630 research outputs found
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
Nonlinear Spectral Geometry Processing via the TV Transform
We introduce a novel computational framework for digital geometry processing,
based upon the derivation of a nonlinear operator associated to the total
variation functional. Such operator admits a generalized notion of spectral
decomposition, yielding a sparse multiscale representation akin to
Laplacian-based methods, while at the same time avoiding undesirable
over-smoothing effects typical of such techniques. Our approach entails
accurate, detail-preserving decomposition and manipulation of 3D shape geometry
while taking an especially intuitive form: non-local semantic details are well
separated into different bands, which can then be filtered and re-synthesized
with a straightforward linear step. Our computational framework is flexible,
can be applied to a variety of signals, and is easily adapted to different
geometry representations, including triangle meshes and point clouds. We
showcase our method throughout multiple applications in graphics, ranging from
surface and signal denoising to detail transfer and cubic stylization.Comment: 16 pages, 20 figure
Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging
Locally adaptive differential frames (gauge frames) are a well-known
effective tool in image analysis, used in differential invariants and
PDE-flows. However, at complex structures such as crossings or junctions, these
frames are not well-defined. Therefore, we generalize the notion of gauge
frames on images to gauge frames on data representations defined on the extended space of positions and
orientations, which we relate to data on the roto-translation group ,
. This allows to define multiple frames per position, one per
orientation. We compute these frames via exponential curve fits in the extended
data representations in . These curve fits minimize first or second
order variational problems which are solved by spectral decomposition of,
respectively, a structure tensor or Hessian of data on . We include
these gauge frames in differential invariants and crossing preserving PDE-flows
acting on extended data representation and we show their advantage compared
to the standard left-invariant frame on . Applications include
crossing-preserving filtering and improved segmentations of the vascular tree
in retinal images, and new 3D extensions of coherence-enhancing diffusion via
invertible orientation scores
Amoeba Techniques for Shape and Texture Analysis
Morphological amoebas are image-adaptive structuring elements for
morphological and other local image filters introduced by Lerallut et al. Their
construction is based on combining spatial distance with contrast information
into an image-dependent metric. Amoeba filters show interesting parallels to
image filtering methods based on partial differential equations (PDEs), which
can be confirmed by asymptotic equivalence results. In computing amoebas, graph
structures are generated that hold information about local image texture. This
paper reviews and summarises the work of the author and his coauthors on
morphological amoebas, particularly their relations to PDE filters and texture
analysis. It presents some extensions and points out directions for future
investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5
(pre-smoothing) extende
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