††thanks: Present address: Wainvam-e, 1 Rue Galilée, 56270 Ploemeur,
France††thanks: Present address: Institute of Physics, Ecole Polytechnique
Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland††thanks: Present
address: Laboratoire de Physique des Matériaux et Surfaces, CY Cergy Paris
Université, 95031 Cergy-Pontoise, France

# Optical properties of SiV and GeV color centers in nanodiamonds under
hydrostatic pressures up to 180 GPa

Baptiste Vindolet  Université Paris-Saclay, CNRS, ENS Paris-Saclay,
CentraleSupelec, LuMIn, F-91190 Gif-sur-Yvette, France  Marie-Pierre Adam
Université Paris-Saclay, CNRS, ENS Paris-Saclay, CentraleSupelec, LuMIn,
F-91190 Gif-sur-Yvette, France  Loïc Toraille  Université Paris-Saclay, CNRS,
ENS Paris-Saclay, CentraleSupelec, LuMIn, F-91190 Gif-sur-Yvette, France  CEA
DAM DIF, F-91297 Arpajon, France  Université Paris-Saclay, CEA, Laboratoire
Matière en Conditions Extrêmes, 91680 Bruyères-le-Châtel, France  Mayeul
Chipaux  Fachrichtung Physik, Universität des Saarlandes, Campus E2.6, 66123
Saarbrücken, Germany  Antoine Hilberer  Université Paris-Saclay, CNRS, ENS
Paris-Saclay, CentraleSupelec, LuMIn, F-91190 Gif-sur-Yvette, France  Géraud
Dupuy  Université Paris-Saclay, CNRS, ENS Paris-Saclay, CentraleSupelec,
LuMIn, F-91190 Gif-sur-Yvette, France  Lukas Razinkovas  Center for Physical
Sciences and Technology (FTMC), Vilnius LT-10257, Lithuania  Audrius Alkauskas
Center for Physical Sciences and Technology (FTMC), Vilnius LT-10257,
Lithuania  Gergő Thiering  Institute for Solid State Physics and Optics,
Wigner Research Centre for Physics, Budapest, POB 49, H-1525, Hungary  Adam
Gali  Institute for Solid State Physics and Optics, Wigner Research Centre for
Physics, Budapest, POB 49, H-1525, Hungary  Department of Atomic Physics,
Institute of Physics, Budapest University of Technology and Economics,
Műegyetem rakpart 3., H-1111, Budapest, Hungary  Mary De Feudis  Laboratoire
des Sciences des Procédés et des Matériaux, CNRS, Université Sorbonne Paris-
Nord, F-93340 Villetaneuse, France  Midrel Wilfried Ngandeu Ngambou
Laboratoire des Sciences des Procédés et des Matériaux, CNRS, Université
Sorbonne Paris-Nord, F-93340 Villetaneuse, France  Jocelyn Achard  Laboratoire
des Sciences des Procédés et des Matériaux, CNRS, Université Sorbonne Paris-
Nord, F-93340 Villetaneuse, France  Alexandre Tallaire  Laboratoire des
Sciences des Procédés et des Matériaux, CNRS, Université Sorbonne Paris-Nord,
F-93340 Villetaneuse, France  Martin Schmidt  Université Paris-Saclay, CNRS,
ENS Paris-Saclay, CentraleSupelec, LuMIn, F-91190 Gif-sur-Yvette, France
Christoph Becher  Fachrichtung Physik, Universität des Saarlandes, Campus
E2.6, 66123 Saarbrücken, Germany  Jean-François Roch  To whom correspondence
should be addressed; E-mail<EMAIL_ADDRESS>Université
Paris-Saclay, CNRS, ENS Paris-Saclay, CentraleSupelec, LuMIn, F-91190 Gif-sur-
Yvette, France

###### Abstract

We investigate the optical properties of silicon-vacancy (SiV) and germanium-
vacancy (GeV) color centers in nanodiamonds under hydrostatic pressure up to
180 GPa. The nanodiamonds were synthetized by Si or Ge-doped plasma assisted
chemical vapor deposition and, for our experiment, pressurized in a diamond
anvil cell. Under hydrostatic pressure we observe blue-shifts of the SiV and
GeV zero-phonon lines by 17 THz (70 meV) and 78 THz (320 meV), respectively.
These measured pressure induced shifts are in good agreement with ab initio
calculations that take into account the lattice compression based on the
equation of state of diamond and that are extended to the case of the tin-
vacancy (SnV) center. This work provides guidance on the use of group-IV-
vacancy centers as quantum sensors under extreme pressures that will exploit
their specific optical and spin properties induced by their intrinsic
inversion-symmetric structure.

##  I Introduction

Quantum sensing consists in using quantum systems to perform measurement of
given physical quantities [1]. Among the various systems that have been
developed, the nitrogen-vacancy (NV) center in diamond has been used to
demonstrate and implement a broad variety of sensing protocols, in particular
for the measurement of magnetic and electric fields, and also for the
detection of stress, temperature, mechanical vibrations, and fluctuating
electromagnetic fields [2]. Due to the stiffness of the hosting diamond
crystal, the NV center is also offering a powerful solution for probing matter
at the extreme static pressures that are routinely achieved in a diamond anvil
cell (DAC) consisting of two anvils that squeeze the sample between their
flattened tips [3], as shown in Fig. 1a. In order to push the pressure limits,
the pressure amplification of the DAC is optimized, essentially by reducing
the culet diameter then putting a constraint on the sample size. For pressures
above 100 GPa this leads to sample chambers of less than 50 $\mu$m diameter
and to the corresponding experimental difficulties in handling and signal
detection. Using the optically detected magnetic resonance (ODMR) of the NV
electronic spin that can be recorded by collecting the luminescence of the NV
centers through the diamond anvil, recent works have shown the applicability
of NV based optical magnetometry to micrometer sized samples under pressure
and external magnetic fields [4, 5, 6]. Since the NV centers can be placed in
close proximity to the sample, the NV based detection can be used to map the
magnetic field distribution created by the sample magnetization, with a
micrometer spatial resolution and with a sensitivity that remains mostly
unaffected by the constraints on the sample size.

However the use of the NV center as a high pressure magnetic sensor suffers
from some limitations, such as the implementation of the microwave excitation
with the constraints associated to the DAC [5] or the detrimental influence of
off-axis magnetic field that may prevent its practical use at high magnetic
field [7]. These features are specific to the NV center and not to diamond in
general. In particular the silicon-vacancy (SiV) and, to a somewhat lesser
extent, germanium-vacancy (GeV) and tin-vacancy (SnV) centers in their
negative charge state are alternative diamond point defects that have
attracted considerable attention in the past decade [8]. These centers,
commonly known as group-IV-vacancy (G4V) centers, share a nearly identical
atomic structure. The reasons why G4V centers have potential advantages
compared to the NV center are two-fold. First, G4V centers exhibit
extraordinary spectral stability due to their intrinsic inversion-symmetric
structure as shown in Fig. 1a [9, 10]. This property is associated to the
$D_{3d}$ point group symmetry of all G4V centers. Second, G4V centers offer
the option of all-optical, microwave free, coherent control of their spin
states [11, 12, 13, 14, 15, 16], allowing for applications where the use of
microwave fields, as required for most NV-based sensing methods, is
detrimental or technically challenging.

As a preliminary step to envisioning the use of G4V centers for high-pressure
sensing, i.e. at pressures above the megabar, we report here the pressure
dependence of the photoluminescence (PL) spectral properties of the SiV and
GeV center at room temperature, using doped nanodiamonds in a DAC. The
evolution of the PL center wavelength with pressure for these two G4V centers
is well reproduced by ab initio density functional theory (DFT) calculation of
the PL zero-phonon line (ZPL). In these calculations the pressure dependence
is computed by varying the lattice parameter according to the equation of
state of diamond that can be taken as a reference for the matrix hosting the
point defect [17].

##  II Experimental set-up

Figure 1:  (a) Description of the high pressure experiment. SiV and GeV-doped
nanodiamonds (shown in blue) are deposited on the tip of one of the two
diamonds (D) assembled in a diamond anvil cell (DAC). The geometry of the SiV
and GeV center of D3d symmetry is shown on the left. The Si/Ge impurity (in
purple) is linked to two vacancies (in dashed lines) aligned along one
crystallographic axis [111] of the lattice of carbon atoms (in black). The
excitation laser (L) is transmitted through an optical fiber, reflected by a
dichroic mirror (DM) and then focused on the anvil tip with a microscope
objective (O). The SiV/GeV photoluminescence (PL) is collected by the same
objective, transmitted by the dichroic mirror and focused in an optical fiber
linked to a photon counting detector or a spectrograph (S). The remaining
parasitic light from L is removed by a longpass filter (F). (b) Image of the
DAC metallic gasket (G), observed through the diamond anvil, at 8.1 GPa during
the GeV spectroscopy experiment. (c) Scanning electron microscopy image of a
typical cluster of GeV-doped nanodiamonds.

The pressure dependence of the G4V center PL spectra is investigated using
nanodiamonds doped with SiV and GeV centers. The nanodiamonds were synthesized
by plasma assisted chemical vapor deposition (CVD) while introducing inside
the plasma a solid silicon or germanium source in the vicinity of a molybdenum
holder [18]. The amount of SiV and GeV centers directly produced in the
nanodiamonds can be controlled by adding N2 and O2 gases to the standard
mixture of H2/CH4 used for the CVD diamond growth [19]. This method is well
suited for the mass production of nanodiamonds doped with SiV or GeV centers.
We estimate the incorporated color center density to a few tens of ppb,
corresponding to several hundreds of color centers per nanodiamond with a
typical size of about 200 nm. The nanodiamonds are then retrieved by rinsing
the holder with ethanol. A drop of $\lesssim 1\leavevmode\nobreak\ \mu$L of
each of these solutions is then deposited on the flattened tips of diamond
anvils. The anvils, made of synthetic ultrapure diamond, are cut with Almax-
Boehler design [20]. The anvil tip is a (100) cristallographic plane and has a
diameter of 100 $\mu$m. After the evaporation of the ethanol solvent, clusters
of the CVD-grown nanodiamonds appear on the tip, as shown in Figs. 1b and 1c.

The anvils are mounted in a non-magnetic DAC with a rhenium metallic gasket
ensuring lateral confinement (Fig. 1a). The DAC is loaded with neon gas as the
pressure transmitting medium. The soft neon environment, which becomes solid
at $4.7\,{\rm GPa}$ [21], ensures the hydrostatic compression of the
nanodiamonds. The pressure in the DAC can be continuously tuned using a
metallic membrane that controls the load applied on the anvils [22]. The DAC
is then integrated in a customized optical confocal microscope equipped with a
microscope objective (0.35 numerical aperture and 18 mm working distance) that
collects the PL of the G4V centers through the diamond anvil on which the
nanodiamonds have been deposited.

##  III Spectroscopy of the silicon-vacancy center

PL spectra of seven clusters of SiV-doped nanodiamonds were recorded for
increasing pressures up to 180 GPa where the failure of an anvil induced an
irreversible decompression of the DAC. The PL was excited using a single-mode
cw laser at 532 nm wavelength. A ruby crystal of micrometer size was
introduced in the DAC as a pressure gauge [23]. The pressure in the DAC was
simultaneously determined from the shifts of the ruby PL and of the first-
order Raman mode of the diamond anvil under load, following the analysis
described in Ref. [24].

Fig. 2 shows the spectra recorded on one cluster of SiV-doped nanodiamonds for
increasing pressure steps of about 10 GPa. The increase of pressure induces a
blue shift of the PL line as expected from the enhanced confinement of the SiV
electronic wavefunctions in the ground and excited states. The spectra are
then fitted by a Lorentzian function in order to determine both the center
emission wavelength and the linewidth. Recorded with a constant laser
excitation power of 15 mW, the total PL intensity associated to a given
nanodiamond slightly decreased with increasing pressure. We attribute this
effect to the shift of the absorption spectrum, leading to a decrease of the
absorption cross-section at 532 nm wavelength.

The pressure dependence of the center energy, averaged over the seven
aggregates that were investigated, is shown on Fig. 3. We estimated the error
of the pressure measurement as $\pm 1$ GPa below 79 GPa, where the pressure
was accurately determined using the Ruby reference, and $\pm 8$ GPa for the
Raman scattering pressure measurement that was used above 79 GPa. The
statistical error of the SiV mean energy is about $\pm 2.5$ meV for 95%
confidence interval. The graph also indicates the corresponding value of the
lattice parameter inferred from the equation of state of diamond under
hydrostatic condition [17]. The results are in good agreement with previous
measurements where the pressure dependence of the SiV PL was measured up to 50
GPa using HPHT grown nanodiamonds loaded in a DAC [25]. Although the size of
the anvil tip prevented us to record a significant number of points at the
start of the pressure exploration, the shift as a function of pressure below
20 GPa is approximately linear with a slope of about 1 meV/GPa. This value
agrees with independent measurements previously performed in this weak strain
regime by bending a diamond cantilever that integrated a single SiV center
[26].

Fig. 2 also shows that the pressure induced shift is associated to a
broadening of the PL. Indeed the ab initio DFT calculation on the strain
induced ZPL shift done in Ref. [27] showed that hydrostatic pressure results
in a blue shift whereas uniaxial stress results in red shifts. The broad
inhomogeneous distribution of the spectral properties of SiV centers that is
observed in milled or CVD grown nanodiamonds was then explained by the
uncontrolled strain environment compared to the highly reproducible properties
of SiV centers designed by ion implantation in high quality bulk diamond
crystals. Such inhomogeneities could be reduced by the synthesis of high-
pressure high-temperature nanodiamonds with Si or Ge precursors [28, 29] or by
improving the CVD growth process [30]. The PL linewidth also depends on the
electron-phonon interaction. Since the electronic states are shifted and mixed
by strain, the electron-phonon scattering might be affected (see e.g. Ref.
[27]) then possibly contributing to a pressure-dependent homogeneous
broadening of the PL spectrum.

Figure 2: Pressure dependence of the photoluminescence (PL) spectra of SiV
centers (shown in red, right) and GeV centers (shown in blue, left) in CVD
grown nanodiamonds. The modulation on the SiV spectra is an artifact due to
parasitic interference on the imaging detector that we first used to record
the PL spectrum of the nanodiamonds. The GeV spectra were recorded with an
improved spectrograph free of this artifact. The increase of pressure induces
a blue shift and a broadening of the PL lines. Pressure steps for SiV (from
lowest to highest curve): 1, 9, 20, 32, 40, 51, 60, 70, 79, 89, 96, 103, 110,
125, 137, 155, 171, and 180 GPa. Pressure steps for GeV (from lowest to
highest curve): 8, 12, 20, 30, 40, 50, 60, 69, 79, 90, 99, 109, 119, 130, 140,
149, 157, and 168 GPa. The plots are separated vertically by the change of
pressure which is indicated by the horizontal, dotted lines. Inset: GeV
spectrum recorded at 140 GPa showing its deconvolution by two shifted
Lorentzian components.

##  IV Spectroscopy of the germanium-vacancy center

A similar and complementary experiment was performed by loading a DAC with
GeV-doped nanodiamonds and recording the evolution of their PL with increasing
pressures up to about 170 GPa. The DAC was prepared following the same
procedure as previously without integrating a ruby crystal since its PL could
induce a parasitic signal superimposed with the GeV PL. The pressure in the
DAC was then determined from the first-order Raman mode associated to the
compression of the diamond lattice, using the same analysis as in the SiV
experiment [24].

Fig. 2 shows the spectra recorded on a given cluster of GeV-doped
nanodiamonds, exhibiting a similar behavior as for the SiV-doped nanodiamonds.
From 8 GPa to 93 GPa, the GeV centers were excited using a single-mode cw
laser at 532 nm wavelength and with a power of 75 mW. Above this pressure, the
laser excitation was switched to a single-mode cw laser at 488 nm wavelength
in order to compensate the blue shift of the GeV absorption spectrum. The
laser excitation power was 37 mW. The PL spectrum could then be recorded until
the failure of the anvils that happened at 168 GPa. Note that above
approximately 100 GPa, the PL line is split in two components as shown in the
inset of figure 2. This splitting could be induced by the non-hydrostatic
stress inside the nanodiamond which then breaks the $D_{3d}$ symmetry that
characterizes the G4V center [31, 32], similarly to previous measurements
realized on the NV center [33]. The experimental spectra were then fitted by
two Lorentzian functions and the PL center energy was taken as the average of
the two center positions of this fit.

Fig. 3 shows the evolution of the PL center energy, averaged over the three
clusters of GeV-doped nanodiamonds that were investigated, as a function of
the pressure in the DAC. The pressure was determined with an uncertainty of
$\pm 1$ GPa and the statistical error of the GeV mean energy is about $\pm 10$
meV for 95% confidence interval. The shift with pressure is about four times
faster for the GeV center than for the SiV center.

##  V Ab initio study of ZPL energies as a function of pressure

###  V.1 Methodology

The electronic structure and the optical excitation energies of the G4V
centers in diamond can be efficiently computed using the spin-polarized DFT
formalism. In the molecular-orbital picture, the ground ${}^{2}\\!E_{g}$ and
excited ${}^{2}\\!E_{u}$ states of these point defects can be expressed as
single Slater determinant wavefunctions with respective electronic
configurations of $e_{u}^{4}e_{g}^{3}$ and $e_{u}^{3}e_{g}^{4}$ [9].
Therefore, in the framework of Kohn–Sham DFT, the energy and geometric
structure of the excited ${}^{2}\\!E_{u}$ state can be calculated by employing
the so-called delta-self-consistent-field ($\Delta$SCF) approximation, whereby
one $e_{u}$ electron in the lower-lying occupied Kohn–Sham level is promoted
to an empty $e_{g}$ level (see, e.g., Refs. [9, 10, 34]).

To describe the SiV and the GeV centers’ electronic structure and extend it to
the case of the SnV center, we used the SCAN exchange–correlation functional
[35] that belongs to the class of so-called meta-GGA functionals. This
functional provides an accurate description of bulk diamond structural
properties, yielding predictions of the diamond lattice constant
$a_{0}=3.554\leavevmode\nobreak\ \mbox{\AA}$ and bulk modulus (based on the
Rose–Vinet equation of state [36]) $B=460\leavevmode\nobreak\ \mbox{GPa}$ in
close agreement with the experimental values $a_{0}=3.555\leavevmode\nobreak\
\mbox{\AA}$ [37] and $B=446\leavevmode\nobreak\ \mbox{GPa}$ [38]. The point
defects were then modeled using $4\times 4\times 4$ supercells with 512 atomic
sites, and the Brillouin zone was sampled at the $\Gamma$ point. We used the
projector-augmented wave (PAW) approach [39] as implemented in the Vienna Ab-
initio Simulation Package (VASP) [40] with a plane-wave energy cutoff of 600
eV. Calculations for non-zero stresses are then performed by modifying the
lattice constant of the defected cell according to the equation of state of
diamond [36, 17] using theoretical parameters calculated for bulk diamond.

Figure 3: Values of the PL center energies obtained from the experimental
measurements of Fig. 2 for the SiV and GeV centers, plotted as a function of
pressure. The error bars indicated in the main text are smaller than the size
of the data points. The upper axis indicates the corresponding values of the
lattice parameter ratio $x=a/a_{0}$, where $a$ is the value deduced from the
equation of state of diamond at a given pressure [17] and $a_{0}$ is the value
at null pressure [36]. The data for the SiV and GeV centers are represented by
blue (lower) and red (upper) dots, respectively. The two solid lines show the
results of the ab initio calculations of the zero-phonon line (ZPL) energy,
extended to the case of the SnV center (in green). The calculated lines have
been shifted to retrieve the ZPL energies at null pressure (1.68 eV for the
SiV center, 2.06 eV for the GeV center, and 2.00 eV for the SnV center,
respectively). The deviation observed for the GeV center below 20 GPa is
attributed to a bias in the pressure estimate when we started to increase the
pressure load applied to the DAC. The measurement of pressure using the Raman
scattering signal is relevant only above 20 GPa, where we observe a good
agreement with the result of the ab-initio calculations. The inset shows the
relative shift of the ZPL energies as calculated from the total energy
differences between excited and ground states, with the influence of the
growing atomic radii of the group-IV atom once embedded in the diamond lattice
as an interstitial impurity.

###  V.2 Results

The ZPL energies at each pressure are calculated as the difference between the
total energies of the excited and ground states using the $\Delta$SCF
approximation. At zero pressure, we obtain ZPL energies of 1.57 eV, 2.00 eV,
and 1.98 eV for the negatively charged SiV, GeV, and SnV centers,
respectively. These values are slightly smaller than the experimentally
measured ZPL energies of 1.68 eV, 2.06 eV, and 2.00 eV. Note that the accuracy
of the $\Delta$SCF method with SCAN functional is close to that of the HSE
functional [10], albeit at much lower computational costs.

The calculated ZPL values of G4V centers as a pressure function are shown in
Fig. 3 by solid lines. For a meaningful comparison with an experiment, a
constant offset is applied to the theoretical curves so that the ZPL energies
at null pressure correspond to the reported experimental values. When aligned
this way, the DFT results agree very well with the center energies that were
previously measured for the SiV and the GeV centers in all the pressure range
that was probed in the experiments.

Figure 4: Relative shift of the ZPL energies as a function of pressure as
calculated from Kohn–Sham eigenvalues $\Delta
E_{\mathrm{ZPL}}^{\mathrm{KS}}(p)=\varepsilon_{e_{g}}(p)-\varepsilon_{e_{u}}(p)$.
The inset shows the relative change of the single-particle Kohn–Sham levels in
the reference system of valence band maximum (VBM). The $e_{g}$ and $e_{u}$
single-particle energies are represented as solid and dashed lines. Dotted
gray line denotes the conduction band minimum (CBM) as calculated in the
$\Gamma$ point of the $4\times 4\times 4$ supercell.

The inset of Fig. 3 shows the relative change of theoretical ZPL energy
($\Delta$ZPL) for the three different G4V centers as a function of pressure.
We see that the rate of change is more pronounced for heavier impurity atoms
with higher atomic radii. Keeping in mind the similarity of the electronic
structure of all G4V defects, this naturally prompts a question regarding the
reason for this difference.

###  V.3 Single-particle picture

Inspection of Kohn–Sham molecular orbital states reveals that the trend can be
explained qualitatively using a single-particle picture. Indeed the single-
particle energies allow for a qualitative chemical insight since the
excitation energy can be roughly approximated as a difference between
unoccupied and occupied states.

Fig. 4 shows the relative change of the ZPL as a function of pressure as
calculated from a difference between $e_{g}$ and $e_{u}$ single-particle
energies in the electronic ground state. To investigate the orbital energy
response to strain, the inset of Fig. 4 shows the change of single-particle
energies in the reference system of valence band maximum (VBM)
$\Delta\varepsilon_{i}(p)\equiv[\varepsilon_{i}(p)-\varepsilon_{\mathrm{VBM}}(p)]-[\varepsilon_{i}(0)-\varepsilon_{\mathrm{VBM}}(0)]$.
Here, $\varepsilon_{i}(p)$ is the Kohn–Sham energy of orbital
$\varepsilon_{i}$ at pressure $p$, and $\varepsilon_{\mathrm{VBM}}$ is the
orbital energy of VBM. One can observe that the major difference between all
three G4V centers lies in the deformation potential of the $e_{g}$ orbital.
Based on the argument that the VBM and conduction band minimum (CBM) states
are of bonding and antibonding characters [41], one can deduce that $e_{g}$
orbital changes its nature from bonding to antibonding as we increase the
atomic number of the group-IV atom. An extended analysis of the difference in
the electronic structure and chemical bonding of G4V centers will be given in
an upcoming study.

##  VI Summary and conclusion

We measured the pressure dependence of the SiV and GeV PL to about 180 GPa by
integrating nanodiamonds in a DAC that were doped with Si or Ge impurities
during their plasma-assisted growth. The experimental results are in good
agreement with ab initio calculations that compute the pressure dependence of
the ZPL of these G4V centers to the equation of state of diamond. This direct
link suggests that SiV and GeV centers could be used as pressure calibration
gauges, adding a new tool to the implementation of a practical pressure scale
above the megabar [23].

The pressure dependence of the PL energies also reveals a difference between
the G4V centers, being more rigidly bonded in the diamond crystal lattice for
increasing atomic radii. These measurements are the first steps to determine
the optical and magnetic properties of G4V centers under a broad set of
parameters that could be explored by combining high pressure and low
temperature: Jahn-Teller relaxation energies, spin-orbit splitting of the
ground and excited states under the influence of high stress, orbital
relaxation rate. Lastly, charge-neutral G4V centers, and in particular the
neutral SiV0 center [42], could be a complementary resource since these
defects can host a coherent spin that can be optically addressed with near
infrared light.

##  VII Acknowledgments

We are grateful to Paul Loubeyre for his insightful advices and comments, and
to Florent Occelli for his constant help and availability in handling high
pressure instrumentation. Funding: This work has received funding from the
QuantERA II program under project no. 4991922368 SENSEXTREME (grant
S-QUANTERA-22-1 from the Research Council of Lithuania), from the Agence
Nationale de la Recherche under the project SADAHPT and the ESR/EquipEx+
program (grant number ANR-21-ESRE-0031), from the EMPIR program co-financed by
the Participating States and the European Union’s Horizon 2020 research and
innovation program (20IND05 QADeT), and from the Paris Île-de-France Région in
the framework of DIM SIRTEQ. Computations were performed on the supercomputer
GALAX of the Center for Physical Sciences and Technology, Lithuania, and on
the High-Performance Computing Center “HPC Sauletekis” in the Faculty of
Physics, Vilnius University. A.G. acknowledges the National Research,
Development, and Innovation Office of Hungary (NKFIH) grant No. KKP129866 of
the National Excellence Program of Quantum-coherent materials project and the
Quantum Information National Laboratory supported by the Ministry of
Innovation and Technology of Hungary. The work of BV was funded by a Ph.D.
research grant from Délégation Générale de l’Armement. JFR acknowledges
support from Institut Universitaire de France. Data and material availability:
All experimental data described here are available at Zenodo [43].

##  VIII Appendix

| SiV center | GeV center | SnV center
---|---|---|---
Measured |  $1.0$ (0-20 GPa) |  $2.7$ (20-40 GPa) |
Computed (below $50\,{\rm GPa}$) | 1.00 | 2.90 | 3.85
Ref. [25] (below $50\,{\rm GPa}$) | 1.09 |  |
Ref. [44] (below $6\,{\rm GPa}$) |  | 3.11 |
Ref. [45] (below $9\,{\rm GPa}$) |  |  | 3.52
Ref. [46] (DFT) | 1.1 | 3.2 | 3.5
Table 1: Pressure dependence of the measured PL mean energies and computed ZPL
energies for the G4V centers. The linear dependence is given in meV/GPa.
Taking into account the bias in the pressure measurement at the start of the
pressure load, the experimental value for the GeV center is determined between
20 to 40 GPa. Extrapolation below 20 GPa might give a result closer to the
computed value due to the nonlinearity of the diamond equation of state.

Table 1 compares our measured and computed values of the linear dependence of
the PL mean energies and ZPL energies in the low pressure regime (up to 20
GPa) with previously published values. The experimental values were obtained
by integrating in a DAC powders of Si [25], Ge [44] and Sn [45] doped
microcrystals that were synthetized from hydrocarbons at high pressures and
high temperatures. The table also indicates the pressure shift that was
previously computed using the Quantum ESPRESSO package implemented with a
computational periodic supercell consisting of 83 atomic sites [46].

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# Segmentation of Lung Tumor from CT Images using Deeply Supervised
MultiResUNet††thanks: Farheen and Shamil contributed equally.

Farhanaz Farheen  Department of CSE, BUET, ECE Building, West Palasi,
Dhaka-1230, Bangladesh  Department of CSE, United International University,
Dhaka, Bangladesh  Md. Salman Shamil  Department of CSE, BUET, ECE Building,
West Palasi, Dhaka-1230, Bangladesh  Department of CSE, United International
University, Dhaka, Bangladesh  Nabil Ibtehaz  Department of CSE, BUET, ECE
Building, West Palasi, Dhaka-1230, Bangladesh  M. Sohel Rahman Corresponding
Author<EMAIL_ADDRESS>Department of CSE, BUET, ECE Building, West
Palasi, Dhaka-1230, Bangladesh

# Segmentation of Lung Tumor from CT Images using Deep Supervision††thanks:
Farheen and Shamil contributed equally.

Farhanaz Farheen  Department of CSE, BUET, ECE Building, West Palasi,
Dhaka-1230, Bangladesh  Department of CSE, United International University,
Dhaka, Bangladesh  Md. Salman Shamil  Department of CSE, BUET, ECE Building,
West Palasi, Dhaka-1230, Bangladesh  Department of CSE, United International
University, Dhaka, Bangladesh  Nabil Ibtehaz  Department of CSE, BUET, ECE
Building, West Palasi, Dhaka-1230, Bangladesh  M. Sohel Rahman Corresponding
Author<EMAIL_ADDRESS>Department of CSE, BUET, ECE Building, West
Palasi, Dhaka-1230, Bangladesh

## Abstract

Lung cancer is a leading cause of death in most countries of the world. Since
prompt diagnosis of tumors can allow oncologists to discern their nature, type
and the mode of treatment, tumor detection and segmentation from CT Scan
images is a crucial field of study worldwide. This paper approaches lung tumor
segmentation by applying two-dimensional discrete wavelet transform (DWT) on
the LOTUS dataset for more meticulous texture analysis whilst integrating
information from neighboring CT slices before feeding them to a Deeply
Supervised MultiResUNet model. Variations in learning rates, decay and
optimization algorithms while training the network have led to different dice
co-efficients, the detailed statistics of which have been included in this
paper. We also discuss the challenges in this dataset and how we opted to
overcome them. In essence, this study aims to maximize the success rate of
predicting tumor regions from two-dimensional CT Scan slices by experimenting
with a number of adequate networks, resulting in a dice co-efficient of
0.8472.
Keywords: Lung tumor, CT scan images, deep learning, discrete wavelet
transform.

##  1 Introduction

Cancer is one of the most fatal afflictions that can affect the human body and
is indisputably a leading cause of death worldwide. Lung cancer is the most
commonly diagnosed cancer in the world with instances constituting 11.6% of
total cancer cases and is also the prime cause of cancer-related fatalities,
covering 18.4% of them [1]. Apart from facing distressing chest pain, weight
loss and cough, lung cancer patients are more likely to suffer from chronic
obstructive pulmonary disease [2]. Mutation of lung cells - often prompted by
imprudent smoking, which is the primary cause of lung cancer or simply due to
exposure to Radon gas [2] \- followed by their disorderly growth, results in
formation of tumors. Lung tumors are mainly aberrant clusters of tissues that
are outcomes of atypical cell division frequency in the lungs [3], [4].
Diagnosis of malignant tumors is often not feasible in early stages for the
lack of symptoms or because the symptoms are indistinguishable from those of a
respiratory infection. Most lung cancer cases are thus diagnosed at an
advanced stage [5], inevitably leading to the patient’s death, which urgently
calls for a coherent approach towards developing a method to deal with lung
cancer.

Since the symptoms of lung cancer appear and the cases are diagnosed at an
advanced stage most of the time [5], it is practically impossible to save the
patient in the end. It is crucial to make an effort to detect it at the
preliminary stages because early diagnosis can allow the patient to go through
radiotherapy or chemotherapy when the tumors haven’t infected neighboring
tissues yet. This is rather convenient for oncologists as they can determine
how to approach the treatment of the patient. An important observation in this
regard is that lung CT scan images have the capability of revealing tumors at
an early stage. The challenge, however, is that these attempts are tedious,
time consuming and more prone to errors in general [6], [7].

Lung cancer prediction pipeline using CT Scan images goes through several
stages including image pre-processing, segmentation, feature extraction and
classification. The pre-processing technique used in [8] involves removing
unwanted artifacts with the help of Median and Wiener filters. Next, a K-means
clustering method is applied for segmentation followed by an EK-Means
clustering. In [9], an SVM classifier is used for early detection of lung
cancer. After pre-processing the CT scan image of the lungs, the Region of
Interest (ROI) is segmented, retained and compressed using Discrete Wavelet
Transform. Another work that uses Support Vector Machines for lung cancer
classification is reported in [10]. Patel et al. used the local energy-based
shape histogram (LESH) feature extraction technique with sensitivity analysis
(SA) to detect lung cancer [11]. In [12], an enhanced artificial bee colony
optimization technique is used for lung cancer detection and classification.
Most common procedures for lung cancer detection have had a significant
reliance on typical Image processing, machine learning based on handcrafted
features and soft computing techniques.

In recent times, deep learning techniques have revolutionized the field of
medical image processing and analysis. Haque et al. in [13] have discussed the
superiority of deep learning techniques for the purpose of medical image
segmentation. Traditional machine learning approaches usually cannot process
natural data in their raw form and are incapable of dynamically adapting to
new information [13]. However, this is something that deep learning techniques
are good at and so they are widely used for handling data in their raw form.
Moreover, with the advent of advanced central processing units and graphic
processing units, training and execution times have reduced as well, making it
more suitable to use deep learning based algorithms. Therefore, there has been
a recent emergence of advanced deep learning techniques [14] including
Convolutional Neural Networks (CNN) [15] in the area of medical image
segmentation. For example, in [16], lung cancer detection and classification
is done using 3D Convolutional Neural Networks. The Kaggle Data Science Bowl
2017 (KDSB17) [17] challenge saw multitudinous applications of Convolutional
Neural Networks on KDSB17 datasets accompanied by LUNA16 dataset in some cases
[18]. On the other hand, the 2018 VIP-CUP Challenge presented the problem of
segmentation and prediction of Lung tumor regions that was addressed with
methodical procedures like Recurrent 3D-DenseUNet architecture using the
tversky loss function [19]. Furthermore, Dilated hybrid 3D Convolutional
Neural Networks have also been experimented with in this context apart from
LungNet and UNet models [20]. All these approaches reported excellent results.

In [21], a study of automatic extraction of features is presented leveraging
deep learning techniques. A CAD system is proposed in [22] that uses deep
features extracted from an autoencoder to classify lung nodules as malignant
or benign. Moreover, three deep learning approaches, namely, Convolutional
Neural Network (CNN), Deep Belief Networks (DBNs) and Stacked Denoising
Autoencoder (SDAE) are applied in [23] to demonstrate the use of deep learning
in lung cancer diagnosis using the Lung Image Database Consortium (LIDC)
database.

The main contribution of this paper is our newly developed pipeline that
consists of a preprocessing phase with efficient feature engineering, an
existing deep learning architecture with some useful enhancements and post-
processing techniques for improvement in the results. 3D Convolutional Neural
Networks, which are quite compute- and memory-intensive, may lead to
overfitting with small datasets because of a larger number of parameters,
which often calls for the alternative of conceptualizing the 3D space as a
collection of 2D planes. To this end, we have converted the problem in such a
way that we can use 2D kernels with our designed feature map and achieved much
better performance while maintaining efficiency in terms of memory usage and
runtime. Thus our technical contribution in this paper involves (a) adopting
deep supervision [24] with MultiResUnet framework - a considerable improvement
from the state of the art models [25]\- after (b) applying two dimensional
discrete wavelet transform on the dataset for inferring the texture better and
(c) analyzing neighboring CT slices for more confident deduction.
Additionally, the concerning bottleneck posed by a small dataset has been
handled by an attempt to diversify it through data augmentation via rotations
by differing angles. All of these phases and their combined impact on accurate
segmentation have been the most important contribution of our project which
ultimately resulted in a dice co-efficient of 0.8472 - a significant
advancement over the prevalent assessments.

##  2 Materials and Methods

###  2.1 Dataset

Our experiments have been conducted on the LOTUS Dataset (supplied by MAASTRO
clinic) - an amended adaptation of the NSCLC-Radiomics Dataset - consisting of
images and annotations of 300 patients in total, i.e., from 260 patients for
the training set and from 40 patients for the validation set [26]. However, we
used the validation set as an independent test set since no labels were
supplied to accompany the original test set. The annotations of this dataset
cover a wide region surrounding the tumor area including both the right and
left lungs. Tumor volumes - Gross Tumor Volume, Planning Tumor Volume and
Clinical Target Volume - have also been annotated in this dataset [26]. It is
a compact collection of DICOM files containing several medical details on each
patient. Our preprocessing methods extract the ${512\times 512}$ CT scan
slices from these DICOM objects that are sent into the pipeline after some
further partitioning and refinements. Table 1 provides a summary of the
dataset [26].

Table 1: Number of tumor and non-tumor slices in dataset Dataset | Number of Subjects | Tumor Slices | Non-Tumor Slices
---|---|---|---
Training Set | 260 | 4296 | 26951
Test Set | 40 | 848 | 3610

Another important detail to be noted is the fact that the CT Scanners differed
for the slices from different patients. Two manufacturers, namely, CMS Imaging
Inc. and SIEMENS were used for this purpose. The relevant statistics have been
reported in Table 2 [26].

Table 2: Dataset statistics with respect to different manufacturers Dataset | Number of Patients | SIEMENS | CMS Imaging Inc.
---|---|---|---
Training Set | 260 | 200 | 60
Test Set | 40 | 6 | 34

The dataset contained folders having the slices and annotation for each
patient. A few of these were dropped owing to missing or inconsistent
annotations. Apart from those, all the other folders contained a number of
DICOM files along with their corresponding contours. There were some minor
inconsistencies involving the identifiers of the annotation files. They were
handled by examining the co-ordinates of the original CT slice.

###  2.2 Proposed Approach

####  2.2.1 Overview of the pipeline

In our study, we have used two dimensional CT slices for our segmentation
task. We have applied two dimensional discrete wavelet transforms on the
original input images. We have also utilized the neighboring CT slices with
each image during the input instance preparation. Next, for training the
dataset, we have used UNet, MultiResUNet as well as deep supervision with both
of these models. We have also used Test Time Augmentation after that.

Challenges in medical image segmentation include variation in the shape, size
and texture of the Region of Interest (ROI) [13]. Our dataset contains a very
small Region of Interest (ROI) in the two dimensional CT slices. If we had
taken three dimensional slices, the proportion of non tumor pixels would have
increased immensely. This would have significantly affected the performance of
the deep learning models as the models would have become biased towards non-
tumor regions. Moreover, the use of three dimensional slices would have
required a huge number of parameters, making the task more computationally
expensive. On the contrary, we have used two dimensional slices which demand
less parameters. To ensure that we are involving the minimum spatial
information in the input instance, we have added the neighboring CT slices
with each original slice. However, unlike a three dimensional approach, it
does not significantly inflate the proportion of blank space in the input,
neither does it increase the parameter usage to a great extent.

Since the ROI is already quite small, capturing the texture of the tumors in
the dataset is a rather arduous task and as mentioned before, texture
variation in ROI can be a challenge. Wavelet transforms can perform this task
of texture analysis very well [27]. It allows the model to identify minute
details in the image because of which, we have chosen to use this in our
preprocessing stage.

####  2.2.2 Preprocessing

Based on the manufacturer, the DICOM files were initially partitioned into two
groups. There was a stark difference in their span of intensity values in
Hounsfield Unit (HU): from -1024 to 3071 for CMS Imaging Inc. and from 0 to
4095 for SIEMENS. Each partition was normalized to establish relative
uniformity in the dataset.

The masks generated had a lot of blank spaces surrounding the tumor region.
This made the tumor fairly insignificant compared to the empty area. The
images were, thus, cropped to a smaller window to ensure that an adequately
amplified tumor portion is supplied to the model. We used the same co-
ordinates to crop both the training and test sets, obtaining this window by
analyzing the masks of the training set.

The preprocessing step also involved gathering more information from
neighboring CT slices. A tumor is a three dimensional structure and these CT
images are only two dimensional slices of them. Principally, this calls for a
three dimensional processing scheme which, however, is memory intensive.
Nevertheless, whether a two dimensional slice would contain a tumor region or
not would depend on its adjacent slices to a great extent. Therefore, to bring
appropriate context and to account for dependencies between consecutive
slices, the neighbors were added to each slice for preparing the input
instance.

A two-dimensional discrete wavelet transform was applied on each CT slice
twice - generating first and second approximations of the image [28]. This
operation simplifies images by leaving out some sharp horizontal, vertical and
diagonal details. By analyzing the original as well as the transformed slices,
the model can perceive tumor textures more minutely by identifying where these
details were lost. In our study, the ${512\times 512}$ images were resized to
${128\times 128}$.

The final feature set comprised five slices concatenated one after another
representing the original image, the previous and the next images, the first
and the second approximations of the original image (by two-dimensional
discrete wavelet transform). The training set was enlarged, or more
accurately, doubled by augmenting the dataset, i.e., flipping or rotating each
image based on a probability. Figure 1 illustrates the pre-processing steps to
prepare the input instances.

Figure 1: Input Instance Preparation

Finally, we performed Test Time Augmentation (TTA) by creating multiple
augmented copies of each image in the test set. This was done by rotating each
image between 20 to 100 times.

####  2.2.3 Description of the Models

Since we experimented with two dimensional U-Net [29], MultiResUNet [25] and
Deeply Supervised [24] networks, the input instances of dimension 128 x 128 x
5 were fed into all the architectures separately.

  1. 1.

U-Net
The U-Net framework consists of an encoding phase and a decoding phase. Each
layer covers two convolutions and a Max-Pooling operation in the encoding
phase whereas the decoding phase replaces the Max-Pooling operation with an
Up-sampling. As the data progresses down the encoders, it gradually secures
more context while leaving out details about location. Consequently, spatial
information is prepended to the contextual data of the decoders via skip
connections.

  2. 2.

MultiResUNet
The generic design of this network is quite similar to that of U-Net, except
for slight differences in the nature of convolutions in each layer and the
residual path from the encoders to the decoders (Figure 2). Each layer of
U-Net is replaced by a MultiRes block that contains 4 convolutions (Figure
2(b)). The skip connections of U-Net are replaced by Res Paths (Figure 2(c))
as described in [25]. The motivation of adopting this network comes from the
idea that an ideal architecture should be able to assess images having
diversified scales in medical image segmentation procedures. For further
details readers are referred to [25].

(a) Network architecture

(b) MultiRes block

(c) Res Path

Figure 2: MultiResUNet architecture. Figure borrowed from [25].

  3. 3.

Deep Supervision
We have applied deep supervision on both U-Net and MultiResUNet models. Rather
than only evaluating the output of the top layer’s decoder, this model
associates loss weights with the outputs of all five layers, in descending
order from top to bottom. In order to achieve this, a simple 1 x 1 convolution
is applied in all the layers after the up-Sampling and convolution operations.
Figure 3 presents Deeply Supervised U-Net and MultiResUNet models.

(a) Deeply Supervised U-Net

(b) Deeply Supervised MultiResUNet

Figure 3: Deeply Supervised Networks

###  2.3 The Baseline Model

We chose U-Net [29] as our baseline model and applied deep supervision on
U-Net as well as MultiResUNet in our experiments. Since the validation set of
the original dataset was used for testing, a 5-fold cross validation was
implemented. For performance evaluation, the metric called dice co-efficient
was calculated. The value of dice co-efficient is always in the range between
0 and 1 (inclusive) and is calculated using the following formula:

$\mathrm{dice~{}co\mathchar 45\relax efficient}=\frac{2*(|x\cap y|)}{|x|+|y|}$

Here, $x$ and $y$ represent the tumor areas of the ground truth and the
prediction, respectively. Following the literature [19], the dice co-efficient
is computed as follows: (i) For True-Negatives (i.e., there is no tumor, and
the processing algorithm correctly detected that), the dice co-efficient would
be 1; and (ii) For False-Positives (i.e., there is no tumor, but the
processing algorithm mistakenly segmented the tumor), the dice co-efficient
would be 0.

###  2.4 Coding and Environment

Our experiments have been conducted in a desktop computer having Intel core
i7-7700 processor (3.6 GHz, 8 MB cache) CPU, 16 GB RAM, and NVIDIA TITAN XP
(12 GB, 1582 MHz) GPU. We have used Python3 programming language [30]. For
implementing the models, we used Keras [31] with Tensorflow backend [32].

##  3 Results

###  3.1 Model Parameters

We have assessed the results by varying different parameters in our model -
optimization algorithm, learning rate and decay of the network. This led to
various dice co-efficients (training accuracy in this case) as reported in
Table 3.

Table 3: Dice Co-efficients for different optimizers, learning rates and decay for UNet and MultiResUNet models Model | Optimization | Learning Rate | Decay | Dice Co-efficient
---|---|---|---|---
| Algorithm |  |  | (Training
|  |  |  | Accuracy)
U-Net | Adam | 0.1 | 0.1/150 | 0.7218
U-Net | Adam | 0.01 | 0.01/150 | 0.7636
U-Net | Adam | 0.001 | 0.001/150 | 0.7591
U-Net | SGD | 0.1 | 0.1/150 | 0.5780
U-Net | SGD | 0.01 | 0.01/150 | 0.4525
MultiResUNet | Adam | 0.1 | 0.1/150 | 0.7437
MultiResUNet | Adam | 0.01 | 0.01/150 | 0.7533
MultiResUNet | Adam | 0.001 | 0.001/150 | 0.7435
MultiResUNet | SGD | 0.5 | 0.5/150 | 0.6556
MultiResUNet | SGD | 0.1 | 0.1/150 | 0.5916

It can be observed from Table 3 that Adam has performed significantly better
than Stochastic Gradient Descent (SGD) for both U-Net and MultiResUNet.
Besides, for both the models, a learning rate of 0.01 has outperformed any
other learning rate. We can infer this from the table since with an increase
of the learning rate from 0.001 to 0.01, the dice co-efficient increases.
However, it falls once the learning rate is raised to 0.1.

Once we have fixed on the Adam optimizer (as the optimization algorithm) and a
learning rate of 0.01, we now focus on deep supervision. Performance of deep
supervision on U-Net and MultiResUNet models involves consideration of loss
weights associated with the outputs from each level. Table 4 presents the dice
co-efficient achieved during the training for various loss weights in
different layers.

Table 4: Dice Co-efficients for deep supervision for various loss weights in different layers Model | Loss | Loss | Loss | Loss | Loss | Dice
---|---|---|---|---|---|---
| Weight | Weight | Weight | Weight | Weight | Coefficient
| (Final | (Level | (Level | (Level | (Level | (Training
| layer) | 1) | 2) | 3) | 4) | Accuracy)
Deeply | 1.00 | 0.8 | 0.6 | 0.4 | 0.2 | 0.7574
Supervised |  |  |  |  |  |
UNet |  |  |  |  |  |
Deeply | 1.00 | 0.7 | 0.5 | 0.3 | 0.1 | 0.7582
Supervised |  |  |  |  |  |
UNet |  |  |  |  |  |
Deeply | 1.00 | 0.8 | 0.6 | 0.4 | 0.2 | 0.7482
Supervised |  |  |  |  |  |
MultiResUNet |  |  |  |  |  |
Deeply | 1.00 | 0.7 | 0.5 | 0.3 | 0.1 | 0.7421
Supervised |  |  |  |  |  |
MultiResUNet |  |  |  |  |  |

###  3.2 Performance on the Test set

We used our test set containing data from 40 subjects for inferring how well
the trained models perform and which ones perform well when supplied with new
instances. We have applied various threshold values and numbers of rotations
during test time augmentation.

####  3.2.1 Tumor Detection

Since the predicted probability of being tumor pixels is between 0 and 1, we
have binarized it based on certain threshold values. For example, if the
probability of a pixel for being a tumor is $x$ and the threshold is $t$ then
for all $x>t$, our model predicts it to be a tumor, whereas for all $x\leq t$,
the model does not recognize it as a tumor pixel. Table 5 gives the true
positives, false positives, true negatives, false negatives and F1 score for
all the model settings.

Table 5: All quantitative results related to tumor detection for different numbers of rotations and thresholds using the test set. Model | Number | Thres | True | False | True | False | F1
---|---|---|---|---|---|---|---
| of | -hold | Positive | Positive | Negative | Negative | Score
| Rotations |  |  |  |  |  |
U-Net | 20 | 0.4 | 104 | 130 | 3502 | 744 | 0.1922
U-Net | 50 | 0.5 | 53 | 58 | 3574 | 795 | 0.1105
MultiResUNet | 20 | 0.4 | 576 | 215 | 3417 | 272 | 0.7028
MultiResUNet | 50 | 0.5 | 447 | 115 | 3517 | 401 | 0.634
Deeply Supervised | 20 | 0.4 | 632 | 520 | 3112 | 216 | 0.6315
U-Net |  |  |  |  |  |  |
Deeply Supervised | 50 | 0.5 | 501 | 210 | 3422 | 347 | 0.6422
U-Net |  |  |  |  |  |  |
Deeply Supervised | 20 | 0.4 | 600 | 268 | 3364 | 248 | 0.6990
MultiResUNet |  |  |  |  |  |  |
Deeply Supervised | 50 | 0.5 | 505 | 123 | 3509 | 343 | 0.6838
MultiResUNet |  |  |  |  |  |  |

####  3.2.2 Tumor Segmentation

Table 6 reports the dice co-efficients for the test set with various numbers
of rotations applied during test time augmentation. Moreover, in addition to
performing standard binarization using a threshold of 0.5, we also
experimented with different threshold values. Evidently, deep supervision has
been able to improve the performance for both U-Net and MultiResUNet and the
latter has performed better. More specifically, deeply supervised MultiResUNet
model (with 50 rotations and 0.5 threshold) is the winner with a dice co-
efficient of 0.8472.

Table 6: Dice co-efficients for different numbers of rotation and thresholds using the test set. Model | Number of | Threshold | Dice
---|---|---|---
| Rotations |  | Co-efficient
|  |  | (Test Accuracy)
U-Net | 20 | 0.4 | 0.7882
U-Net | 50 | 0.4 | 0.7890
U-Net | 20 | 0.5 | 0.7984
U-Net | 50 | 0.5 | 0.8003
MultiResUNet | 20 | 0.4 | 0.8327
MultiResUNet | 50 | 0.4 | 0.8363
MultiResUNet | 20 | 0.5 | 0.8373
MultiResUNet | 50 | 0.5 | 0.8382
Deeply Supervised | 20 | 0.4 | 0.7645
U-Net |  |  |
Deeply Supervised | 50 | 0.4 | 0.7858
U-Net |  |  |
Deeply Supervised | 20 | 0.5 | 0.8158
U-Net |  |  |
Deeply Supervised | 50 | 0.5 | 0.8224
U-Net |  |  |
Deeply Supervised | 20 | 0.4 | 0.8294
MultiResUNet |  |  |
Deeply Supervised | 50 | 0.4 | 0.8324
MultiResUNet |  |  |
Deeply Supervised | 20 | 0.5 | 0.8434
MultiResUNet |  |  |
Deeply Supervised | 50 | 0.5 | 0.8472
MultiResUNet |  |  |

A qualitative analysis of our results reveals the strengths and weaknesses of
our proposed model. In most cases, regardless of the size of the ground truth,
our model predicts the tumor shapes very well. This is evident from Figure 4
where the ground truth and the prediction (by Deeply Supervised MultiResUNet)
are shown in red and blue respectively. Although the tumors are in various
arbitrary locations within the lung and appear in diverse sizes, the red and
blue margins appear to coincide almost perfectly.

Figure 5 shows a comparison between predictions by the MultiResUNet model and
Deeply supervised MultiResUNet model. It can be seen that the latter can
delineate the tumor edges more accurately than the former. The ground truth
(shown in red) and the prediction (shown in blue) have a more consistent
alignment with each other in Deeply Supervised MultiResUNet’s prediction.

However, in a few rogue cases, where the shapes of the ground truth are
exceedingly uncoordinated, perhaps with fissures in the middle or with erratic
outlines, it is seen that the predicted tumor regions are prone to
imperfections. Although for these cases, our model can predict the existence
of tumors, the shapes can often appear to have disfigurements. This is
demonstrated in Figure 6. We plan on addressing this issue in our future work.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 4: Strength of our model. The ground truth (in red) and prediction (in
blue) for Deeply Supervised MultiResUNet model.

(a)

(b)

(c)

(d)

Figure 5: Deeply Supervised MultiResUNet outperforms MultiResUNet
significantly in terms of capturing the range of the tumor. The ground truth
is shown in red whereas the prediction is given in blue.

(a)

(b)

(c)

Figure 6: Limitation of our model. Tumors with tremendously erratic boundaries
are predicted imperfectly. The ground truth is shown in red whereas the
prediction is given in blue.

###  3.3 Comparison with other models

A comparative analysis involving other state-of-the-art models shows that our
model outperforms all of them by a significant margin. This is presented in
Table 7 which shows the mean dice co-efficient obtained using our model and
several others.

At this point a brief discussion on the (unusual) dice calculation of Hossain
et al. [20] is in order, which differs from the calculation followed in [19]
(and this work). The test set in [20] contained 4478 slices from 40 subjects.
Their frontend binary classifier produced 1158 false negatives out of those
but this huge number of misclassifications did not affect the dice score, as
only the slices with tumor pixels in the ground truth were considered during
their dice score calculation. Although they mentioned that the number of false
positives was reduced by approximately 50% through segmentation and post-
processing, the paper makes no attempt to address what happened to the true
positives reported by the binary classifier after passing them through the
segmentation model and therefore, conveniently ignores the possibility of a
reduction in the number of true positives which is a major issue.

Let us now analyze the the quantitative results reported in [19]. The highest
dice co-efficient achieved by them is 0.7228. For this result, the false
positives and false negatives are 321 and 331 in number, respectively [19]. In
our case, the best dice co-efficient (of 0.8472) is achieved by the Deeply
Supervised MultiResUnet which gives 123 false positives (much less than [19])
and 343 false negatives (close to [19]). Notably, we have already achieved far
less false negatives for Deeply Supervised MultiResUnet with 20 rotations and
0.4 threshold (248 in number) at the cost of a slightly worse dice score
(i.e., 0.8294) and false positives (268 in number)- both far better than that
of [19]. However, we still plan on exploring ways to reduce both false
positives and negatives further while maintaining a high dice co-efficient.

Table 7: Dice co-efficients obtained using different models in lung tumor segmentation task. Values for the other models have been taken from the respective papers ([20] and [19]) Model | Mean Dice Co-efficient
---|---
2D-LungNet [33] | 0.6267
3D-LungNet [20] | 0.6577
3D-DenseUNet [19], [34] | 0.6884
Recurrent 3D-DenseUNet [19] | 0.7228
Deeply Supervised | 0.8472
MultiResUNet |

###  3.4 Ablation Study

We conducted an ablation study to analyze the performance of our overall
pipeline. In particular, we check what happens if wavelet transforms are not
applied to the dataset in the preprocessing step. We preprocessed the images
without wavelet transforms and only kept the neighboring slices along with the
original image. This resulted in a 3-channel input instead of a 5-channel one
wherewith we then trained the Deeply Supervised MultiResUNet with loss weights
of [1.00,0.8,0.6,0.4,0.2] while keeping all other parameters same as before.
This same model when trained on the dataset containing wavelet transforms
gives a dice co-efficient of 0.8294 on the test set (after applying 20
rotations and with a threshold of 0.4). On the other hand, the model trained
on the dataset without wavelet transforms gives a dice co-efficient of 0.7649
with the same setting.

Moreover, we performed a qualitative analysis on the results produced from the
two cases. We observed two things that happen in the absence of wavelet
transforms -

  1. 1.

The predicted tumors seem to have frequent outliers

  2. 2.

In most cases, the predicted tumor seems to be enlarged and the edges of the
tumors are not properly detected

These observations have been demonstrated in Figure 7.

(a)

(b)

(c)

(d)

Figure 7: Application of wavelet transform reduces the frequency of outliers
and avoids an inflated predicted tumor size. The ground truth is shown in red
whereas the prediction is given in blue.

##  4 Discussions

MultiResUNet outperforms U-Net in segmentation of lung tumor from CT slices
and deeply supervised MultiResUNet performs even better. In particular, due to
deep supervision the best MultiResUNet model registers an improvement from
0.8382 to 0.8472 in terms of dice co-efficient. Since deep supervision
considers the outputs from the lower levels of the decoder, the reconstruction
phase of the model begins at a very deep level. This positively affects the
final dice co-efficient calculated on the predictions. Besides, we believe,
wavelet transforms combined with using neighboring CT slices during input
instance preparation have allowed our model to analyze tumor textures more
accurately.

Table 5 demonstrates various quantitative results for tumor detection. A
crucial observation is that, for every model, application of deep supervision
reduces the number of false negatives. Reducing false negatives is crucial as
failing to identify a sick patient with tumor has serious detrimental effects.
Tables 5 and 6 illustrate another pattern. The models which give a higher F1
score also yield better dice co-efficients although the margin may not be very
high.

Table 6 shows a pattern of increase in dice co-efficients as we increase the
thresholds and number of rotations. For each segmentation model, keeping the
threshold constant, with the increase of rotations, the dice co-efficient
increases as well. The rationality behind this is that, when the number of
rotations is low, it is difficult to filter out the false positive pixels as
opposed to a greater number of rotations where such pixels receive a very low
probability of being tumors. When rotations are more, the ability to
confidently claim that a certain pixel will be part of the tumor is more.
Having a higher threshold has a similar effect on the predictions. This is
because a pixel is only considered a part of the tumor if the predicted
probability is quite high. Otherwise, it is discarded. This effectively
filters out the false positive pixels.

Another observation from Table 6 is that, with the increase in threshold, the
performance of deep supervision improves as well. This can be seen in the case
of both U-Net and MultiResUnet. Keeping the number of rotations constant, an
increase in threshold results in a improved dice co-efficient for deep
supervision. We observed that the deeply supervised versions of the model
almost consistently had probability scores higher than 0.5 in the tumor
regions. So, when we consider threshold values less than 0.5 (i.e., 0.4), very
little additional actual tumor pixels were considered compared to the
background pixels having scores at the range of 0.4-0.5. As a result, it
slightly dips the performance. On the other hand, for models without deep
supervision, there exists a bigger ratio of tumor pixels in the 0.4-0.5 range,
thus the performance is better compared to the deep supervised models. Our
takeaway point was that, apparently, for deep supervised models, the
separation between background and foreground is a bit better.

Figure 7 shows the occurrence of outliers in the absence of wavelet transforms
and an inability to accurately determine tumor edges in this case. The
intuition concerning the former observation is that without wavelet
transforms, texture information is relatively lost and the model perceives
similarly shaped structures to be tumors as well. The second observation is
also related to the fact that wavelet transforms can capture the texture
better. In absence of it, the model cannot predict or justifiably limit the
extent of the area that the tumor boundary should encompass. This results in
inflated tumor areas and inaccurate tumor sizes.

The mechanism that we have proposed in this paper is unique, resulting in a
procedure that returns an excellent dice co-efficient value of 0.8472. The
technique of combining neighboring slices for more detail and applying wavelet
transforms for texture analysis have never been implemented in this way
before. The first and second approximations of the original slice, obtained
from two-dimensional discrete wavelet transform, have allowed the model to
peruse details that are lost, concluding with a finer interpretation of the
input. We have also implemented Deeply Supervised MultiResUNet, assigning
priorities to the outputs of lower layers of the model. Apart from these,
application of Test Time Augmentation has assisted the network to execute
better when supplied with new instances.

##  5 Conclusion

The battle against lung cancer has been going on for a very long time. To this
end, a pivotal field of research has emerged and is gaining traction with the
help of deep learning in the recent years. The proposed methods in our paper
performed significantly better than other existing approaches in this attempt
towards detecting lung tumors with CT Scan images. The strategy that we
undertook included two-dimensional discrete wavelet transform during the
preprocessing step and experimenting with multiple models that led to splendid
results - in terms of dice co-efficient - especially in the case of Deeply
Supervised MultiResUNet model which ensured more accurate delineation of faint
boundaries.

We believe that our approach can make the tasks of oncologists much easier and
help detect tumors at an early stage. We have planned for further research
regarding this particular topic that encompasses refining the pipeline in
order to achieve even better results. For example, we plan to explore other
preprocessing techniques apart from wavelet transforms thereby redesigning the
pipeline. Moreover, we plan on experimenting with additional techniques that
could improve the performance of the models that we used. One such interesting
avenue to explore is to use attention mechanism with the MultiResUnet model.

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