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

On 2019-10-01 11:00:00 at G205, Karlovo náměstí 13, Praha 2
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
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.
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
information, are known to
have advantage in tracking curved fibers and in presence of noise. The choice
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.

[Sumit Kaushik is finishing a PhD at Masaryk University and is currently
for a postdoc position.]
Responsible person: Petr Pošík