Gengyan Zhao^{1}, Fang Liu^{2}, Jonathan A. Oler^{3}, Mary E. Meyerand^{1,4}, Ned H. Kalin^{3}, and Rasmus M. Birn^{1,3}

Brain extraction of MR images is an essential step in
neuroimaging, but current brain extraction methods are often far from
satisfactory on nonhuman primates. To overcome this challenge, we propose a
fully-automated brain extraction framework combining deep Bayesian convolutional
neural network and fully connected three-dimensional conditional random field. It
is not only able to perform accurate brain extraction in a fully
three-dimensional context, but also capable of generating uncertainty on each
prediction. The proposed method outperforms six popular methods on a 100-subject
dataset, and a better performance was verified by different metrics and
statistical tests (Bonferroni corrected p-values<10^{-4}).

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Figure 1. Work flow of the
proposed brain extraction framework, a combination of Bayesian SegNet and fully
connected three-dimensional CRF.

Figure 2. Evaluation metrics for the compared methods. (A) and (B)
are Dice coefficient and average symmetric surface distance on each subject
from different brain extraction methods. Higher Dice coefficients or lower
average symmetric surface distance indicates better agreement between the
automatically-extracted and manually-labeled (ground truth) brain masks. For
all subjects, BSegNetCRF resulted in better brain extraction than all other
methods tested. (C) and (D) are the Dice
coefficient and average symmetric surface distance in boxplots for different
brain extraction methods. In the figure points are drawn as outliers with red
‘+’ symbols, if they are greater than q3+1.5(q3-q1) or less than q1-1.5(q3-q1),
where q1 and q3 are the first and third quartiles respectively. AFNI: 3dSkullStrip in AFNI; AFNI+: 3dSkullStrip in AFNI with reduced
coronal slice thickness to one half of the original value; BET: Brain
Extraction Tool; BSE: Brain Surface Extractor; HWA: Hybrid Watershed Algorithm;
NMT: National Institute of Mental Health Macaque Template; BSegNet: Bayesian SegNet;
BSegNetCRF: the combination of Bayesian SegNet and fully connected
three-dimensional conditional random field.

Figure 3. Comparison the performances of different brain
extraction methods. (A) The brain masks extracted by different methods on a
representative subject: subject 007. Note that many of the automated brain
extraction algorithms include parts of the skull (e.g. BSE, HWA), include
adipose tissues near the eyes (AFNI, AFNI+, BET, NMT), remove portions of the
frontal or occipital lobes (AFNI, BET, NMT), or include non-brain areas out of
the edge of the brain (BET, BSE, HWA, NMT). (B) Averaged absolute error maps
for compared methods. For display purposes, the natural logarithm of the
averaged map collapsed (averaged) along each axis is shown.

Figure 4. Uncertainty maps generated by Monte Carlo dropout testing.
(A) The uncertainty map generated for a representative subject, subject 007.
(B) The averaged uncertainty map across all the 100 subjects in the template
space. For display purposes, the natural logarithm of the averaged uncertainty
map collapsed (averaged) along each axis is shown.