=Paper=
{{Paper
|id=None
|storemode=property
|title=MFC: A Morphological Fiber Classification Approach
|pdfUrl=https://ceur-ws.org/Vol-715/bvm2011_75.pdf
|volume=Vol-715
}}
==MFC: A Morphological Fiber Classification Approach==
https://ceur-ws.org/Vol-715/bvm2011_75.pdf
MFC: A Morphological Fiber Classification
Approach
Diana Röttger, Viktor Seib, Stefan Müller
Computer Graphics Working Group, University of Koblenz
droettger@uni-koblenz.de
Abstract. Diffusion imaging is a magnetic resonance imaging (MRI)
technique that provides the examination of neuronal pathways in vivo.
High angular resolution diffusion imaging (HARDI) is able to recon-
struct more than one fiber population within one voxel and hence, over-
comes the limitations of diffusion tensor imaging (DTI). Fiber tracking
approaches can benefit from the additional data, but require informa-
tion about the real fiber population to reconstruct fiber bundles. In this
paper we evaluate recent scalar measures on HARDI data and introduce
a novel global approach, a morphological filtering, to identify multiple
fiber populations per voxel.
1 Introduction
One of the most popular HARDI reconstruction techniques is Q-ball imaging [1].
It’s output is the local probability density function on a sphere, the orientation
distribution function (ODF). HARDI data can be beneficial in fiber tracking,
where DTI-based reconstructions suffer from weak directional information, e.g.,
in fiber crossings, fannings or kissings. However, with multiple orientations per
voxel it is not clear which is the most appropriate one for a specific fiber bundle
reconstruction. Therefore, fiber tracking techniques using HARDI data must
distinguish between one and more fiber populations per voxel.
Anisotropy measures provide information in terms of fiber tract integrity
and can act as a stopping criteria for fiber tracking. The generalized fractional
anisotropy (GFA) [1] is an important criterion for HARDI, as an extension to
the fractional anisotropy (FA) in DTI
√ ∑
n 2
std(Ψ ) n i=1 (Ψ (ui ) − ⟨Ψ ⟩)
GF A = = ∑n 2 (1)
rms(Ψ ) (n − 1) i=1 Ψ (ui )
Here, ⟨Ψ ⟩ is the mean of the ODF and Ψ (ui ) is the ODF value of the i-th
diffusion direction u.
In addition, different approaches exist to delineate the intra-voxel fiber pop-
ulation. Frank et al. [2] introduced the fractional multi-fiber index (1823-02) for
determining the model order, l, of the current voxel
∑ 2
j:l≥4 |cj |
FMI = ∑ 2 (2)
j:l≥2 |cj |
Morphological Fiber Classification 365
Here, c are the spherical harmonics (SH) coefficients, used for ODF reconstruc-
tion.
Another approach was introduced by Chen et al. [3] and Descoteaux et al. [4],
which incorporates the variance of the measurements (in the following named
Chen’s classifier)
∑ ∑
|c0 | j:l=2 |cj | j:l≥4 |cj |
R0 = ∑ R2 = ∑ Rmulti = ∑ (3)
j |cj | j |cj | j |cj |
If R0 is large, the voxel’s diffusion is considered to be isotropic, if R2 is
large, a one-fiber population is present in the specific voxel. A large Rmulti -value
indicates two or more fibers’ diffusion.
In this paper, we introduce the morphological fiber classification (MFC)
method, which is a global heuristic to differentiate between voxels with one
or more fiber populations. We will demonstrate that our approach is advan-
tageous in challenging cases, for example acquisitions with low b-values, where
other classifier fail to detect the multiple maxima.
2 Materials and Methods
We performed our initial experiments on a phantom dataset. This phantom was
originally provided by the Laboratoire de Neuroimagerie Assistée par Ordina-
teur (LNAO, France) for the Fiber Cup, a tractography contest at the MICCAI
conference in 2009. A ground truth of the fibers in the phantom was provided as
well. We use this ground truth to evaluate the results of our proposed approach
in terms of multiple fiber populations per voxel. The phantom data was acquired
with two repetitions and 64 image encoding gradients, uniformly distributed over
a sphere. The two repetitions were averaged before further processing. Dataset
size was 64 × 64 voxels with an uniform voxel size of 3 mm. Of the different
diffusion sensitizations provided, we use the dataset with b-value 2000 s/mm2 .
To be able to characterize voxels as containing zero (isotropic), one or multi-
ple fiber populations, first their respective diffusion profile has to be calculated.
We use the Q-ball reconstruction based on SH as proposed by Descoteaux et
al. [5]. The regularization parameter for the Laplace-Beltrami smoothing ma-
trix is λ = 0.006 and the employed SH order is l = 4. This order is high enough
to classify multiple fiber populations in a voxel [2, 3], and low enough to avoid
over-modeling perturbations due to noise in the input diffusion MRI signal [5].
The main idea of MFC is to morphologically eliminate fibers from the white
matter mask so that only clusters remain. These clusters represent an estimation
of voxels with multiple fiber populations. A mask is generated in the first step
and separates isotropic voxels from voxels with at least one fiber population.
Ideally, a mask image separates all white matter voxels from all gray matter
voxels. Since the white matter mask features gaps due to the thresholding pro-
cedure, the second step is to close these gaps. We apply morphological closing
with different kernel sizes for filtering. With reasonable threshold choices, the
gaps in the white matter mask that need to be closed are small. Closing consists
366 Röttger, Seib & Müller
of a morphological dilation (2 × 2 × 2) followed by an erosion (4 × 4 × 4). Since
our goal is to eliminate fibers, the erosion is performed with a larger kernel size.
This kernel eliminates the additional white matter voxels from dilation and thins
out white matter. The third step is morphological opening with a kernel size of
3 × 3 × 3. The resulting image contains clusters located at positions where mul-
tiple fibers meet. In the fourth step the median filtered mask image is combined
with the cluster image to form the final result. Voxels marked in both images are
characterized as containing multiple fiber populations, whereas voxels marked
only in the mask image as containing only one fiber population. Due to the
dilation in the third step some clusters might have been enlarged beyond the
actual white matter mask. Therefore voxels marked only in the cluster image
are ignored.
3 Results
Figure 1a shows the ground truth of the phantom dataset, containing the most
challenging fiber courses: crossing, kissing, and fanning. The result obtained
from MFC with a standard deviation mask image is presented for comparison in
Fig. 1b. MFC is able to identify all areas of multiple fiber populations.
For our experiments thresholded mask images are calculated based on GFA,
FMI, Chen’s method, and the standard deviation (sDEV) of the diffusion ODF.
The respective thresholds are chosen carefully to find a proper balance between
gaps in the mask and false positives. The computed masks are shown with
their corresponding MFC in Figure 2. GFA is not able to separate the white
(a) Ground truth (b) MFC from sDEV
Fig. 1. Ground truth of the phantom dataset. This image is adapted from the Fiber
Cup website. The multiple fiber populations per voxel are shown as light voxels in
Fig. 1(b), whereas dark voxels represent one fiber population.
Morphological Fiber Classification 367
and gray matter of this dataset (Fig. 2a). Hence, its MFC provides no useful
information. FMI and Chen’s method separate the white and gray matter well,
but fail to detect multiple fiber populations per voxel in this dataset (Fig. 2b, 2c,
top row). However, their respective MFCs perform significantly better, albeit
fail to detect some multiple fiber population areas. Also, the MFC computed
from Chen’s mask image detects one false positive cluster (Fig. 2c). The best
separation of white and gray matter was obtained from the standard deviation
(Fig. 2d). Further, the corresponding MFC detects all multiple fiber areas with
no false positives.
Our experiments show that the selection of proper thresholds in step one is
crucial for the success of the MFC algorithm. Further, median filtering the mask
image before or instead of step two to close gaps and eliminate false positives
yields worse classification results.
For further evaluation we used a human brain dataset (dataset size 128 ×
128 × 60, voxel size 1.875 × 1.875 × 2 mm), which is courtesy of Poupon et al. [6].
Data was acquired with a uniform gradient direction scheme with 41 directions
and a b-value of 700 s/mm2 . We tested our method in the region of the centrum
semiovale, where a known crossing of the corpus callosum, the corticospinal tract
and the superior longitudinal fasciculus exist. The resulting MFC with properly
adjusted kernel sizes (Fig. 3).
4 Discussion
In neuro-visualizations the extraction of fiber tracts connecting functional areas
of the brain is of major intrest. Our approach can pose an improvement in
(a) GFA (b) FMI (c) Chen’s method (d) sDEV
Fig. 2. Each column represents a seperation criterion for white matter. The top row
shows the different mask images. The bottom row shows the corresponding MFC
results (dark voxels: one fiber population, light voxels: multiple fiber populations).
368 Röttger, Seib & Müller
Fig. 3. MFC classification result of the centrum semiovale with superimposed local
ODF maxima.
detecting voxels traversed by more than one fiber and hence, influence fiber
tracking methods for HARDI. Additionally, the MFC can be used to distinguish
isotropic diffusion from multiple intra-voxel fiber population and thus, provide
information about fiber tract integrity. Future work will include the integration
of the proposed classifier into a fiber tracking algorithm.
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