48 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
Invertible Orientation Scores of 3D Images
The enhancement and detection of elongated structures in noisy image data is
relevant for many biomedical applications. To handle complex crossing
structures in 2D images, 2D orientation scores were introduced, which already
showed their use in a variety of applications. Here we extend this work to 3D
orientation scores. First, we construct the orientation score from a given
dataset, which is achieved by an invertible coherent state type of transform.
For this transformation we introduce 3D versions of the 2D cake-wavelets, which
are complex wavelets that can simultaneously detect oriented structures and
oriented edges. For efficient implementation of the different steps in the
wavelet creation we use a spherical harmonic transform. Finally, we show some
first results of practical applications of 3D orientation scores.Comment: ssvm 2015 published version in LNCS contains a mistake (a switch
notation spherical angles) that is corrected in this arxiv versio
Extrapolating fiber crossings from DTI data : can we gain the same information as HARDI?
High angular resolution diffusion imaging (HARDI) has proven to better characterize complex intra-voxel structures compared to its predecessor diffusion tensor imaging (DTI). However, the benefits from the modest acquisitions and significantly higher signal-to-noise ratios (SNRs) of DTI make it more attractive for use in clinical research. In this work we use contextual information derived from DTI data, to obtain similar crossing information as from HARDI data. We conduct synthetic phantom validation under different angles of crossing and different SNRs. We corroborate our findings from the phantom study to real human data. We show that with extrapolation of the contextual information the obtained crossings are the same as the ones from the HARDI data, and the robustness to noise is significantly better
Diffusion, convection and erosion on R3 x S2 and their application to the enhancement of crossing fibers
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations (erosions) on the space R3 x S2 of 3D-positions and orientations naturally embedded in the group SE(3) of 3D-rigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossing-preserving fiber enhancement on probability densities defined on the space of positions and orientations. The linear left-invariant (convection-)diffusions are forward Kolmogorov equations of Brownian motions on R3 x S2 and can be solved by R3 x S2-convolution with the corresponding Green’s functions or by a finite difference scheme. The left-invariant Hamilton-Jacobi equations are Bellman equations of cost processes on R3 x S2 and they are solved by a morphological R3 x S2-convolution with the corresponding Green’s functions. We will reveal the remarkable analogy between these erosions/dilations and diffusions. Furthermore, we consider pseudo-linear scale spaces on the space of positions and orientations that combines dilation and diffusion in a single evolution. In our design and analysis for appropriate linear, non-linear, morphological and pseudo-linear scale spaces on R3 x S2 we employ the underlying differential geometry on SE(3), where the frame of left-invariant vector fields serves as a moving frame of reference. Furthermore, we will present new and simpler finite difference schemes for our diffusions, which are clear improvements of our previous finite difference schemes. We apply our theory to the enhancement of fibres in magnetic resonance imaging (MRI) techniques (HARDI and DTI) for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles. We provide experiments of our crossing-preserving (non-linear) left-invariant evolutions on neural images of a human brain containing crossing fibers
Diffusion on the 3D Euclidean motion group for enhancement of HARDI data
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclidean motion group SE(2), for the purpose of crossing-preserving coherence-enhancing diffusion on 2D images. In this paper we study left-invariant diffusion on the 3D Euclidean motion group SE(3), which is useful for processing three-dimensional data. In particular, it is useful for the processing of High Angular Resolution Diffusion Imaging (HARDI) data, since these data can be considered as orientation scores directly, without the need to transform the HARDI data to a different form. In principle, all theory of the 2D case can be mapped to the 3D case. However, one of the complicating factors is that all practical 3D orientation scores are not functions on the entire group SE(3), but rather on a coset space of the group. We will show how we can still conceptually apply processing on the entire group by requiring the operations to preserve the introduced notion of alpha-right-invariance of such functions on SE(3). We introduce left-invariant derivatives and describe how to estimate tangent vectors that locally fit best to the elongated structures in the 3D orientation score. We propose generally applicable techniques for smoothing and enhancing functions on SE(3) using left-invariant diffusion on the group. Finally, we will discuss implementational issues and show a number of results for linear diffusion on artificial HARDI data
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