Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
The Topology of Symmetric, Second-Order 3D Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
Topological Lines in 3D Tensor Fields
VIS '04 Proceedings of the conference on Visualization '04
Visualization and Processing of Tensor Fields: Advances and Perspectives
Visualization and Processing of Tensor Fields: Advances and Perspectives
Geodesic-loxodromes for diffusion tensor interpolation and difference measurement
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
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Interpolating diffusion tensor fields is a key technique to visualize the continuous behaviors of biological tissues such as nerves and muscle fibers. However, this has been still a challenging task due to the difficulty to handle possible degeneracy, which means the rotational inconsistency caused by degenerate points. This paper presents an approach to interpolating 3D diffusion tensors in 2D planar domains by aggressively locating the possible degeneracy while fully respecting the underlying transition of tensor anisotropy. The primary idea behind this approach is to identify the degeneracy using minimum spanning tree-based clustering algorithm, and resolve the degeneracy by optimizing the associated rotational transformations. Degenerate lines are generated in this process to retain the smooth transitions of anisotropic features. Comparisons with existing interpolation schemes will be also provided to demonstrate the technical advantages of the proposed approach.