Abstract
The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.
Highlights
Many approaches to the visualization of vector and tensor fields involve reducing the dense input data to a sparse set of features that are more displayed and understood
We explore the use of differential operators to extract features from tensor fields
We present a novel approach to tensor field visualization which builds upon our previously developed tensor decomposition method 2
Summary
Many approaches to the visualization of vector and tensor fields involve reducing the dense input data to a sparse set of features that are more displayed and understood. Topological approaches to vector field visualization attempt to reduce the input data to a simpler representation of the structure of the field in terms of critical points such as foci of sources and sinks, or the centers of vortices for, example and a few separating streamlines separatrices. These points and curves comprise a skeleton description of the flow field 1. Feature points are local extrema and segmenting curves are isocontours This approach has the benefit of being very general with respect to tensor order.
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