Computer Science Department, University of California, Santa Cruz
Abstract:
Visualization of 3D tensor fields continues to be a major challenge in terms
of providing intuitive and uncluttered images that allow the users to better
understand their data. The primary focus of this paper is on finding a
formulation that lends itself to a stable numerical algorithm for extracting
stable and persistent topological features from 3D tensors.
While features in 2D
tensors can be identified as either wedge or trisector points, in 3D, the
corresponding stable features are lines, not just points. These topological
feature lines provide a compact representation of the 3D tensor field and
are essential in helping scientists and engineers understand their complex
nature. Existing techniques work by finding degenerate points and are not
numerically stable, and worse,
produce both false positive and false negative feature points.
This paper seeks to address this problem with a robust
algorithm that can extract these features in a numerically stable, accurate,
and complete manner.
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