final portion of the segments joining ${\mathbb{X}}_{t-1}^{\epsilon}$ and
${\mathbb{X}}_{t}^{\epsilon}$.

Thus, at each step, we arrive at a vertex of a hexagon. For this Exploration
Process we still maintain the following properties.

######  Proposition 4.5 (Proposition 4.3, [6]).

Let $\gamma_{\epsilon}([0,t])$ be the line segments formed by the process up
until time $t$, and $\Gamma_{\epsilon}([0,t])$ be the hexagons revealed by the
Exploration Process. Let
$\partial\Omega_{\epsilon}^{t}=\partial\Omega_{\epsilon}\cup\Gamma_{\epsilon}([0,t])$
and let
$\Omega_{\epsilon}^{t}=\Omega_{\epsilon}\backslash\Gamma_{\epsilon}([0,t]).$
Then, the quadruple
$(\Omega_{\epsilon}^{t},\partial\Omega_{\epsilon}^{t},{\mathbb{X}}_{\epsilon}^{t},c_{\epsilon})$
is admissible. Furthermore, the Exploration Process in $\Omega_{\epsilon}^{t}$
from ${\mathbb{X}}_{\epsilon}^{t}\text{ to }c_{\epsilon}$ has the same law as
the original Exploration Process from $a_{\epsilon}$ to $c_{\epsilon}$ in
$\Omega_{\epsilon}$ conditioned on $\Gamma_{\epsilon}([0,t]).$

Percolation satisfies the KS Condition.

It is well known that the Exploration Process produces in any critical
percolation configuration $\Omega_{\epsilon}$, the unique interface connecting
$a_{\epsilon}$ to $c_{\epsilon}$ denoted by $\gamma_{\epsilon}$, i.e. the
unique curve which separates the blue connected cluster of the boundary from
the yellow connected cluster of the boundary. Let
${\mathbb{P}}_{\Omega_{\epsilon}}$ be the law of this interface. Let
$\mu_{\epsilon}$ be the probability measure on random curves induced by the
Exploration Process on $\Omega_{\epsilon}$, and let us endow the space of
curves with the sup-norm metric
$\mathrm{dist}(\gamma_{1},\gamma_{2})=\inf\limits_{\varphi_{1},\varphi_{2}}\sup\limits_{t}|\gamma_{1}(\varphi_{1}(t))-\gamma_{2}(\varphi_{2}(t))|$
over all possible parameterizations $\varphi_{1},\varphi_{2}$.

The proof of the fact that the collection
$({\mathbb{P}}_{\Omega}\;:\;\Omega\text{ admissible})$ satisfies the KS
Condition follows directly from [17, Proposition 4.13] since this generalized
percolation model still satisfies Russo-Seymour-Welsh (RSW) type correlation
inequalities.

######  Remark 4.6.

As long as $a^{2}\geq 2s^{2}$, then a restricted form of Harris-FKG property
holds for all paths and path type events, see [10, Lemma 6.2]. Since we have
this essential ingredient in the RSW type arguments, we are indeed free to use
RSW sort of correlation inequalities.

######  Proposition 4.7 (Proposition 4.13 in [17]).

The collection of the laws of the interface of the modified bond percolation
model described above on the hexagonal lattice.

$\Sigma_{\mathrm{Percolation}}=\\{(\Omega_{\epsilon},\phi(\Omega_{\epsilon}),{\mathbb{P}}_{\Omega_{\epsilon}}):\Omega_{\epsilon}\text{
an admissible domain}\\}$ (4.1)

satisfies the KS Condition.

###### Proof.

First, notice that for percolation, we do not have to consider stopping times.
Indeed, by Proposition (4.5) if
$\gamma:[0,N]\rightarrow\Omega_{\epsilon}\cup\\{a,c\\}$ is the interface
parameterized so that $\gamma(k),\;k=0,1,\cdots,N$ are vertices along the
path, then $\Omega_{\epsilon}\backslash\gamma(0,k]$ is admissible for any
$k=0,1,\cdots,N$ and there is no information gained during $(k,k+1)$. Also,
the law of percolation satisfies the domain Markov property so the law
conditioned to the vertices explored up to time $n$ is the percolation measure
in the domain where $\gamma(k),\;k=0,1,\cdots,n$ is erased. Thus, the family
((4.1)) is closed under stopping.

Since crossing an annuli is a translation invariant event for percolation, for
any $\Omega_{\epsilon}$, we can apply a translation and consider the annuli
around the origin. Let $B_{n}$ be the set of points on the triangular lattice
that are graph distance less than or equal to $n$ from $0$. Consider the
annulus $B_{9^{N}n}\backslash B_{n}$ for any $n,N\in{\mathbb{N}}$. We can
consider concentric balls $B_{3n}$ inside the annulus $B_{9^{N}n}\backslash
B_{n}$. Then for an open crossing of the annulus $B_{9^{N}n}\backslash B_{n}$,
there needs to be an open path inside each annulus $A_{n}=B_{3n}\backslash
B_{n},A_{3n}=B_{9n}\backslash B_{3n},\cdots$ etc. The probability that $A_{n}$
contains an open path separating $0$ from $\infty$ and $A_{3n}$ contains a
closed path separating $0$ from $\infty$ are independent. Hence, by Russo-
Seymour-Welsh (RSW) theory, we know that there exists a $q>0$ for any $n$

$\mu_{\epsilon}\left(\text{open path inside }A_{n}\cap\text{ closed path in
}A_{3n}\text{ both separating 0 from }\infty\right)\geq q^{2}$

Since a closed path in one of the concentric annuli prohibits an open crossing
of $B_{9^{N}n}\backslash B_{n}$, we conclude that

${\mathbb{P}}_{\epsilon}\left(\gamma\text{ makes an unforced crossing of
}B_{9^{N}n}\backslash B_{n}\right)\leq(1-q^{2})^{N}\leq\frac{1}{2}$

for large enough $N$. ∎

The observable.

Consider two addition marked points (or prime ends) b,d so that a,b,c,d are in
cyclic order. Let $\Omega_{n}$ be the admissible domain described above at
lattice scale $n^{-1}$ to the domain $\Omega$. More details of the
construction can be found in [6, §3 and §4] and [7, §4.2]. Furthermore, the
boundary arcs can be appropriately coloured and the lattice points
$a_{n},b_{n},c_{n},d_{n}$ can be selected. The main objects of study for
percolation is the crossing probability of the conformal rectangle
$\Omega_{n}$ from $(a_{n},b_{n})$ to $(c_{n},d_{n})$, denoted by
${\mathcal{C}}_{n}$ and ${\mathcal{C}}_{\infty}$ its limit in the domain
$\Omega$, i.e., Cardy’s formula in the limiting domain. Geometrically,
${\mathcal{C}}_{n}$ produces in any percolation configuration on $\Omega_{n}$,
the unique interface connecting $a_{n}$ to $c_{n}$, i.e. the curve separating
the blue lattice connected cluster of the boundary from the yellow. Let us
temporarily forget the marked point $a_{n}$ and consider the conformal
triangle $(\Omega_{n};b_{n},c_{n},d_{n})$.

We will briefly recall the observable function introduced in [28] which we
will denote by $S_{b},S_{c},S_{d}$. For a lattice point $z\in\Omega_{n}$,
$S_{d}(z)$ is the probability of a yellow crossing from $(c_{n},d_{n})$ to
$(d_{n},b_{n})$ separating $z$ from $(b_{n},c_{n})$. Notice that $S_{d}$ has
boundary value $0$ on $(b_{n},c_{n})$ and $1$ at the point $d_{n}$. $S_{b}$
and $S_{c}$ are defined similarly. We define the complexified function
$S_{n}:=S_{b}+\tau S_{c}+\tau^{2}S_{d}$ with $\tau=e^{2\pi i/3}$, called the
Carleson-Cardy-Smirnov (CCS) function. The following lemma due to Smirnov
shows that CCS observable is a martingale.

######  Lemma 4.8.

The CCS observable is a martingale observable.

###### Proof.

Parameterize the interface $\gamma^{\epsilon}$ and draw the exploration
process up to time $t$, $\gamma^{\epsilon}[0,t]$. By convention/definition,
the faces on the left and right side of the exploration process are yellow and
blue, respectively. Then any open crossing (yellow crossing) from arc $bc$ to
the arc $db$ inside $\Omega$ is either disjoint from $\gamma^{\epsilon}[0,t]$
or hits its ”open” (yellow) arc of $\gamma^{\epsilon}[0,t]$. Either case
produces an open crossing from the arc $\gamma^{\epsilon}(t)c$ to the arc
$d\gamma^{\epsilon}(t)$ inside $\Omega\backslash\gamma^{\epsilon}[0,t]$. The
converse also holds. Thus, we have the following observation: crossing
probabilities conditioned on $\gamma^{\epsilon}[0,t]$ coincide with crossing
probabilities in the slit domain $\Omega\backslash\gamma^{\epsilon}[0,t].$

Let $Q$ denote the area above the lowest (i.e. closest to arc $bc$) open
crossing from arc $cd$ to arc $db$. Then $S_{d}(z)={\mathbb{P}}(z\in Q)$. We
can view the other crossing probabilities $S_{b}$ and $S_{c}$ in the same way.
By the above observation, we know that this probability conditioned on
$\gamma^{\epsilon}[0,t]$ will coincide with the probability in the slit domain
$\Omega\backslash\gamma^{\epsilon}[0,t].$ The same holds true for $S_{b}(z)$
and $S_{c}(z)$.

Figure 5: Observe that the lowest yellow crossing cannot cross the curve
$\gamma$ since it is blocked by the blue side of the curve.

Thus, one sees for every realization of $\gamma^{\epsilon}[0,t]$, the CCS
function conditioned on $\gamma^{\epsilon}[0,t]$ coincides with the CCS
function in the slit domain, an analogue of the Markov property. Stopping the
curve at times $0<t<s$, say with the least discrete time such that the path
has capacity $\geq t$, and using the total probability for every realization
of $\gamma^{\epsilon}[0,t]$ we get the martingale property:

${\mathbb{E}}_{\mu_{\epsilon}}\left[S_{\epsilon}(\Omega_{\epsilon}\backslash\gamma^{\epsilon}[0,s],\gamma^{\epsilon}(s),b,c,d)|\gamma^{\epsilon}[0,t]\right]=S_{\epsilon}(\Omega_{\epsilon}\backslash\gamma^{\epsilon}[0,t],\gamma^{\epsilon}(t),b,c,d).$

∎

The CCS functions $S_{n}$ are not discrete analytic but are “almost” discrete
analytic in the following sense, see [8, §4]:

######  Definition 4.9 ($(\sigma,\rho)-$Holomorphic).

Let $\Lambda\subseteq\mathbb{C}$ be a simply connected domain and
$\Lambda_{\epsilon}$ be the (interior) discretized domain given as
$\Lambda_{\epsilon}:=\bigcup_{h_{\epsilon}\subseteq\Lambda}h_{\epsilon}$ and
let $(Q_{\epsilon}:\Lambda_{\epsilon}\to\mathbb{C})_{\epsilon\searrow 0}$ be a
sequence of functions defined on the vertices of $\Lambda_{\epsilon}$. We say
that the sequence $(Q_{\epsilon})$ is _$(\sigma,\rho)$ –holomorphic_ if there
exist constants $0<\sigma,\rho\leq 1$ such that for all $\epsilon$
sufficiently small:

  1. 1.

$Q_{\varepsilon}$ is Hölder continuous up to $\partial\Lambda_{\epsilon}$:
There exists some small $\psi>0$ and constants $c,C\in(0,\infty)$ (independent
of domain and $\epsilon$) such that

    1. (a)

if $z_{\epsilon},w_{\epsilon}\in\Lambda_{\epsilon}\setminus
N_{\psi}(\partial\Lambda_{\epsilon})$ such that
$|z_{\epsilon}-w_{\epsilon}|<\psi$, then
$|Q_{\epsilon}(z_{\epsilon})-Q_{\epsilon}(w_{\epsilon})|\leq
c\left(\frac{|z_{\epsilon}-w_{\epsilon}|}{\psi}\right)^{\sigma}$ and

    2. (b)

if $z_{\epsilon}\in N_{\psi}(\partial\Lambda_{\epsilon})$, then there exists
some $w_{\epsilon}^{\star}\in\partial\Lambda_{\epsilon}$ such that
$|Q_{\epsilon}(z_{\epsilon})-Q_{\epsilon}(w_{\epsilon}^{\star})|\leq
C\left(\frac{|z_{\epsilon}-w_{\epsilon}^{\star}|}{\psi}\right)^{\sigma}$.

  2. 2.

For any simply closed lattice contour $\Gamma_{\epsilon}$,

$\left|\oint_{\Gamma_{\epsilon}}Q~{}dz\right|=\left|\sum_{h_{\epsilon}\subseteq\Lambda_{\epsilon}^{\prime}}\oint_{\partial
h_{\epsilon}}Q~{}dz\right|\leq c\cdot|\Gamma_{\epsilon}|\cdot\epsilon^{\rho},$
(4.2)

with $c\in(0,\infty)$ (independent of domain and $\epsilon$) and
$\Lambda_{\epsilon}^{\prime},|\Gamma_{\epsilon}|$ denoting the region enclosed
by $\Gamma_{\epsilon}$ and the Euclidean length of $\Gamma_{\epsilon}$,
respectively.

######  Proposition 4.10 (Proposition 4.3, [8]).

Let $\Lambda$ denote a conformal triangle with marked points (or prime ends)
$b$, $c$, $d$ and let $\Lambda_{\epsilon}$ denote an interior approximation
(see [7, Definition 3.1]) of $\Lambda$ with
$b_{\epsilon},c_{\epsilon},d_{\epsilon}$ the associated boundary points. Let
$S_{\epsilon}(z)$ denote the CCS function defined on $\Lambda_{\epsilon}$.
Then for all $\epsilon$ sufficiently small, the functions
$(S_{\epsilon}:\Lambda_{\epsilon}\rightarrow\mathbb{C})$ are
$(\sigma,\rho)$–holomorphic for some $\sigma,\rho>0$.

Polynomial convergence of the observable function to its continuous
counterpart.

Observe that ${\mathcal{C}}_{n}$ can be realized from $S_{d}(a_{n})$ as
${\mathcal{C}}_{n}=\frac{-2}{\sqrt{3}}\cdot\operatorname{Im}[S_{n}(a_{n})]$.
Since it is already known that $S_{n}$ converges to $H:D\to T$, a conformal
map to equilateral triangle $T$ which sends $(b,c,d)$ to $(1,\tau,\tau^{2})$,
we can see that
${\mathcal{C}}_{\infty}=\frac{-2}{\sqrt{3}}\operatorname{Im}[H(a)]$ (see,
[28], [2], and [7]). Thus, when establishing a rate of convergence of
${\mathcal{C}}_{n}$ to ${\mathcal{C}}_{\infty}$, it is sufficient to show that
there exists $\psi>0$ such that

$|S_{n}(a_{n})-H(a)|\leq C_{\psi}\cdot n^{-\psi}$

for some $C_{\psi}<\infty$ independent of the domain. Indeed, a polynomial
rate of convergence is shown in [8, Main Theorem]. This is a slight
reformulation of the theorem in which we have that the constant $\psi$ is
independent of the domain $\Omega$. Indeed, a direct reconstruction of the
proof in [8] gives this result.

######  Theorem 4.11.

Let $\Omega$ be a domain with two marked boundary points (or prime ends) $a$
and $c$. Let $(\Omega_{n},a_{n},c_{n})$ be its admissible discretization.
Consider the site percolation model or the models introduced in [10] on the
domain $\Omega_{n}$. In the case of the latter we also impose the assumption
that the boundary Minkowski dimension is less than 2 (in the former, this is
not necessary). Let $\gamma$ be the interface between $a$ and $c$. Consider
the stopping time $T:=\inf\\{t\geq 0\;:\;\gamma\text{ enters a
}\Delta\text{-neighbourhood of }c\\}$ for some $\Delta>0$. Then there exists
$n_{0}<\infty$ depending only on the domain $(\Omega;a,b,c,d)$ and $T$ such
that the following estimate holds: There exists some $\psi>0$ (which does not
depend on the domain $\Omega$) such that $\mathscr{C}_{n}$ converges to its
limit with the estimate

$|\mathscr{C}_{n}-\mathscr{C}_{\infty}|\leq C_{\psi}\cdot n^{-\psi},$

for some $C_{\psi}<\infty$ provided $n\geq n_{0}(\Omega)$ is sufficiently
large.

Polynomial convergence of critical percolation on the triangular lattice.

By a straightforward computation, we can see that the martingale observable is
a nondegenerate solution to BPZ equation ((1.4)). Thus, by Proposition (4.7),
Lemma (4.8), Proposition (4.10), and Theorem (4.11), we can now apply Theorem
(1.23) to obtain:

######  Theorem 4.12.

Let $\gamma_{n}$ be the percolation Exploration Process defined above on the
admissible triangular lattice domain $\Omega_{n}$. Let $\tilde{\gamma}_{n}$ be
its image in $({\mathbb{H}};0,\infty)$ parameterized by capacity. There exists
stopping time $T<\infty$ and $n_{1}$ such that
$\displaystyle\sup_{n}\sup_{t\in[0,T]}n_{1}(\Omega_{t})<\infty$. Then if
$n\geq n_{1}$, there is a coupling of $\gamma_{n}$ with Brownian motion
$B(t),\;t\geq 0$ with the property that if $\tilde{\gamma}$ denotes the
chordal SLE6 path in ${\mathbb{H}}$,

${\mathbb{P}}\left\\{\sup_{t\in[0,T]}|\tilde{\gamma}_{n}(t)-\tilde{\gamma}(t)\;|\;>n^{-u}\right\\}<n^{-u}$

for some $u\in(0,1)$ and where both curves are parameterized by capacity.

Moreover, if $\Omega$ is an $\alpha$-Hölder domain, then under the same
coupling, the SLE curve in the image is polynomially close to the original
discrete curve:

$\mathbb{P}\left\\{\sup_{t\in[0,T]}d_{*}\left(\gamma^{n}(t),\phi^{-1}(\tilde{\gamma}(t))\right)>n^{-v}\right\\}<n^{-v}$

where $v$ depends only on $\alpha$ and $u$.

######  Remark 4.13.

The authors believe that modifications of the arguments in [8] could lead to a
full convergence statement.

######  Remark 4.14.

Notice that under this modified percolation model, we still maintain the
reversibility of the exploration path. Let $\omega$ be a simple polygonal path
from $a^{\delta}$ to $c^{\delta}$. Suppose that the corresponding path
designate is the sequence

$\left[H_{0,1},(\mathcal{F}_{1},h_{1}^{e},h_{1}^{x}),H_{1,2},(\mathcal{F}_{2},h_{2}^{e},h_{2}^{x}),H_{2,3},\cdots,(\mathcal{F}_{K},h_{K}^{e},h_{K}^{x}),H_{K,K+1}\right]$

where $\mathcal{F}_{1},\cdots\mathcal{F}_{K}$ are flowers in $\Omega^{\delta}$
with $h_{j}^{e}$ and $h_{j}^{x}$ are the entrance and exit petals in the
$j^{th}$ flower and for $1\leq j\leq K-1,\;H_{j,j+1}$ is a path in the
complement of flowers which connects $h_{j}^{x}$ to $h_{j+1}^{e}$. That is, we
are not viewing the microscopic description where we have to specifying how
the path got between entry and exit petals. With a small loss of generality we
are also assuming that the path only visits the flower once else we would have
to specify the first entrance and exit petals, the second entrance and exit
petals, etc.

Let $\gamma^{\delta}$ be a chordal exploration process from $a^{\delta}$ to
$c^{\delta}$ in $\Omega^{\delta}$ and $\hat{\gamma}^{\delta}$ be a chordal
exploration process from $c^{\delta}$ to $a^{\delta}$ in $\Omega^{\delta}$.
Recall that all petal arrangements are independent, all flowers are configured
independently and these in turn are independent of the background filler
sites. Thus the exploration process generated by the colouring algorithm given
previously, excluding colouring of flowers, is independent and flowers are
independent of background filler sites. Thus, by the colouring algorithm we
have:

$\displaystyle{\mathbb{P}}(\gamma^{\delta}=\omega)=\left(\frac{1}{2}\right)^{l(H_{0,1})}p_{1}\left(\frac{1}{2}\right)^{l(H_{1,2})}\cdots
p_{K}\left(\frac{1}{2}\right)^{l(H_{K,K+1})}$

where $l(H_{j,j+1})$ is the number of coloured hexagons in $H_{j,j+1}$
produced by the colouring algorithm on the event $\gamma^{\delta}=\omega$ and
$p_{j}$ is the appropriate conditional probabilities on each flower of a petal
or iris given by the colouring algorithm. Notice that on the event
$\gamma^{\delta}=\hat{\gamma}^{\delta}=\omega$ for any hexagon in
$\Omega^{\delta}$ either it is coloured by both the colouring algorithm for
$\gamma^{\delta}$ and the colouring algorithm for $\hat{\gamma}^{\delta}$ or
by neither. Therefore, we have the following lemma:

######  Lemma 4.15.

Suppose $\Omega^{\delta}$ is a simply connected domain in the
$\delta$-hexagonal lattice with a predetermined flower arrangement. For any
simple polygonal path $\omega$ from $a^{\delta}$ to $c^{\delta}$ we have

${\mathbb{P}}(\gamma^{\delta}=\omega)={\mathbb{P}}(\hat{\gamma}^{\delta}=\omega)$

This lemma directly implies the following lemma.

######  Lemma 4.16.

For any simply connected domain $\Omega^{\delta}$ with predetermined flower
arrangement, the percolation exploration path from $a^{\delta}$ to
$c^{\delta}$ in $\Omega^{\delta}$ has the same distribution as the time-
reversal of the percolation exploration path from $c^{\delta}$ to $a^{\delta}$
in $\Omega^{\delta}$.

######  Question 4.17.

Is it possible to use reversibility to extend the polynomial convergence for
the whole curve percolation exploration process?

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# Ethics of Generating Synthetic MRI Vocal Tract Views from the Face
CVPR Responsible Generative AI Workshop

Muhammad Suhaib Shahid
University of Nottingham
NG8 1BB, UK
<EMAIL_ADDRESS>Gleb E. Yakubov
University of Nottingham
LE12 5RD, UK
Andrew P. French
University of Nottingham
NG8 1BB, UK

###### Abstract

Forming oral models capable of understanding the complete dynamics of the oral
cavity is vital across research areas such as speech correction, designing
foods for the aging population, and dentistry. Magnetic resonance imaging
(MRI) technologies, capable of capturing oral data essential for creating such
detailed representations, offer a powerful tool for illustrating articulatory
dynamics. However, its real-time application is hindered by expense and
expertise requirements. Ever advancing generative AI approaches present
themselves as a way to address this barrier by leveraging multi-modal
approaches for generating pseudo-MRI views. Nonetheless, this immediately
sparks ethical concerns regarding the utilisation of a technology with the
capability to produce MRIs from facial observations.

This paper explores the ethical implications of external-to-internal
correlation modeling (E2ICM). E2ICM utilises facial movements to infer
internal configurations and provides a cost-effective supporting technology
for MRI. In this preliminary work, we employ Pix2PixGAN to generate pseudo-MRI
views from external articulatory data, demonstrating the feasibility of this
approach. Ethical considerations concerning privacy, consent, and potential
misuse, which are fundamental to our examination of this innovative
methodology, are discussed as a result of this experimentation.

##  1 Introduction

The ability to model the complete oral cavity holds significant utility across
various domains, notably in dentistry, where understanding how dental
prosthetics impact speech and mastication is crucial in forming personalised
dental devices. However, achieving comprehensive oral cavity modeling presents
challenges, including limitations in technique availability, articulator
capture capacity, and associated costs. Researchers often face the dilemma of
selecting a suitable technique tailored to their specific objectives. Among
the available methods, magnetic resonance imaging (MRI) stands out for its
capability to provide detailed representations of all articulators,
particularly when augmented with real-time functionality, offering insights
into dynamic movements. Nonetheless, the practicality of real-time MRI is
hindered by its costliness and the need for specialised expertise, rendering
it less feasible for routine use.

This raises the question, is it possible to use generative AI approaches to
achieve a complete model of the oral cavity, encompassing all articulators in
motion, without incurring excessive expenses? This is where the concept of
external-to-internal correlation modeling (E2ICM) emerges as a potential
solution. By observing the external facial movements, particularly those of
visible articulators such as the lips, and jaw, we investigate if we can in
any way reconstruct the internal configurations of the oral cavity. This
approach leverages the inherent relationship between external facial gestures
and internal vocal tract configurations. Such an approach aims to address the
cost and complexity concerns associated with MRI and other experimental
techniques. Clearly there are limitations to this approach, but here we
consider exploring the feasibility of such a technology, and bring to the fore
the ethical questions such an approach might raise.

As advancements in AI-based approaches continue to progress, questions
regarding ethical implications become increasingly pertinent. The ability to
record or photograph individuals during articulation and mastication, followed
by the generation of MRI-like images of the internal oral cavity, raises
several ethical considerations and potential concerns regarding privacy,
consent, and misuse.

This paper explores the application of generative deep learning models to
create pseudo-MRI views of the oral cavity. Specifically, it employs the
Pix2PixGAN network to transform external views of a participant during
articulation into predicted MRI representations, in a limited speech-
reconstruction scenario. For the purpose of demonstrating the feasibility of
the proposed approach we briefly evaluate the challenges associated with
determining the quality of the generated images. This is followed by a
discussion focused on possible ethical dilemmas associated with the use of
such generated data.

##  2 Background

Real time MRI (RtMRI) of the vocal tract is one of the very few techniques
capable of displaying, frame by frame, the movements of all articulators
during speech[6]. The method allows researchers to explore a wide range of
applications from articulatory studies, to oral health and food oral
processing. Despite the prospects RtMRI presents, there are some underpinning
issues that hinder its widespread use. These limitations are a result of the
cost and expertise requirements for collecting RtMRI data on an individual
subject basis [10, 3]. One possible generative solution to this is by forming
predictive models capable of using external observations of the face to
synthesise a representation of the vocal tract MRI view.

The feasibility of such an approach relies on investigating the
interrelationship between the internal vocal tract and external face views.
Such research has explored correlations between the two views by linking
facial movements, captured via video, with vocal tract dynamics, captured
through rtMRI [7]. The main focus is to identify whether there is sufficient
mutual information between the forward coronal view of the face and the
sagittal MRI to make reconstruction procedures possible. Employing Principal
Component Analysis (PCA), Scholes et al. (2020) simplified the data and
identified key patterns of change in both modalities. Through this process,
they uncovered connections between facial gestures and vocal tract
configurations, showcasing the potential for mutual reconstruction between the
two modalities. The findings concluded that facial information may hold
sufficient data to recover certain vocal tract shapes during speech
production.

While the PCA-based analysis-by-synthesis technique showcases an
interrelationship between the two modalities, it comes short of addressing key
barriers that prevent the widespread use of MRI. In order to reconstruct an
MRI representation of the vocal tract, a corresponding PCA matrix must
accompany each specific external view. However, the PCA representation is
derived from the MRI image, and consequently, the MRI data are still necessary
each time the representation is created.

Paving the way to addressing this problem are generative machine learning
models capable of performing cross-modality synthesis of unseen MRI
configurations when presented with a novel face view for a specific individual
[11]. This technique is commonly used in computer vision and machine learning
to create mappings between different visual styles, attributes, or
characteristics. It is the process of transforming an input image from one
domain into a corresponding output image in another domain, while preserving
meaningful content and maintaining consistency between the two domains; it
involves changing how an image looks while keeping its underlying meaning
intact. In the application of this task, it would involve shifting from a face
view to a MRI vocal tract view for any two paired frames; this pairing being
key to the approach.

The Pix2PixGaN framework [1] serves as the translation network chosen for this
task. The architecture comprises two key components: a generator and a
discriminator. The generator works to produce a realistic mapping from the
input domain to the desired output, while the discriminator’s role is to
determine whether an image is real or synthesised. The generator and
discriminator train in an adversarial fashion, each trying to optimise ahead
of the other. This approach drives the mapping of images from one domain to
another in a supervised manner. Once trained, the system has the potential to
operate in an autonomous manner and predict internal views based on the
outside image or video only. If successful, such approaches can enable
generating synthesised views without specialised equipment and a person’s
consent, which raises important ethical questions and considerations that need
to be addressed.

Existing research has explored the (bio)ethical considerations surrounding the
use of Generative Adversarial Networks (GANs) for generating medical images.
The integration of AI technologies in healthcare raises complex legal,
ethical, and technical challenges. In their work [5], the authors underscore
the necessity for a regulatory framework to ensure the safe integration of
generative technologies in medical contexts. A systematic review conducted by
[2] examined recent GAN architectures utilised in medical image analysis,
revealing imbalances in their capabilities, particularly with smaller
datasets. These findings align with the observations of [4], regarding the
imbalanced class distributions often observed in datasets, thereby raising
ethical concerns.

##  3 Framework and Implementation

In this study we used a dual-modal dataset used for this study, comprising
registered videos captured during speech, this has been previously
published[8]. Initial data collection involved 13 participants articulating a
predetermined set of 10 sentences. Participants underwent two recording
sessions: first, speaking the sentences in front of a camera, and second,
repeating the same sentences during MRI scans. Subsequently, these video sets
were then aligned. Initially, data from 13 participants were collected for the
study. However, only data from 11 participants were ultimately included in the
published datasets as the study focused on British English speakers. The
dataset encompasses videos providing a frontal view of the face alongside
sagittal MRI views. For the purposes of this preliminary study, only data from
one subject was utilised, as they were the only participant for whom all 10
videos were available across all sentences. Across these 10 videos, a total of
461 frames were available, considering the videos were recorded at a frame
rate of 15 frames per second (fps). The shortest video contained 30 frames,
while the longest comprised 59 frames.

An implementation of Pix2PixGaN framework was used as the image-to-image
translation network. Based on the conditional generative adversarial network
(CGaN), the architecture consists of a generator and a discriminator. The
generator aims to produce realistic images based on the input, while the
discriminator’s job is to distinguish between real and generated images. The
generator employs a U-Net-inspired encoder-decoder architecture with skip
connections. The encoder module is formed of only convolutional layers,
omitting dropout. This structure forms the following sequence of layers:
C64-C128-C256-C512-C512-C512-C512-C512. The decoder integrates dropout layers
with a dropout rate of 0.5 in the first, second, and third layers. The
decoder’s structure is as follows: CD512-CD512-CD512-C512-C256-C128-C64. This
combination establishes a proficient generator capable of producing coherent
translations for this dataset. The model was optimised using the Adam
optimiser with hyperparameters $\alpha$ = 0.0002, $\beta_{1}$ = 0.5,
$\beta_{2}$ = 0.999, and $\epsilon$ = 1e-08. The training was done with a
batch size of 16, for 200 epochs. Tanh activation function was used.

##  4 Results

The Fréchet Inception Distance (FID) metric and Structural Similarity Index
Measure (SSIM) were used to accesses the quality of image examination. FID
provides a quantitative measure of similarity between the distribution of
generated and authentic images, with lower scores indicating higher quality.
SSIM considers the structural information of images, accounting for spatial
relationships beyond pixel values. Additionally, a qualitative evaluation was
conducted by observing the movements of each articulator frame by frame,
drawing conclusions regarding which articulators are constructed most
effectively. The FID score for generated images compared to ground truth is
30.80, though establishing an understanding of what a ”good” FID score is when
transitioning from RGB to MRI domains remains challenging. To gain some
insight, an FID was calculated for various ground truth frames to assess how
well the FID performs with real images but of different vocal tract views,
yielding a score of 19.75. While FID offers valuable insight into image
similarity, it doesn’t directly consider the spatial representation of vocal
tract structure. Therefore, SSIM might be more suitable for this task. The
average SSIM score for all 46 test images was 0.7961, with higher scores
indicating better image quality on a scale from -1 to 1. We recognise, and
highlight, that interpreting these scores in this application domain is
challenging.

As illustrated in Figure 1, the generative models demonstrate some proficiency
in generating images with realistic appearances, particularly showcasing
discernible movements in the jaw regions. However, upon closer examination,
specific articulatory details are challenging to determine. Despite reasonable
FID and SSIM scores indicating overall good image similarity, inconsistencies
between generated articulators and ground truth are apparent in certain
frames. These discrepancies could potentially lead to misleading
interpretations in clinical applications, where images resembling plausible
MRI scans but with incorrect articulator configurations may pose risks. Moving
forward, vocal tract segmentation could serve as a promising avenue for
enhancing the clinical relevance in assessing the quality of generated vocal
tract views [9].

Figure 1: Still frames sample the external view (left), ground truth MRI frame
(middle) and generated frame (right).

##  5 Discussion of Ethics and Responsible Use

The ethical dimensions surrounding the potential of such generative medical
approaches demand scrutiny. There are concerns associated with the generation
and utilisation of synthetic views, the accuracy and reliability of the data,
and potential misuse.

###  5.1 Synthetic dataset enlargement

The fundamental principle of informed consent and participant autonomy is
central. Ethical protocols governing the collection of MRI data are
universally stringent, dictating both the type of data collected and its
storage practices. Participants are provided with comprehensive information
about the study, including potential risks and the intended utilisation of
their data, to make informed decisions regarding consent. The integration of
generative AI raises logistical and ethical considerations perhaps not
originally conceived. In a practical application, MRI data might initially be
collected for a limited set of sentences, such as the 10 here. Subsequently,
using generative techniques, additional MRI data could be synthesised for
sentences that were not originally captured via MRI. When using a trained
model, it’s possible to employ readily available facial data, especially from
public spaces where recording may be allowed by law. However, the ethical
dilemma arises: Is it acceptable and responsible to generate new data
modalities without obtaining explicit consent? While enlarging datasets using
generative AI techniques is not novel and has been applied in various domains,
the unique aspect here lies in the translation from an external view to an
internal view. Accessing and utilising facial data for such a task, even if
publicly available, must be carefully assessed to uphold principles of
privacy.

###  5.2 Accuracy of generated images

Responsible use of generative AI necessitates addressing concerns surrounding
the accuracy and integrity of synthesised data. As demonstrated here, methods
such as FID are employed to help assess the ”quality” of images. However, it
is evident from the outset that these methods do not adequately evaluate
specific spatial information in the generated images. In other words, the
morphology of clinically-relevant structures is not captured well by these
metrics. Often, it is also hard to identify subtle features even directly in
the dataset (see Figure 1), so interpreting the quality of synthesised data in
this domain is a challenge.

Questions will arise regarding the potential misuse or misinterpretation of
inaccurate synthetic information. Poorly performing models could lead to
misdiagnosis or misinterpretation. Therefore, it is imperative to remain
vigilant and implement rigorous validation procedures to ensure the
reliability and accuracy of synthesised data. More work is needed to develop
approaches to assess the usefulness and trustworthiness of generated images.

###  5.3 Data storage of generated images

The stringent protocols governing the storage and anonymisation of MRI data
are imperative to safeguard individuals’ sensitive health information.
However, the creation of additional synthetic MRI data, which may still
contain identifiable features or morphology, may not always undergo comparable
protocol scrutiny as the original data. While large scale MRI datasets could
potentially advance medical research and clinical applications, relaxed
protocols for synthesised data may compromise privacy and data security. Thus,
careful ethical consideration is warranted here for future research.

Furthermore, there are broader societal implications to consider, particularly
regarding the potential impact of synthesised medical views on areas such as
identity verification. If such technology were to be deployed in contexts such
as security or law enforcement, there could be implications for individuals’
rights and freedoms, including the risk of discrimination or misuse of
biometric data.

###  5.4 Dataset and model biases

The publicly available dataset used in this study exhibited a bias towards
speakers of British English. Though it is understandable from the associated
papers that this is likely an attempt to standardise an already small and
challenging data set, it nevertheless highlights concerns regarding potential
biases in future datasets and the models trained upon them. Certain
demographic groups may be favoured in inferences, while for others the model
could perform poorly. Likewise, the application of the model would likely be
limited to the application studied in the dataset (e.g. speech versus chewing,
for example); wrong application would lead to misleading results.

The concern extends beyond data representation to the broader implications for
societal equity and fairness. Though this is a problem not only relevant to
this application, occurrence of such a scenario could also exacerbate existing
disparities in access to resources and opportunities, with models not being
tailored to regional use. Proactive measures must be implemented to mitigate
bias and promote inclusivity in dataset curation and model development.
Strategies may include diversifying dataset sources to encompass a broader
spectrum of linguistic and cultural backgrounds, and implementing robust
validation techniques to identify and mitigate bias in model predictions.

##  6 Conclusion

A demonstration of an exploratory method for generating MRI images of the
vocal tract has been presented. Leveraging the Pix2PixGAN architecture, this
study demonstrates the application of Generative AI to synthesise previously-
unseen vocal tract configurations from external facial views. The quality of
the generated images has been evaluated using the Fréchet Inception Distance
(FID) metric, alongside the observation of distinct articulator movements.
Results are by no means conclusive at this stage, but certainly raise the
question of whether this is a valid line of research in generative AI for
future researchers.

Furthermore, an initial discussion regarding the responsible use of generative
AI in such applications has been provided. This discussion presents
considerations that must be taken into account when employing such techniques.
These encompass various aspects, including the enlargement of synthetic
datasets, the accuracy of generated images, the storage protocols employed,
and the potential biases inherent in both the dataset and the models utilised.

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