# Entanglement based tomography to probe new macroscopic forces

Peter. F. Barker  Department of Physics and Astronomy, University College
London, Gower Street, WC1E 6BT London, United Kingdom.  Sougato Bose
Department of Physics and Astronomy, University College London, Gower Street,
WC1E 6BT London, United Kingdom.  Ryan J. Marshman  Centre for Quantum
Computation and Communication Technology, School of Mathematics and Physics,
University of Queensland, Brisbane, Queensland 4072, Australia  Anupam
Mazumdar  Van Swinderen Institute, University of Groningen, 9747 AG Groningen,
The Netherlands.

###### Abstract

Quantum entanglement provides a novel way to test short distance physics in
the non-relativistic regime. We will provide a protocol to potentially test
new physics by bringing two charged massive particle interferometers adjacent
to each other. Being charged, the two superpositions will be entangled via
electromagnetic interactions mediated by the photons, including the Coulomb
and the Casimir-Polder potential. We will bring a method of entanglement based
tomography to seek time evolution of very small entanglement phases to probe
new physical effects mediated by hitherto unknown macroscopic force which
might be responsible for entangling the two charged superpositions modelled by
the Yukawa type potential. We will be able to constrain the Yukawa couplings
$\alpha\geq 10^{-35}$ for $r\geq 10^{-6}$m for new physics occurring in the
electromagnetic sector, and in the gravitational potential $\alpha_{g}\geq
10^{-8}$ for $r\geq 10^{-6}$m. Furthermore, our protocol can also constrain
the axion like particle mass and coupling, which is complimentary to the
existing experimental bounds.

One critical observation which parts from the classical world is the notion of
quantum entanglement [1, 2]. The latter provides the evidence of quantum
correlation which a classical world cannot replicate. In particular, it is
known that a classical interaction cannot entangle the two quantum systems (if
they were not entangled to begin with) [3]. Since all the known Standard Model
(SM) interactions and mediators are quantum in nature, entanglement formation
becomes inevitable. The SM interactions are fairly well constrained by the
collider [4], non-collider [5], the electron-dipole-moment (EDM) [6]
experiments. However, there are consistent effort in constraining weakly
coupled bosons such as axion like particle, majorons, or light dark matter
searches [7, 9]. Given these advancements it is now paramount to seek a
complimentary avenue to test new physics in the infrared (IR) and in a non-
relativistic (NR) limit.

The aim of this paper will be to provide a simple quantum-information lead
entanglement protocol to confirm the SM interactions and to probe new physics
in the particle physics and gravitational sectors. Very light and weakly
coupled bosons could couple to the SM degrees of freedom, such as axion like
particle, Kaluza-Klein modes from the extra dimensions, hidden sector photon
[8, 7, 5, 9, 10]. Axions with varied mass range are also expected in string
theory [11], which provide a significant motivation to look for these light
bosons experimentally. In the NR limit such corrections will generically yield
Yukawa modifications to the potential mediated by these light bosons either at
the tree or at the loop level [8]. Similarly, the quantum nature of the
graviton within general relativity (GR) and beyond GR also tend to modify the
gravitational potential which can be tested via entanglement witness [12, 13,
14, 15].

In this paper, we will probe the nature of beyond the SM physics and the
gravitational sector by witnessing the quantum entanglement between the two
charged massive particle interferometers. Specifically, we will assume the
interferometers induce a spatial superposition of size $\Delta x$. For details
about explicit schemes of the sorts of intereferometers considered, see Refs.
[12, 16, 17].

To model this, we take an electronic spin in a host crystal, with a spin-
spatial state coupling allowing us to measure the entanglement. We will assume
a nitrogen-vacancy (NV) centre spin in a diamond nano/micro-crystal, although
qualitatively our results and analysis will hold for similar materials. We
will further assume that the nano-crystal can be electrically charged. If we
bring another such quantum superposition of a charged nano-crystal and keep
them apart by a distance $d$, then the two nano-crystals will be entangled via
the exchange of a virtual photon (Coulomb), via the vacuum induced dipole-
dipole type interactions mediated by the two photon exchange giving rise to
the Casimir-Polder (CP) potential [18, 19], and any additional particle-
particle interactions which may occur. Since, at sufficiently short distances
both the contributions will dominate the electromagnetic (EM) interactions, we
study how to disentangle or mitigate the EM induced entanglement to probe new
macroscopic forces in the EM sector and in the gravitational sector

In this paper, we will show that there exists parameter regions, where we can
cancel the entanglement phase due to the Coulomb and the CP potential, and
probe the configuration where the net entanglement phase due to the EM induced
interactions vanishes (when $\Delta\phi_{em}=2n\pi$, for $n=0,1,2\cdots$). We
will then show how by studying the entanglement entropy in the bipatrite
system, namely the von-Neumann entropy, we can probe for unknown force of
nature in the IR. To detect a new force, we consider that the resulting
particle-particle interactions produce different quantum correlations, which
are captured by the time evolution of the entanglement entropy, i.e.
entanglement based tomography. In general, we will describe this new force by
a Yukawa potential without going into the details of model building.

Figure 1: Configuration where the two spatial superpositions with the
splitting $\Delta x$ are kept parallel to each other separated by a distance
$r,~{}d$. The two spin states have been shown, the radius of the spherical
nano-crystal is $R$.  Figure 2: von Neumann entropy with respect to time for
all the interactions. The shaded region shows the uncertainty in the
experimental parameters where the EM induced entanglement is used as a
baseline. Here we have taken $R=10^{-4}{\rm
m},\alpha_{g}=0.01,\lambda=10^{-3}$.

Let us consider a setup where we have two charged nano-crystals, with an
embedded, addressable spin, we will assume that they have the same mass $m$
with a radius $R=\left({3m}/{4\pi\rho}\right)^{1/3}$ where $\rho=3.5\times
10^{3}$ kgm-3 is the density of the nano-crystals, similar to that of the
diamond, see Fig. (1). Each mass, labelled $a$ and $b$, will be assumed to
have a net charge $(q_{a}e,~{}q_{b}e)$ where $q_{i}\in\mathbb{Z}$ and $e$ is
the charge of an electron. The interactions are expected to be in the IR and
are thus limited to EM, gravitational and the unknown interactions mediated by
beyond SM quanta. Since the nano-crystals have diamagnetic properties, typical
for a diamond, there will be a CP potential on top of the Coulomb interaction.
These will be the dominant EM interactions the crystals will face at
relatively short distances, but still in the IR. The known potentials are

$\displaystyle U_{cp}(x)$ $\displaystyle=$ $\displaystyle-\frac{23\hbar
c}{4\pi}\frac{\epsilon-1}{\epsilon+2}\frac{R^{6}}{\left(x-2R\right)^{7}}$ (1)
$\displaystyle U_{c}(x)$ $\displaystyle=$
$\displaystyle\frac{e^{2}}{4\pi\varepsilon_{0}}\frac{q_{a}q_{b}}{x}$ (2)

where $\epsilon$ is the diamagnetic susceptibility. We consider the masses to
be placed in a spatial superposition of size $\Delta x$ in the parallel
arrangement as shown in Fig.(1). For this configuration of masses, the joint
quantum state of the spins
$\left|\Psi(0)\right\rangle=\frac{1}{2}\left(\left|\uparrow,\uparrow\right\rangle+\left|\downarrow,\downarrow\right\rangle+\left|\uparrow,\downarrow\right\rangle+\left|\downarrow,\uparrow\right\rangle\right)$
will evolve to [12, 13] 111The analogous system of quantum spatial
superposition but with the neutral masses have been considered in Ref. [12,
13]. The details of the entanglement phase evolution can be found in Refs.
[12, 13, 20]. In these papers, the quantum nature of the graviton (spin-2 and
spin-0 components of the quantum nature of graviton was responsible for
entangling the two superpositions, see for a quantum field theory description
[13, 15]. Here, instead, we consider the quantum nature of the photon to
entangle the two charged nano-crystals. Even the vacuum induced dipole-dipole
interaction which gives rise to CP potential is being mediated by the virtual
exchange of the photons [19].:

$\left|\Psi(t)\right\rangle=\frac{1}{2}\left[\left|\uparrow,\uparrow\right\rangle+\left|\downarrow,\downarrow\right\rangle+e^{i\Delta\phi(d,r)}\left(\left|\uparrow,\downarrow\right\rangle+\left|\downarrow,\uparrow\right\rangle\right)\right]$
(3)

where the phase $\phi$ is determined by the interaction considered:
$\phi_{i}(x)=({t}/{\hbar})U_{i}(x)$, see [16, 15], and is a function of the
particle-particle distance $d$ between the $\left|\uparrow\right\rangle_{a}$
and $\left|\uparrow\right\rangle_{b}$ states (which is the same as that for
the joint state $\left|\downarrow,\downarrow\right\rangle$) and
$\Delta\phi(d,r)=\phi(r)-\phi(d)$ where $r=\sqrt{d^{2}+\Delta x^{2}}$ is the
particle-particle distance for the joint states
$\left|\uparrow,\downarrow\right\rangle$ (and equivalently
$\left|\downarrow,\uparrow\right\rangle$). As such, there is only one
important phase $\Delta\phi(d,\Delta x)$, which dictates whether or not the
masses are entangled, which is why this arrangement is preferred. Further to
these potentials, we will consider as an example of the Yukawa potential where
we will constrain $(\alpha,\lambda)$, see [8, 10].

$U_{Y}(x)={\alpha e^{-{x}/{\lambda}}}/{x}\,,$ (4)

$\alpha$ dictates the interaction strength of the new physics and $\lambda$
determines the effective range of the interaction, or related to the Compton
wavelength $\lambda\sim 1/m_{\ast}$, where $m_{\ast}$ denotes the particle
mass which interacts with the EM photons. We will now discuss how, by
carefully selecting the experimental parameters, we might hope to detect new
close range forces and the modifications to these by eliminating the competing
effects of the Coulomb and the CP interactions. To determine the parameter
space in which the Coulomb and the CP interactions cancel, we will consider
the entanglement phase due to each:

$\displaystyle\Delta\phi_{c}$ $\displaystyle=$
$\displaystyle\frac{t}{\hbar}\frac{e^{2}}{4\pi\varepsilon_{0}}\left(\frac{q_{a}q_{b}}{r}-\frac{q_{a}q_{b}}{d}\right)\,,$
$\displaystyle\Delta\phi_{cp}$ $\displaystyle=$
$\displaystyle-\frac{t}{\hbar}\frac{23\hbar
c}{4\pi}\frac{\epsilon-1}{\epsilon+2}\left(\frac{R^{6}}{\left(r-2R\right)^{7}}-\frac{R^{6}}{\left(d-2R\right)^{7}}\right).$
(5)

Thus, we require $\Delta\phi_{c}(d,r)=-\Delta\phi_{cp}(d,r)$. To consider a
general situation, we use the parametrisation; $\Delta x=\beta d$,
$r=\sqrt{1+\beta}d$. This constrains

$d=\left(\frac{\sqrt{1+\beta}-\left(1+\beta\right)^{-3}}{\sqrt{1+\beta}-1}\frac{23\hbar
c\varepsilon_{0}}{e^{2}}\frac{\epsilon-1}{\epsilon+2}\frac{1}{q_{a}q_{b}}\right)^{1/6}R.$
(6)

These results suggest that there are no solutions when
$\textrm{sign}(q_{a})\neq\textrm{sign}(q_{b})$ as this leads to a complex
valued $d$. The ability to detect a close range interaction within this regime
will then be determined by the parameter stability, and the certainty from one
run to the next. There is however a significant issue of the acceleration
induced by the CP and the Coulomb interactions.

The two accelerations fail to cancel one another out, and leave a significant
residual acceleration, which is only made larger by increasing the charges of
the masses ($q_{a}$ and $q_{b}$). This poses a strong limiting factor without
some further mitigation strategy, which is what we will now present.

Now, we will present the analysis of the experimental configuration where we
optimise the separation between the two superpositions involved, such that the
CP and the Coulomb forces cancel. So that we are no longer optimising over
both the average distance $d$ and $\Delta x$. The two EM forces are given by;
$F_{cp}(x)=-({161\hbar
c}/{4\pi})({\epsilon-1}/{\epsilon+2}){R^{6}}/{\left(x-2R\right)^{8}}$, and
$F_{c}(x)=({e^{2}}/{4\pi\varepsilon_{0}})({q_{a}q_{b}}/{x^{2}})$. We can
eliminate the net EM forces at a single distance $d$, which gives
$F_{cp}(d)=-F_{c}(d)$. Setting $d=nR$ gives:

$\displaystyle\frac{n^{2}}{\left(n-2\right)^{8}}=$
$\displaystyle\frac{4\pi}{161\hbar
c}\frac{\epsilon+2}{\epsilon-1}\frac{q_{a}q_{b}e^{2}}{4\pi\varepsilon_{0}}\,,$
(7)

which gives $d\sim 6R,~{}{\rm for}~{}~{}q_{a}=q_{b}=1$, $d\sim 4R,~{}{\rm
for}~{}~{}q_{a}=q_{b}=10$, and $d\sim 3R,~{}{\rm for}~{}~{}q_{a}=q_{b}=100$.

This limits the charges to be, $q\lesssim{\cal O}(10)$. To allow a significant
separation between the two nano-crystals, we will need to move into the regime
where the forces only approximately cancel. To do this, we would set the
minimum distance between the masses, $d$, to be such that the force between
them cancels. The superposition size $\Delta x$ can then be increased until
the force between the distant states (each at a distance of $r$ from one
another) becomes significant. We will again use $d=nR$ to represent the exact
distance for which the forces cancel, and write $r=nR+r^{\prime}$. The
residual force is then

$F_{\textrm{net}}=\left(\frac{161\hbar
c}{4\pi}\frac{\epsilon-1}{\epsilon+2}\frac{8}{\left(n-2\right)^{9}}-\frac{e^{2}q_{a}q_{b}}{4\pi\varepsilon_{0}}\frac{2}{n^{3}}\right)\frac{r^{\prime}}{R^{3}}$
(8)

Therefore, for example, when we take $q_{a}=q_{b}=1$, and $n=6$, we obtain
$F_{\textrm{net}}\sim 10^{-29}{r^{\prime}}/{R^{3}}$. This suggests that,
depending on the tolerable force, even $r^{\prime}\leq R$ could be possible.
In this case, the superposition size is $\Delta
x=((nR+r^{\prime})^{2}-n^{2}R^{2})^{1/2}$. For the purpose of illustration and
in remainder of the paper, and specifically for Figs.(2,3,5), we will take
these optimised parameters,

$d=6R,~{}r=7R,~{}\Delta x\approx 3.6R,~{}q_{1}=q_{2}=1\,.$ (9)

We consider $R\in\left\\{10^{-4}\textrm{ m},10^{-5}\textrm{ m},10^{-6}\textrm{
m}\right\\}$, equivalently $m\in\left\\{10^{-8}\textrm{ kg},10^{-11}\textrm{
kg},10^{-14}\textrm{ kg}\right\\}$. It is, however, known that for a given
mass $m$, the graviton vacuum gets displaced and this corresponds to the
number of excited gravitons around the Minkowski vacuum which can be estimated
by the Bekenstein’s entropy [21]: $N_{g}=S_{BEK}\sim(m/M_{p})^{2}$ [22]. For
$m\sim 10^{-8}$kg, it is actually $N_{g}\sim 1$, and for lighter mass
$N_{g}\ll 1$. It appears that $N_{g}\sim{\cal O}(1)$ might dictate this subtle
distinction between one graviton excitation with many graviton excitations in
the vacuum. Here we have kept all our masses below the Planck mass, i.e.
$m\leq 10^{-8}$kg.

We will now consider a novel strategy to mitigate the EM induced phase through
the tomography, i.e. experimental timing. Specifically, given the total EM-
induced entanglement phase is
$\Delta\phi_{em}=\Delta\phi_{c}+\Delta\phi_{cp}$, and provided the
experimental parameters ($m$, $t$, $d$ and $\Delta x$) are tuned sufficiently
well, then ensuring

$\Delta\phi_{em}=\Delta\phi_{c}+\Delta\phi_{cp}=2\pi n$ (10)

where $n\in\mathbb{Z}$ will remove any EM signal, leaving only the discovery
potential for the other macroscopic forces beyond the SM.

This can be achieved by choosing an appropriate interaction time. If we are
constraining the Yukawa potential, then by using our set-up we can utilise the
force cancelling region to enable a relative stable particle-particle
interaction. That is, little or no deflection of the masses due to their EM
interactions throughout the interferometry process. This can be seen in Fig.
(2), where the entanglement entropy induced by the EM interaction between the
two sub-systems vanishes, while the other interactions do not vanish at a
specific point. Indeed, we have chosen a small snap-shot of time for the
purpose of illustration, we can indeed take a larger time evolution. Just as
an example, we have shown here the entanglement entropy for the gravitational
induced Yukawa potential between the two systems do not vanish at that
specific time. The shaded region in the EM induced entanglement denotes the
uncertainties in the Coulomb and CP potential due to uncertainties in the
experimental parameters, as discussed below.

Figure 3: $\alpha-\lambda$ plot showing the region in which the Yukawa
potential dominates over the Casimir and Coulomb interactions for different
values of $R$. The solid and dashed lines correspond to a total interaction
time $t=10^{-3},t=10^{-6}$ s, respectively.

The EM induced entanglement phases per unit time are given by:

$\displaystyle\frac{\Delta\phi_{c}}{t}$ $\displaystyle=$
$\displaystyle\frac{1}{\hbar}\frac{e^{2}}{4\pi\varepsilon_{0}}\left(\frac{q_{a}q_{b}}{r}-\frac{q_{a}q_{b}}{d}\right)\sim({5\times
10^{4}}/{R})\textrm{rad s}^{-1}$ $\displaystyle\frac{\Delta\phi_{CP}}{t}$
$\displaystyle=$ $\displaystyle\frac{1}{\hbar}\frac{23\hbar
c}{4\pi}\frac{\epsilon-1}{\epsilon+2}\left(\frac{R^{6}}{\left(r-2R\right)^{7}}-\frac{R^{6}}{\left(d-2R\right)^{7}}\right)$
(11) $\displaystyle\sim$ $\displaystyle-({2\times 10^{4}}/{R})\textrm{rad
s}^{-1}.$

For any interaction time $t\gtrsim 10^{-4}R$ sec, the condition set out in
Eq.(10) can be readily made true. We will consider the merit of two different
scenarios of new physics.

$\bullet$ Departure from the Coulomb and the CP potential:
We will consider the acceptable levels of uncertainties in the experimental
parameters. To determine, approximately, we will consider the uncertainties by
taylor expanding arond their target values which suggests the Coulomb
interaction will be

$\displaystyle\Delta\phi_{c}(d,r)+\delta\left(\Delta\phi_{c}(d,r)\right)=$
$\displaystyle\Delta\phi_{c}(d,r)(1+{\delta t}/{t}+{\delta d}/{d}+{\delta
r}/{r})$ $\displaystyle\equiv\Delta\phi_{c}(d,r)(1+3\tilde{\delta}),$ (12)

where we have assumed every parameter has an equal relative error
$\tilde{\delta}$ for simplicity. Similarly for the CP interaction, we obtain

$\Delta\phi_{cp}(d,r)+\delta\Delta\phi_{cp}(d,r)\approx\Delta\phi_{cp}(d,r)(1+15\tilde{\delta}).$
(13)

To ensure that the entanglement phases induced by the EM interactions does not
remove that sourced by the Yukawa, $\delta\Delta\phi_{em}\ll\Delta\phi_{Y}$
and $\delta\Delta\phi_{em}\ll 1$, where $\Delta\phi_{Y}$ is the entanglement
phase induced by the Yukawa term. Thus we will require
$\left|\delta\Delta\phi_{em}\right|<1$, which implies
$\tilde{\delta}\left|\left(3\Delta\phi_{c}+15\Delta\phi_{cp}\right)\right|<1$,
or using Equation 11: $\tilde{\delta}\leq 10^{-6}{R}/{t}$. Similarly, we must
ensure that the gravitational interaction between the masses do not induce a
coherence destroying noise. Given the gravitational entanglement phase is
given by: $\Delta\phi_{g}={Gm^{2}t}\left(r^{-1}-d^{-1}\right)/\hbar$, to keep
the variance below the unit phase will require
$\delta\Delta\phi_{g}\approx\frac{40\pi^{2}\rho^{2}GR^{5}t}{189\hbar}\tilde{\delta}<1$.
Substituting known values and assuming diamond is used gives then gives the
bound $\tilde{\delta}\lesssim 5\times 10^{-32}t^{-1}R^{-5}$. If we thus set
$\tilde{\delta}\approx\textrm{min}\left\\{10^{-6}{R}/{t},10^{-32}t^{-1}R^{-5}\right\\}$,
then the Yukawa potential will be the dominant entangling signal, provided
$\left|\Delta\Phi_{y}\right|\geq 1$. We then have a detectable Yukawa signal
provided

$\frac{\alpha t}{42\hbar
R}\left(6e^{-\frac{7R}{\lambda}}-7e^{-\frac{6R}{\lambda}}\right)\geq 1\,.$
(14)

The Yukawa induced correction to the EM interaction is shown in Fig. 3. Its
worth noting that this corresponds to the actual parameter uncertainties of:
$\delta d=\textrm{min}\left\\{10^{-6}\times({R^{2}}/{t}){\rm
sec~{}m^{-1}},~{}10^{-32}\times t^{-1}R^{-4}{\rm sec~{}m^{5}}\right\\},$ and
$\delta t=\textrm{min}\left\\{10^{-6}\times R\textrm{
sec~{}m}^{-1},~{}10^{-32}\times R^{-5}\textrm{ sec~{}m}^{5}\right\\}$. This
suggests that for a nano-crystal with a radius $R\sim 10^{-6}$m we will need
the precision in time for the measurement to be around $10^{-12}$ sec. This
may pose a challenge but the recent advancements of keeping track of the
frequency ratio measurements at 18-digit accuracy may be the way to track the
time evolution of the entanglement [23].

Figure 4: Plot showing the region in which the Axion modified Coulomb
interaction is detectable using this entanglement based detection for the two
configurations. The _Observations_ shown by the grey shaded region correspond
to the combined results of many separate observations, such as CAST+SUMICO,
cosmology, supernovae-1987A, electron-positron collider (LEP), OSCAR and PVLAS
collaborations, compiled from the Refs. [5, 7, 45, 46, 47, 48].

$\bullet$ Axion like particle detection:  We can also consider how our
protocol may be sensitive to the axion modified Coulomb potential. Following
previous analyses [48], assuming that the experiment involves distances larger
than the Compton wavelength of the axion mass, the axion modified Coulomb
potential is approximately given by:
$U_{ac}(x)=U_{c}(x)\left(1+\frac{g^{2}\lambda^{2}\hbar^{2}}{\pi^{2}c^{2}x^{4}}e^{-x/\lambda}\right)$
where $g$ is the coupling strength and $\lambda=\frac{\hbar}{m_{a}c}$ is the
Compton wavelength of the axion of mass $m_{a}$. The entanglement phase
detectability requires
$\Delta\phi_{ac}-\delta\left(\Delta\phi_{ac}\right)>\Delta\phi_{c}+\delta\left(\Delta\phi_{c}\right)$,
which leads to $\Delta\phi_{a}>2\delta\left(\Delta\phi_{c}\right)$. The latter
condition gives the bound for a detectable $g$ as

$g\gtrsim\sqrt{6\frac{\pi^{2}c^{2}}{\lambda^{2}\hbar^{2}}\left(\frac{1}{r}-\frac{1}{d}\right)\left(\frac{e^{-r/\lambda}}{r^{5}}-\frac{e^{-d/\lambda}}{d^{5}}\right)^{-1}\tilde{\delta}}.$
(15)

We can see that the current observational bounds arising from [5, 7, 45, 46,
47, 48] cover a large range of parameter space in $g,~{}m_{a}$. We see that
our current protocol will be sensitive to constrain masses below $m_{a}\leq
10^{-21}$ eV in future.

As such, taking the experimental set-up discussed above with $R=10$ $\mu$m
suggests a the detectable coupling strength will be

$g\gtrsim\frac{10^{35}}{\lambda}\left(2e^{-\frac{6}{10^{-5}\lambda}}-e^{-\frac{7}{10^{-5}\lambda}}\right)^{-1/2}\textrm{
kg}^{-1}$ (16)

as shown in Figure 4.

Figure 5: $\alpha_{g}-\lambda$ plot showing the region in which the Yukawa
modified Newtonian potential dominates over the Casimir and the Coulomb
interactions for different values of $R$. The solid and dashed lines
correspond to the total interaction time $t=10^{-3},t=10^{-6}$ s,
respectively. The two black lines (solid and dashed) correspond to the
experimental results from the years 2007, 2020, see [25]. The horizontal grey
area shows the region in which $n$-compact extra dimensions may be observable
where $\alpha_{g}=2n$. The typical range for $\alpha_{g}\leq 20$ from string
theory compactification on a Calabi Yau manifold, see [28].

$\bullet$ Departure from the Newtonian potential: Following the above
discussion, we can evaluate the entanglement phase as sourced by the quantum
origin of the gravitational interaction [12, 16, 15] or as we will do here, a
modification to the Newtonian potential. We can parameterise the departure
from Newton’s law by the Yukawa potential [24]:

$U_{Y_{g}}=\frac{Gm^{2}}{r}\left(1+\alpha_{g}e^{-{r}/{\lambda}}\right)$ (17)

In this case, a similar analysis as above, see Eq.(14) translates to a
sensitivity in the effective gravitational coupling $\alpha_{g}$ given by
Fig.(5). Note that the sensitivity to probe $\alpha_{g}$ in the vicinity of
$10^{-5}$ m is far improved than what we have achieved in the torsion-balance
experiments $\alpha_{g}\sim 10^{-3}$ in the ${\mu m}$ range [25]. Fig.(5)
shows the experimental constraints from 2000 and 2007 of the same group, see
[25].

Large extra spatial dimensions [26, 27] also modify the gravitational
potential very similar to the Yukawa modification, Eq.(17), see [28]. The
extra dimensions are compactified, which depends on the geometry of the
compactification. However, different compactification will give rise to
different $\alpha_{g}$ in Eq.(17). If $n$ extra dimensions are compactified on
a n-torus, then $\alpha_{g}=2n$, when on n-spehere $\alpha_{g}=n+1$, and in
the case of string theory compactification on a Calabi-Yau manifold it should
be $\alpha_{g}\leq 20$ [28]. The corresponding $\alpha_{g}-\lambda$ plot is
shown in Figure 5 which suggests that our setup with entanglement tomography
is capable of detecting modifications to the Newtonian potential for
$\lambda\gtrsim 10^{-6}$ m, and eventually can probe certain aspects of string
theory or the presence of large extra dimensions 222Similarly, we can also
constrain the hidden sector photon, for which the modified Coulomb potential
can be derived very similar to the modification to the gravitational potential
[29], $V(r)=[e^{2}/(4\pi\epsilon_{0}r)][1+\alpha e^{-m_{\gamma^{\prime}}r}]$.
Here $m_{\gamma^{\prime}}$ is the mass of the hidden photon and
$\sqrt{\alpha}$ designates the coupling between the hidden sector photon and
the Standard Model photon, i.e. $(\sqrt{\alpha}/2)X_{\mu\nu}F^{\mu\nu}$.
$X_{\mu\nu}$ denotes the hidden sector photon and $F_{\mu\nu}$ denotes the
Standard Model photon, and $\mu\nu=0,1,2,3$. In this scenario we can constrain
$m_{\gamma^{\prime}}\leq 10^{-17}$ eV for $\alpha\geq 10^{-4}$. The current
constraints on the hidden sector photon mostly arises from astrophysics, and
they can constrain $m_{\gamma^{\prime}}\sim{\cal O}(10^{-10}-10^{-15})$eV, see
[29].

To summarise, all the examples capture the importance of entanglement based
tomography as a protocol to test new physics - whether it is in the EM sector
or in the gravitational sector. Indeed, there are many challenges from
creating charged superposition [34] in a levitated ion trap, see [35, 36, 37,
38, 39, 40], to preparing and cooling the ground state of the nano-crystal
[41]. There will be constraints on the decoherence [42], but we expect the
decoherence rates will be very similar to the case of the neutral crystal, as
far as the blackbody and the atmospheric interactions are concerned for a
micron size crystal with a mass of $\sim 10^{-17}$Kg [20, 43]. However, there
are possible ways of mitigating EM induced decoherence by creating Faraday
cage, and also the gravity gradient and relative acceleration noise [44].

To conclude, the entanglement based tomography could potentially be a powerful
protocol to detect new physics in the IR. One can apply this technique to
probe modifications to GR including local [30] and non-local modifications of
classical and quantum gravity [31, 32, 33]. In physics beyond the SM, we will
be able to probe certain model dependent parameters case by case [8, 9, 47].
The last reference considered axion induced entanglement, however, not in the
context of EM background effects arising from Coulomb and CP-induced
entanglement.

In a model independent fashion the entanglement based tomography can constrain
the Yukawa parameters $\alpha\geq 10^{-35}$ for $r\geq 10^{-6}$m for the new
forces, and a similar modification in the gravitational potential would yield
constraining $\alpha_{g}\geq 10^{-8}$ for $r\geq 10^{-6}$m, nearly five-orders
of magnitude better than the current bounds arising from the classical
torsion-balanced experiment [25]. In this way we can also place future
constraints on the large extra compact dimensions. Furthermore, in the case of
axion like particle detection, we are sensitive to even smaller axion masses
(smaller than the existing constraints from various astrophysical and
cosmological observations), but not for small couplings, see Fig. (4).
Nevertheless, entanglement tomography in conjunction with other data set will
be extremely helpful to probe axion masses below $10^{-21}$eV, thereby probing
both Yukawa type correction as well as more sophisticated potentials arising
due to axion-like particles.

Acknowledgements: PFB. acknowledges funding from the EPSRC Grant No.
EP/N031105/1 and the H2020-EU.1.2.1 TEQ project Grant agreement ID: 766900. SB
acknowledges the EPSRC grant EP/S000267/1, AM acknowledges (NWO) grant number
680-91-119 and RJM was supported by the Australian Research Council (ARC)
under the Centre of Excellence for Quantum Computation and Communication
Technology (CE170100012).

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# A Screen-Shooting Resilient Document Image Watermarking Scheme using Deep
Neural Network

Sulong Ge, Zhihua Xia, Yao Tong, Jian Weng, and Jianan Liu  Sulong Ge is with
Engineering Research Center of Digital Forensics, Ministry of Education,
School of Computer and Software, Nanjing University of Information Science &
Technology, Nanjing, 210044, China. Zhihua Xia, Jian Weng, and Jianan Liu are
with College of Cyber Security, Jinan University, Guangzhou, 510632, China.
Zhihua Xia is also with Engineering Research Center of Digital Forensics,
Nanjing University of Information Science & Technology, Nanjing, 210044,
China. Zhihua Xia and Jian Weng are the corresponding authors. e-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>The code of our scheme can be found
at https://github.com/gslxr/Screen-Shooting-Resilient-Document-Image-
Watermarking

###### Abstract

With the advent of the screen-reading era, the confidential documents
displayed on the screen can be easily captured by a camera without leaving any
traces. Thus, this paper proposes a novel screen-shooting resilient
watermarking scheme for document image using deep neural network. By applying
this scheme, when the watermarked image is displayed on the screen and
captured by a camera, the watermark can be still extracted from the captured
photographs. Specifically, our scheme is an end-to-end neural network with an
encoder to embed watermark and a decoder to extract watermark. During the
training process, a distortion layer between encoder and decoder is added to
simulate the distortions introduced by screen-shooting process in real scenes,
such as camera distortion, shooting distortion, light source distortion.
Besides, an embedding strength adjustment strategy is designed to improve the
visual quality of the watermarked image with little loss of extraction
accuracy. The experimental results show that the scheme has higher robustness
and visual quality than other three recent state-of-the-arts. Specially, even
if the shooting distances and angles are in extreme, our scheme can also
obtain high extraction accuracy.

###### Index Terms:

watermark, screen-shooting resilient watermarking, document image, deep neural
network

##  1 Introduction

With the popularity of smart phones, taking photographs has become the most
simple and efficient way of information transmission, which brings a threat to
information security. The commercialization process generates lots of valuable
secret files, anyone who has access to the files, can simply steal information
by taking photographs without leaving any records [1]. In addition, the
screen-shooting process is difficult to prohibit from the outside, so it is
very important to design a screen-shooting resilient (SSR) document
watermarking scheme to solve this problem. As shown in Fig. 1, we can embed
watermark such as identity information in the document, so when the document
after the screen-shooting process, we can also extract the identification from
the captured photographs.

Figure 1:  A framework of the screen-shooting resilient image watermarking.

Screen-shooting process is the process of capturing images displayed on the
screen with a camera. It can be seen as one of the called cross-media
information transmission processes, and the other are print-scanning process
and print-camera process [2]. In previous years, the print-scanning resilient
(PSR) watermarking schemes and the print-camera resilient (PCR) watermarking
schemes have been extensively studied. Print-scanning process is the process
of printing image on paper and then scanning through a scanner. Rotation,
scaling, and translation (RST) are the common distortions during the process.
So far, PSR watermarking scheme can be broadly divided into two categories
that are template-based methods [3, 4, 5] and transform invariant domain-based
methods [6, 7, 8, 9]. Besides, Print-camera process can be seen as an addition
to the print-scanning process, which means printing image on paper and taking
a photograph of the printed image. The watermark must be robust to more
distortions, such as camera distortion, shooting distortion and so on. PCR
watermarking schemes can be roughly divided into three categories. One is
template-additive based methods [10, 11, 12]. The other two are transformed
invariant domain-based methods [13, 14, 15] which is developed from PSR
watermarking scheme, and the DNN-based (deep neural network) methods [16, 17].

With the advent of screen-reading era, the screen-shooting process is becoming
common, and using this way to leak files is the most difficult problem at this
stage. Compared with the print-scanning process and the print-camera process,
the watermarked image undergoes a series of analog-to-digital (AD) and
digital-to-analog (DA) conversion processes in the screen-shooting process,
which will be manifested as a combination of strong distortions [18].
Therefore, it becomes impractical to design watermarking algorithms by seeking
transformed invariant domain, like [2, 19, 15], we need to analyze all the
distortions in the screen-shooting process and design corresponding
compensation operations for the distortions. With the development of deep
learning, deep learning instead of artificial design has become the mainstream
of natural image watermarking algorithms, and has achieved good results in
robustness and visual quality. However, according to the peculiarity of text
content, these algorithms cannot be applied to document images without
adjustments. In this paper, we propose a screen-shooting resilient document
image watermarking scheme using deep neural network. The main contributions of
this paper are listed as follows:

  * •

We propose a document image watermarking scheme which is resilient to the
screen-shooting process. Our scheme outperforms the recent state-of-the-arts
in both the visual quality and robustness.

  * •

During the training process, a distortion layer is designed to simulate the
distortions caused by the screen-shooting process, including the camera
distortion, shooting distortion, light source distortion, and etc. Such design
is quite helpful in improving the robustness.

  * •

Redundancy space in model parameters during the training process provides
possibility for image co-encoding. An embedding strength adjustment strategy
is proposed to improve the visual quality of the watermarked image, which
almost has no effect on the extraction accuracy.

The rest of this paper is organized as follows. The Section 2 introduces the
related works. The screen-shooting distortions is analyzed in Section 3. In
the Section 4 shows the details of the proposed scheme. The Section 5
discusses the experimental results and analysis. The Section 6 draws the
conclusion.

##  2 Related works

In this section, we summarize the image watermarking schemes about the cross-
media information transmission process in recent years, including the print-
scanning resilient (PSR) schemes, the print-camera resilient (PCR) schemes,
and the screen-shooting resilient (SSR) schemes.

###  2.1 Print-scanning resilient watermarking

Print-scanning process means printing image on paper and then scanning through
a scanner. PSR schemes can be broadly divided into two categories: the
template-based methods and the transform invariant domain-based methods.

The template-based methods. This kind of methods design template for watermark
to resist print-camera process. Pereira and Pun [3] proposed a templete
watermarking scheme using discrete Fourier transform (DFT). The authors proved
that watermark embedding into the DFT domain can resist affine transformation.
Based on this, Kang _et al._ [4] proposed a watermarking using discrete
wavelet transform (DWT) and DFT. Watermark is embedded in the coefficients of
the LL subband in the DWT domain. To resist affine transformation, a template
is embedded in the middle frequency components in the DFT domain. Pramila _et
al._ [5] proposed a watermarking scheme in multiple domains. To resist
rotation and scaling after print-scan process, a circular template is embedded
in the DFT domain. To resist translations, another template is embedded in
spatial domain. To achieve high robustness and visual quality, the watermark
is embedded in the wavelet domain.

The transform invariant domain-based methods. This kind of methods design
watermarking schemes in the transform invariant domain that can resist the
print-camera process. He and Sun [6] proposed a watermarking scheme using DFT.
The cover is divided into the non-overlapping blocks, in which watermark is
embedded into the middle frequency DFT coefficients block by block. The
watermark extraction is an inverse procedure of the watermark embedding
process. Solanki _et al._ [7] proposed a watermarking scheme using the
analytical modeling of the print-scan process, in which geometric
transformations, nonlinear effects, and colored noise are main components.
Watermark is embedded into high-magnitude of low-frequency DFT coefficients.
Besides, A novel approach was proposed for estimating the rotation that an
image might undergo during the scanning process. Kang _et al._ [8] proposed a
watermarking scheme using uniform log polar mapping (ULPM), which is resilient
to both geometric distortion and the print-scan process. To obtain a discrete
log polar point, the authors apply ULPM to the frequency index in the
Cartesian system. Then the watermark is embedded in the corresponding 2D-DFT
coefficients in the Cartesian system. Amiri and Jamzad [9] proposed a
watermarking scheme using DWT and discrete cosine transform (DCT). The authors
apply Two-dimensional DWT to the cover for obtaining the mid-frequency
subbands, then apply DCT to the selected subbands for embedding the watermark.
Besides, a Genetic Algorithm is used to achieve image quality.

###  2.2 Print-camera resilient watermarking

Print-camera process means printing image on paper and then taking a
photograph of the printed image. PCR schemes can be roughly divided into two
categories: the template-based methods, the transformed invariant domain-based
methods and the DNN-based methods.

The template-based methods. This kind of methods design templates for
watermarks to resist print-camera process. Nakamura _et al._ [10] proposed a
fast watermark detection scheme from a captured image. The method consists of
two processes, one is to correct geometric distortion of the captured image,
and the other is to detect watermark from the rectified image. Kim _et al._
[11] proposed an watermarking scheme for the print-camera process. They embed
watermark into the spatial domain of a color image, print out using a printer,
and extract the watermark from the image captured by a digital camera. Pramila
_et al._ [12] proposed a directed periodic pattern-based watermarking scheme.
This scheme generate a periodic template and embed the watermark by modulating
the direction of the template. At the extraction side, the Hough transform is
used to detect the angle of template.

The transform invariant domain-based methods. This kind of methods design
watermarking schemes in the transform invariant domain that can resist the
print-camera process. Delgado-Guillen _et al._ [13] proposed a watermarking
scheme for mobile platforms. The embedding and extracting algorithms are based
on the scheme proposed by Kang _et al._ [8]. Gourrame _et al._ [14] proposed a
watermarking scheme using DFT. The watermark is embedded into the luminance
channel by adjusting the coefficient of the DFT. For the perspective
distortions, the 3D rotation of the image and camera position are simulated
simultaneously. Liang and Wang [15] proposed a watermarking scheme using DCT
and scale-invariant feature transform (SIFT). This method embed watermarks
into middle frequency of the DCT coefficients. The SIFT is used to revert the
geometric distortions and correct blurred pixel values.

The DNN-based methods. This kind of methods train network to simulate the
print-camera process. Tancik _et al._ [16] proposed an end-to-end watermarking
scheme for print-camera process. The authors use a set of differentiable image
perturbations (Perspective Warp, Color Manipulation, and JPEG Compression)
between the encoder and decoder to approximate the distortions in print-camera
process. It proved that this method has a quite high robustness to the print-
camera distortions. On this basis, Jia _et al._ [17] proposed a watermarking
scheme using differentiable 3D rendering and just noticeable difference (JND)
loss. To make the watermark resilient to print-camera process during training
process, this method introduce a distortion network (DL) using differentiable
3D rendering to augment the encoded images, in which almost all distortions in
print-camera process are simulated. Besides, the JND-based loss is helpful to
maintain image quality.

###  2.3 Screen-shooting resilient watermarking

Screen-shooting process means capturing images displayed on the screen with a
camera. SSR schemes can be roughly divided into two categories: the
transformed invariant domain-based methods and the DNN-based methods.

The transform invariant domain-based methods. This kind of methods design
watermarking schemes in the transform invariant domain that can resist the
screen-shooting process. Fang _et al._ [2] proposed a watermarking scheme
using an intensity-based scale-invariant feature transform (I-SIFT) algorithm
and DCT transform. It proved that this method has good robustness to the
screen-shooting process and visual quality. However, compared with natural
images, the simple texture and color of the document would result in the weak
strength of I-SIFT key point, so that the watermark region cannot be
accurately located. Subsequently, Fang _et al._ [19] proposed the flip-based
watermarking scheme to better synchronize the watermark region. Li _et
al._[20] proposed a watermarking scheme using learned invariant keypoints,
quaternion discrete Fourier transform (QDFT), and tensor decomposition
(TD).They apply feature regions filtering model to SuperPoint (FRFS) to locate
the embedding regions, then the watermarks are embedded by using the QDFT and
TD algorithm. To enhance robustness, the watermarks are repeatedly embedded
into different regions in an image.

The DNN-based methods. This kind of methods train network to simulate the
screen-shooting process. Wengrowski and Dana [21] proposed an end-to-end
watermarking for the screen-shooting process. To learn the camera-display
transfer function (CDTF), they introduce a dataset (Camera-Display) of
1,000,000 camera-captured images collected from 25 camera-display pairs. This
method significantly outperformed existing methods, even when camera and
display were at high perspective angles, but seriously driven by datasets
[22]. Zhang _et al._ [23] proposed a watermarking shceme with Universal Deep
Hiding (UDH). The authors proved that only adding a perspective transformation
layer between the encoder and decoder, which can resist the distortions
introduced by screen-shooting process to a certain extent. Unlike the above
schemes, Fang _et al._ [24] proposed a watermarking scheme using DNN. The
scheme is not end-to-end, the watermark template and the locating template are
generated by template generation scheme, and then embedded into the red or
blue channel of the cover respectively. Watermark extraction is designed by
DNN, which is composed of an enhancing network and a classification network.
Subsequently, Fang _et al._ [25] also proposed a watermarking scheme named
”TERA”. The scheme is like [24], watermark embedding depends on manual design
named superposition-based embedding scheme and watermark extraction is
designed by deep neural network (DNN). Extraction network is composed of an
enhancing network, an attention-guided network [26] and a regression network.

##  3 Screen-shooting distortion analysis

Combined with the analysis of Fang _et al._ [2] and Jia _et al._ [17], we
summarize the distortions in the screen-shooting process into three aspects:
camera distortion, shooting distortion and light source distortion.

###  3.1 Camera Distortion

Camera distortion mainly comes from the distortion when taking photographs
with the camera, and different types of cameras produce different camera
distortions. The sources of these distortions are generally classified into
three categories: 1) the distortion caused by electronic components inside the
camera system. 2) the distortion from camera parameters. 3) the distortion
caused by image compression. The electronic components in the camera system
can introduce a series of noises in the imaging process, including photon
noise, dark noise and lens noise [27]. The camera parameters mainly affect the
focusing in the imaging process, and the defocusing phenomenon will lead to
blurred images. Photographs are usually saved in a lossy format (JPEG
compression) after being shot, and JPEG compression will bring image loss to
the captured photographs.

###  3.2 Shooting Distortion

Due to the diversity of camera angles and the distances between the object and
the camera lens, when we use a camera to capture the image displayed on the
screen, the image will be firstly affected by perspective deformation from the
original 3D space to the 2D plane, and then followed by rotation, scaling, and
translation distortions.

###  3.3 Light Source Distortion

Our ability to see the world depends on the reflection of light from the
surface of any object. Therefore, lighting conditions are the most important
and complex environmental factors in the camera imaging process. For light
source distortion, in addition to the external light, the screen itself is
also a light source. The unevenness of the screen light source will produce
brightness, contrast and saturation distortions [17].

Figure 2:  The overview of the proposed scheme.

##  4 proposed scheme

In this section, we firstly give an overview of our scheme. Then, the encoder,
distortion layer, decoder, and loss function are specified.

###  4.1 The overview of the proposed scheme

As shown in Fig. 2, the overall architecture of our scheme is introduced,
which is an end-to-end training pipeline composed of three components, namely
encoder (E), distortion layer (DL) and decoder (D). In the training stage, the
watermark $w$ is expanded, reshaped, and concatenated with the cover image
$I_{c}$. Then, combination of $I_{c}$ and $w$ are encoded to generate the
watermarked $I_{w}$. Next, $I_{w}$ is input into the distortion layer which
simulates the screen-shooting process, generating the distorted and
watermarked image $I^{\prime}_{w}$. Finally, $I^{\prime}_{w}$ is input into
the Decoder D to extract the watermark $w^{\prime}$. After training, the
Encoder E is used to embed the watermark and the Decoder D is used to extract
the watermark.

###  4.2 Encoder

Figure 3:  The structure of the Encoder E.

Encoder E is a network trained to embed the watermark into the cover image as
illustrated in Fig. 3. Since the U-Net [28] like architectures has proved its
capability in many image-to-image translation tasks, we use the U-Net style
architecture as our E, which receives a six-channel input tensor and outputs a
three-channel mask image. The watermark is represented as a binary bit string
with L bits. To enhance the robustness to distortions in training stage, the
watermark is expanded by a fully connected layer to bring in redundancy, and
then up-sampled to the same size as the cover image. The expanded watermark
with the cover are concatenated and input to E, and finally outputs a mask
image which represent the watermark. Therefore, the watermarked image is the
combination of cover image and mask image, that is

$I_{w}=I_{c}+\alpha\cdot m_{w},$ (1)

where $\alpha$ is an embedding strength factor.

###  4.3 Distortion layer

Figure 4:  The structure of Distortion Layer DL.

In the Section 3, we divide the screen-shooting distortions into camera
distortion, shooting distortion and light source distortion. To resist the
distortions introduced in the screen-shooting process, we can simulate it in
the training process. So, the process is added to the output of the Encoder E
as Distortion Layer DL.

Camera distortion. Electronic components in the camera system introduce
multiple noises in the imaging process. To simulate the random noises, we use
a random Gaussian noise ($\alpha$ = U[0, 0.02]). To simulate defocus blur, we
apply Gaussian kernel with width from 1 to 3 pixels and variance from 0.01 to
1. To simulate motion blur, we use a straight line blur kernel with a width
from 3 to 7 pixels and a random angle from 0 to 2 $\pi$. To compensate the
JPEG compression loss, as the quantization of JPEG compression is not
differentiable, we use the trick proposed by Shin and Song [29], which is a
differentiable operation to approximate the quantization step close to 0.

Shooting distortion. The camera angles and distances make the camera lens
deviate from the image plane, resulting in the perspective deformation. To
simulate perspective deformation, we randomly perturb the four corners of the
watermarked image in a fixed range (up to $\pm$ 40 pixels, i.e. $\pm$ 10%),
then applying homography to restore the watermarked image into the new
locations.

Light source distortion. Compared with the entire RGB color space, the color
area of the display is very limited. The camera system uses many manipulations
to modify its output, such as exposure settings, color correction matrix, and
white balance. For convenience, we use a series of random affine color
transformations to approximate these pixel distortions, including global
contrast, brightness, and hue adjustments, which can achieve a similar effect
to light reflection. Please note that, the details can be found from the link:
https://github.com/gslxr/Screen-Shooting-Resilient-Document-Image-
Watermarking.

###  4.4 Decoder

Figure 5:  The structure of the Decoder D.

Decoder D is a network trained to extract the watermark from the distorted and
watermarked image $I^{\prime}_{w}$ as illustrated in Fig. 5. D is composed of
a series of convolution layers, a flatten layer, and a fully connected layer.
The output of the Distortion Layer DL is input into D to extract the
watermark. Finally, the sigmoid function is used to activate the output of the
fully connected layer.

###  4.5 Loss function

In this section, we will give the loss function, which consists of three
parts: image loss, text sensitive loss and watermark loss.

Image loss. Image loss is used to make the watermarked image $I_{w}$ and the
cover $I_{c}$ look the same. We consider the image in YUV color space and try
to make little change on the Y component as the human eyes are more sensitive
to it. The image loss is designed as follows,

$\begin{split}L_{I}&=MSE(I_{w}^{Y},I_{c}^{Y})\times s_{Y}\\\
&+MSE(I_{w}^{U},I_{c}^{U})\times s_{U}\\\ &+MSE(I_{w}^{V},I_{c}^{V})\times
s_{V},\end{split}$ (2)

where $MSE$ denotes the mean squared error, and $s_{Y}$, $s_{U}$ and $s_{V}$
are the weights for YUV channels.

Text-sensitive loss. Readers will pay more attention to the text content in
the reading process, so the modification on characters can be more conspicuous
than on background [30]. Thus, text-sensitive loss is designed to restrain the
modification on characters as follows,

$\begin{split}L_{T}&=\mid I_{w}^{R}-I_{c}^{R}\mid\cdot\tilde{I_{c}^{R}}\times
s_{R}\\\ &+\mid I_{w}^{G}-I_{c}^{G}\mid\cdot\tilde{I_{c}^{G}}\times s_{G}\\\
&+\mid I_{w}^{B}-I_{c}^{B}\mid\cdot\tilde{I_{c}^{B}}\times s_{B},\end{split}$
(3)

where $\tilde{I_{c}^{*}}=\frac{255-I_{c}^{*}}{255}$ assigns larger punishment
to the text content, and $s_{*}$ denotes the weights for different color
components, $*\in\\{R,G,B\\}$.

Watermark loss. Watermark loss is used to minimize the difference between the
extracted and the original watermark. Binary cross entropy function is used
for it as follows,

$L_{W}=-\sum_{i=1}^{N}{(w_{i}\cdot\log(w^{\prime}_{i})+(1-w_{i})\cdot\log(1-w^{\prime}_{i}))},$
(4)

where $w_{i}$ refers to the original watermark, $w^{\prime}_{i}$ denotes the
extracted watermark, and $N$ is the watermark length.

Finally, the total training loss can be calculated as

$L_{total}=\lambda_{I}L_{I}+\lambda_{T}L_{T}+\lambda_{W}L_{W}.$ (5)

where $\lambda_{I}$, $\lambda_{T}$, and $\lambda_{W}$ are weight factors.

##  5 Experimental results and analysis

In this section, we show the implementation details and experimental results.
Besides, an embedding strength adjustment strategy is discussed.

###  5.1 Implementation Details

We respectively select the first 100,000 document images from DocImgEN and
DocImgCN training sets [31] as our training sets, and then selected the first
100 document images from DocImgEN and DocImgCN test sets as our test sets. In
the experiment, the size of the cover is 400 $\times$ 400 pixels, and the
length of the watermark is 100 bits which is random bit string.

In the training stage, we feed the document images and watermark into the
Encoder E by batches, and the size of each batch is 4. To accelerate the
convergence of model parameters, we set the learning rate to 0.0001 and use
the Adam optimizer [32] to optimize the model parameters. An NVIDIA 1080Ti GPU
is used as the training environment for model training.

In addition, we find that even with many rounds of training, the decoding
accuracy is still difficult to increase. So, we froze the encoder at the first
3000 iterations, just training the decoder and distortion layer. Besides, to
make the Decoder D gradually adapt to the distortions, the parameters
$\lambda_{I}$, $\lambda_{T}$, and $\lambda_{W}$ are set to be 0 at the
beginning, and increase linearly to 1.5, 1.5, and 2.0 at the first 15,000
iterations. Please note that, the other parameters can be found from the link:
https://github.com/gslxr/Screen-Shooting-Resilient-Document-Image-
Watermarking.

###  5.2 The quality of the watermarked document image

In this section, to evaluate the quality of watermarked images, we select Peak
Signal to Noise Ratio (PSNR) and Structural Similarity Metric (SSIM) [33] as
our metrics. Considering that readers may be more sensitive to the characters
while reading the documents, we use the text-sensitive loss to ensure less
modification on text pixels. Here we use the Change Intensity Per Text-Pixel
(CPP) designed in [31] to evaluate the modification on text pixels. The CPP
metric is designed as follows,

$\begin{split}CPP&=\frac{\sum_{i=1}^{n_{t}}{\mid
I_{c}^{tR}(i)-I_{w}^{tR}(i)\mid}}{n_{t}}\\\ &+\frac{\sum_{i=1}^{n_{t}}{\mid
I_{c}^{tG}(i)-I_{w}^{tG}(i)\mid}}{n_{t}}\\\ &+\frac{\sum_{i=1}^{n_{t}}{\mid
I_{c}^{tB}(i)-I_{w}^{tB}(i)\mid}}{n_{t}},\end{split}$ (6)

where $I_{\\#}^{t*},\\#\in{c,w},*\in\\{R,G,B\\}$ refers to the set of text
pixels in the cover and watermarked images, and $n_{t}$ denotes the total
number of the text pixels.

The PSNR, SSIM and CPP values are listed in Table I, and some example pairs of
cover and watermarked images are shown in Fig. 6. As listed in Table I, the
incorporation of text-sensitive loss $L_{T}$ make little influence on PSNR and
SSIM values but decrease CPP value by up to 53.84% averagely. It indicates
that $L_{T}$ loss decreases the modification on text pixels and has little
effect on image quality of the watermarked image.

TABLE I:  PSNR, SSIM, and CPP of our scheme with the text-sensitive loss $L_{T}$ or not. Schemes | PSNR (dB) | SSIM | CPP
---|---|---|---
On DocImgEN without $L_{T}$ | 32.90 | 0.916 | 15.55
On DocImgEN with $L_{T}$ | 34.10 | 0.914 | 6.88
On DocImgCN without $L_{T}$ | 35.70 | 0.946 | 11.40
On DocImgCN with $L_{T}$ | 33.20 | 0.928 | 5.56
Figure 6:  Example pairs of cover and watermarked images and their difference
with the text-sensitive loss $L_{T}$ or not.

###  5.3 Comparisons with previous methods

In this section, we will compare the visual quality and robustness with
different schemes. Due to the lack of SSR image watermarking algorithms for
document, we have to choose three schemes for natural images as comparison
schemes. We compare the proposed scheme with the schemes in [2] (Transform
invariant domain-based), [16] (DNN-based) and [23] (DNN-based). As shown in
the Fig. 7, the environmental scenario is set as similar as possible to the
description of [19]. Because the watermark capacity in [19] is different from
other schemes, so to measure the robustness, we change bit error rate (BER) to
average bit accuracy for fair comparison.

(a) The front view of the screen-shooting test.

(b) The vertical view of the screen-shooting test.

Figure 7:  Experimental scenario of our scheme. As shown in the Fig. 7a, the
environmental scenario is set as similar as possible to the description of
[19]. As shown in the Fig. 7b, the dots in the red circle are examples of the
shooting point in the experimental test. Figure 8:  Example pairs of the
captured images with different horizontal perspective angles (first row) and
the corresponding recovered images (second row). These photographs are
captured with a Huawei Mate 30 Pro.

####  5.3.1 The visual quality with different schemes

To better evaluate the visual quality, in addition to calculating PSNR and
SSIM values, we also perform the Change Intensity Per Text-Pixel (CPP) test.
As is listed in Table II, the CPP value of the proposed scheme is much lower
than that of other schemes. It indicates that the less modification on the
characters of the text pixels on DocImgEN and DocImgCN testsets. In addition,
the PSNR values of our scheme are higher than that of two DNN-based methods,
which means our scheme has better image quality than two DNN-based methods.
Finally, the watermarked images by [2], [16] and [23] are illustrated in Fig
9.

TABLE II:  Visual quality of watermarked images with different schemes on DocImgEN and DocImgCN testsets. Schemes | PSNR (dB) | SSIM | CPP
---|---|---|---
Fang _et al._ [2] (On DocImgEN) | 35.42 | 0.975 | 15.12
Tancik _et al._ [16] (On DocImgEN) | 22.02 | 0.940 | 81.58
Zhang _et al._ [23] (On DocImgEN) | 27.30 | 0.947 | 35.34
Proposed (On DocImgEN) | 34.10 | 0.914 | 6.88
Fang _et al._ [2] (On DocImgCN) | 35.50 | 0.977 | 14.57
Tancik _et al._ [16] (On DocImgCN) | 20.30 | 0.922 | 88.58
Zhang _et al._ [23] (On DocImgCN) | 28.75 | 0.944 | 27.69
Proposed (On DocImgCN) | 33.20 | 0.928 | 5.56
Figure 9:  Examples of the watermarked images from three state-of-the-arts and
our scheme.

####  5.3.2 The robustness with different schemes

In the real scenes, different screen-shooting settings can be used. Therefore,
we evaluate the robustness of our scheme under different conditions on
DocImgEN and DocImgCN testsets, including different shooting distances, angles
(horizontal and vertical perspective angles) and devices.

1) The Impact of Distance on Robustness: The average bit accuracy obtained
under different shooting distances is listed in Table III. Compared with
natural images, the simple texture of the document would result in the weak
strength of I-SIFT key point, so the domain-based method ([2]) can not achieve
satisfying results as shown in Fig. 10. Besides, it is easy to see that our
scheme has better performance than other two DNN-based methods in all test
distances. When the shooting distance is in a short distance, Moiré pattern
occurs in the captured photographs as descripted in [2]. However, the Moiré
pattern almost has no effect on the robustness of the proposed method, and the
bit accuracy is no less than 97%. Therefore, the proposed scheme has certain
robustness to distance change and Moiré pattern.

TABLE III:  Average bit accuracy of the extracted watermark with different shooting distances on DocImgEN and DocImgCN testsets. Distance (cm) | 15 | 25 | 35 | 45 | 55 | 65 | 75 | 85 | 95
---|---|---|---|---|---|---|---|---|---
Fang _et al._ [2] (On DocImgEN) | 68.01 | 66.01 | 59.80 | 68.80 | 64.21 | 63.19 | 63.55 | 60.58 | 55.34
Tancik _et al._ [16] (On DocImgEN) | 98.30 | 97.33 | 95.70 | 99.58 | 98.20 | 98.84 | 98.31 | 97.63 | 97.33
Zhang _et al._ [23] (On DocImgEN) | 87.96 | 74.20 | 79.68 | 83.14 | 73.08 | 65.86 | 59.72 | 51.67 | 49.89
Proposed (On DocImgEN) | 99.97 | 99.98 | 99.97 | 99.95 | 99.78 | 99.89 | 99.86 | 98.87 | 98.21
Fang _et al._ [2] (On DocImgCN) | 69.02 | 73.37 | 68.67 | 65.62 | 65.59 | 63.52 | 65.11 | 60.41 | 58.69
Tancik _et al._ [16] (On DocImgCN) | 95.48 | 98.98 | 92.02 | 99.32 | 98.36 | 98.63 | 97.69 | 97.47 | 96.98
Zhang _et al._ [23] (On DocImgCN) | 76.77 | 83.92 | 87.77 | 90.15 | 83.92 | 61.14 | 59.25 | 55.24 | 52.14
Proposed (On DocImgCN) | 99.98 | 99.98 | 99.92 | 99.98 | 99.98 | 99.55 | 98.88 | 98.10 | 97.54
Figure 10:  Average bit accuracy of the extracted watermarks with different
shooting conditions on DocImgEN and DocImgCN testsets.

2) The Impact of Horizontal Perspective Angle on Robustness: Table IV shows
the bit accuracy of different schemes at the same shooting distance of 40 cm
but different horizontal shooting angles. We can see that the robustness of
the proposed algorithm is higher than that of other schemes from Left
65$\degree$ to Right 65$\degree$ and the bit accuracy is no less than 98%.
Therefore, the proposed scheme has certain robustness to horizontal
perspective angle change.

TABLE IV:  Average bit accuracy of the extracted watermarks with different horizontal perspective angles on DocImgEN and DocImgCN testsets. Horizontal angle ($\degree$) | Left 65 | Left 60 | Left 45 | Left 30 | Left 15 | 0 | Right 15 | Right 30 | Right 45 | Right 60 | Right 65
---|---|---|---|---|---|---|---|---|---|---|---
Fang _et al._ [2] (On DocImgEN) | 59.63 | 64.00 | 63.76 | 72.81 | 70.05 | 68.80 | 75.54 | 69.79 | 60.63 | 63.53 | 61.52
Tancik _et al._ [16] (On DocImgEN) | 98.95 | 99.03 | 99.47 | 99.87 | 99.75 | 99.58 | 99.57 | 99.15 | 98.50 | 98.57 | 98.40
Zhang _et al._ [23] (On DocImgEN) | 83.56 | 84.84 | 83.22 | 83.04 | 83.76 | 83.14 | 88.62 | 90.44 | 86.12 | 82.62 | 82.46
Proposed (On DocImgEN) | 98.53 | 98.86 | 99.62 | 99.96 | 99.94 | 99.98 | 99.96 | 99.92 | 99.98 | 99.92 | 98.92
Fang _et al._ [2] (On DocImgCN) | 65.62 | 72.46 | 73.73 | 71.69 | 67.49 | 68.80 | 77.01 | 64.50 | 63.38 | 53.15 | 60.81
Tancik _et al._ [16] (On DocImgCN) | 98.44 | 98.50 | 99.38 | 98.86 | 99.62 | 99.32 | 99.40 | 98.84 | 97.68 | 98.26 | 98.10
Zhang _et al._ [23] (On DocImgCN) | 80.87 | 81.65 | 84.10 | 82.42 | 83.07 | 90.15 | 84.05 | 86.65 | 85.22 | 84.02 | 81.60
Proposed (On DocImgCN) | 98.72 | 98.84 | 99.46 | 99.56 | 99.94 | 99.98 | 99.64 | 99.96 | 99.66 | 99.54 | 99.06

3) The Impact of Vertical Perspective Angle on Robustness: Table V show that
the bit accuracy obtained by different schemes at the same shooting distance
of 40 cm but different vertical shooting angles. It is easy to see that the
robustness of the proposed algorithm is higher than that of other schemes from
Up 65$\degree$ to Down 65$\degree$ and the bit accuracy is no less than 97%.
Therefore, the proposed scheme has certain robustness to vertical perspective
angle change.

TABLE V:  Average bit accuracy of the extracted watermarks with different vertical perspective angles on DocImgEN and DocImgCN testsets. Vertical angle ($\degree$) | Up 65 | Up 60 | Up 45 | Up 30 | Up 15 | 0 | Down 15 | Down 30 | Down 45 | Down 60 | Down 65
---|---|---|---|---|---|---|---|---|---|---|---
Fang _et al._ [2] (On DocImgEN) | 52.23 | 55.34 | 56.69 | 53.46 | 55.05 | 68.80 | 64.35 | 61.23 | 54.19 | 51.91 | 50.45
Tancik _et al._ [16] (On DocImgEN) | 97.86 | 98.07 | 98.03 | 98.81 | 98.54 | 99.58 | 98.85 | 98.86 | 98.63 | 97.60 | 97.13
Zhang _et al._ [23] (On DocImgEN) | 60.56 | 63.18 | 66.71 | 67.92 | 75.09 | 83.14 | 72.29 | 67.89 | 62.57 | 51.37 | 50.12
Proposed (On DocImgEN) | 98.37 | 99.12 | 99.45 | 99.58 | 99.98 | 99.98 | 99.98 | 99.72 | 99.55 | 99.05 | 98.57
Fang _et al._ [2] (On DocImgCN) | 53.11 | 55.58 | 58.24 | 56.27 | 57.95 | 68.80 | 62.27 | 58.35 | 58.09 | 55.04 | 57.67
Tancik _et al._ [16] (On DocImgCN) | 97.93 | 98.43 | 98.37 | 99.00 | 99.34 | 99.32 | 98.95 | 98.47 | 99.18 | 98.41 | 98.10
Zhang _et al._ [23] (On DocImgCN) | 56.95 | 60.47 | 67.39 | 70.75 | 73.54 | 90.15 | 71.20 | 67.65 | 63.35 | 52.94 | 49.68
Proposed (On DocImgCN) | 98.42 | 99.63 | 99.74 | 99.90 | 99.83 | 99.98 | 99.83 | 99.62 | 99.26 | 98.33 | 97.56

4) The Impact of Different Devices on Robustness: To test the robustness for
different devices, we use multiple device combinations (phone-display) in the
testing stage. To display watermarked images, we choose five types of
displays, namely AOC Q271PQ, HP P224, AOC Q2490PXQ, ThinkVision T27h-20, and
Dell S2721DS. To take photographs, we choose five phone devices with cameras,
namely Huawei nova 2s, Huawei mate 30 pro, MEIZU M3X, Mi 8 UD, and IPhone 11
Pro Max. For each combination of display-phone tests, the shooting angle is 0
degrees and shooting distance is 40 cm. The bit accuracy obtained by different
combinations of devices is listed in Table VI. For all combination of display-
phone tests, the extraction accuracy is no less than 97%, it indicates the
scheme has good applicability to phones and displays used in the testing
stage.

TABLE VI:  Average bit accuracy of the extracted watermarks with different devices on DocImgEN testset. Screens Phones | Huawei Nova 2S | Huawei Mate 30 Pro | MEIZU M3X | Mi 8 UD | IPhone 11 Pro Max
---|---|---|---|---|---
HP P224 (On DocImgEN) | 99.55 | 99.93 | 99.16 | 98.90 | 98.41
CHANGHONG 27P620F (On DocImgEN) | 99.69 | 99.84 | 98.91 | 98.64 | 98.88
AOC Q271PQ (On DocImgEN) | 97.46 | 99.99 | 99.81 | 99.95 | 99.91
Dell U2720Q (On DocImgEN) | 99.51 | 99.95 | 98.05 | 98.04 | 99.99
ThinkVision T27h-20 (On DocImgEN) | 99.86 | 99.98 | 99.83 | 99.68 | 99.33
HP P224 (On DocImgCN) | 98.96 | 99.62 | 98.59 | 97.63 | 98.66
CHANGHONG 27P620F (On DocImgCN) | 99.02 | 99.15 | 98.46 | 98.43 | 99.24
AOC Q271PQ (On DocImgCN) | 99.64 | 99.91 | 98.59 | 99.19 | 98.10
Dell U2720Q (On DocImgCN) | 99.03 | 99.42 | 97.38 | 98.23 | 99.89
ThinkVision T27h-20 (On DocImgCN) | 99.24 | 99.98 | 98.65 | 99.66 | 99.99

###  5.4 Further improvement by adjusting embedding strength

Although the PSNR and SSIM values in Table II is acceptable, the examples in
Fig. 9 still shows clear traces due to the obvious contrast between the
foreground and background in the document image. So, we try to alleviate this
phenomenon by adjusting the embedding strength in the training and testing
process.

According to the Formula 1, the adjustment of the embedding strength factors
$\alpha$ can influence the quality of watermarked image and the bit accuracy.
As shown in Table IV and Table V, our scheme achieves high bit accuracy during
testing in real scenes. It means that redundancy space is existed during
training, the quality of watermark image can be improved by decreasing the
embedding strength factors $\alpha$ without much loss in the bit accuracy. It
indicates that we can set a higher embedding strength during training, and
decrease the embedding strength to apply in the real scenes after the model is
fully trained.

In this subsection, we try to set the embedding strength factors
$\alpha=1.0,2.0,3.0,4.0,5.0$ in the training process and keep $\alpha$ to be
1.0 in the testing process. As shown in Table VII and Fig. 11, with larger
initial $\alpha$, better image quality is achieved. While as shown in Table
VIII, Table IX and Table X, the bit accuracy is not decreased a lot, including
in different shooting distances, horizontal perspective angles, and vertical
perspective angles tests.

TABLE VII:  PSNR, SSIM and CPP of our scheme with different embedding strength factors during the testing stage on DocImgEN and DocImgCN testsets. Schemes | PSNR (dB) | SSIM | CPP
---|---|---|---
On DocImgEN with $\alpha$=1.0 | 34.10 | 0.914 | 6.88
On DocImgEN with $\alpha$=2.0 | 38.50 | 0.938 | 4.89
On DocImgEN with $\alpha$=3.0 | 39.40 | 0.973 | 3.50
On DocImgEN with $\alpha$=4.0 | 42.10 | 0.949 | 3.32
On DocImgEN with $\alpha$=5.0 | 43.70 | 0.963 | 2.95
On DocImgCN with $\alpha$=1.0 | 33.20 | 0.928 | 5.56
On DocImgCN with $\alpha$=2.0 | 38.90 | 0.937 | 5.13
On DocImgCN with $\alpha$=3.0 | 39.50 | 0.950 | 4.34
On DocImgCN with $\alpha$=4.0 | 40.90 | 0.957 | 3.42
On DocImgCN with $\alpha$=5.0 | 42.58 | 0.966 | 3.51
Figure 11:  Visual examples of our scheme with different embedding strength factors during the testing stage on DocImgEN and DocImgCN testsets. TABLE VIII:  Average bit accuracy of our scheme with the different embedding strength factors and distances during the testing process on DocImgEN and DocImgCN testsets. Distance (cm) | 15 | 25 | 35 | 45 | 55 | 65 | 75 | 85 | 95
---|---|---|---|---|---|---|---|---|---
On DocImgEN with $\alpha$=1.0 | 99.97 | 99.98 | 99.97 | 99.95 | 99.78 | 99.89 | 99.86 | 98.87 | 97.33
On DocImgEN with $\alpha$=2.0 | 99.92 | 99.90 | 98.35 | 99.93 | 99.80 | 99.56 | 99.39 | 98.59 | 97.02
On DocImgEN with $\alpha$=3.0 | 99.22 | 99.36 | 97.48 | 99.48 | 99.28 | 98.13 | 96.74 | 96.84 | 95.25
On DocImgEN with $\alpha$=4.0 | 98.76 | 98.92 | 98.96 | 98.53 | 98.96 | 98.64 | 97.66 | 96.83 | 96.10
On DocImgEN with $\alpha$=5.0 | 95.16 | 98.50 | 97.86 | 97.60 | 97.74 | 97.51 | 96.63 | 96.29 | 94.32
On DocImgCN with $\alpha$=1.0 | 99.98 | 99.98 | 99.92 | 99.98 | 99.98 | 99.55 | 98.88 | 98.10 | 96.98
On DocImgCN with $\alpha$=2.0 | 99.74 | 99.45 | 98.60 | 99.53 | 98.70 | 98.64 | 98.43 | 98.48 | 97.60
On DocImgCN with $\alpha$=3.0 | 99.70 | 98.85 | 97.30 | 98.90 | 98.70 | 98.58 | 98.40 | 98.21 | 96.01
On DocImgCN with $\alpha$=4.0 | 97.35 | 97.50 | 94.26 | 97.83 | 98.26 | 97.91 | 97.78 | 95.83 | 95.01
On DocImgCN with $\alpha$=5.0 | 93.22 | 95.36 | 94.92 | 96.59 | 95.02 | 94.37 | 95.77 | 94.68 | 94.82
TABLE IX:  Average bit accuracy of our scheme with the different embedding strength factors and horizontal perspective angles during the testing stage on DocImgEN and DocImgCN testsets. Horizontal angle ($\degree$) | Left 65 | Left 60 | Left 45 | Left 30 | Left 15 | 0 | Right 15 | Right 30 | Right 45 | Right 60 | Right 65
---|---|---|---|---|---|---|---|---|---|---|---
On DocImgEN with $\alpha$=1.0 | 98.53 | 98.86 | 99.62 | 99.96 | 99.94 | 99.98 | 99.96 | 99.92 | 99.98 | 99.92 | 98.92
On DocImgEN with $\alpha$=2.0 | 97.45 | 98.95 | 99.10 | 99.85 | 99.72 | 99.93 | 99.33 | 99.42 | 99.27 | 99.10 | 97.62
On DocImgEN with $\alpha$=3.0 | 97.16 | 98.62 | 99.18 | 99.54 | 99.50 | 99.48 | 98.54 | 99.08 | 99.02 | 98.52 | 97.06
On DocImgEN with $\alpha$=4.0 | 96.91 | 98.96 | 98.96 | 98.13 | 98.29 | 98.53 | 98.48 | 98.36 | 98.29 | 98.54 | 96.60
On DocImgEN with $\alpha$=5.0 | 96.02 | 97.30 | 98.86 | 98.82 | 98.76 | 97.60 | 98.68 | 98.86 | 98.92 | 96.76 | 95.62
On DocImgCN with $\alpha$=1.0 | 98.72 | 98.84 | 99.46 | 99.56 | 99.94 | 99.98 | 99.64 | 99.96 | 99.66 | 99.54 | 99.06
On DocImgCN with $\alpha$=2.0 | 98.35 | 98.69 | 99.80 | 99.94 | 99.80 | 99.53 | 99.91 | 99.91 | 99.77 | 99.54 | 98.66
On DocImgCN with $\alpha$=3.0 | 97.72 | 97.73 | 99.81 | 99.82 | 99.87 | 98.90 | 99.86 | 99.89 | 99.83 | 98.86 | 96.81
On DocImgCN with $\alpha$=4.0 | 96.41 | 97.53 | 98.63 | 98.61 | 98.52 | 97.83 | 98.71 | 98.60 | 98.83 | 98.59 | 96.55
On DocImgCN with $\alpha$=5.0 | 95.38 | 95.19 | 96.60 | 96.15 | 97.47 | 97.59 | 97.10 | 96.86 | 96.48 | 96.38 | 96.06
TABLE X:  Average bit accuracy of our scheme with the different embedding strength factors and vertical perspective angles during the testing stage on DocImgEN and DocImgCN testsets.  Vertical angle ($\degree$) | Up 65 | Up 60 | Up 45 | Up 30 | Up 15 | 0 | Down 15 | Down 30 | Down 45 | Down 60 | Down 65
---|---|---|---|---|---|---|---|---|---|---|---
On DocImgEN with $\alpha$=1.0 | 98.37 | 99.12 | 99.45 | 99.58 | 99.98 | 99.98 | 99.98 | 99.72 | 99.55 | 99.05 | 98.57
On DocImgEN with $\alpha$=2.0 | 97.02 | 97.50 | 98.58 | 98.89 | 99.86 | 99.93 | 99.58 | 98.84 | 98.87 | 98.32 | 97.85
On DocImgEN with $\alpha$=3.0 | 96.14 | 96.51 | 97.64 | 98.70 | 98.88 | 99.48 | 98.52 | 97.73 | 96.12 | 95.52 | 94.33
On DocImgEN with $\alpha$=4.0 | 96.33 | 96.92 | 97.35 | 98.86 | 98.36 | 98.53 | 97.97 | 98.33 | 95.89 | 94.36 | 94.10
On DocImgEN with $\alpha$=5.0 | 93.15 | 94.20 | 96.76 | 97.45 | 97.69 | 97.60 | 96.57 | 95.88 | 96.51 | 93.11 | 92.82
On DocImgCN with $\alpha$=1.0 | 98.42 | 99.63 | 99.74 | 99.90 | 99.83 | 99.98 | 99.83 | 99.62 | 99.26 | 98.33 | 97.56
On DocImgCN with $\alpha$=2.0 | 98.17 | 98.90 | 98.97 | 99.54 | 99.94 | 99.53 | 99.80 | 99.50 | 98.93 | 97.70 | 97.17
On DocImgCN with $\alpha$=3.0 | 97.51 | 97.56 | 98.60 | 98.51 | 98.52 | 98.90 | 98.64 | 98.61 | 97.41 | 97.96 | 97.02
On DocImgCN with $\alpha$=4.0 | 96.55 | 96.90 | 97.10 | 97.47 | 98.57 | 97.83 | 97.41 | 97.76 | 96.57 | 96.03 | 95.83
On DocImgCN with $\alpha$=5.0 | 95.39 | 96.54 | 97.71 | 96.60 | 97.08 | 97.59 | 96.87 | 97.44 | 96.32 | 94.03 | 94.96

##  6 Conclusions

In this paper, we propose an end-to-end screen-shooting resilient document
image watermarking scheme using deep neural network. Our scheme consists of
three core components: Encoder, Distortion Layer, and Decoder. The Encoder is
designed to embed watermark into document images. The Distortion Layer is
added to compensate a series of distortions in the screen-shooting process
(such as camera distortion, shooting distortion, and light source distortion),
which enables the watermarked image can be resilient to the distortions in
real screen-shooting scenes. The Decoder is designed to extract the watermark
from the captured photographs. Besides, An embedding strength adjustment
strategy is discusses to decrease the embedding trace with little loss of
extraction accuracy, and the experimental results show the feasibility of our
proposed scheme.

## Acknowledgment

This work is supported in part by the National Key Research and Development
Plan of China under Grant 2020YFB1005600, in part by the National Natural
Science Foundation of China under grant numbers 62122032, 62172233, 62102189,
U1936118, 61825203, U1736203, and 61732021, in part by the Major Program of
Guangdong Basic and Applied Research Project under Grant 2019B030302008, in
part by Six Peak Talent project of Jiangsu Province (R2016L13), Qinglan
Project of Jiangsu Province, and ‘333‘ project of Jiangsu Province, in part by
the National Joint Engineering Research Center for Network Security Detection
and Protection Technology, in part by the Priority Academic Program
Development of Jiangsu Higher Education Institutions (PAPD) fund, in part by
the Collaborative Innovation Center of Atmospheric Environment and Equipment
Technology (CICAEET) fund, China. Zhihua Xia is supported by BK21+ program
from the Ministry of Education of Korea.

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|  Sulong Ge received his BE degree in Software Engineering from TianGong
University in 2020. He is currently pursuing master degree in School of
Computer Science in Nanjing University of Information Science and Technology.
His research interests include data hiding and information forensics.
---|---
|  Zhihua Xia received his Ph.D. degree in computer science and technology
from Hunan University, China, in 2011, and worked successively as a lecturer,
an associate professor, and a professor with College of Computer and Software,
Nanjing University of Information Science and Technology. He is currently a
professor with the College of Cyber Security, Jinan University, China. He was
a visiting scholar at New Jersey Institute of Technology, USA, in 2015, and
was a visiting professor at Sungkyunkwan University, Korea, in 2016. He serves
as a managing editor for IJAACS. His research interests include AI security,
cloud computing security, and digital forensic. He is a member of the IEEE
since Mar. 1, 2014.
---|---
|  Yao Tong is an adjunct professor in the South China University of
Technology, GuangZhou. Currently, she is the CEO of Guangzhou Fongwell Data
Limited Company. Her research interests include data security, big data
applications.
---|---
|  Jian Weng received the Ph.D. degree in computer science and engineering
from Shanghai Jiao Tong University, Shanghai, China, in 2008. He is currently
a Professor and the Dean with the College of Information Science and
Technology, Jinan University, Guangzhou, China. His research interests include
public key cryptography, cloud security, and blockchain. He was the PC Co-
Chairs or PC Member for more than 30 international conferences. He also serves
as an Associate Editor for the IEEE TRANSACTIONS ON VEHICULART ECHNOLOGY.
---|---
|  Jianan Liu (S’17) received the B.S. degree and M.S. degree from Zhengzhou
University and Jinan University in 2013 and 2016 respectively. He is currently
a Ph.D. candidate of Jinan University and a visiting scholar of Wilfrid
Laurier University, Canada. His research interesting includes cryptography,
smart grid security and cloud computing security.
---|---