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   -> Volume 5, Issue 4

Answer: Wavelets and pattern recognition (WD 5.3 #20)
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Naoki Saito (

PostPosted: Wed Dec 04, 2002 9:52 am    
Subject: Answer: Wavelets and pattern recognition (WD 5.3 #20)
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Answer: Wavelets and pattern recognition (WD 5.3 #20)

This is an answer to the question by Kevin Englehart (WD 5.3 #20) about the
wavelet research applied to pattern recognition.

Kevin Englehart wrote (
> I am interested in determining the reason for the apparent sparsity
> of wavelet research as applied to pattern recognition. Is there an
> intrinsic problem with wavelet-based coefficients (or features
> derived thereof) that preclude their use as a feature set for
> pattern recognition or classification applications?

One of the problems of wavelets is a lack of shift invariance of the
expansion coefficients as Stefan Mallat has been mentioning in his
papers for some time. This may a problem for pattern recognition
applications in general, but it really depends on the problem. It may
not be necessary to have complete shift invariance for a particular
pattern recognition problem. To circumvent this problem, many papers
have been written, e.g., [1], [2], [3], [4]. One of the procedures is
the so-called "Spin Cycle" proposed by Prof. Coifman and Prof. Donoho
[1]. The basic strategy is to create several shifted versions of the
original signals and used them for the training data. Of course, one
can perform the shift invariant wavelet transforms [2], [3], [4] and
use all the coefficients too.

In my opinion, the wavelets and their relatives are excellent tools
for pattern recognition and classification, in particular, extracting
important local features. I have been advocating this for some time
now. I would like to list some of our papers for reference, [5], [6],
[7], [8]. We are also working on an improved version of our local
discriminant basis algorithm [9] which should be available soon.

To the best of my knowledge, there are at least several groups working
on the applications of wavelets (and their relatives) to pattern
recognition and classification including I and Prof. Raphy Coifman's
group at Yale, Prof. Donoho's group at Stanford. If texture
segmentation is considered as a part of pattern recognition (I think
it is), then many more people are working on this field using wavelets
and their relatives, e.g., Prof. Alan Bovik at Univ. Texas at Austin,
Prof. Dennis Healy at Dartmouth, Prof. Jay Kuo at Univ. Southern
California, Prof. Andrew Laine at Univ. Florida, Dr. Michael Unser at
NIH, Prof. Hiro Yoshida and Prof. Kunio Doi at Univ. Chicago,
Prof. Josh Zeevi at Technion, ..., to name a few. I'm sure that there
are many more people working in this field.

So, I don't think the wavelet research in this area is not "sparse" at

Best regards,
Naoki Saito

[1] R. R. Coifman and D. Donoho, Translation-invariant de-noising, in
Wavelets and Statistics (Eds. A. Antoniadis and G. Oppenheim),
Lecture Note in Statistics, Springer-Verlag, pp.125--150, 1995.

[2] G. P. Nason and B. W. Silverman, The stationary wavelet transform and some
statistical applications, in Wavelets and Statistics
(Eds. A. Antoniadis and G. Oppenheim), Lecture Notes in Statistics,
Springer-Verlag, pp.281--299, 1995.

[3] J. Liang and T. W. Parks, A translation-invariant wavelet representation
algorithm with applications, IEEE Trans. Sig. Proc., vol.44, no.2,
pp.225-- 232, 1996.

[4] J.-C. Pesquet, H. Krim, and H. Carfantan, Time invariant orthonormal
wavelet representations, IEEE Trans. Sig. Proc., 1996, to appear.

[5] N. Saito, Local Feature Extraction and Its Applications Using a Library of
Bases, Ph.D. Thesis, Dept. of Math., Yale University, 1994.

[6] N. Saito and R. R. Coifman, Local discriminant bases and their
applications, Journ. Math. Imaging and Vision, vol.5, No.4,
pp.337--358, Dec., 1995.

[7] R. R. Coifman and N. Saito, Constuctions of local orthonormal bases for
classification and regression, Comptes Rendus Acad. Sci., Paris,
Serie I, vol.319, no.2, pp.191--196, 1994.

[8] R. R. Coifman and N. Saito, The local Karhunen-Loeve bases, in Proc.
of IEEE International Symposium on Time-Frequency and Time-Scale
Analysis, June 18--21, 1996, in Paris, to appear.

[9] N. Saito and R. R. Coifman, Improved local discriminant bases using
empirical probability density estimation, in Proc. Joint
Statistical Meeting, Aug. 4--8, 1996, in Chicago, to appear.

Naoki Saito, Ph.D. Schlumberger-Doll Research
Email: Old Quarry Road
Voice: (203) 431-5209 Fax: (203) 438-3819 Ridgefield, CT 06877 USA
All times are GMT + 1 Hour
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