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   -> Volume 6, Issue 10

Preprint: High-Dimensional Wavelet Data Compression
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Krasimir Kolarov (

PostPosted: Thu Dec 05, 2002 8:56 am    
Subject: Preprint: High-Dimensional Wavelet Data Compression
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#2 Preprint: High-Dimensional Wavelet Data Compression

Dear Wavelet Digest Readers,

There are a number of papers and reports on the topic of
High-Dimensional Wavelet Data Compression, from our
research group at Interval Research Corporation, available at .

The list below includes papers published at DCC'97, SPIE'97,
Sequences'97 as well as Interval external technical reports. Some of
the abstracts are also included.

Communication and comments are greatly appreciated.

1.) Authors: Krasimir Kolarov and William Lynch

Title: "Compression of Functions Defined on Surfaces of 3D Objects"

Published: Data Compression Conference, J. Storer and M. Cohn, editors,

IEEE Computer Society Press, March 1997.


We present a technique to compress scalar functions defined on
2-manifolds. Our approach combines discrete wavelet transforms with
zerotree compression, building on ideas from three previous
developments: the lifting scheme, spherical wavelets, and embedded
zerotree coding methods. Applications lie in the efficient storage
and rapid transmission of complex data sets. Typical data sets are
earth topography, satellite images, and surface parametrizations. Our
contribution in this paper is the novel combination and application of
these techniques to general 2-manifolds.

2.) Authors: Krasimir Kolarov and Wiliiam Lynch

Title: "Optimization of the SW Algorithm for High-Dimensional Compression"

Published: Compression and Complexity of SEQUENCES 1997,

IEEE Computer Society Press, June 1997.


This paper describes an algorithm and a software package SW (Spherical
Wavelets) that implements a method for compression of scalar functions
defined on 3D objects. This method combines discrete second generation
wavelet transforms with an extension of the embedded zerotree coding
method. We present some results on optimizing the performance of the
SW algorithm via the use of arithmetic coding, different scaling and
norms of the wavelet coefficients. We describe an extension of the SW
algorithm using different prediction schemes in the zerotree
mechanism. The combined use of those techniques leads to a significant
improvement of the compression performance of SW.

3.) Authors: Krasimir Kolarov and William Lynch

Title: "Wavelet Compression for 3D and Higher-Dimensional Objects"

Published: Invited paper, Proc. of SPIE Conference on Applications of
Digital Image Processing, Volume 3164, San Diego,
California, July 1997.

4.)Authors: Thomas Yu, Krasimir Kolarov and William Lynch

Title: "Barysymmetric Multiwavelets on Triangle"

Published: Interval Research Corp. Technical Report IRC 1997-006,
March 11, 1997.


Wavelets are typically designed on simple domains like
R<smaller>n</smaller> or rectangular subsets of
R<smaller>n</smaller>. Motivated by applications on more general
domains, for example, compression of data defined on the sphere or
more general surfaces, we tackle the problem of designing
multiresolution analysis on general manifolds.

In this paper, we give explicit construction of multiwavelets on
polygonal region in R<smaller>2</smaller> that is associated with a
nested triangular tessellation. Two different constructions will be
presented. The first construction is very similar to Alpert's
construction. Unlike the Alpert's 1-D construction, in which case
symmetry of basis functions comes in almost automatically, the
multiwavelets from our first construction possess no symmetry of any
sort. We define a form of symmetry for functions that "live" on
triangles, which we call barysymmetry, and establish various results
about it. We then show that by sacrificing some vanishing moments in
the first construction, we can construct multiwavelets which possess
barysymmetry - our second construction.

Typical members of the bases from both constructions have at least M>0
vanishing moments, but are discontinuous. We discuss how to apply
moment-interpolation schemes to improve these orthonormal bases, which
gives rise to their smooth biorthogonal counterparts.

5.) Authors: Krasimir Kolarov and William Lynch

Title: "Compression of Scalar Functions Defined on 2-Manifolds"

Published: Interval Research Corp. Technical Report 1996-012,
September 13, 1996.
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