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A survey on visualization of tensor field

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Abstract

Tensor field has been widely used in various applications, such as medical imaging, industrial manufacturing, high-dimensional data analysis, and so forth. However, it is a challenging task to understand tensor field intuitively. Therefore, tensor field visualization has become an important research topic. In this survey, we present a comprehensive survey for two kinds of visualization methods for tensor fields: glyphs and streamlines. For glyphs, the eigenvalues of tensor fields will be used to classify existing visualization methods. There are mainly three types of eigenvalues: diffusion tensor fields with all positive real eigenvalues; the tensor field with negative real eigenvalues; the tensor field with imaginary eigenvalues. The methods showing the difference between two tensors (glyphs) are also introduced. For streamlines, there are mainly three important issues: the selection of seed points (streamlines), interpolation of tensor fields, the singularity problem around isotropic tensors. Finally, we discuss challenges and open questions for future studies.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 61702360, 61572057, 61836001, partly by the Tianjin Natural Science Foundation of China under Granted No. 16JCQNJC04100.

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  1. College of Intelligence and Computing, Tianjin University, Tianjin, 300350, China

    Chongke Bi

  2. School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China

    Lu Yang

  3. Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing, 100081, China

    Yulin Duan & Yun Shi

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Bi, C., Yang, L., Duan, Y. et al. A survey on visualization of tensor field. J Vis 22, 641–660 (2019). https://doi.org/10.1007/s12650-019-00555-8

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