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Degenerate 3D Tensors

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Executive Summary

Topological analysis of 3D tensor fields starts with the identification of degeneracies in the tensor field. In this paper, the authors present a new, intuitive and numerically stable method for finding degenerate tensors in symmetric second order 3D tensors. This method is formulated based on a description of a tensor having an isotropic spherical component and a linear or planar component. As such, they refer to this formulation as the geometric approach. In this paper, they also show that the stable degenerate features in 3D tensor fields form lines. On the other hand, degenerate features that form points, surfaces or volumes are not stable and either disappear or turn into lines when noise is introduced into the system.

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