CTU Events

«  October  2019  »
Mo Tu We Th Fr Sa Su
  1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31      

Back to calendar

Higher Order Tensor Framework for Segmentation and Fiber Tracking in DWMR Images

01 Oct 2019   11:00-12:30

Clinically DTI (Diffusion Tensor Imaging) is a widely used image modality for diagnosis and study of progression of neuro diseases. In DTI, 2nd order tensors are ensured to have symmetric positive definite property. Thus, lie in well studied Riemann geometric space. But these 2nd order tensors are unable to resolve the white matter fibers in regions of crossing/merging. Higher order tensors appear naturally to deal this issue. The higher order tensors are comparatively less explored, specifically for their use in applications like segmentation and fiber tractography in the crossing/ merging regions.
There do exist some applications where the rotation invariants of these tensors gives rise to new set of bio-markers and are robust than existing ones due to 2nd order tensors in DTI. In this work, 4th order tensors have been explored which is extendable to higher order tensors. The initial idea is to use the known Riemann geometry for the higher 4th order tensors. Three different 2nd order projections of 4th order tensors have been utilized under three anisotropy preserving similarity measures for the geometric space. Spectral quaternion similarity measure is known to better preserve the anisotropy of 2nd order tensors than Log Euclidean metric.
An extension of this measure called SlerpSQ (spherical linear interpolation spectral quaternion) produces smoother interpolation curves.
The spectral metric approach is known to behave robustly under noise. It is observed that the diagonal components of the flattened fourth-order tensors live in the well-known Riemannian symmetric space of symmetric positive-definite matrices. The projection under spectral similarity measure proved effective for
segmentation of white matter complex structures with high curvatures and
crossings. Experimentally, in the work it is confirmed that this projection unfolds the geometry and hence, effective in revealing directions of underlying fibers than existing method known as cartesian tensor orientation
distribution function (CT- ODF). In the fiber tracking application, the algorithms relying upon full tensor information, are known to have advantage in tracking curved fibers and in presence of noise. The choice of
metric tensor for such geometric space is crucial. So far, inverse of the tensor is widely used as a metric tensor. It has also been showed that activation function can also be used for rescaling of this metric tensor (β scaled), so as to minimize the Riemann cost in anisotropic regions (or maximizing the cost in isotropic regions) while fiber tracking. Further, the known ray tracing algorithm is also modified to counter the deviation of fiber from actual path under the β scaled metric tensor and compared to the recent adjugate and standard inverse metric tensor. Various synthetic and real images are used for testing the segmentation and fiber tracking methods.

KN:G-205, FEL ČVUT, Karlovo náměstí 13, Praha 2
Katedra kybernetiky FEL ČVUT
Contact person
prof. Dr. Ing. Jan Kybic, kybicjan@fel.cvut.cz
More information