R. Daniel Bergeron (*)

John P. McHugh (**)

(*) Department of Computer Science

(**) Department of Mechanical Engineering

University of New Hampshire

Kingsbury Hall

Durham, NH 03824

*Phone: *(603) 862-3780
*Fax:* (603) 862-3493
*Email: *rdb@cs.unh.edu

jpm@alma.unh.edu
*www: *www.cs.unh.edu/~rdb

**WWW PAGE**

www.cs.unh.edu/projects/vis/mdr

**List of Supported Students**

Tao Ouyang, Graduate Research Assistant

Award Number: 9871859

Duration: 9/15/1998 - 8/31/2001

Title: Adaptive Multiresolution Data Representation

**Keywords**

multiresolution data, hierarchical data, level of detail, error representation,
orthogonal wavelets.

**Project Summary**

This project is based on the development and evaluation of a multiresolution
data representation model for interactive visualization and exploration
of very large multidimensional multivariate scientific data. The combination
of wavelets and multidimensional visualization techniques provides a powerful
and effective basis for real-time visualization of very large data sets.
We believe that compactly supported orthogonal wavelets can be used effectively
to furnish an authentic representation of very large scientific data, and
at the same time, provide a fine to coarse hierarchy for detail investigations.
An essential component of our wavelet-based multiresolution data representation
model is the ability to provide a meaningful *localized* error estimation
for each level of the representation. Preliminary results show that large
data sets can be effectively viewed at low resolutions. A scientist can
search the coarse representation for interesting patterns, and can use
the local error display to identify areas of the coarse representation
where the visual representation has too much error to be trusted. In both
cases, the scientist can then explore the identified areas at a higher
resolution. This research is an interdisciplinary effort aimed at
developing and evaluating tools to support the interactive exploration
of computational fluid dynamics (cfd) output representing the turbulence
generated by gravity waves in the atmospheres of the Earth and the outer
planets.

**Publications
and Products**

Laramee,
Robert and R. Daniel Bergeron, Adaptive Resolution Isosurface Rendering,
submitted to *IEEE Visualization 2001.*

Laramee,
Robert, *Adaptive Resolution Isosurface Rendering*, M.S. Thesis, Computer
Science Department, University of New Hampshire, December 2000.

Completed Software:

- C++ wavelet-based utility library to generate multiresolution representations
of a dataset

C++ utility to generate generate an adaptive resolution data set from a multiresolution hierarchy based on a user specified error.

An efficient adaptive resolution data description language and C++ utilities to store, read and access the representation

One M.S. student, Robert Laramee worked on project-related research, although he was funded by a teaching assistantship. He will be starting a Ph.D. program in Austria this summer. A Ph.D. student, Tao Ouyang, is currently being funded.

**Goals, Objectives, and Targeted Activities**

The principal immediate goal for this project is to develop the basic
software that allows us to use the multiresolution data representation
with the computational fluid dynamics (cfd) simulation output. The principal
goal of the past year has been to develop the software infrastructure support
for representing our cfd data as a hierarchy of adaptive resolution data
representations at different error levels. Our current goals are to deploy
this software to the remote supercomputer sight where the simulation is
being done, and to integrate the data representation software with local
rendering tools to facilitate interactive exploration of the data.

**Project References**

Wong, P.C. and R.D. Bergeron, Authenticity analysis of wavelet approximations
in visualization. *Proc IEEE Visualization '95*, pp 184-191,
October 1995. IEEE Computer Society Press.

Wong, P.C. and R.D. Bergeron, Multiresolution
Multidimensional Wavelet Brushing. *Proceedings of IEEE Visualization
'96*, pp 141-148, October 1996. ACM Press.

Wong, P.C. and R.D. Bergeron, Brushing
Techniques for Exploring Scientific Volume Datasets.
*Proceedings of
IEEE Visualization '97*, October 1997. ACM Press.

**Area Background**

Scientific data visualization [Nielson and Shriver, 1990; Rosenblum
et al., 1994] is an emerging multidisciplinary research area that incorporates
aspects of data modeling, data access and storage, interactive techniques,
understanding of human perception and considerable emphasis on domain-specific
needs and visualization goals. The notion of
*exploratory data
analysis* [Tukey, 1977] has been a fundamental component of much scientific
data visualization research and corresponds closely to recently developed
ideas of *data mining * and knowledge-directed data discovery.
In recent years, significant research efforts have been devoted to development
of multiresolution data representations including notions of multiple levels
of detail for rendering purposes. One particularly significant development
in this area is the use of wavelet transformations [Strang, 1989; Stollnitz
et al. 1995] which were originally used primarily for data compression.
Mallat's seminal paper [Mallat, 1989] was a primary motivation for much
of the later use of wavelets for volume rendering and surface representation
and for our data modeling work. A basic one-dimensional wavelet transform
of *n* data elements produces two sets of *n/2* coefficients,
called the *summary* and *detail *components. The operation
is invertible, so that the original signal can be reconstructed from the
coefficients. The coefficients are essentially weights applied to
wavelet basis functions which have compact and limited support. Consequently,
small coefficients can be discarded (treated as 0) without major impact
on the reconstructed signal. This characteristic makes wavelets useful
for data compression. The multiresolution application of wavelets
arises because the *summary *coefficients essentially act as a lower
resolution approximation to the original data and recursive applications
of the wavelet transform produce a hierarchy of resolutions. For
our purposes, however, it is just as important that (for *orthogonal*
wavelets) we can treat the *detail* coefficients as representing
the locally-defined
*error* of the associated *summary *coefficients
at each level of the hierarchy.

**Area References**

Mallat, S.G. A theory for multiresolution signal decomposition: the
wavelet representation. *IEEE Trans. Pattern Analysis and Machine Intelligence.*
11(7):674-693, July 1989.

Nielson, G. and B. Shriver, editors.
*Visualization in Scientific
Computing. * IEEE Computer Society Press, 1990.

Rosenblum, L., R. Earnshaw, J. Encarnacao, H. Hagen, A. Kaufman, S.
Klimenko, G. Nielson, F. Post, and D. Thalmann, editors. *Scientific
Visualization: Advances and Challenges. *Academic Press, 1994.

Stollnitz, E.J., T.D. DeRose and D.H. Salesin. Wavelets for computer
graphics: a primer, Parts 1 and 2.
*IEEE Computer Graphics and Applications*,
15(3):76-84 (May 1995) and 15(4):75-85 (July 1995).

Strang, G. Wavelets and dilation equations: a brief introduction.
*Siam Review,
*31(4):614-627, December 1989.

Tukey, J.D. *Exploratory Data Analysis. * Addison-Wesley,
1977.

**Potential Related Projects**

The data modeling aspect of this project is closely related to ongoing
research based on a comprehensive data model for scientific data. In particular
we are developing components of the model to represent distributed adaptive
multiresolution scientific data. This work is being carried out in
collaboration with Ted M. Sparr and several computer science graduate students
at UNH.