain a new integral transform, in the range, which
has similar properties to the original
transform. The authors illustrate this idea with a
variant of the Mellin-Fourier transform, applied to
an image which has been transformed by a log-polar
mapping. The kernel obtained, which the authors call
an ``exponential chirp'' has properties (unlike the
Mellin-Fourier transform) which are both consistent
with the spatial nature of human vision and can be
applied directly in the space-variant image
plane. The authors outline applications to visual
template matching and auto-correlation, and show a
one-dimensional example of a generalization of
cepstral auto-correlation using this method.},
keywords = {geometric invariance; space-variant vision systems;
exponential chirp transform; symmetry properties;
Fourier kernel; Jacobian; integral transform;
Mellin-Fourier transform; log-polar mapping;
space-variant image plane; cepstral
auto-correlation},
}