Wavelets for volume graphics

Abstract

In recent years, there has been a shift in the paradigm from surface-based graphics to volume graphics. Volume graphics uses a three-dimensional unit cube, known as a voxel, as its primitive, whereas surface-based graphics use pixels, lines, and surfaces. Voxel-based graphics is becoming increasingly popular due to the inherent advantages it offers over surface graphics. Although volume graphics involves working with larger datasets, the availability of faster processors and inexpensive memory has made it feasible. Recently, there has been considerable research on the application of wavelet theory to problems in graphics and visualization. In this thesis, wavelets are applied to three key problems in volume graphics:

Volume Fusion: This refers to the technique of building volume data by merging two or more similar volumes such that the new volume includes significant details from each of the original volumes. A wavelet-based technique for volume fusion has been developed, along with a scheme to evaluate the performance of various fusion methods.

Internal Detail Visualization: Although ray casting provides realistic volume visualizations, it may obscure internal details. Wavelets are used to extract multilevel isosurfaces, enabling the visualization of significant internal features.

Volume Morphing: This is the process of simulating a smooth deformation from one model to another. Wavelets are used to ensure smooth transitions. Although computationally intensive, the algorithm has been implemented on a multiprocessor system, achieving good speed-up and near real-time performance due to its high degree of parallelizability.

The thesis begins with an introduction to wavelet theory, followed by a survey of its applications in computer graphics, particularly volume graphics. Detailed descriptions of the three algorithms and their implementations are provided, along with experimental results. The thesis concludes with suggestions for future research directions.