Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators
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 representation...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/142923 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548433090576384 |
|---|---|
| author | Tim McGraw Takamitsu Kawai Inas Yassine Lierong Zhu |
| author_facet | Tim McGraw Takamitsu Kawai Inas Yassine Lierong Zhu |
| author_sort | Tim McGraw |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-de691f26d04a461cba3db6f5dbb3014d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-de691f26d04a461cba3db6f5dbb3014d2025-02-03T06:14:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/142923142923Visualizing High-Order Symmetric Tensor Field Structure with Differential OperatorsTim McGraw0Takamitsu Kawai1Inas Yassine2Lierong Zhu3West Virginia University, Department of Computer Science and Electrical Engineering, Morgantown, WV 26506, USAWest Virginia University, Department of Computer Science and Electrical Engineering, Morgantown, WV 26506, USAWest Virginia University, Department of Computer Science and Electrical Engineering, Morgantown, WV 26506, USAWest Virginia University, Department of Computer Science and Electrical Engineering, Morgantown, WV 26506, USAThe 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.http://dx.doi.org/10.1155/2011/142923 |
| spellingShingle | Tim McGraw Takamitsu Kawai Inas Yassine Lierong Zhu Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators Journal of Applied Mathematics |
| title | Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators |
| title_full | Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators |
| title_fullStr | Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators |
| title_full_unstemmed | Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators |
| title_short | Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators |
| title_sort | visualizing high order symmetric tensor field structure with differential operators |
| url | http://dx.doi.org/10.1155/2011/142923 |
| work_keys_str_mv | AT timmcgraw visualizinghighordersymmetrictensorfieldstructurewithdifferentialoperators AT takamitsukawai visualizinghighordersymmetrictensorfieldstructurewithdifferentialoperators AT inasyassine visualizinghighordersymmetrictensorfieldstructurewithdifferentialoperators AT lierongzhu visualizinghighordersymmetrictensorfieldstructurewithdifferentialoperators |