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   -> Volume 4, Issue 10

Preprint: Gaussian and Gabor wavelets and image processing
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Author Message (Gabriel Cristobal)

PostPosted: Fri Dec 06, 2002 9:34 am    
Subject: Preprint: Gaussian and Gabor wavelets and image processing
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Preprint: Gaussian and Gabor wavelets and image processing

The following two papers are now available electronically:

"Image representation with Gaussian wavelets and its applications"
by Navarro, R., Tabernero, A. and Cristobal, G. to be published
in Advances in Imaging and Electronic Physics (P.W. Hawkes, ed.),
Academic Press. (97 pages and 39 figures).

The figures of the previous paper have been tared in separate files,*

I. Introduction
II. Joint space-frequency representations and wavelets
A. Joint representations. Wigner distribution, spectrogram and
block transforms.
B. Wavelets
C. Multiresolution pyramids.
D. Vision oriented models.
III. Gabor schemes of representation
A. Exact Gabor expansion for a
continous function.
B. Gabor expansion of discrete signals.
C. Quasicomplete Gabor transform.
IV. Vision modeling.
A. Image representation in the
visual cortex.
B. Gabor functions and the RFs of
cortical cells.
C. Sampling in the human
visual system.
V. Image coding, enhancement
and reconstruction.
A. Image coding and compression.
B. Image enhancement and
VI. Image analysis and machine vision.
A. Edge detection.
B. Texture.
C. Motion analysis.
D. Stereo.
VII. Conclusions

The second Technical Report available electronicaly is
the following:

"Several experiments on texture analysis, coding and
synthesis by Gabor wavelets", by Navarro, R., Nestares, O.,
Portilla, J. and Tabernero, A. (31 pags, 12 figures).

Gabor functions, and other related wavelets have shown to be
useful for different applications such as texture analysis.
The most interesting feature of such functions is that they
permit a joint sampling of the space and frequency domains,
with a maximum joint localization in both domains; i.e. they
permit a simultaneous local analysis of both domains.
Concretely, several authors have proposed the application
of Gabor functions for texture analysis. Most of these
proposed schemes share a common pattern to obtain a set
of descriptors: the application of a bank of Gabor
(or similar) filters, followed by one (or more) non
linear operation, and local averaging (some schemes
include further processing), whereas the Gabor phase
is typically ignored. Here we propose another similar
scheme, that has the additional advantage of producing
a quasi complete image representation, and therefore it
can be used not only for analysis, but also for coding
and synthesis. We have constructed different sets of
local descriptors, by applying different operations to
the outputs of either complex or even filters, and their
performance in segmentation and classification experiments
was compared. The modulus of Gabor complex, or demodulated
even, channels provided the best performance. Then, global
descriptors, corresponding to a parametric characterization
of the first and second order statistics (histogram and
autocorrelation), are used for coding and synthesis of
pure textures. The visual resemblance of the synthetic
image with respect to the original is very good for
those textures with a low degree of structure (with a
nearly random Fourier phase), but it is poor for textures
composed by structured elements.

Gabriel Cristobal
Phone: (34)-1-561-6800 FAX: (34)-1-564-5557
Instituto de Optica (CSIC) Serrano 121. 28006 Madrid
All times are GMT + 1 Hour
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