Direct Volume Rendering

A Thesis Presented to the Faculty of the Graduate School of

Cornell University

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

by

January 1999

## Abstract:

Finding appropriate transfer functions for direct volume rendering is a difficult problem because of the large amount of user experimentation typically involved. Ideally, the dataset being rendered should itself be able to suggest a transfer function which makes the important structures visible. We demonstrate that this is possible for a large class of scalar volume data, namely that where the region of interest is the boundary between different materials. A transfer function which makes boundaries readily visible can be generated from the relationship between three quantities: the data value and its first and second directional derivatives along the gradient direction. A data structure we term the

histogram volumecaptures the relationship between these quantities throughout the volume in a position independent, computationally efficient fashion. We describe the theoretical importance of the quantities measured by the histogram volume, the implementation issues in its calculation, and a method for semi-automatic transfer function generation through its analysis. The techniques presented here make direct volume rendering easier to use, not only because there are much fewer variables for the user to adjust to find an informative rendering, but because using them is more intuitive then current interfaces for transfer function specification. Furthermore, the results are derived solely from the original dataset and its inherent patterns of values, without the introduction of any artificial structures or limitations. Examples with volume datasets from a variety of disciplines illustrate the generality and strength of the techniques.

© 1999 Gordon Lothar Kindlmann

ALL RIGHTS RESERVED

You may also be interested in my VolVis '98 paper, which is essentially an 8-page version of this thesis, or the software which implements all the algorithms described here. |

**Biographical Sketch****Dedication****Acknowledgements****Chapter 1**Introduction**Chapter 2**Previous work**Chapter 3**Mathematical foundations**Chapter 4**Histogram volume calculation**Chapter 5**Opacity function generation**Chapter 6**Results**Chapter 7**Conclusions and future work**Appendix A**Bandlimiting and the ``thickness'' of boundaries**Appendix B**Generating masks for volume derivative measurement**Appendix C**Evaluating the performance of the derivative measures- Bibliography
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