Adaptive Multiresolution Data Representation

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


List of Supported Students

              Tao Ouyang, Graduate Research Assistant
Project Award Information

              Award Number:    9871859
              Duration: 9/15/1998 - 8/31/2001
              Title: Adaptive Multiresolution Data Representation

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:

Project Impact
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.