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RESEARCH ARTICLE
Optimized 3D co-registration of ultra-low-field
and high-field magnetic resonance images
Roberto Guidotti
1,2
*, Raffaele Sinibaldi
1,2
, Cinzia De Luca
1,2
, Allegra Conti
1,2
, Risto
J. Ilmoniemi
3
, Koos C. J. Zevenhoven
3
, Per E. Magnelind
4
, Vittorio Pizzella
1,2
, Cosimo Del
Gratta
1,2
, Gian Luca Romani
1,2
, Stefania Della Penna
1,2,5
1Department of Neuroscience, Imaging and Clinical Science, Chieti, Italy, 2Institute for Advanced
Biomedical Technologies, University G. D’Annunzio of Chieti and Pescara, Chieti, Italy, 3Department of
Neuroscience and Biomedical Engineering, Aalto University School of Science, FI, Aalto, Finland, 4Applied
Modern Physics Group, Physics Division MS-D454, Los Alamos National Laboratory, Los Alamos, NM,
United States of America, 5Consiglio Nazionale delle Ricerche, Istituto SPIN, UOS L’Aquila, Sede di lavoro
CNR-SPIN c/o Universitàdi Chieti-Pescara “G. D’Annunzio”, Chieti, Italy
*r.guidotti@unich.it
Abstract
The prototypes of ultra-low-field (ULF) MRI scanners developed in recent years represent
new, innovative, cost-effective and safer systems, which are suitable to be integrated in
multi-modal (Magnetoencephalography and MRI) devices. Integrated ULF-MRI and MEG
scanners could represent an ideal solution to obtain functional (MEG) and anatomical (ULF
MRI) information in the same environment, without errors that may limit source reconstruc-
tion accuracy. However, the low resolution and signal-to-noise ratio (SNR) of ULF images,
as well as their limited coverage, do not generally allow for the construction of an accurate
individual volume conductor model suitable for MEG localization. Thus, for practical usage,
a high-field (HF) MRI image is also acquired, and the HF-MRI images are co-registered to
the ULF-MRI ones. We address here this issue through an optimized pipeline (SWIM—Slid-
ing WIndow grouping supporting Mutual information). The co-registration is performed by an
affine transformation, the parameters of which are estimated using Normalized Mutual Infor-
mation as the cost function, and Adaptive Simulated Annealing as the minimization algo-
rithm. The sub-voxel resolution of the ULF images is handled by a sliding-window approach
applying multiple grouping strategies to down-sample HF MRI to the ULF-MRI resolution.
The pipeline has been tested on phantom and real data from different ULF-MRI devices,
and comparison with well-known toolboxes for fMRI analysis has been performed. Our pipe-
line always outperformed the fMRI toolboxes (FSL and SPM). The HF–ULF MRI co-registra-
tion obtained by means of our pipeline could lead to an effective integration of ULF MRI with
MEG, with the aim of improving localization accuracy, but also to help exploit ULF MRI in
tumor imaging.
1. Introduction
In the last 15 years, new instrumental apparatuses have been developed to perform Magnetic
Resonance Imaging (MRI) at low fields (LF MRI, B<10 mT), in contrast to the general
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 1 / 19
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OPEN ACCESS
Citation: Guidotti R, Sinibaldi R, De Luca C, Conti
A, Ilmoniemi RJ, Zevenhoven KCJ, et al. (2018)
Optimized 3D co-registration of ultra-low-field and
high-field magnetic resonance images. PLoS ONE
13(3): e0193890. https://doi.org/10.1371/journal.
pone.0193890
Editor: Chin-Tu Chen, University of Chicago,
UNITED STATES
Received: September 27, 2017
Accepted: February 19, 2018
Published: March 6, 2018
Copyright: This is an open access article, free of all
copyright, and may be freely reproduced,
distributed, transmitted, modified, built upon, or
otherwise used by anyone for any lawful purpose.
The work is made available under the Creative
Commons CC0 public domain dedication.
Data Availability Statement: Raw data used are
from two studies: "Hybrid ultra-low-field MRI and
magnetoencephalography system based on a
commercial whole-head neuromagnetometer"
whose authors may be contacted at panu.
vesanen@aalto.fi, and "Microtesla MRI of the
human brain combined with MEG" whose authors
may be contacted at vzotev@lanl.gov. Processed
data is available at Zenodo: https://doi.org/10.5281/
zenodo.1161054.
tendency to increase the magnetic field strength for higher spatial resolution (see [1,2] for
reviews on actual LF NMR/MRI instruments and applications). These devices operate at field
levels ranging from ~1 μT (Ultra Low Field, ULF [3,4]) to ~10 mT (Very Low Field, VLF [3–
6]).
The advantages of LF MRI include: i) safer operation for specific patient populations (chil-
dren, pregnant women, patients with metallic prostheses or electronic implants), due to the
lower static field; ii) detection in the presence of metals, thanks to the reduced sensitivity to
magnetic susceptibility; iii) lower cost compared to HF devices; iv) possibility of integration
with other instruments such as Magnetoencephalography (MEG) systems [7,8]; v) possibility
of directly imaging neural currents in cerebral regions responding to a stimulus [9]; and vi)
enhanced contrast of the relaxation time T
1
at low static magnetic fields. In particular, ULF
MRI has been proven to be able to differentiate healthy and cancerous tissues on the basis of
the T
1
relaxation time without the need of contrast agents [10,11].
The integration of LF-MRI and MEG devices and the subsequent possibility to assess the
anatomical brain structure and to record MEG activity with the same instrument [7,12] would
remove the contribution of the MEG and MRI co-registration error considerably improving
MEG spatial accuracy, which is often worse than 5 mm. Drawbacks of the existing LF-MRI
prototypes are the lower spatial resolution and lower signal-to-noise ratio (SNR) than in high-
field scanners (HF MRI). Additionally, due to the use of pulsed pre-polarization techniques to
increase the SNR [13–16], acquisition times are considerably longer than in HF MRI, so that
only part of the subject’s head is usually scanned. As a consequence, today’s ULF images of the
brain cannot be directly used to construct the volume conductor model for MEG. A possible
solution to this problem is to acquire a separate set of HF-MR images covering the whole head,
for reference, and then to co-register these images to the ULF-MR ones. To effectively improve
the MEG localization error, it is of paramount importance that the co-registration between the
HF-MRI and the original LF-MRI be performed as accurately as possible.
Well-assessed co-registration procedures are already available for specific types of biomedi-
cal images, such as multimodal images acquired with different devices, e.g., MRI and CT or
MRI and PET, the outputs of which are co-registered in the same standard space [17,18].
Among the existing procedures, the best candidates able to co-register LF and HF MRIs are
those used to co-register functional and anatomical MRIs produced by the same scanner and
implemented in fMRI processing software (e.g., SPM, FSL and many others; [19,20]).
To this end, Mutual Information (MI) based algorithms [21–23] are widely used to find the
best co-registration transformation. In particular, MI was demonstrated to be optimal for mul-
timodal data analysis where images recorded from different devices or with different contrasts,
such as fMRI and MRI, must be aligned in a common space, whereas many other mathemati-
cal cost functions can be misleading when handling images with different SNR and sensitivity
[24]. Of note, this approach was tested for co-registering fMRI and MRI images with high SNR
and contrast on the whole brain volume. On the contrary, if the image SNR is low, such as in
current ULF MRI, then the cost function will have more local minima where the minimization
process could be trapped [18], thus disturbing the co-registration process.
To the best of our knowledge, there is no efficient tool for the co-registration of low-resolu-
tion, low-contrast images with high-contrast, high-resolution 3D images. Ultrasound images
used for multimodal co-registration have also low SNR, but they have a high spatial resolution
[25,26]. Additionally, this tool should co-register the whole volume imaged with HF systems
to only a portion of this volume recorded by ULF MRI.
We present here a new pipeline (SWIM—Sliding WIndow grouping supporting Mutual
information) specifically designed to co-register HF MRIs to LF MRIs, with a low SNR, low
contrast, low resolution, and only partial coverage of the imaging volume. This pipeline is
Optimized co-registration of ULF and HF MRI
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Funding: This project has received funding from
the European Union’s Horizon 2020 research and
innovation programme under grant agreement No
686865. The present work reflects only the
authors’ view; the Commission is not responsible
for any use that may be made of the information it
contains.
Competing interests: The authors have declared
that no competing interests exist.
based on Normalized Mutual Information (NMI) [17], supported by an accurate sub-voxel
sampling procedure based on a sliding window. The results obtained on three different data-
sets were analyzed to validate this method. Specifically, we carried out a first test on datasets of
a phantom with a known geometry. We then performed two tests on in-vivo human brain data
recorded at Los Alamos National Laboratory [12], and at AALTO University [7]. Our results
were then compared with those from standard software for the co-registration of fMRI to ana-
tomical images.
2. Materials and methods
Ethics statement: The MRI experiments performed at AALTO University were approved by the
Ethics Committee of the Hospital District of Helsinki and Uusimaa. The human subject experi-
ments, acquired at Los Alamos, were approved by the Los Alamos Institutional Review Board.
2.1 SWIM Co-registration pipeline
2.1.1 Mutual information based registration. The goal of the image co-registration is to
find the set of parameters t, defining the transformation Tthat brings an image Ainto the best
possible spatial correspondence with a second image B.
arg min
tðBTAÞ
The affine transformation Tcan be composed by a product of multiple independent trans-
formations; here, Tconsists of a rigid transformation defined by 6 parameters representing 3
translations and 3 rotations around the x,y,zaxes of the reference system of image A, and a
scaling transformation to match for possible anisotropic distortions across images with 3
parameters, one for each spatial dimension. From now on, we will name as rigid the transfor-
mation with 6 parameters and as rigid+scaling the transformation with both rigid and scaling
parameters with a total of 9 parameters.
According to information theory and literature on image analysis [27], MI is a suitable cost
function to find the best transformation T. Specifically, the MI criterion states that Tmaxi-
mizes the MI between Aand B.
For two images Aand B, MI is defined as follows:
MIðA;BÞ ¼ HðBÞ þ HðAÞ HðA;BÞ ¼ HðAÞ HðAjBÞ ¼ HðBÞ HðBjAÞ ð1Þ
Where H(X) is the Shannon entropy of image X,H(A|B) is the conditional entropy of A
given Band H(A,B) is the joint entropy, defined as in the following:
HðAÞ ¼ PapAðaÞlogpAðaÞ ð2Þ
HðA;BÞ ¼ Pa;bpABða;bÞlogpABða;bÞ ð3Þ
HðAjBÞ ¼ Pa;bpABða;bÞlogpAjBðajbÞ ð4Þ
Here, p
A
(a) and p
B
(b) are the marginal probability distributions of images Aand B,
obtained as the frequency of a grey voxel intensity yin an image Y. The joint probability distri-
bution p
AB
(a,b) is obtained from the joint histogram of Aand B, where each {i,j} entry repre-
sents the frequency of a voxel intensity iin the first image (A) and voxel intensity jin the
second image (B) at the same coordinate.
The probability distribution p
AB
(a,b) depends on the alignment between the two images,
and thus on the transformation Tapplied to image A.
Optimized co-registration of ULF and HF MRI
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SWIM uses a modified MI, the Normalized Mutual Information (NMI) [17], which has
been demonstrated to be less sensitive than MI (Eq 1) to the size of the overlapping part of the
two 3D structures; it is better suited for our requirements (see previous subsection). NMI is
defined as:
NMI A;Bð Þ ¼ HðAÞ þ HðBÞ
HðA;BÞð5Þ
In addition, SWIM uses a reverse mapping procedure [28] and a trilinear interpolation [29]
to prevent the generic transformation Tfrom creating empty voxels in the transformed image,
altering the NMI value [30]. These empty voxels could be caused by the discrete sampling of
the image space, implying that after a generic transformation T, the new position of each voxel
may not coincide with a point on the grid described by the coordinate set. Moreover, numeri-
cal truncation may lead to two or more voxels being transformed in the same one after direct
transformation.
2.1.2 Minimization and grouping procedures. We used Adaptive Simulated Annealing
(ASA) [31] to find the parameters of the transformation Tthat minimize the reciprocal 1/
NMI.NMI
–1
is not a convex function of the set of parameters t, and although it has been
shown that there is no optimization method that is superior to others [32], ASA is a robust
method less prone to be trapped in local minima or funnels [31] that characterize the space of
co-registration parameters for noisy and low-contrast images. We ran the ASA algorithm 10
times, each with a different starting configuration, using 500 runs for each configuration.
There is an additional issue we had to face during minimization of 1/NMI. Since NMI-
based co-registration must be applied to pairs of images with the same spatial resolution, we
down-sampled the HF images to the ULF image resolution. To this aim, we applied a grouping
procedure, namely the sliding window approach, as described in the following: In the HF
images, once a voxel was selected as the origin of the HF grid, we averaged in each direction a
number of voxels equal to the ratio between the voxel size of the low- and high-resolution
images. The total number of voxels to be averaged in the 3D grouping window ðNav
3DÞis equal
to the product of the ratio between the voxel size of the low- and high-resolution images in
three dimensions:
Nav
3D¼Yd¼x;y;z
sizeðvLR
dÞ
sizeðvHR
dÞ
ð6Þ
In Eq (6), the size function gives the resolution of voxel vin the ddimension for low-resolu-
tion (LR) and high-resolution (HR) images. The size of the 3D window described in Eq (6) is
fixed. However, the co-registration accuracy depends on the position of the 3D window.
Before the ASA minimization procedure, the 3D window can be slid onto the high-resolution
image: this implies that the voxels constituting the grouping window depend on three transla-
tion parameters. The number of trials for the selection of the best position of the grouping win-
dow is equal to the number of voxels included in the window.
This effect is illustrated in Fig 1 in a simple 2D case: an image with a voxel size equal to 1×1
mm
2
is down-sampled to a resolution of 2×2 mm
2
. We have four possible 2D window posi-
tions (from Eq 6) to down-sample the image with voxel size 1×1 mm
2
. In the figure, each offset
individuates a window with a different edge color and it is clear that different offsets produce
different average values over the 2D window and thus different image contents. In general, a
shift in one direction will modify the group of voxels participating at each 3D window, so that
the number of voxels constituting the intersection between the shifted and 0-shift windows is
Optimized co-registration of ULF and HF MRI
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equal to
Qd¼x;y;zðsizeðvLR
dÞ
sizeðvHR
dÞ
offsetdÞ ð7Þ
This number could be relatively small, thus suggesting how the position of the grouping
sliding window influences the mutual information value and the whole co-registration
process.
In summary, the SWIM pipeline explores all possible positions of the sliding window and
selects the most informative tessellation for the image-registration algorithm. Eventually, a
minimization run is performed for different tessellations, searching for the highest NMI value,
which corresponds to the best transformation found by the algorithm. In this optimization
step, only three translational parameters are involved and a minimization procedure based on
the Downhill Simplex Method in multi-dimensions [33] is rather efficient and less time con-
suming than ASA. We used 500 runs for the optimization pipeline.
The output is the set of transformed high-resolution images to be superimposed with the
low-resolution one, and the best NMI value obtained. For qualitative evaluation of the co-reg-
istration results, we computed the difference images between the two sets of aligned image
stacks at low spatial resolution. This requires that a threshold is applied on both ULF and HF
image stacks. This threshold is automatically selected using an adaptive procedure based on
the image histogram [28,34].
All the algorithms were written in C and ran on a standard Linux desktop PC with a quad-
core CPU and 4 GB of RAM.
Two different open-source software packages, commonly used in the neuroscience commu-
nity, were used to compare and validate our approach: FSL [20] and SPM [35]. In this compar-
ison, the NMI values were calculated using the output images of all the different software tools
as input to SWIM, without any optimization, to be sure that the calculation of the NMI value
was performed exactly with the same procedure and using the same volumes.
Fig 1. Schematic drawing illustrating the grouping procedure. The figure shows an example of the grouping
procedure to down-sample a 2D image with a voxel size 1×1 mm
2
into another one with 2x2mm
2
resolution. We have
four possible groupings, shown here in different colors (red, green, orange and pink). Each grouping relates to a
different offset out of the possible four. Notably, at each grouping window a different value is obtained when voxels are
averaged, showing how this procedure modifies the information content of the image, particularly when the image to
be down-sampled has a large number of edges.
https://doi.org/10.1371/journal.pone.0193890.g001
Optimized co-registration of ULF and HF MRI
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In addition to NMI values, we also calculated a group of image similarity indices to further
evaluate the co-registration. These indices are commonly used in the image-processing litera-
ture [36,37]; their mathematical formulations are reported in Table 1.
2.2 Datasets
2.2.1 Phantom images acquired at 8.9 mT and at 3T. We first tested the SWIM pipeline
on MR images of a phantom with a known 3D geometry, which is free from possible image
blurring and motion artifacts. The phantom was a hollow cylinder with an asymmetrical hole
filled with doped water (770 mg of CuSO
4
in 1 dm
3
of H
2
O, 1 ml Arquad, 0.15 ml H
2
SO
4
), and
contained in a volume of 5×5×4 cm
3
. HF-MR images were recorded on a Philips 3T scanner
using a knee coil and an Ultra Fast Gradient Echo sequence, with 1×1×1 mm
3
resolution,
12×12×18 cm
3
FOV, TR = 8.5 ms, TE = 3.9 ms, NEX = 3, and total acquisition time = 6 min.
VLF MRIs were recorded on a prototype operating at a static field of 8.9 mT inside a mag-
netically shielded room [6]. We used a Spin Echo (SE) sequence, cartesian sampling with
1×1×1 mm
3
resolution, 6.4×6.4×6.4 cm
3
FOV, TR = 500 ms, TE = 19 ms, NEX = 37 and total
acquisition time of 8.5 min for each volume. To save time, only 32×32 phase encoding steps
and zero filling were used. Note that in this first dataset, the whole phantom was imaged with
the LF and HF devices.
2.2.2 Brain images acquired at 46 μT and at 1.5 T. Our pipeline was applied to a second
dataset consisting of images of a human brain acquired with HF- and ULF-MRI scanners at
Los Alamos National Laboratory (LANL), Applied Modern Physics Group [12]. The HF data-
set was acquired with a conventional 1.5 T scanner using an SE sequence with TE = 64 ms and
TR = 9000 ms. The HF image size is 256×256×192 cubic voxels, with side length of 1 mm. The
ULF-MRI brain dataset was acquired in a static field of 46 μT, using pre-polarizing pulses of
30 mT [12]. The voxel resolution of the ULF 3D acquisition was 6×3×3 mm
3
, NEX = 6. The
detection coil array was placed above the right temporal lobe. The total number of voxels was 6
in the xdirection, 45 in the ydirection and 40 in the zdirection. Note that, as observed above,
only a portion of the left hemisphere was imaged with ULF MRI, and this portion had to be
co-registered to the whole head volume acquired with the HF set-up.
2.2.3 Brain images acquired at 50 μT and at 3 T. Finally, we tested SWIM on a dataset
acquired with the ULF-MRI apparatus installed at Aalto University [7]. Images of the brain
Table 1. Mathematical formulation of similarity measures. We used these measures to evaluate the performances of
SWIM. In the first column containing the index names, S stands for similarity measure while D stands for dissimilarity
measure.
Jaccard (S) Pn
i¼1minðai;biÞ
Pn
i¼1maxðai;biÞ
R
2
score (S) 1Pn
i¼1ðbiaÞ2
Pn
i¼1ðaiaÞ2
Where a¼1
nPn
iai
Kendall tau (S) CD
nðn1Þ
2
C is the number of concordant pairs while D is the number of discordant
pairs.
A pair [(a
i
, bi), (a
j
, bj)] is defined concordant if sign(a
i
-a
j
) = sign(b
i
-b
j
).
They are said to be discordant, in other cases.
Bray Curtis (D) Pn
i¼1ðaibiÞ
Pn
i¼1ðaiþbiÞ
Mean Squared Error
(D) 1
nX
n
i¼1ðaibiÞ2
Correlation distance
(D) 1Pn
i¼1ðaiaÞðbi
bÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pn
i¼1ðaiaÞPn
i¼1ðbi
bÞ
q
https://doi.org/10.1371/journal.pone.0193890.t001
Optimized co-registration of ULF and HF MRI
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were acquired with a static field of 50 μT and a prepolarization field of 22 mT, using a 3D SE
sequence with NEX = 8. The detection coils were placed above the occipital lobe. The resolu-
tion was 4×6×4 mm
3
and an image matrix of 50×16×38 voxels was reconstructed. In this case
as well, only a portion of the brain was imaged at ULF. The HF MRI of the brain was acquired
with a Siemens 3T MRI scanner, using a Turbo SE with a TR = 4920 ms and TE = 121 ms. The
HF images had a voxel resolution of 1×5×1 mm
3
, resulting in an image grid composed of
256×79×256 voxels.
3. Results
3.1 Phantom data recorded at 8.9 mT and 3T
In Fig 2, we show the result of the SWIM pipeline applied on the phantom images acquired at
HF and VLF. Although in these images the signal is generated by the doped water in the phan-
tom, they differ due to the following reasons: i) the respective upper parts of the images are
different since the phantom was closed by a cap during the HF scan, while the cap was not in-
serted during the VLF recordings; ii) the SNR is clearly lower in LF images than in HF images;
iii) in the VLF images, although it is not difficult to recognize the phantom shape, the upper
and bottom parts are blurred due to the fading of the sensitivity profile of the RF coils along
the vertical direction. Despite these differences, we show that the images of the phantom are
aligned by our co-registration pipeline, using the 9-parameter transformation (rigid + scaling).
In this procedure, we did not use the sliding-window approach since the image resolution
was the same for the LF and HF datasets.
3.2 Brain data recorded at 46 μT and 1.5 T
We here describe features of ULF-MR brain images that make the co-registration with HF
MRI nontrivial. First, the resolution of the ULF images is much poorer than that of HF images.
While the HF images are recorded with a cubic voxel with 1-mm side, the voxels in the ULF
MRIs are “rectangular cuboids” with size along the axial direction (6 mm) being twice the in-
plane size (3 mm). These voxels are considerably larger than in HF images in order to increase
the SNR and to reduce the recording time. In addition, the ULF dataset of the human brain
acquired at LANL, as for the phantom dataset, is characterized by a resolution and contrast
Fig 2. Co-registration of the phantom dataset. Images of the phantom dataset acquired at VLF (left panel) and at HF,
after co-registration (right panel) at 6 different depths (4–9 mm).
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Optimized co-registration of ULF and HF MRI
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considerably lower than for the corresponding HF dataset. Finally, due to the smoothing
effects of the large voxel size of the ULF images, a considerable blurring reduces the contrast
between brain tissues, smoothing edges between different anatomical compartments and at
the head edges. Indeed, edges detected by ULF are never sharp, in contrast with the HF images,
making the detection of anatomical features and the co-registration between the two image
sets harder.
The spectral content of both ULF and the re-sampled HF images was evaluated by means of
the 2D power spectrum density (2D PSD). In S1 Fig, we show the 2D PSD for two slices of the
dataset, calculated with ImageJ [38] using no-padding and a triangular filter window. The
spectra of the HF images were calculated following the grouping procedure to reduce the reso-
lution of HF images down to the ULF ones. The spatial frequency content of the two images is
very different, with HF MRIs exhibiting higher frequencies (reflecting the edge sharpness
between anatomical features) than ULF MRIs (due to the smoother edges).
In Fig 3, the results from the SWIM co-registration of the in-vivo dataset are shown. In Fig
3A, we show a composite panel including three columns: the ULF dataset on the left side, the
HF images after a rigid+scaling transformation in the centre, and the two overlapped datasets
on the right, qualitatively suggesting that our approach was correctly co-registering the two
sets of images. The value of the Normalized Mutual Information is 1.105.
In Fig 3B and 3C we show the joint histogram before and after co-registration, respectively.
As explained in [18], if the images are correctly aligned and co-registered, the joint histogram
Fig 3. Co-registration of brain data recorded at 46 μT and 1.5 T. Panel a) Co-registration results on an in-vivo brain dataset recorded at 46 μT. a) Four sample slides.
The left column represents the target ULF images, the middle column contains the HF co-registered images and the right column shows the overlap between the two
image sets, where HF images are in grey tones and ULF images in green tones. b) and c) The joint histogram before and after co-registration, respectively. The red
ellipses demarcate background voxels. These are badly aligned in the starting histogram, as suggested by the spread peak along the column corresponding to the
background in the ULF image (0 gray value) and to background and head voxels in the HF image. In the final histogram the peak is concentrated close to the origin of
the joint histogram, suggesting that background voxels are aligned in the final histogram. The violet ellipses represent some brain and skull structures that are
misaligned in the starting configuration (the peak is wide); while in the final histogram a sharper peak is shown around ULF gray-level of 50. The yellow ellipses
represent some structures with highest gray value like eyes and white matter that are less sharp in the starting joint histogram, while have a more clear structure in final
configuration, demonstrating the good alignment of the images.
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is characterized by the presence of sharp peaks related to the aligned image features. Compar-
ing the pre- and post-co-registration histograms, a visible modification of the histogram pat-
tern can be appreciated. The red ellipses in Fig 3B and 3C mark a peak involving the small
values of grey level in the ULF image, which are mainly associated with the background voxels.
While before co-registration this peak spreads along the vertical axis (peak value = 1.23 e
3
,
standard deviation on the xaxis σ
x
= 5, σ
y
= 83), after co-registration it is restricted to small
grey values for ULF and HF-MRI, suggesting a good overlap of background voxels (peak
value = 7.25 e
4
,σ
x
= 8, σ
y
= 22). Peaks in Fig 3B and 3C highlighted by the violet ellipses are
possibly related to part of the brain tissue and scalp represented by grey values ~40 in ULF
images. These are misaligned in the histogram in Fig 3B, as indicated by the wide peak (peak
value = 28, σ
x
= 63, σ
y
= 45); while a sharper peak (peak value = 87, σ
x
= 32, σ
y
= 23) in the his-
togram in Fig 3C is clearly visible, suggesting a good alignment. Finally, some structures with
high grey value (eyes, white matter) are surrounded by the yellow contour. Again, the histo-
gram before co-registration shows a smaller peak (peak value = 17, σ
x
= 75, σ
y
= 43) while the
final histogram has a clearer pattern (peak value = 27, σ
x
= 39, σ
y
= 40), which demonstrates an
alignment of these head structures. Note that the peaks representing the head structures do
not lay on the bisection line, since the voxels within these structures are described by different
distributions of grey values, which may depend on the different contrast at the two MRI fields.
In Fig 4, we show the interpolated NMI as a function of the sliding window offsets in each
direction at a fixed offset. According to formula (6), 6 offset values are possible along the x
direction and 3 along the yand zdirections. NMI changes with the offset values, suggesting
that SWIM optimized the co-registration thanks to the sliding window approach. The cross-
hair marks the best offset found by SWIM, corresponding to a window with an initial position
with offsets equal to x
off
= 5, y
off
= 1 and z
off
= 0.
In Fig 5, the goodness of the co-registration obtained with SWIM is compared with the
results obtained by FSL and SPM. In the first column, the target ULF images at four different x
Fig 4. NMI as a function of different positions of the grouping window. The figure shows the interpolated NMI
obtained by SWIM sliding the grouping window over the three direction of the xyz space. a) NMI for different offsets
in xand zdirection at y
off
= 1; b) NMI for offsets in yand zdirections at x
off
= 5; panel c) shows the NMI for different
offsets in xand ydirection at x
off
= 1. The cross-hair shows the highest value of NMI obtained at x
off
= 5, y
off
= 1, z
off
=
0.
https://doi.org/10.1371/journal.pone.0193890.g004
Optimized co-registration of ULF and HF MRI
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depths are shown, while the outputs of SWIM, and of FSL and SPM, applied on the HF images
are shown in the other columns. Notably, the different software packages produce different
alignments between the HF and ULF images, as suggested by the NMI values indicating the
goodness of co-registration. We obtained the highest value of NMI by using our pipeline, dem-
onstrating that the new procedure reaches the best performance in the superposition of
HF-MRI images with the corresponding low resolution, noisy ULF-MRI images of the brain.
This indication is strengthened by analyzing the overlaps of the ULF and HF structures as
obtained with the three methods, which are shown in Fig 6. The images were binarized after
co-registration using an adaptive threshold filter [28,34] based on the grey level histograms of
the two image sets. Fig 6 shows that using SWIM, anatomical features such as nasal sinuses
and the cortical surface are well aligned. Conversely, using FSL and SPM, despite the good
NMI value and plausible brain orientation, we did not obtain a good match of these structures
(second and third row of Fig 6). The percentage of overlapping voxels is calculated considering
only those voxels contained inside the HF head volume, while the external background voxels
are not considered. Also ULF bright outliers outside the head surface marked by the HF struc-
ture were excluded. The final superposition found by our pipeline is characterized by the high-
est percentage of overlapping voxels.
Moreover, we report in Table 2 additional indices of either similarity (the higher the value,
the higher the similarity–Kendall tau, Jaccard correlation, R
2
score in addition to NMI) or dis-
similarity (the lower the value, the higher the similarity—Correlation distance, Bray–Curtis
Fig 5. Comparison between SWIM and fMRI software packages. The results obtained with SWIM on the brain
images recorded at 46 μT are compared with the outcomes of two different co-registration software packages routinely
used for fMRI analysis. The corresponding NMI coefficients obtained after optimization are reported in the last row.
The best result is obtained with SWIM. The co-registration procedure of fMRI processing software is very fast and
efficient for fMRI analysis, but it is not adequate for co-registering ULF and HF images.
https://doi.org/10.1371/journal.pone.0193890.g005
Optimized co-registration of ULF and HF MRI
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distance, Mean squared error) estimated according to formulas shown in Table 1. Both simi-
larity and dissimilarity indexes confirm the goodness of the alignment using our approach,
which outperforms the co-registration results of the fMRI software packages.
3.3 ULF brain data recorded at 50 μT
Finally, we evaluated our pipeline using a dataset of the brain acquired with the system devel-
oped at Aalto University. This device records data from the occipital part of the brain. These
LF images are blurred at the bottom and top due to the limited field of view. Fig 7A shows the
coronal view of the ULF- and HF-aligned brain images, obtained with the rigid+scaling trans-
formation. In Fig 7B, we show the interpolated NMI as a function of the sliding window offset
in each direction at a fixed offset. According to formula (6), 4 offset values are possible along
the xand zdirections and 2 along the ydirection. The intersection of plot lines marks the best
offset found by SWIM, corresponding to a window with an initial position with offsets equal
to x
off
= 1, y
off
= 1 and z
off
= 0. The similarity/dissimilarity indices for this transformation are:
Fig 6. Overlap between the co-registered images. Segmented images are converted into binary format and the
percentage of voxel overlap is reported on the last column for the three different co-registration procedures.
Overlapping voxels are shown in white, light gray voxels are the HF voxels not matched in ULF image, dark gray
indicates the ULF voxels not present in the brain shown in the HF scans and black indicates matching of the
background. The matching of anatomical features is maximal for SWIM.
https://doi.org/10.1371/journal.pone.0193890.g006
Table 2. Similarity/dissimilarity indices for co-registration of HF and ULF MRI at 46 μT. Different values obtained
for the indices in Table 1 applied to images co-registered using SWIM, FSL and SPM are reported in the table. The best
values are highlighted in bold.
SWIM SPM FSL
Jaccard similarity 0.36 0.34 0.32
R
2
index 0.46 0.28 0.20
Kendall similarity 0.65 0.62 0.55
Bray-Curtis 0.30 0.38 0.42
Mean Squared Error 793 1671 1978
Correlation distance 0.26 0.40 0.44
https://doi.org/10.1371/journal.pone.0193890.t002
Optimized co-registration of ULF and HF MRI
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Jaccard similarity = 0.393, R
2
score = 0.354, Kendall’s similarity = 0.654, Bray–Curtis dissimi-
larity = 0.370, MSE = 1066, correlation distance = 0.293. In summary, also in the case of the
images obtained from the Aalto system, SWIM was successful in the alignment, providing sim-
ilarity/dissimilarity indices comparable with those of the Los Alamos system data.
3.4 Control analysis using a shear transformation
We further evaluated the performance of the SWIM approach, using only a rigid transformation,
a rigid+scaling transformation, as well as using a shear transformation in addition to the rigid and
scaling transformations described above. We always obtained an increase of NMI by including a
scaling transformation, compared to a rigid transformation only, for all the datasets (~1.5% for
the phantom, 0.15% for brain images). In contrast, we did not obtain better values of NMI by
including a shear transformation, neither by tuning all parameters in a single run (~ –0.1% for the
phantom, ~ –0.05% for brain images), nor by tuning separately the 3 shear parameters (~0.05%
for the phantom, <0.01% for brain images). These results suggest that, at least for the analyzed
datasets, the rigid+scaling transformation already provides a reliable co-registration.
3.5 Statistical assessment of SWIM
There is no ground truth to evaluate the accuracy of the registration of human brain images
[39]. Therefore we applied two different approaches to assess the significance of our results: we
estimated i) the robustness of the co-registration results using a consistency test and ii) the sig-
nificance of our method using a permutation test.
The robustness of co-registration results was analyzed using the consistency test developed
in Jenkinson et. al [39]. Specifically, a hundred randomly generated transformation matrices
were used to modify the starting co-registration of the HF dataset to the ULF-MRI (first
guess), without distorting the image structure. Then the coregistration pipeline was applied
using these new images and the reference ULF images recorded at 46 μT.
Fig 7. Co-registration of HF and ULF images at 50 μT. a) Co-registration of the dataset acquired at Aalto University. On the left the ULF image of the brain and
on the right the down-sampled co-registered image at HF. b) NMI as function of the sliding window offset on the three (x,y,z) directions for x
off
= 1, y
off
= 1,
z
off
= 0.
https://doi.org/10.1371/journal.pone.0193890.g007
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 12 / 19
The RMS deviation error is calculated between the transformation obtained with the gener-
ated images and the original one, using the following formula:
dRMS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
5R2TrðMTMÞ þ tTt
rð8Þ
Where d
RMS
is the deviation RMS measured, R is the radius of the ULF voxel and M and t
are obtained from M t
0 0
!¼TjAjT1
0, where T
j
is the initial random transformation
matrix, A
j
is the matrix obtained after running the coregistration algorithm and T
0
is the trans-
formation obtained using the original HF dataset.
We calculate this index using both SWIM and FSL in order to get a distribution of errors.
The mode of the deviation error for SWIM was about the size of the largest voxel dimensions
(6mm) in the low resolution image, while for FSL two modes are found at about 2 and 3 times
this size, respectively. The error of SWIM was significantly lower than that of FSL (p<0.001;
unpaired t-test).The error distributions of SWIM and FSL are plotted in Fig 8.
We then used permutation test [40] to further evaluate if the transformation generated
using the original dataset is obtained by chance. We shuffled voxels position of the HF image,
destroying the structural information contained in the image but maintaining the distribution
of the gray values. One hundred (100) randomly shuffled images were generated, and these
were coregistered with the original LF image by our pipeline, in order to build a null distribu-
tion of the NMI. This distribution was used to evaluate if our coregistration transformation
was obtained by chance.
Fig 8. Distribution of d
RMS
for SWIM and FSL. The violin plot of the distribution of d
RMS
after running the consistency test over one hundred of different starting
images for both SWIM and FSL, suggests that SWIM error is significantly lower than FSL coregistration error.
https://doi.org/10.1371/journal.pone.0193890.g008
Optimized co-registration of ULF and HF MRI
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For the ULF images recorded at 46 μT, the null distribution had a mean of 1.029 with a SD
of 0.001. SWIM produced an NMI 1.105 which is significantly above chance level (p<0.01).
4. Discussion and conclusions
Here, we demonstrated that our approach based on minimization of the reciprocal of NMI
supported by the sliding window grouping is robust to low SNR and contrast and is suitable to
co-register ULF- and HF-MR images from phantom and in-vivo recordings obtained by differ-
ent systems. The matching between image sets was quantified through a set of similarity indi-
ces in addition to NMI, proving that our approach provided transformation parameters which
were more reliable than the ones obtained by other software packages used in the neuroscience
community. Notably, we also demonstrated that 9 parameters (rigid transformation plus scal-
ing) are adequate to achieve a reliable co-registration.
4.1 Methodological considerations
SWIM was designed to be robust to images with different SNR and contrast levels and with very
different resolution. In a setting with different voxel resolutions in x,y,zdirections, it is manda-
tory to scale the high-resolution images. This process leads to an information loss, which
increases when the resolution difference becomes higher [28]. We used the sliding window to
avoid bias due to unsuitable resampling of high-resolution images that could compromise
image registration in the case of lower-resolution images with lesser SNR and contrast. As an
example, co-registration results obtained by FSL were suboptimal, despite the relatively high
NMI, probably due to a down-sampling strategy not adequate for this type of images. To speed
up processing time, the initial coarse registration step in FSL is realized by sub-sampling the
original images at a resolution of 8×8×8 mm
3
. In this way, the software quickly calculates a first
guess before starting the co-registration using the original spatial resolution [41]. This method
allows faster registration at a finer scale as a result of a reasonable initial estimate. Although the
FSL procedure is very fast and efficient in fMRI analysis, in this particular case of ULF and HF
brain images, the initial sub-sampling could cause a loss of information in the ULF structures,
implying the calculation of a bad first guess for the subsequent image co-registration.
Moreover, the fact that the FOV in ULF-MR images represents only a part of the volume
imaged by HF MRI could negatively affect the co-registration process since it limits the in-
formation contained in the dataset. In addition, the cost function (the reciprocal of NMI)
includes a large number of local minima also due to the lower SNR of ULF-MRI images, and
this number increases with the number of parameters used in the co-registration procedure.
Overall, these effects generate a complex minimization hypersurface full of local minima
where a minimization algorithm could be trapped [18,31]. The ASA algorithm, together with
the sliding window down-sampling, is less sensitive to local minima, although the processing
time is longer than in other minimization algorithms.
Our results suggest that, for the analyzed image sets, possible distortions are accounted for
by different scaling parameters in the three dimensions of the HF and ULF grids, and only
marginally by shear parameters, as suggested by the negligible increase of NMI when these are
included. Future studies could test whether the use of regularization techniques may further
improve the co-registration of this kind of datasets [42].
We designed SWIM to ensure portability across different VLF-HF and ULF-HF MRI sce-
narios. In this perspective, the pipeline could be improved using ad-hoc cost functions or min-
imization algorithms, leveraging on particular features of the imaging instruments. However,
using a customized configuration would prevent from generalizing the pipeline to other MRI
systems.
Optimized co-registration of ULF and HF MRI
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Moreover, SWIM could be effectively adapted to images from different modalities to track
changes in tissues or in material structures in order to detect the effect of therapeutic treat-
ments or micro-morphology changes [30,43]. Since the implementation of reliable and robust
methods of multimodal image co-registration and image fusion [44–46] is central in several
medicine-related research and clinical fields [42], it would be worth exploiting our pipeline in
other imaging modalities in the future.
4.2 Impact of optimized co-registration on LF-MRI
The application of optimized co-registration software would support the exploitation of LF
MRI for the following reasons. Co-registering ULF MRI to HF MRI is of fundamental impor-
tance for instruments integrating MRI with MEG in the same setup, with the aim at improving
the spatial accuracy of MEG. Source localization requires the solution of an ill-posed inverse
problem [47], for which, in addition to source models, head (volume conductor) models are
used to restrict the possible solutions, and to associate magnetic field sources to specific brain
areas. These models are usually obtained from the HF MRI of the subject’s head, which should
be co-registered in the same reference system as the MEG.
This is achieved through two co-registrations, one between the fiducial markers and the
anatomical image of the subject’s head and the other between the reference systems of the sub-
ject’s head and the MEG sensor space. Thus, co-registration of HF-MRI to MEG [48,49] has
an influence on MEG spatial accuracy and reliability. Measuring both MEG and ULF MRI
with the same sensor setup implies, assuming that proper calibrations have been performed,
that anatomical and functional images are already co-registered, together with the position of
the subject’s head in the MEG sensor space (thanks to the image of the head produced by
ULF-MRI) [7,12,14]. On the other hand, for practical usage of present day ULF-MRI and
MEG systems, due to the low resolution of ULF-MRI images, a co-registration of HF-MRI to
ULF-MRI is needed. This co-registration relies on a larger number of points than the one
using fiducial markers, and it can therefore be expected to be far more reliable and accurate. In
this work, we have presented a new co-registration method and we have compared it to other
existing methods. We found that our method has greater robustness. The impact of this
improved co-registration on MEG localization is under investigation and will be the subject of
another work.
In addition, ULF MRI could provide information on electrical conductivity of different
head compartments; this information could be used to further improve localization accuracy
[50]. However, current ULF-MRI systems compatible with MEG allow to image only a part of
the brain to keep the measurement duration reasonable; also, the contrast and resolution in
these images are still inadequate to build an accurate volume-conductor model. Therefore,
data analysis would still require an independently acquired high-resolution MRI. Our
approach was able to successfully co-register phantom and in-vivo LF images obtained with
different systems to the respective HF images. The obtained co-registration was better than the
one obtained with fMRI analysis packages, as assessed through multiple similarity/dissimilarity
indices.
The development of a new generation of NMR and MRI apparatuses working at ultra-low
measurement fields is opening up new possibilities to image and characterize properties of bio-
logical structures. ULF MRI can be used to detect different brain tissues, usually not distin-
guishable at HF strengths, using particular sequences and leveraging on different tissue
relaxation times, with the possibility to discriminate between different brain tumors without
contrast agents [51]. ULF MRI has already revealed abnormal relaxation rates in prostate can-
cer tissues, which correlated with the percentage of prostate tumor tissue [11]. For practical
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 15 / 19
scientific and clinical applications on living tissues, instruments capable of providing images
with very high quality and good spatial resolution in a reasonable recording time are needed.
The present-day ULF MRI systems are still at an early stage although their output could in
principle be used in a multimodal approach together with HF MRI and/or other diagnostic
techniques such as X-ray computed tomography, ultrasonography and biopsy. In this perspec-
tive, our approach could enhance exploitation of multimodal imaging involving VLF and ULF
MRI.
Supporting information
S1 Fig. Power spectrum density of HF and ULF MRI at 46 μT. a) Spectrum of the ULF
image. The spectrum is mainly characterized by low-frequency components, indicating low
contrast and blurring. b) Spectrum of the HF image. The spectrum includes also high frequen-
cies and indeed the edges between different anatomical regions are clearly detectable. Notably,
the HF image was down-sampled to the same spatial resolution as the ULF image.
(PNG)
Acknowledgments
We would like to thank Dr. Panu T. Vesanen and Dr. Andrei Matlashov for gently providing
us the datasets.
Author Contributions
Conceptualization: Roberto Guidotti, Risto J. Ilmoniemi, Stefania Della Penna.
Data curation: Cinzia De Luca, Allegra Conti, Koos C. J. Zevenhoven, Per E. Magnelind.
Formal analysis: Roberto Guidotti, Raffaele Sinibaldi.
Methodology: Roberto Guidotti, Raffaele Sinibaldi, Stefania Della Penna.
Resources: Cinzia De Luca, Allegra Conti, Koos C. J. Zevenhoven, Per E. Magnelind.
Software: Roberto Guidotti, Raffaele Sinibaldi.
Writing – original draft: Roberto Guidotti, Raffaele Sinibaldi, Risto J. Ilmoniemi, Per E. Mag-
nelind, Vittorio Pizzella, Cosimo Del Gratta, Stefania Della Penna.
Writing – review & editing: Roberto Guidotti, Raffaele Sinibaldi, Cinzia De Luca, Allegra
Conti, Risto J. Ilmoniemi, Koos C. J. Zevenhoven, Per E. Magnelind, Vittorio Pizzella,
Cosimo Del Gratta, Gian Luca Romani, Stefania Della Penna.
References
1. Ko
¨rber R, Storm J-H, Seton H, Ma
¨kela
¨JP, Paetau R, Parkkonen L, et al. SQUIDs in biomagnetism: a
roadmap towards improved healthcare. Supercond Sci Technol. IOP Publishing; 2016; 29: 113001.
https://doi.org/10.1088/0953-2048/29/11/113001
2. Della Penna S, Pizzella V, Romani GL. Impact of SQUIDs on functional imaging in neuroscience.
Supercond Sci Technol. 2014; 27: 044004. https://doi.org/10.1088/0953-2048/27/4/044004
3. Clarke J, Hatridge M, Mo
¨ssle M. SQUID-detected magnetic resonance imaging in microtesla fields.
Annu Rev Biomed Eng. 2007; 9: 389–413. https://doi.org/10.1146/annurev.bioeng.9.060906.152010
PMID: 17328671
4. Hilschenz I, Ko
¨rber R, Scheer HJ, Fedele T, Albrecht HH, Mario Cassara
´A, et al. Magnetic resonance
imaging at frequencies below 1 kHz. Magn Reson Imaging. 2013; 31: 171–177. https://doi.org/10.1016/
j.mri.2012.06.014 PMID: 22898690
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 16 / 19
5. Sarracanie M, LaPierre CD, Salameh N, Waddington DEJ, Witzel T, Rosen MS, et al. Low-Cost High-
Performance MRI. Sci Rep. Nature Publishing Group; 2015; 5: 15177. https://doi.org/10.1038/
srep15177 PMID: 26469756
6. Galante A, Sinibaldi R, Conti A, De Luca C, Catallo N, Sebastiani P, et al. Fast room temperature very
low field-magnetic resonance imaging system compatible with MagnetoEncephaloGraphy environment.
Lin F-H, editor. PLoS One. 2015; 10: e0142701. https://doi.org/10.1371/journal.pone.0142701 PMID:
26630172
7. Vesanen PT, Nieminen JO, Zevenhoven KCJ, Dabek J, Parkkonen LT, Zhdanov A V, et al. Hybrid ultra-
low-field MRI and magnetoencephalography system based on a commercial whole-head neuromagnet-
ometer. Magn Reson Med. 2013; 69: 1795–804. https://doi.org/10.1002/mrm.24413 PMID: 22807201
8. Zotev VS, Matlashov AN, Volegov PL, Urbaitis A V, Espy M a, Kraus Jr RH. SQUID-based instrumenta-
tion for ultralow-field MRI. Supercond Sci Technol. 2007; 20: S367–S373. https://doi.org/10.1088/0953-
2048/20/11/S13
9. Ko
¨rber R, Nieminen JO, Ho
¨fner N, Jazbins
ˇek V, Scheer H-J, Kim K, et al. An advanced phantom study
assessing the feasibility of neuronal current imaging by ultra-low-field NMR. J Magn Reson. 2013; 237:
182–190. https://doi.org/10.1016/j.jmr.2013.10.011 PMID: 24252245
10. Myers RW. Potential Applications of Microtesla Magnetic Resonance Imaging Detected Using a Super-
conducting Quantum Interference Device. University of California, Berkeley. 2006.
11. Busch S, Hatridge M, Mo
¨ßle M, Myers W, Wong T, Mu¨ck M, et al. Measurements of T(1) -relaxation in
ex vivo prostate tissue at 132 μT. Magn Reson Med. 2012; 67: 1138–45. https://doi.org/10.1002/mrm.
24177 PMID: 22294500
12. Zotev VS, Matlashov AN, Volegov PL, Savukov IM, Espy M a, Mosher JC, et al. Microtesla MRI of the
human brain combined with MEG. J Magn Reson. 2008; 194: 115–20. https://doi.org/10.1016/j.jmr.
2008.06.007 PMID: 18619876
13. McDermott R, Lee S, ten Haken B, Trabesinger AH, Pines A, Clarke J. Microtesla MRI with a supercon-
ducting quantum interference device. Proc Natl Acad Sci U S A. National Academy of Sciences; 2004;
101: 7857–7861. https://doi.org/10.1073/pnas.0402382101 PMID: 15141077
14. Magnelind PE, Gomez JJ, Matlashov AN, Owens T, Sandin JH, Volegov PL, et al. Co-Registration of
Interleaved MEG and ULF MRI Using a 7 Channel Low-Tc SQUID System. IEEE Trans Appl Super-
cond. 2011; 21: 456–460. https://doi.org/10.1109/TASC.2010.2088353
15. Zotev VS, Volegov PL, Matlashov AN, Espy M a, Mosher JC, Kraus RH. Parallel MRI at microtesla
fields. J Magn Reson. 2008; 192: 197–208. https://doi.org/10.1016/j.jmr.2008.02.015 PMID:
18328753
16. Vesanen PT, Nieminen JO, Zevenhoven KCJ, Dabek J, Simola J, Sarvas J, et al. The spatial and tem-
poral distortion of magnetic fields applied inside a magnetically shielded room. IEEE Trans Magn. 2012;
48: 53–61. https://doi.org/10.1109/TMAG.2011.2167627
17. Studholme C, Hill DLG, Hawkes DJ. An overlap invariant entropy measure of 3D medical image align-
ment. Pattern Recognit. 1999; 32: 71–86. https://doi.org/10.1016/S0031-3203(98)00091-0
18. Maes F, Collignon A, Vandermeulen D, Marchal G, Suetens P. Multimodality image registration by max-
imization of mutual information. IEEE Trans Med Imaging. 1997; 16: 187–98. https://doi.org/10.1109/
42.563664 PMID: 9101328
19. Ashburner J. SPM: A history. Neuroimage. 2012; 62: 791–800. https://doi.org/10.1016/j.neuroimage.
2011.10.025 PMID: 22023741
20. Jenkinson M, Beckmann CF, Behrens TEJ, Woolrich MW, Smith SM. FSL. Neuroimage. 2012; 62:
782–790. https://doi.org/10.1016/j.neuroimage.2011.09.015 PMID: 21979382
21. Maintz JBA, Viergever MA. A survey of medical image registration. Med Image Anal. 1998; 2: 1–36.
https://doi.org/10.1016/S1361-8415(01)80026-8 PMID: 10638851
22. Pluim JPW, Maintz JBA, Viergever MA. Mutual-information-based registration of medical images: a sur-
vey. IEEE Trans Med Imaging. 2003; 22: 986–1004. https://doi.org/10.1109/TMI.2003.815867 PMID:
12906253
23. Zitova B. Image registration methods: a survey. Image Vis Comput. 2003; 21: 977–1000. https://doi.
org/10.1016/S0262-8856(03)00137-9
24. Liao Y-L, Sun Y-N, Guo W-Y, Chou Y-H, Hsieh J-C, Wu Y-T. A hybrid strategy to integrate surface-
based and mutual-information-based methods for co-registering brain SPECT and MR images. Med
Biol Eng Comput. 2011; 49: 671–85. https://doi.org/10.1007/s11517-010-0724-9 PMID: 21191661
25. Mercier L, Del Maestro RF, Petrecca K, Araujo D, Haegelen C, Collins DL. Online database of clinical
MR and ultrasound images of brain tumors. Med Phys. American Association of Physicists in Medicine;
2012; 39: 3253–61. https://doi.org/10.1118/1.4709600 PMID: 22755708
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 17 / 19
26. Fuerst B, Wein W, Mu¨ller M, Navab N. Automatic ultrasound-MRI registration for neurosurgery using
the 2D and 3D LC2 Metric. Med Image Anal. 2014; 18: 1312–1319. https://doi.org/10.1016/j.media.
2014.04.008 PMID: 24842859
27. MacKay DJC. Information Theory, Inference and Learning Algorithms [Internet]. Cambridge University
Press; 2003. p. 640. Available: http://www.amazon.com/Information-Theory-Inference-Learning-
Algorithms/dp/0521642981
28. Ja
¨hne B. Digital Image Processing [Internet]. Springer; 2002. p. 622. Available: http://www.amazon.
com/Digital-Image-Processing-Bernd-Jhne/dp/3540240357
29. Lehmann TM, Go
¨nner C, Spitzer K. Survey: interpolation methods in medical image processing. IEEE
Trans Med Imaging. 1999; 18: 1049–75. https://doi.org/10.1109/42.816070 PMID: 10661324
30. Sinibaldi R, Conti A, Pecci R, Plotino G, Guidotti R, Grande NM, et al. Software tools for the quantitative
evaluation of dental treatment effects from μCT scans. J Biomed Graph Comput. 2013; 3: 85–100.
https://doi.org/10.5430/jbgc.v3n4p85
31. Ingber L. Adaptive simulated annealing (ASA): Lessons learned [Internet]. Control and Cybernetics;
1996. pp. 33–54. Available: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.2777
32. Wolpert DH, Macready WG. No Free Lunch Theorems for Search. IEEE Trans Evol Comput. 1995; 1:
67–82. Available: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.5447
33. Press WH, Teukolsky SA, Vettering WT, Flannery BP. Numerical recipes: the art of scientific comput-
ing. Cambridge University Press; 2007.
34. Otsu N. A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern. 1979;
9: 62–66. https://doi.org/10.1109/TSMC.1979.4310076
35. Ashburner J. SPM: A history. Neuroimage. 2012; 62: 791–800. https://doi.org/10.1016/j.neuroimage.
2011.10.025 PMID: 22023741
36. Cha S-H. Comprehensive Survey on Distance / Similarity Measures between Probability Density Func-
tions. Int J Math Model Methods Appl Sci. 2007; 1: 300–307.
37. Choi S-S, Cha S-H, Tappert CC. A survey of binary similarity and distance measures. J Syst Cybern
Informatics. 2010; 8: 43–48.
38. Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image analysis. Nat Meth-
ods. Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.; 2012;
9: 671–675. https://doi.org/10.1038/nmeth.2089 PMID: 22930834
39. Jenkinson M, Smith S. A global optimisation method for robust affine registration of brain images. Med
Image Anal. 2001; 5: 143–156. https://doi.org/10.1016/S1361-8415(01)00036-6 PMID: 11516708
40. Nichols TE, Holmes AP. Nonparametric permutation tests for functional neuroimaging: a primer with
examples. Hum Brain Mapp. 2002; 15: 1–25. Available: http://www.ncbi.nlm.nih.gov/pubmed/
11747097 PMID: 11747097
41. Jenkinson M, Bannister P, Brady M, Smith S. Improved Optimization for the Robust and Accurate Lin-
ear Registration and Motion Correction of Brain Images. Neuroimage. 2002; 17: 825–841. https://doi.
org/10.1006/nimg.2002.1132 PMID: 12377157
42. Viergever MA, Maintz JBA, Klein S, Murphy K, Staring M, Pluim JPW. A survey of medical image regis-
tration–under review. Med Image Anal. 2016; 33: 140–144. https://doi.org/10.1016/j.media.2016.06.
030 PMID: 27427472
43. Sinibaldi R, Conti A, Sinjari B, Spadone S, Pecci R, Palombo M, et al. Multimodal-3D imaging based
on μMRI and μCT techniques bridges the gap with histology in visualization of the bone regeneration
process. J Tissue Eng Regen Med. 2017; https://doi.org/10.1002/term.2494 PMID: 28593731
44. Sarkar A, Santiago RJ, Smith R, Kassaee A. Comparison of manual vs. automated multimodality (CT-
MRI) image registration for brain tumors. Med Dosim. 2005; 30: 20–24. https://doi.org/10.1016/j.
meddos.2004.10.004 PMID: 15749007
45. Zaveri T. A Novel Region Based Multimodality Image Fusion Method. Comput Eng. 2011; 2: 140–153.
https://doi.org/10.13176/11.175
46. Sannazzari GL, Ragona R, Redda MGRUO, Giglioli FR, Isolato G, Guarneri A. CT–MRI image fusion
for delineation of volumes in three-dimensional conformal radiation therapy in the treatment of localized
prostate cancer. Br J Radiol. British Institute of Radiology; 2002; 75: 603–607. https://doi.org/10.1259/
bjr.75.895.750603 PMID: 12145134
47. Del Gratta C, Pizzella V, Tecchio F, Romani GL. Magnetoencephalography—a noninvasive brain imag-
ing method with 1 ms time resolution. Reports Prog Phys. 2001; 64: 1759–1814. https://doi.org/10.
1088/0034-4885/64/12/204
48. Adjamian P, Barnes GR, Hillebrand a, Holliday IE, Singh KD, Furlong PL, et al. Co-registration of
magnetoencephalography with magnetic resonance imaging using bite-bar-based fiducials and
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 18 / 19
surface-matching. Clin Neurophysiol. 2004; 115: 691–8. https://doi.org/10.1016/j.clinph.2003.10.023
PMID: 15036065
49. Troebinger L, Lo
´pez JD, Lutti A, Bradbury D, Bestmann S, Barnes G. High precision anatomy for MEG.
Neuroimage. 2014; 86: 583–591. https://doi.org/10.1016/j.neuroimage.2013.07.065 PMID: 23911673
50. Vesanen PT, Nieminen JO, Zevenhoven KCJ, Hsu YC, Ilmoniemi RJ. Current-density imaging using
ultra-low-field MRI with zero-field encoding. Magn Reson Imaging. 2014; 32: 766–770. https://doi.org/
10.1016/j.mri.2014.01.012 PMID: 24731792
51. Inglis B, Buckenmaier K, Sangiorgio P, Pedersen AF, Nichols MA, Clarke J. MRI of the human brain at
130 microtesla. Proc Natl Acad Sci U S A. National Academy of Sciences; 2013; 110: 19194–201.
https://doi.org/10.1073/pnas.1319334110 PMID: 24255111
Optimized co-registration of ULF and HF MRI
PLOS ONE | https://doi.org/10.1371/journal.pone.0193890 March 6, 2018 19 / 19
