1992
@article{SFA1992,
vgclass = {refpap},
author = {Simoncelli, Eero P. and Freeman, Wiliam T. and Adelson,
Edward H. and Heeger, David J.},
title = {Shiftable multiscale transforms},
journal = {IEEE Transactions on Information Theory},
volume = {38},
number = {2},
pages = {587--607},
month = {March},
year = {1992},
url = {http://ieeexplore.ieee.org/iel1/18/3425/00119725.pdf},
abstract = {One of the major drawbacks of orthogonal wavelet
transforms is their lack of translation invariance: the content of
wavelet subbands is unstable under translations of the input signal.
Wavelet transforms are also unstable with respect to dilations of the
input signal and, in two dimensions, rotations of the input signal. The
authors formalize these problems by defining a type of translation
invariance called shiftability. In the spatial domain, shiftability
corresponds to a lack of aliasing; thus, the conditions under which the
property holds are specified by the sampling theorem. Shiftability may
also be applied in the context of other domains, particularly
orientation and scale. Jointly shiftable transforms that are
simultaneously shiftable in more than one domain are explored. Two
examples of jointly shiftable transforms are designed and implemented:
a 1-D transform that is jointly shiftable in position and scale, and a
2-D transform that is jointly shiftable in position and orientation.
The usefulness of these image representations for scale-space analysis,
stereo disparity measurement, and image enhancement is demonstrated.},
}