Pectoral Muscle Segmentation in Tomosynthesis Images using Geometry

Information and Grey Wolf Optimizer

Mohamed Abdel-Nasser

1,2 a

, Francesc Porta Solsona

and Domenec Puig

1 b

Computer Engineering and Mathematics Department, University Rovira i Virgili, Tarragona, Spain

Electrical Engineering Department, Aswan University, Aswan, Egypt

Keywords:

Tomosynthesis, Breast Cancer, Pectoral Muscle, CAD Systems.

Abstract:

Digital breast tomosynthesis (DBT) is quickly replacing full-ﬁeld digital mammography because it allows

a more efﬁcient breast cancer diagnostic workﬂow and yields a more conﬁdent interpretation. The visual

characteristics of the pectoral muscle on mediolateral oblique (MLO) views may increase the false positive rate

in computer-aided diagnosis systems. Therefore, the pectoral muscle should be extracted from MLO images

before further analysis. Notably, most pectoral muscle segmentation method has a ﬁxed parameter setting

that may yield good results with some images and fail with others due to the variations in breast density. In

this paper, we propose a promising method to segment pectoral muscles from tomosynthesis images based on

geometric information of the pectoral muscle and a meta-heuristic optimization algorithm. Concretely, our

method involves four steps: 1) a preprocessing step, 2) obtaining of geometric information of pectoral muscle,

3) selection of pectoral muscle pixels, and 4) ﬁnding the optimal parameters using the grey wolf optimizer

(GWO). The GWO optimizer gets different parameters for each input image as they depend on the visual

characteristics of the images (i.e., breast density). With each input image, the GWO optimizer determines

different values of the parameters because they rely on the visual characteristics of tomosynthesis images that

are highly related to breast density. The proposed method is evaluated with a set of tomosynthesis images

obtaining a Dice score of 0.823 and an IoU score of 0.726.

1 INTRODUCTION

Breast cancer is one of the common cancers occur-

ring in women. Statistics reveal that the number of

predicted deaths due to breast cancer in the European

Union for the year 2019 is 92800 (Malvezzi et al.,

2019). However, there is evidence that early diagno-

sis and treatment of breast cancer can signiﬁcantly

raise the probability of survival (Lee et al., 2010).

Mammography (X-ray images of the breast) is, un-

til now, the most useful tool for global population

screening. However, the precise detection and diag-

nosis of a breast tumor completely based on mam-

mography ﬁndings is hard and really depends on the

expertise of the radiologist, which may yield a high

number of false positives and extra screenings and ex-

aminations (Hubbard et al., 2011). Computer-aided

detection and diagnosis (CAD) systems are already

being adopted to help radiologists in the decision-

making process (Abdel-Nasser et al., 2016a; Abdel-

Nasser et al., 2016b). Such systems may highly de-

https://orcid.org/0000-0002-1074-2441

https://orcid.org/0000-0002-0562-4205

crease the amount of effort necessitated for the eval-

uation of a lesion in clinical practice while decreas-

ing the number of false positives that may yield unde-

sirable biopsies. Nowadays, digital breast tomosyn-

thesis (DBT) is speedily succeeding in full-ﬁeld digi-

tal mammography because it enables a more effective

breast cancer diagnostic and produces a more trusting

interpretation.

Breast masses are seen as white regions in mam-

mograms. Hence CAD systems encounter difﬁculty

when analyzing these images in the mediolateral

oblique (MLO) view due to the appearance of the pec-

toral muscle, which has an appearance similar to the

pixels of the breast region that increases the false pos-

itive rate in CAD systems. Therefore, the pectoral

muscle should be removed from the breast region in

MLO images before additional analysis. The higher

number of images that need to be reviewed encoun-

ters a challenge for segmenting the pectoral muscle

manually (a time-consuming task). One of the main

steps of these CAD systems is the automated removal

of pectoral muscle from mammograms and tomosyn-

thesis images and leaving the breast region only.

It worth remarking that DBT images contain the

Abdel-Nasser, M., Solsona, F. and Puig, D.

Pectoral Muscle Segmentation in Tomosynthesis Images using Geometry Information and Grey Wolf Optimizer.

DOI: 10.5220/0009156408290836

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 5: VISAPP, pages

829-836

ISBN: 978-989-758-402-2; ISSN: 2184-4321

829

following kinds of pectoral muscles, namely, regu-

lar, convex, concave, and combinatorial. In the liter-

ature, numerous methods have been suggested to ex-

tract pectoral muscles. For example, in (Taghanaki

et al., 2017a), geometric rules with a region growing

algorithm are employed to segment pectoral muscles.

Few publicly available mammographic image anal-

ysis tools, such as LIBRA (Keller et al., 2015) and

OpenBreast (Pertuz et al., 2019), embrace the pectoral

muscle segmentation step.

Most pectoral muscle segmentation method set

a ﬁxed parameter setting that may work with some

images and fail with others due to the variations in

the density of breasts. In this paper, we propose a

promising method to automatically segment pectoral

muscles from tomosynthesis images based on geo-

metric information of the breast and a meta-heuristic

optimization algorithm. Speciﬁcally, the proposed

method comprises the following four steps: 1) a pre-

processing step, 2) obtaining of geometric informa-

tion of pectoral muscle, 3) selection of pectoral mus-

cle pixels, and 4) ﬁnding the optimal parameters using

the grey wolf optimizer (GWO). The GWO algorithm

determines different parameters for each input image

as they depend on the visual characteristics of the im-

ages (i.e., breast density). With each input image, the

GWO optimizer determines different values of the pa-

rameters because they rely on the visual characteris-

tics of tomosynthesis images that are highly related to

breast density.

The remaining of this paper comprises the sub-

sequent sections. Section 2 presents related work.

Section 3 explains the proposed method. Section 4

presents the results. Section 5 summarizes the paper.

2 RELATED WORK

There are several pectoral muscle segmentation tech-

niques, such as thresholding methods, active contours

methods, K-means clustering methods, region grow-

ing methods, edge detection using Gabor ﬁlters meth-

ods, statistical region properties methods, and deep

learning-based methods. Each of these methods has

a different complexity that varies from highly sophis-

ticated to low complex. Below, we present examples

of these methods and explain how they address the

problem of segmenting pectoral muscle.

In (Sreedevi and Sherly, 2015) and (Unni et al.,

2018), a global threshold is used to estimate an initial

pectoral muscle boundary, and a morphology-based

boundary reﬁnement algorithm is applied. The re-

sulting pectoral muscle region is then segmented by

a combination of global thresholding and connected

components methods. With a subset of 161 images

from the mini-MIAS mammographic images dataset,

(Sreedevi and Sherly, 2015) achieved an accuracy of

90.06% of based on visual observation of the correct-

ness of segmented images. The use of intensity only

for segmenting the pectoral muscle from the breast

region cannot produce a precise segmentation in most

cases. That happens because there is no signiﬁcant

variation in texture and intensity between the pectoral

muscle tissue and the other tissues of the breast.

The authors of (Ergin et al., 2016) proposed a

region growing algorithm, in which he positions of

initial seeds for the pectoral muscle region are de-

termined based on the intensity of the region. As

the intensity cannot be effectively used for detecting

complex textures such as muscles, (Taghanaki et al.,

2017b) proposed to use a set of geometric rules and a

region growing method to segment pectoral muscles.

Using the MIAS and DDSM mammographic images

datasets, they achieved segmentation accuracy of 95%

and 94%, respectively. Based on the assumption that

pectoral muscles are near the chest wall on the upper-

right or the upper-left of mammographic images, the

authors of (Selvathi and Poornila, 2018) used only a

single seed for region growing algorithm. If the pec-

toral muscle is at right, they set the seed point into

the last 5th column in the input images; otherwise,

they set it set into (5th column of and 5th row). The

pectoral muscle boundary is then reﬁned using mor-

phology operations.

Furthermore, line estimation methods are popular

pectoral muscle segmentation approaches, in which a

straight or a curve can represent the boundary of the

pectoral muscle. Hough transform is one of the most

popular line estimation method used for pectoral mus-

cle segmentation. Based on the Canny edge detector,

the authors of (Qayyum and Basit, 2016) proposed a

method for removing the pectoral muscle region from

mammograms. Firstly, a 3x3 median ﬁlter was used

to reduce the noise in input images. Then, they seg-

mented the initial pectoral muscle region by a com-

bination of the Canny edge detector and the inten-

sity of the region. The ﬁnal pectoral muscle bound-

ary was determined using a straight-line estimation

method applied to the boundary. They achieved an ac-

curacy of 93% accuracy with the mini-MIAS dataset.

Besides, the authors of (Palkar and Agrawal, 2016)

proposed a straight-line estimation method for remov-

ing the pectoral muscle from mammograms based on

the fact that the pectoral muscle is at the upper-left

region of the breast. In the case of the original im-

ages in which the chest wall is not on the left side

of the image, they ﬂipped them horizontally. Then,

the position of the middle-top pixel of the image was

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

830

computed and connected to the lowest-left pixel of the

rectangle approximating the pectoral muscle with the

straight-line connecting these pixels taken as the pec-

toral muscle boundary. Finally, the pectoral muscle

was segmented based on the approximated triangle

of the pectoral muscle boundaries. With the MIAS

dataset, they achieved an accuracy of 80%.

Shi et al. (Shi et al., 2018) used the four-class

K-means clustering method to segment the pectoral

muscles. First, they used a 5x5 median ﬁlter to reduce

the noise in the images and normalized the image in

order to enhance the contrast. Then, they clustered

the pixels and assigned the potential pectoral muscle

region candidate to the cluster with the highest inten-

sity. Next, they employed a Hough transform method

to extract the initial pectoral muscle boundary and re-

ﬁned the ﬁnal boundary by a polynomial curve ﬁtting

method.

Pavan et al. (Pavan et al., 2019) used a Canny

method for extracting the initial pectoral muscle re-

gion based on rules dervided from the location of

pectoral muscle in mammograms. To accurately seg-

ment the pectoral muscles, they used a contour grow-

ing technique with seeds deﬁned based on the ini-

tial pectoral muscle boundary. With a private dataset

(30 images), they achieved a mean Jaccard index of

0.92. Besides, Toz et al. (Toz and Erdogmus, 2018)

used neighborhood relations and geometrical proper-

ties for locating the pectoral muscle region. As the

pectoral muscle region often represented as a trian-

gle with high but homogeneous intensity, an initial

pectoral muscle region is determined using edge de-

tection at angles of 30

◦

–45

◦

. The resulting pectoral

muscle boundary was reﬁned using a linear interpo-

lation method to ﬁll any missing boundaries. With a

subset of 60 images from the INbreast dataset, they

achieved a mean sensitivity of 95.6%, a false positive

rate of 2.74%, and a false negative rate of 4.33%.

As shown above, almost all pectoral muscle seg-

mentation method has a ﬁxed parameter setting that

may perform well with some images and fail with oth-

ers due to the variations in the density of breasts. To

address this point, in this paper, we propose the use of

a GWO optimizer to determine the optimal parame-

ters required for segmenting the pectoral muscle from

the input image. Notably, GWO determines the dif-

ferent parameters for each input image as they depend

on the visual characteristics of the images (i.e., breast

density).

3 PROPOSED ALGORITHM

The proposed method comprises the following steps:

1) a preprocessing step, 2) obtaining of geometric in-

formation of pectoral muscle, 3) selection of pectoral

muscle pixels and 4) ﬁnding the optimal parameters

using the GWO optimizer.

3.1 Preprocessing of Tomosynthesis

Images

The preprocessing stage of the proposed algorithm in-

cludes three main steps: removing the outliers, align-

ing the orientation of images, and determining the

view of the images.

S1) Removing the Outliers: Figure 1 demon-

strates that tomosynthesis images contain the breast

region as well as outliers (small objects that exist in

tomosynthesis images). To segment the breast region

from other objects existing in images, we create a bi-

nary mask from the original image using a threshold

of 100, select the most prominent object in it (which

will presumably be the breast region), and suppress all

other small objects. This produces a mask that will be

smoothed and applied to the original image to obtain

the breast region only. Note that this region will also

contain the pectoral muscle that exists in MLO views

only.

S2) Aligning the Orientation of Images: To-

mosynthesis images could be left-oriented (the chest

on the left side of the image) or right-oriented. Here

we work with left-oriented images. As depicted in

Figure 2, we create two 3x3 windows, one on the

left side and one on the right side of the image. The

one that has the greater mean of intensity values in-

dicates the orientation of the image. If the image is

right-oriented, the image and the mask of the breast

area will be ﬂipped. Note that in the case of right-

oriented tomosynthesis images, the algorithm would

not be able to determine correctly whether the view

is craniocaudal (CC) or MLO, nor ﬁnd the pectoral

muscle if there is any.

S3) Determining the View of the Images: To

check if the input image has CC or MLO view, we

use prior information about the shape of the breast.

In the case of CC views, the breast regions tend to

have a semi-circular shape, while in the case of MLO

views, the top part of the breast is almost has a ver-

tical line shape. As shown in Figure 3, we set two

points at the top part of the breast edge (p1 and p2),

and then we ﬁnd the slope of the line that connects

p1 with p2. If this slope is close to the vertical line

slope, the view will be MLO. Differently, If this slope

is close to the horizontal line slope, the view will be

Pectoral Muscle Segmentation in Tomosynthesis Images using Geometry Information and Grey Wolf Optimizer

831

Figure 1: Preprocessing of tomosynthesis images. (a) original tomosynthesis image, (b) objects existing in the image, and (c)

segmented breast region.

Figure 2: Aligning the orientation of images. (a) a 3x3 Win-

dows, and (b) Flipped Image.

CC. Empirically, we set the slope limit to 45

. If the

slope is higher than the limit, the view will be MLO;

otherwise, CC. If the view is MLO, the next steps of

the proposed method will be carried out; differently,

and the algorithm will be terminated.

3.2 Obtaining of Geometric Rules

As shown in Figure 4, the edge of the pectoral muscle

is located at the point A (the top of the image–ﬁrst

row of image). To ﬁnd A, we compute the average of

the intensities in the breast region for the ﬁrst 30 rows

of the image. Then, this average value is used as a

threshold to create a binary image of the pixels with

a higher intensity in the 10th-row region at the top of

the image. As the images are prone to be affected by

noise, we do not directly take the last white pixel on

the ﬁrst row in the mask, and we smooth the shape of

this binary mask before locating where the edge is. To

smooth the mask, we take the edge location of the ﬁrst

ﬁve rows and compute the mean of the column value

of them, as it is still possible to ﬁnd some essential

variances in the mask even after the smoothing.

As depicted in Figure 5(a), we ﬁrst determine the

maximum inscribed circle (MIC) inside the breast re-

gion, by implementing the algorithm introduced in

(Xia et al., 2007). The MIC algorithm applies a vec-

tor distance transformation to create a distance ﬁeld,

and an intensity value is set for each pixel of the im-

age depending on the distance from that pixel to the

edges of the breast. Then, it globally searches for the

radius and center of the MIC. The center point O is

determined by selecting the pixel with the highest in-

tensity on the distance ﬁeld, and the radius r is the

distance from that pixel to the nearest edge point.

As shown in Figure 5(b), we determine the tangent

line from A to MIC. We can express this process as

follows:

• Calculate AO vector: AO = (x

− x

− y

)

• Get middle point in AO: C

= (

)

where C

is the center of a second circle with radius

that intersects with MIC in two points, and by

solving the formulas of the two circles, we can get the

intersections. It worth noting that the possible num-

ber of solutions (intersection points) of this problem

are:

• Two intersection points (crossing circles).

• One intersection point (tangent circles).

• No intersection (separated circles).

As the line AO includes the radius of MIC, our case

will always be the ﬁrst case (two crossing circles with

two intersection points). Therefore, we will choose

the leftmost point (lower x value) and deﬁne it as

point D. The line AD is extruded until it reaches the

left edge of the image to ﬁnd point B (see Figure 5(b)).

This extrusion is made by calculating the straight line

formula for AD y = m ∗ x +b, where m =

∆y

∆x

−y

−x

and b = y

− m ∗ x

, and set x

= 1 to ﬁnd y

using

the same formula. Note that we need to ﬁnd the point

B to create the right-angled triangle. The point B is at

the edge of the pectoral, in the ﬁrst column. It is difﬁ-

cult to ﬁnd B in the same way as A because, generally,

the intensity of the pectoral pixels is more similar to

the intensity of the breast ones due to the increasing

density of the breast. Notably, a bit similar steps are

employed in (Taghanaki, 2017).

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

832

Figure 3: Determining the view of the images. (d) Binary mask over the breast and point A location.

Figure 4: Obtaining of geometric rules.

3.3 Selection of Pectoral Muscle Pixels

We implement a region growing process inside the

triangle previously deﬁned by the geometrics of the

breast. The starting seed point is placed near the cen-

ter of this triangle to make sure that the seed is in-

side the pectoral region. The intial seed point is set to

(

). We formulate threshold of the selection

as follows:

th = I

− (dev) ∗ I

(1)

where I

is the average value of the intensities of the

accepted pixels in the region growing process (only

the seed at ﬁrst iteration).

As noise may cause deviations in intensity values,

and thus we do not calculate

from the intensities

of pixels directly. Instead, we apply a mean ﬁlter by

creating a 75x75 window around each pixel and com-

pute the average of the intensities inside this window.

Thus, I

is deﬁned as follows:

∑

i=1

(2)

here n is the number of pixels accepted in the region

growing, and px is the window average of a pixel.

px =

x,y=l1

∑

x,y=l1

px(X + x,Y + y)

(3)

where px(X,Y ) is the intensity of the selected pixel,

and x and y are the increments referring to the position

inside the window, and we set l1 to 37.

In each iteration of the selection of pectoral mus-

cle pixels, we perform the following:

• Select new pixel from the neighbour list (starts

with seed).

• Recalculate I

and th.

• Calculate the intensity px of the selected pixel.

• Compare px and th. If px is higher, accept pixel

and update n and the sum for I

• Add neighbouring non-selected pixels to the

neighbour list.

To add the neighboring pixels, we get the eight adja-

cent pixels around the selected pixel. In order to limit

the method inside the geometry triangle and avoid

adding the same pixel twice, we create a binary mask,

as shown in Fig.6. We will mark neighboring pixels

as zeros after adding them to the list, so if we mark a

neighbor of the current iteration as zero, we will not

include it again. The region growing process ﬁnishes

when there are no more pixels in the neighbor list.

3.4 Determining the Optimal

Parameters using the Grey Wolf

Optimizer (GWO)

Note that AB is a straight-line approximation, but the

edge of the pectoral muscle normally has a concave or

convex shape. Concave pectorals will always inside

the limit of the triangle, but for the convex ones, some

pixels might be outside this limit. To avoid the under-

segmentation of the pectoral muscle, we shift the line

AB to the right by a factor δ from the top-left corner to

B (see Figure 7). This is achieved by modifying the y-

intercept term in the straight-line formula b

= b + S,

where S = δ ∗ B

, and recalculating the x

and y

of A

and B

, respectively.

Here, we use the GWO optimizer proposed in

(Mirjalili et al., 2014) to ﬁnd the optimal values of

the shift δ of the line AB and the threshold parameter

dev. The GWO optimizer simulates the social hier-

archy of grey wolves, in order, alpha (α), beta (β),

delta (∆), and omega(ω) wolves. Alpha wolves are

the leaders that manage and conduct the whole pack

of wolves. They formulated the hunting mechanism

Pectoral Muscle Segmentation in Tomosynthesis Images using Geometry Information and Grey Wolf Optimizer

833

(a) (b)

Figure 5: (a) A-MIC intersection points, (b) AD extrusion to point B.

Figure 6: Position of the seed over the binary mask.

Figure 7: Original AB line and shifted AB’ line (hand-

drawn pectoral edge in orange).

of grey wolves using three steps: tracking and dimin-

ishing the prey, surrounding the prey until it stops, and

hitting it. The prey encircling is expressed as follows:

D =



C ·

(I) −



(4)

X(I +1) =

(I) −

A ·

D (5)

where I indicates the current iteration,

A and C are

coefﬁcient vectors,

(I) is the position vector of the

prey,

X refers to the position vector of a grey wolf,

and

C can be calculated as

A = 2~a ·~r

−~a,

C = 2~r

The wolf alpha guides the hunting process. Mir-

jalili et al. (Mirjalili et al., 2014) formulated this pro-

cess as

· X

− X

(6)



· X

− X



(7)

∆

· X

∆

− X

(8)

where

−

· (

−





∆

−

· (

∆

), and

X(I + 1) =

(

(I) +

(I)) /3. Finally, they model

the process of approaching and hunting the prey

by decreasing the value of A randomly in the range

[−wd, wd], and reduce the value of wd from 2 to 0

over the iteration.

In our experiments, we set the search ranges of

dev and δ, number of iteration, number of agents to

[0.3, 0.7], [-1/4, 1/4], 10, and 5, respectively. We cal-

culate the ﬁtness of each search agent using the seg-

mented pectoral regions. In this paper, we use en-

tropy, which is a statistical measure of randomness. It

can be used to characterize the texture of an image.

Entropy is deﬁned as follows:

E = −sum(p.∗ log2(p)) (9)

where p contains the normalized counts of the his-

togram of input image. The ﬁtness function is ex-

pressed as follows:

f it = 1 −

entropy

(10)

The Homogeneity measure the closeness of the distri-

bution of the elements in the image. Homogeneity is

deﬁned as follows (Y. Li, H. Chen, Y. Yang, N. Yang,

2013):

H =

∑

i=0

∑

j=0

1 +(i − j)

× p

(i, j) (11)

where p

(i, j) are the pixel intensities of the image,

and the homogeneity ﬁtness is expressed as follows:

f itH = 1 − homogeneity (12)

In future studies, we will use an artiﬁcial neural net-

work (Abdel-Nasser et al., 2018) instead of GWO to

ﬁnd the best parameters.

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

834

4 RESULT AND DISCUSSION

In our experiments, a total of 16 tomosynthesis im-

ages are employed to evaluate the performance of the

proposed method. We gathered the images from a

hospital in Spain (Hospital Universitario Puerta del

Mar). This paper used manually segmented pectoral

muscle regions as the ground-truth. Utilizing a com-

puter graphic user interface (GUI) tool in MATLAB,

we outlined pectoral muscle regions on tomosynthesis

images in the dataset of this research.

In this study, we use two metrics for evalu-

ating the efﬁcacy of the proposed method: Dice

and intersection-over-union (IoU). The Dice and IoU

scores can be deﬁned as follows:

Dice =

∩ Im

(13)

Jaccard =

∩ Im

∪ Im

(14)

where R

and R

are the segmentation masks of the

proposed method and the ground truth, respectively.

The values of Jaccard and Dice metrics vary from 0

to 1. If any of the two metrics have a value of 0, it

indicates that two masks have no common elements,

while we obtain a value of 1 with Jaccard and Dice

metrics if and only if the masks are identical. The

larger the values of the Jaccard and Dice metrics, the

more accurate the segmentation obtained by the pro-

posed method.

In Table 1 we show the Dice of the IoU scores of

the proposed method when using the Entropy and Ho-

mogeneity ﬁtness function. As shown, the proposed

method achieves the best results with the Homogene-

ity ﬁtness function with Dice score of 0.823 and an

IoU score of 0.726.

Table 1: Segmentation results of the proposed method.

Fitness Dice IoU

Entropy ﬁtness 0.816±0.11 0.702±0.15

Homogeneity ﬁtness 0.823±0.09 0.726±0.13

Figure 8 shows an example of pectoral muscle

segmentation in tomosynthesis images. Figure 8(a)

shows the input tomosynthesis image, Figure 8(b)

presents the binary mask generated by the proposed

method. The binary mask is multiplied with the

the input tomosynthesis image to suppress the pec-

toral muscle. As shown in Figure 8(c), the proposed

method accurately segment the pectoral muscle from

the breast area.

5 CONCLUSIONS

In this paper, we have presented a promising method

for pectoral muscle segmentation from tomosynthesis

images automatically. The proposed method includes

four steps: 1) a preprocessing step, 2) obtaining of

geometric information of pectoral muscle, 3) selec-

tion of pectoral muscle pixels, and 4) ﬁnding the opti-

mal parameters using the grey wolf optimizer (GWO).

The optimizer determines distinct parameters setting

for each input image as they depend on its breast den-

sity. The proposed method is assessed with a set of

tomosynthesis images and achieved a Dice score of

0.823 and an IoU score of 0.726. The future work will

be focused on the use of various ﬁtness function as

well as evaluating the proposed with a larger dataset

of tomosynthesis images.

ACKNOWLEDGEMENTS

This research was partly supported by the Spanish

Govern-ment through project DPI2016-77415-R.

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