This paper derives a multiresolution analysis technique for performing
correlations on wavelet representations of images. The technique
maps the images into the wavelet-frequency domain to take advantage
of high-speed correlation in the frequency domain. It builds on Vaidyanathan's
(1993) wavelet correlation theorem, which shows that subsamples of
correlations of two signals can be obtained from a sum of correlations
of subbands of wavelet representations of those signals. Our algorithm
produces the correlations at lowest resolution by applying the convolution
theorem to subband correlations. A new multiresolution technique
fills in the missing correlation data by incrementally inverting
the wavelet transform and refining the Fourier transform. When applied
to JPEG representations of data, the lowest resolution correlations
can he performed directly on the JPEG images to produce 1/64th of
the correlation points. Each of three incremental steps quadruple
the number of correlation points, and the process can be halted at
any point if the intermediate results indicate that the correlation
will not find a match
%0 Journal Article
%1 StoneJan1999
%A Stone, H.S.
%D 1999
%I IEEE Computer Society
%K Fourier JPEG analysis, coding, compressed compression, convolution convolution, correlation correlation, correlations, data data, domain frequency-domain high-speed image images, inverse inversion, methods, missing multiresolution problems, progressive representation, representations, resolution, sampling, subband subsamples, theorem, transform transform, transforms, transformsFourier wavelet wavelet-frequency
%N 1
%P 97-107
%R 10.1109/78.738243
%T Progressive wavelet correlation using Fourier methods
%V 47
%X This paper derives a multiresolution analysis technique for performing
correlations on wavelet representations of images. The technique
maps the images into the wavelet-frequency domain to take advantage
of high-speed correlation in the frequency domain. It builds on Vaidyanathan's
(1993) wavelet correlation theorem, which shows that subsamples of
correlations of two signals can be obtained from a sum of correlations
of subbands of wavelet representations of those signals. Our algorithm
produces the correlations at lowest resolution by applying the convolution
theorem to subband correlations. A new multiresolution technique
fills in the missing correlation data by incrementally inverting
the wavelet transform and refining the Fourier transform. When applied
to JPEG representations of data, the lowest resolution correlations
can he performed directly on the JPEG images to produce 1/64th of
the correlation points. Each of three incremental steps quadruple
the number of correlation points, and the process can be halted at
any point if the intermediate results indicate that the correlation
will not find a match
@article{StoneJan1999,
abstract = {This paper derives a multiresolution analysis technique for performing
correlations on wavelet representations of images. The technique
maps the images into the wavelet-frequency domain to take advantage
of high-speed correlation in the frequency domain. It builds on Vaidyanathan's
(1993) wavelet correlation theorem, which shows that subsamples of
correlations of two signals can be obtained from a sum of correlations
of subbands of wavelet representations of those signals. Our algorithm
produces the correlations at lowest resolution by applying the convolution
theorem to subband correlations. A new multiresolution technique
fills in the missing correlation data by incrementally inverting
the wavelet transform and refining the Fourier transform. When applied
to JPEG representations of data, the lowest resolution correlations
can he performed directly on the JPEG images to produce 1/64th of
the correlation points. Each of three incremental steps quadruple
the number of correlation points, and the process can be halted at
any point if the intermediate results indicate that the correlation
will not find a match},
added-at = {2011-03-27T19:35:34.000+0200},
author = {Stone, H.S.},
biburl = {https://www.bibsonomy.org/bibtex/24c8a4db84f71064849aa2fc01205470e/cocus},
doi = {10.1109/78.738243},
file = {:./00738243.pdf:PDF},
interhash = {2979622e92ba54dc68ee0a362ebc4f5d},
intrahash = {4c8a4db84f71064849aa2fc01205470e},
issn = {1053-587X},
journaltitle = {#ieeetsp#},
keywords = {Fourier JPEG analysis, coding, compressed compression, convolution convolution, correlation correlation, correlations, data data, domain frequency-domain high-speed image images, inverse inversion, methods, missing multiresolution problems, progressive representation, representations, resolution, sampling, subband subsamples, theorem, transform transform, transforms, transformsFourier wavelet wavelet-frequency},
location = {#ieeeaddr#},
month = jan,
number = 1,
pages = {97-107},
publisher = {{IEEE} Computer Society},
timestamp = {2011-03-27T19:35:43.000+0200},
title = {Progressive wavelet correlation using Fourier methods},
volume = 47,
year = 1999
}