Date of Award

Spring 1997

Project Type


Program or Major

Computer Science

Degree Name

Doctor of Philosophy

First Advisor

R Daniel Bergeron


The sizes of today's scientific datasets range from megabytes to terabytes, making it impossible to directly browse the raw datasets visually. This presents significant challenges for visualization scientists who are interested in supporting these datasets. In this thesis, we present an adaptive data representation model which can be utilized with many of the commonly employed visualization techniques when dealing with large amounts of data. Our hierarchical design also alleviates the long standing visualization problem due to limited display space. The idea is based on using compactly supported orthogonal wavelets and additional downsizing techniques to generate a hierarchy of fine to coarse approximations of a very large dataset for visualization.

An adaptive data hierarchy, which contains authentic multiresolution approximations and the corresponding error, has many advantages over the original data. First, it allows scientists to visualize the overall structure of a dataset by browsing its coarse approximations. Second, the fine approximations of the hierarchy provide local details of the interesting data subsets. Third, the error of the data representation can provide the scientist with information about the authenticity of the data approximation. Finally, in a client-server network environment, a coarse representation can increase the efficiency of a visualization process by quickly giving users a rough idea of the dataset before they decide whether to continue the transmission or to abort it. For datasets which require long rendering time, an authentic approximation of a very large dataset can speed up the visualization process greatly.

Variations on the main wavelet-based multiresolution hierarchy described in this thesis also lead to other multiresolution representation mechanisms. For example, we investigate the uses of norm projections and principal components to build multiresolution data hierarchies of large multivariate datasets. This leads to the development of a more flexible dual multiresolution visualization environment for large data exploration.

We present the results of experimental studies of our adaptive multiresolution representation using wavelets. Utilizing a multiresolution data hierarchy, we illustrate that information access from a dataset with tens of millions of data values can be achieved in real time. Based on these results, we propose procedures to assist in generating a multiresolution hierarchy of a large dataset. For example, the findings indicate that an ordinary computed tomography volume dataset can be represented effectively for some tasks by an adaptive data hierarchy with less than 1.5% of its original size.