The Topology of Symmetric, Second-Order 3D Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
The topology of symmetric, second-order tensor fields
VIS '94 Proceedings of the conference on Visualization '94
Topological Lines in 3D Tensor Fields and Discriminant Hessian Factorization
IEEE Transactions on Visualization and Computer Graphics
Segmentation of Discrete Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Topological Visualization of Brain Diffusion MRI Data
IEEE Transactions on Visualization and Computer Graphics
Invariant Crease Lines for Topological and Structural Analysis of Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
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We present new scalar measures for diffusion-weighted MRI visualization which are based on operations of tensor calculus and have a connection to topological visualization. These operators are generalizations of the familiar divergence and curl operations in vector calculus. We also present a method for computing the Helmholtz decomposition of tensor fields which can make the new scalar measures more robust. The methods we present are general with respect to tensor order, so they apply to traditional 2nd order diffusion tensor MRI, as well as 4th and high order models used in high angular resolution diffusion imaging. Results are shown for synthetic tensor fields of orders 2 and 4 and also real diffusion tensor MRI data of orders 2 and 4.