we conclude that the trigonometric operator $\cos(\hat{\varphi}(t))$ can be
expressed as

$\cos(\hat{\varphi}(t))=\\!\\!\sum_{k_{a},k_{c}}\hat{a}^{\dagger\,k_{a}}\hat{c}^{\dagger\,k_{c}}f(\hat{n},k_{a},\varphi_{a})f(\hat{n}_{c},k_{c},\varphi_{c})e^{i(k_{a}\omega_{a}+k_{c}\omega_{c})t}\,\,\delta_{(k_{a}+k_{c})\,\mathrm{mod}\,2,0}\,.$
(49)

The expression for $\sin(\hat{\varphi}(t))$ is similar, but with the Kronecker
delta $\delta_{(k_{a}+k_{c})\,\mathrm{mod}\,2,1}$ and a global phase $-\pi/2$.
We can now apply the rotating wave approximation to the previous Hamiltonian
by selecting in Eq. (49) only the terms that oscillate with $\omega_{p}$. For
$p_{a},p_{c}>0$, the Hamiltonian reads

$\hat{H}\approx-
E_{J}\,f(\hat{n},0,\varphi_{a})\,f(\hat{n}_{c},0,\varphi_{c})-iE_{J}\varphi_{c}\xi_{p}\,\hat{a}^{\dagger\,p_{a}}\hat{c}^{\dagger\,p_{c}}f(\hat{n},p_{a},\varphi_{a})f(\hat{n}_{c},p_{c},\varphi_{c})\delta_{(p_{a}+p_{c})\,\mathrm{mod}\,2,1}+\mathrm{H.c.}$
(50)

For $p_{a},p_{c}<0$, replace
$\hat{a}^{\dagger\,p_{a}}f(\hat{n},p_{a},\varphi_{a})$ by
$f(\hat{n},p_{a},\varphi_{a})\hat{a}^{p_{a}}$ correspondingly. For standard
reservoir engineering schemes, one typically requires $p_{c}=1$, which in this
context necessitates that $p_{a}$ be even. Therefore, we get the Hamiltonian
in Eq. (27) when considering two microwave drives and setting $p_{a}=r/l$ and
$p_{c}=1$. It comes however with an additional first term that originates from
the zeroth order expansion from Eq. (47). This expression corresponds to an
always-on resonance condition $k_{a}=k_{c}=0$ and gathers various effects such
as AC Stark shift, self-Kerr and cross-Kerr terms, all being energy conserving
(i.e. it can be diagonalized using Fock states).

This leads to some restrictive conditions. The first requirement is that this
energy-conserving term must be compensated or be negligible compared to the
desired stabilizing Hamiltonian. The coefficients of the function
$f(\hat{n},0,\varphi_{a})$ written as power series of $\hat{n}$ fall with
powers of $\varphi_{a}$ and factorial denominator. Since the phase
fluctuations are typically small, the first few terms of this series dominate
the dynamics of which the leading one (AC Stark shift) can be compensated
using the drive frequency $\omega_{p}$ [36, 37]. The second requirement is
that the Rabi frequencies $\tilde{f}$ and $\tilde{g}$ must be engineered to
satisfy the conditions of the NLRE method. The strengths of the microwave
drives $\epsilon_{r/l}$ are the only free parameters that can allow an in situ
engineering of the crossing points between the Rabi frequencies $\tilde{f}$
and $\tilde{g}$. The range of their tunability is limited by the condition
${\varphi_{c}\absolutevalue{\xi_{r/l}}\ll 1}$ (see Eq. (47)).

The different constraints imposed by the use of a single Josephson junction to
stabilize cat-like state manifolds can be resolved by substituting it with
some alternative nonlinear elements. Using for example a superconducting
quantum interference device (SQUID) which allows to tune the Josephson energy
using an external flux and to add a phase offset to the phase operator in Eq.
(46). When this phase offset equals $\pi/2$, the trigonometric term changes
from a cosine to a sine function allowing to construct models with odd indices
$r,l$. Although SQUIDs may add some additional tunable parameters, the energy-
conserving term from Eq. (27) will persist.

In the scenario when the nonlinear element is an ATS, the system Hamiltonian
reads

$\begin{split}\hat{H}_{\mathrm{sys}}\\!=\,&\omega_{a}\hat{a}^{\dagger}\hat{a}+\omega_{c}\hat{c}^{\dagger}\hat{c}-2E_{J}\cos\\!\left(\varphi_{\Sigma}\right)\cos\\!\left(\hat{\varphi}+\varphi_{\Delta}\right)\\\
&+2\scalebox{0.7}{$\Delta$}E_{J}\sin\\!\left(\varphi_{\Sigma}\right)\sin\\!\left(\hat{\varphi}+\varphi_{\Delta}\right)\end{split}$
(51)

where $\varphi_{\Sigma}$ and $\varphi_{\Delta}$ are the sum and difference of
the external fluxes, respectively, and $\scalebox{0.7}{$\Delta$}E_{J}$
captures the asymmetry between Josephson energies of the junctions composing
the ATS. Considering the same parameter regime as in Sec. VI, the Hamiltonian
in the rotating frame takes a similar form as Eq. (26) but with
$\omega_{V}=0$. Because of the absence of the zeroth order terms as in single
Josephson junction case, the rotating wave approximation reveals only the
operators necessary to the NLRE Hamiltonian. Moreover, the expressions
$iE_{J}\varphi_{c}\xi_{p}$ and $\delta_{(p_{a}+p_{c})\,\mathrm{mod}\,2,1}$
from Eq. (50) are in this case replaced by $E_{J}\epsilon_{p}$ and
$\delta_{(p_{a}+p_{c})\,\mathrm{mod}\,2,0}$, preserving the parity constraint
on $p_{a}$ and $p_{c}$. This approach thus alleviates some of the constraints
associated with using a single Josephson junction. However, the two approaches
presented so far show another fundamental limitation when one desires to
implement models with large orders $r,l$ which is the fact that the normalized
Rabi frequencies $\tilde{f}(k)/\Omega_{r}$ and $\tilde{g}(k)/\Omega_{l}$ scale
as $\mathcal{O}\left(\varphi_{a}^{\nu}/\nu!\right)$ with $\nu$ being $r$ or
$l$ (straightforward from Eq. (24)). This means that the normalized Rabi
frequencies become exponentially small with the order and must be compensated
by some exponentially large driving strengths $\epsilon_{r/l}$.

To solve this issue, one can envisage using instead a KITE device [75, 76]
which resembles a SQUID whose Josephson junctions are each connected in series
to a large inductance. This creates a generalized Josephson element which when
shunted with another large inductance (see Fig. 13) gives a system Hamiltonian

$\hat{H}_{\mathrm{sys}}=\omega_{a}\hat{a}^{\dagger}\hat{a}+\omega_{c}\hat{c}^{\dagger}\hat{c}+(-1)^{\mu}E_{J}\cos\\!\left(\mu\hat{\varphi}\right)\,.$
(52)

Here, $\mu\in\mathbb{N}$ represents the number of Cooper pairs that tunnel
through the element. This expression is identical to the Hamiltonian of a
single Josephson junction discussed earlier (up to the drive term), and thus
yields similar results but with larger zero-point fluctuations. For large
$\varphi_{a/c}$, the energy-conserving term in Eq. (50) will become negligible
leaving room to the desired Hamiltonian of the NLRE toy model. The NLRE method
we propose is then highly relevant to current research and introduces a novel
approach to studying the dissipative stabilization of cat-like state
manifolds. As shown the method can explain past and present circuit QED
experiments, allowing us to identify challenges and conditions for different
schemes to work. Notably, all existing schemes are still subject to the
restrictive requirement that process orders $r$ and $l$ be either even or odd
integers. The novel scheme we presented in Sec. VI overcomes this limitation
using a voltage-biased nonlinear element.

It is important to note that in all the examples discussed above, the rotating
wave approximation remains valid as long as the oscillators’ frequencies
$\omega_{a}$ and $\omega_{b}$ are much larger than the coupling strengths
(i.e. the Rabi frequencies $\tilde{f}$ and $\tilde{g}$). This condition is
typically satisfied in all the presented cases, as we engineer the external
drives to allow the use of a small angle approximation. Quantitatively,
$\omega_{a/b}$ are of the order of $\unit{}$ while as seen in Fig. 10 the Rabi
frequencies are of the order of $\unit{}$.

##  Appendix F Bosonic Hamiltonians using voltage-biased nonlinear circuits

Figure 14: Matrix elements of the Hamiltonian $\hat{H}_{\mathrm{avg}}$
obtained by time averaging the Hamiltonian in Eq. (53) over $\quantity{10}{}$.
The parameters of the considered system are identical to those used in Fig.
10. The plotted functions correspond to the matrix off-diagonals
$f(k,k_{a},k_{c})=\absolutevalue{\bra{k+k_{a},k_{c}}\hat{H}_{\mathrm{avg}}\ket{k,0}}$
with $k_{a/c}\in\mathbb{Z}$. We see that the resonant terms of the Hamiltonian
follow the analytically derived Rabi frequencies $\tilde{f}$ and $\tilde{g}$.

In this section we present the derivation of the Hamiltonian for a voltage-
biased nonlinear circuit in the rotating frame. We consider a nonlinear
circuit with an ATS biased by a DC voltage source $V$. For simplicity we
assume no asymmetry between the Josephson junctions energies (i.e.
${\scalebox{0.7}{$\Delta$}E_{J}=0}$) and two external fluxes such that
$\varphi_{\Delta}=\pi/2$ and $\varphi_{\Delta}=\pi/2+\epsilon(t)$. We modulate
the fluxes using $\epsilon(t)=\epsilon_{p}\cos\\!\left(\omega_{p}t\right)$
with $\epsilon_{p}\ll 1$ and $\omega_{p}=p_{a}\omega_{a}+p_{c}\omega_{c}$,
where $p_{a},p_{c}\in\mathbb{Z}$. The Hamiltonian of the system in the
oscillator’s rotating frame and in the small angle approximation reads

$\hat{H}=-E_{J}\epsilon_{p}\left(e^{i\omega_{p}t}+e^{-i\omega_{p}t}\right)\sin\\!\left(\hat{\varphi}(t)+\omega_{V}t\right)\,.$
(53)

Here, $\omega_{V}\equiv 2eV/\hbar=v_{a}\omega_{a}+v_{c}\omega_{c}$ with
$v_{a},v_{c}\in\mathbb{Z}$ is the frequency associated with the DC voltage
source which, as in the main text, we assume to be much smaller than the
superconducting gap voltage of the junctions composing the ATS.

Due to the additional term in the trigonometric function it cannot be
rewritten in the form of Eq. (49). This means each operator $\exp(\pm
i(\hat{\varphi}(t)+\omega_{V}t))$ must be treated separately when performing
the rotating wave approximation. Together with $e^{\pm i\omega_{p}t}$, the two
resonant conditions are

$\omega_{p}\pm\omega_{V}=k_{a}^{\pm}\omega_{a}+k_{c}^{\pm}\omega_{c}\,\,\,\Leftrightarrow\,\,\,\left\\{\begin{matrix}p_{a}\pm
v_{a}=k_{a}^{\pm}\\\ p_{c}\pm v_{c}=k_{c}^{\pm}\end{matrix}\right.$ (54)

where $k_{a}^{\pm},k_{c}^{\pm}\in\mathbb{Z}$ are free variables determining
the order of the resonant processes. Explicitly, after the rotating wave
approximation the Hamiltonian reads ($k_{a}^{\pm},k_{c}^{\pm}>0$)

$\begin{split}\hat{H}&\propto\hat{a}^{\dagger\,k_{a}^{+}}\hat{c}^{\dagger\,k_{c}^{+}}f(\hat{n},k_{a}^{+},\varphi_{a})f(\hat{n}_{c},k_{c}^{+},\varphi_{c})\,+\\\
&+\hat{a}^{\dagger\,k_{a}^{-}}\hat{c}^{\dagger\,k_{c}^{-}}f(\hat{n},k_{a}^{-},\varphi_{a})f(\hat{n}_{c},k_{c}^{-},\varphi_{c})+\mathrm{H.c.}\end{split}$
(55)

As before, for $k_{a}^{\pm},k_{c}^{\pm}<0$, replace
$\hat{a}^{\dagger\,k_{a}^{\pm}}f(\hat{n},k_{a}^{\pm},\varphi_{a})$ by
$f(\hat{n},k_{a}^{\pm},\varphi_{a})\hat{a}^{k_{a}^{\pm}}$ correspondingly. The
bias voltage thus introduces an additional degree of freedom and helps lift
the parity constraint on $p_{a}$ and $p_{c}$ observed in previous examples. We
choose $k_{a/c}^{+}$ to be the orders of the desired processes. Therefore, the
objective is to engineer $\omega_{p}$ and $\omega_{V}$ such that either their
difference prevents the resonant condition from being satisfied (i.e., there
exist no ${k_{a/c}^{-}\in\mathbb{Z}}$ that fulfill Eq. (54)), or such that the
orders $k_{a/c}^{-}$ of the undesired processes are large enough to be
negligible due to the exponential suppression of the Rabi frequencies for
large orders. We opt for the first solution as it is more versatile and
straightforward to engineer as we can simply impose

$\omega_{p}-\omega_{V}=\frac{1}{2}\left(k_{a}^{-}\omega_{a}+k_{c}^{-}\omega_{c}\right)\quad\mathrm{for}\quad
k_{a,c}^{-}\in\mathbb{Z}\,.$ (56)

As an example let us take the situation presented in the main text and
depicted in Fig. 10. We consider the same set of parameters and numerically
average the Hamiltonian in Eq. (53) over a time span of $\quantity{10}{}$
(integration step $\quantity{1}{}$). The result $\hat{H}_{\mathrm{avg}}$
corresponds to the first term in the Magnus expansion of the time evolution
operator and effectively to the rotating wave approximation Hamiltonian. We
extract the off-diagonal elements of this operator in the Fock basis.
Specifically, we evaluate the function
$f(k,k_{a},k_{c})=\absolutevalue{\bra{k+k_{a},k_{c}}\hat{H}_{\mathrm{avg}}\ket{k,0}}$
for various integers $k_{a/c}\in\mathbb{Z}$ and plot them over the Fock number
$k$. The results are shown in Fig. 14. We observe that the resonant terms of
the Hamiltonian follow the analytically derived Rabi frequencies $\tilde{f}$
and $\tilde{g}$, confirming the validity of the rotating wave approximation.
The off-resonant terms are average out to values close to zero and thus can be
neglected in the analysis of the system’s dynamics. In particular, this is
also the case for the off-diagonals that are the closest to our engineered
off-resonant condition from Eq. (56), namely
$\omega_{r}-\omega_{V}=6.5\omega_{a}-5.5\omega_{c}$ and
$\omega_{l}-\omega_{V}=2.5\omega_{a}-5.5\omega_{c}$.

##  Appendix G Rabi frequencies in the generalized NLRE model

In this section, we derive the expressions for the functions $\tilde{f}$ and
$\tilde{g}$ in the generalized NLRE model. As described in the Sec. VII, the
NLRE method can be extended to stabilize bosonic state that are linked to
nonlinear cat states presented in this work as long as there exist an
isomorphic transformation $\hat{U}$ between the two. The stabilization
operator in the standard ladder picture then reads

$\hat{K}=\hat{U}\left(\hat{a}^{\dagger\,r}f(\hat{n})-g(\hat{n})\hat{a}^{l}\right)\hat{U}^{\dagger}$
(57)

with the expression in the parentheses being the NLRE toy model from Eq. (2).
After performing the transformation the stabilization operator $\hat{K}$ will
have the general form presented in Eq. (28) where we extend the definition of
the Rabi frequencies to

$\tilde{f}_{j}(k)\\!=\\!\bra{k+j}\\!\hat{K}\\!\ket{k}\quad\mathrm{and}\quad\tilde{g}_{j}(k)\\!=\\!\bra{k}\\!\hat{K}\\!\ket{k+j}.$
(58)

In the Fock basis, these functions are defined using the matrix elements of
the transformation $\hat{U}$ and the functions $\tilde{f}$ and $\tilde{g}$ of
the underlying NLRE toy model. Explicitly, we have

$\begin{split}\tilde{f}_{j}(k)=\sum_{k^{\prime}=0}^{\infty}&\quad\bra{k+j}\\!\hat{U}\\!\ket{k^{\prime}+r}\,\bra{k^{\prime}}\\!\hat{U}^{\dagger}\\!\ket{k}\,\tilde{f}(k^{\prime})\,-\\\
&-\bra{k+j}\\!\hat{U}\\!\ket{k^{\prime}}\,\bra{k^{\prime}+l}\\!\hat{U}^{\dagger}\\!\ket{k}\,\tilde{g}(k^{\prime})\end{split}$
(59)

and similarly for $\tilde{g}_{j}(k)$. The matrix elements can be calculated
numerically for an arbitrary transformation $\hat{U}$. However, the analytical
form of some interesting transformations are know and can thus be utilized for
designing new models.

For the specific example from the main text, the transformation $\hat{U}$
corresponds to a single-mode unitary Bogoliubov transformation decomposed in
general into squeezing and rotation of phase space. Since the orientation of
the cat states can be adjusted using the relative phase of the boson raising
and lowering processes (see Sec. III), we focus exclusively on squeezing
transformations $\hat{S}(\zeta)$ with $\zeta\in\mathbb{C}$. The matrix
elements of the squeezing operator in the Fock basis are given by [141]

$\bra{k}\\!\hat{S}\\!\left(\absolutevalue{\zeta}e^{i\phi}\right)\\!\ket{k^{\prime}}=\sqrt{\cos(\theta)}\,X_{n}^{m}(\theta,\phi)$
(60)

where ${\cos(\theta)=\mathrm{cosh}(\absolutevalue{\zeta})^{-1}}$,
${n=(k+k^{\prime})/2}$ and ${m=(k-k^{\prime})/2}$. The function $X_{n}^{m}$ is
the non-normalized spherical harmonics defined as

$X_{n}^{m}(\theta,\phi)=\sqrt{\frac{4\pi}{2l+1}}\,Y_{n}^{m}(\theta,\phi)$ (61)

and captures the peculiar property of the squeezing operator that it only
couples states with the same parity. In other words, the matrix elements in
Eq. (60) are non-zero only if $k$ and $k^{\prime}$ have the same parity. Given
this and Eq. (59), we conclude that the Rabi frequencies $\tilde{f}_{j}$ and
$\tilde{g}_{j}$ will be non-zero only if $j$ shares the same parity than $r$
or $l$. In particular, schemes stabilizing two dimensional manifolds will be
composed of Rabi frequencies with either even $j$ if $(r,l)=(0,2)$ or $(2,0)$;
or odd $j$ for $(1,1)$ schemes.

This opens the way towards the design of novel stabilization schemes through
reverse engineering. Let us consider a system where jump operators $\hat{K}$
with two pairs of boson raising and lowering processes can be implemented
(e.g., using two bichromatic laser beams in a trapped ions setup or a four-
tones drive in cavity QED systems). Then fixing the orders of the drives to be
$(r_{1},r_{2},l_{1},l_{2})=(1,3,1,3)$ and carefully tuning the system
parameters (drive strengths, LD parameters,…), one would be able to stabilize
a squeezed cat manifold which in the transformed basis would be similar to a
$(1,1)$ scheme. The reverse engineering consists then in finding numerically
the right parameters such that $\tilde{f}$ and $\tilde{g}$ cross adequately.
The analytical form of these functions will be similar to Eq. (59).

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# Teeth3DS: a benchmark for teeth segmentation and labeling from intra-oral 3D
scans

Achraf Ben-Hamadou  Centre de Recherche en Numérique de Sfax, Technopôle de
Sfax, 3021 Sfax, Tunisia  Udini, 37 BD Aristide Briand, 13100 Aix-En-Provence,
France  corresponding author: Achraf Ben-Hamadou
<EMAIL_ADDRESS> Oussama Smaoui  Udini, 37 BD Aristide
Briand, 13100 Aix-En-Provence, France  Houda Chaabouni-Chouayakh  Centre de
Recherche en Numérique de Sfax, Technopôle de Sfax, 3021 Sfax, Tunisia  Udini,
37 BD Aristide Briand, 13100 Aix-En-Provence, France  Ahmed Rekik  Centre de
Recherche en Numérique de Sfax, Technopôle de Sfax, 3021 Sfax, Tunisia  Udini,
37 BD Aristide Briand, 13100 Aix-En-Provence, France  Sergi Pujades  Inria,
Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, France  Edmond Boyer  Inria,
Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK, France  Julien Strippoli
Centre de Recherche en Numérique de Sfax, Technopôle de Sfax, 3021 Sfax,
Tunisia  Aurélien Thollot  Centre de Recherche en Numérique de Sfax,
Technopôle de Sfax, 3021 Sfax, Tunisia  Hugo Setbon  Centre de Recherche en
Numérique de Sfax, Technopôle de Sfax, 3021 Sfax, Tunisia  Cyril Trosset
Centre de Recherche en Numérique de Sfax, Technopôle de Sfax, 3021 Sfax,
Tunisia  Edouard Ladroit  Centre de Recherche en Numérique de Sfax, Technopôle
de Sfax, 3021 Sfax, Tunisia

###### Abstract

Teeth segmentation and labeling are critical components of Computer-Aided
Dentistry (CAD) systems. Indeed, before any orthodontic or prosthetic
treatment planning, a CAD system needs to first accurately segment and label
each instance of teeth visible in the 3D dental scan, this is to avoid time-
consuming manual adjustments by the dentist. Nevertheless, developing such an
automated and accurate dental segmentation and labeling tool is very
challenging, especially given the lack of publicly available datasets or
benchmarks. This article introduces the first public benchmark, named
Teeth3DS, which has been created in the frame of the 3DTeethSeg 2022 MICCAI
challenge to boost the research field and inspire the 3D vision research
community to work on intra-oral 3D scans analysis such as teeth
identification, segmentation, labeling, 3D modeling and 3D reconstruction.
Teeth3DS is made of 1800 intra-oral scans (23999 annotated teeth) collected
from 900 patients covering the upper and lower jaws separately, acquired and
validated by orthodontists/dental surgeons with more than 5 years of
professional experience.

## Background & Summary

Computer-aided design (CAD) tools are becoming increasingly popular in modern
dentistry for highly accurate treatment planning. Advanced intra-oral scanners
(IOSs) are particularly popular in orthodontic CAD softwares as they provide
accurate digital surface 3D representation of the dentition. Such 3D
representation can greatly assist dentists in simulating tooth extraction,
realignment, and smile design, making the treatment final results more
predictable. As a result, digital teeth models have the potential to relieve
dentists from time-consuming and tedious tasks.

Although IOSs are becoming ubiquitous in clinical dental practice, there are
only few contributions on teeth segmentation/labeling available in the
literature, e.g., [1, 2, 3, 4, 5, 6], and, most importantly, no publicly
available benchmark. A fundamental challenge in IOS data analysis is the
ability to accurately segment and identify teeth. Teeth segmentation and
labeling is challenging due to inter-class variations, such as inherent
similarities between tooth shapes and ambiguous positions on jaws, as well as
intra-class variations such as damaged teeth or braces. This is in addition to
the tight borders between surrounding teeth and gingiva as well as
abnormalities like crowded, misaligned, or missing teeth.

Despite several efforts, developing an accurate and a fully automated dental
segmentation and labeling tool remains challenging. Most former approaches are
based on the teeth geometric characteristics, such as curvature thresholding
[7] or active contour computing [8] in order to separate between teeth and
gingiva. However, these solutions lack robustness with respect to teeth shape
variations and usually require additional manual interventions that include
teeth pre-selection or contour initialization. Recent advances in 3D shape
analysis based on machine learning techniques can also be used for 3D dental
scan analysis. In general, they follow two main strategies. Some researchers
proposed to convert the 3D scans into 2D images so that existing convolutional
neural networks (CNNs) can be used for both teeth segmentation and
classification [9]. This strategy may lead to acceptable results in the 2D
space. Meanwhile, the reconstruction of the obtained segmentation into the 3D
space will systematically decrease the segmentation accuracy. Other studies
proposed to directly process the 3D scans and to apply deep learning
architectures [10] with the aim of detecting and segmenting teeth present in
the IOSs. Although this approach may be faster, it still has to deal with
different challenges such as point cloud irregularity, downsampling, and 3D
pose variations. Overall, it should also be noted that the lack of a publicly
available dataset or benchmark is an obstacle to the development of this
research area, as no fair comparison can be conducted among state-of-the-art
approaches.

In this article, we introduce a freely available teeth dataset of 1800 intra-
oral scans collected from 900 patients covering the upper and lower jaws
separately. The split into training and testing subsets was used and validated
for the 3DTeethSeg 2022 scientific challenge held during the 25th
International Conference on Medical Image Computing and Computer Assisted
Intervention (MICCAI) (https://3dteethseg.grand-challenge.org/), which
reflects the research community’s interest in our proposed dataset. The
provided data can be used by researchers of different backgrounds for the
development and evaluation of machine learning methods not only for teeth
detection, segmentation and labeling, but also other tasks such as 3D shape
modeling and reconstruction from 2D intra-oral photos.

##  1 Methods

###  1.1 Patients and intra-oral scans collection

In compliance with the European General Data Protection Regulation (GDPR)
agreement, we obtained 3D intra-oral scans for 900 patients acquired by
orthodontists/dental surgeons with more than 5 years of professional
experience from partner dental clinics located mainly in France and Belgium.
All data is completely anonymized, and the identity of the patients cannot be
revealed. Two 3D scans are acquired for each patient, covering the upper and
lower jaws separately. The following IOSs were used for scan acquisition: the
Primescan from Dentsply, the Trios3 from 3Shape, and the iTero Element 2 Plus.
These scanners are representative and generate 3D scans with an accuracy
between 10 and 90 micrometers and a point resolution between 30 and 80
pts/mm2. No additional equipment other than the IOS itself was used during the
acquisitions. All acquired clinical data are collected for patient requiring
either orthodontic ($50\%$) or prosthetic treatment ($50\%$). The provided
dataset follows a real-world patient age distribution: $50\%$ male $50\%$
female, about $70\%$ under 16 years-old, about $27\%$ between 16-59 years-old,
about $3\%$ over 60 years old.

###  1.2 Data annotation and processing

The data annotation, i.e., teeth segmentation and labeling, was performed in
collaboration with clinical evaluators with more than 10 years of expertise in
orthodontistry, dental surgery and endodontics. The detailed process is
depicted in Figure 1. It consists of eight steps. First, the 3D scans are
preprocessed (steps 1 and 2 in Figure 1) by removing all degenerated and
redundant mesh faces, as well as duplicated and irrelevant vertices. The
dental mesh coordinates are then automatically centered and aligned with the
occlusal plane by principle component analysis. This improves teeth visibility
while also normalizing the 3D pose of all the input 3D IOSs. Then, we used a
custom tool to manually crop each tooth from the 3D scans with a tight sphere
that includes the detected tooth as well as its surroundings (i.e.,
neighboring teeth and gingiva). We decided to perform UV mapping in step 3 to
flatten the cropped 3D meshes and show the maximum 3D curvature to make the
annotation of tooth boundaries easier. This transformation is ensured by
harmonic parameterization, a fixed boundary parameterization algorithm that
calculates the 2D coordinates of the flattened cropped tooth as two harmonic
functions [11]. These vertices are then mapped to a circle, and the 2D
coordinates of the remaining vertices are calculated using two harmonic
functions and the circle boundary constraints. The benefits are twofold: the
annotator can annotate the 2D polygons delimiting the tooth without changing
the 3D point of view, and the 3D curvature overlay is informative on the
boundaries of teeth.

After the manual annotation of the UV maps (step 4 of Figure 1), we back-
propagate the tooth boundaries to the 3D crops in step 5. At this point each
separate tooth candidate has been manually segmented, however they have been
represented in the same 3D coordinate system. The aim of the next step is to
gather all the teeth crowns and prepare them for manual labeling as shown in
step 7 of Figure 1. We followed the FDI World Dental Federation numbering
system for teeth labeling depicted in Figure 2.

Figure 1: Illustration of our annotation process. An input 3D IOS is annotated
following eight steps, beginning with preprocessing and pose normalization and
ending with clinical validation. The clinical validator can return the
annotation to steps 2, 4, or 7, depending on the raised issue, which
respectively correspond to missing teeth, teeth border issues, or incorrect
teeth instance labeling. Figure 2: FDI World Dental Federation notation222FDI
World Dental Federation numbering system, Wikipedia, last modified May 20,
2022.
https://en.wikipedia.org/wiki/FDI$\\_$World$\\_$Dental$\\_$Federation$\\_$notation.

The final step 8 of the annotation process consists of the visual inspection
and validation of the produced annotated 3D IOS. This step is carried out by
our clinical partners, who are experienced orthodontists, dental surgeons, and
endodontists. Their inspection targeted the identification of annotation
issues, such as a missing tooth annotation (return to step 2), inaccurate
tooth boundary annotation (return to step 4), or incorrect tooth labels
(return to step 7). This validation/correction cycle was repeated until the
entire dataset was correctly annotated and clinically validated.

##  2 Data records

Figure 3: Frontal and occlusal rendering of annotated jaws for 6 randomly
selected patients.

A total of 1800 3D intra-oral scans have been collected for 900 patients
covering their upper and lower jaws separately. Figure 3 shows some examples.

The data will be hosted at the Figshare platform. For the purpose of the
segmentation and labeling challenge held at MICCAI 2022, the 3D scans data
(obj format) are separated into training (1200 scans, 16004 teeth) and test
data (600 scans, 7995 teeth). The dataset structure is depicted in Figure 4.
Patients are anonymized by their universally unique identifier (uuid). The
ground truth tooth labels and tooth instances for each vertex in the obj files
are provided in JavaScript Object Notation (JSON) format. A JSON file example
is shown below:

⬇

1{

2 "id_patient": "YNKZHRPO",

3 "jaw": "upper",

4 "labels": [0, 0, 44, 33, 34, 0, 0, 45, 0, ... , 41, 0, 0, 37, 0, 34, 45, 0,
31, 36],

5 "instances": [0, 0, 10, 2, 12, 0, 0, 9, 0, ... , 10, 0, 0, 8, 0, 1, 9, 0, 1,
8]

6}

Figure 4: Dataset structure for both training and testing phases. All data are
structured by jaws and patient ID. Stl files represent the raw intra-oral
scans (3D mesh). They are converted to obj files for commodity. Json files
provide the annotation corresponding to the obj files.

The length of the tables "labels" and "instances" is the same as the total
number of vertices in the corresponding 3D scan. The label and instance "0"
are reserved by default for gingiva. And, other than "0", the unique numbers
in table "instances" indicate the number of teeth in the 3D scan.

## Technical Validation

As previously mentioned, the annotation of our dataset was performed and
validated in collaboration with clinical evaluators with over ten years of
experience in orthodontistry, dental surgery and endodontics. We divided the
dataset into training and testing subsets as detailed in Table 1. We selected
two-thirds of the scans for training and the rest for testing, totaling 1200
and 600 scans, respectively. The scan selection is performed in such a way
that the same training/testing proportion is validated at the level of tooth
labels as well, ensuring balanced data. For example, there are 591 teeth in
the training subset out of a total of 888 teeth with the label 12, which reads
approximately $66.55\%$.

We also validated the statistics related to teeth distributions across upper
and lower jaws. As depicted in figure 5, we observe a comparable distributions
of number of teeth per jaw when comparing the upper and lower jaws. For
example, we find 10.7% for 13-teeth upper jaws while 13-teeth lower jaw
represent 10.3%. From another perspective, jaws with 14 teeth are the most
representative, accounting for 53.4% and 58.9% for upper and lower jaws,
respectively. Even if there are significantly less jaws with missing teeth
(e.g., 0.1 % and 0.8 % for 8 and 9 teeth on the upper jaws), the overall
statistics are still representative according to our clinical experts.

To provide use case scenarios for our Teeth3DS dataset, it was successfully
processed by the competing algorithms in the 3DTeethSeg 2022 challenge. The
obtained results showed that the majority of the proposed deep learning
algorithms can perform accurate and reliable 3D teeth localization, 3D scan
segmentation and labeling tasks. In terms of evaluation metrics, they obtained
a teeth localization accuracy between $45.3\%$ and $96.58\%$, a teeth
segmentation accuracy between $81.26\%$ and $98.59\%$ and a teeth
identification rate between $68.36\%$ and $91\%$. These results demonstrate
that Teeth3DS can be useful for segmenting and labeling each instance of
visible teeth in 3D dental scans, allowing for example orthodontists to
simulate teeth extraction, deletion, and rearrangement and improve the
treatment outcome prediction. Nevertheless, in order to develop a fully
automated CAD system, all of these three mainstream tasks should be
significantly improved. For example, depending on the application
requirements, teeth miss detection should ideally be lower than 1/100. Also,
we envision to further refine the tasks and metrics in order to evaluate the
quality of the algorithms in the accurate delimitations of these limits.
Beyond the explored tasks, this dataset will be also useful for a wider range
of applications such as 3D teeth modeling and reconstruction or dentition
anomalies detection.

Table 1:  Teeth3DS dataset description. |  | Training | Testing | Total
---|---|---|---|---
| # patients | 600 | 300 | 900
| # scans | 1200 | 600 | 1800
| # teeth | 16004 | 7995 | 23999
Upper jaw | Label 18 | 28 | 14 | 42
Label 17 | 417 | 205 | 622
Label 16 | 592 | 298 | 890
Label 15 | 591 | 290 | 881
Label 14 | 586 | 293 | 879
Label 13 | 556 | 278 | 834
Label 12 | 591 | 297 | 888
Label 11 | 599 | 300 | 899
Label 21 | 599 | 300 | 899
Label 22 | 598 | 299 | 897
Label 23 | 561 | 283 | 844
Label 24 | 592 | 297 | 889
Label 25 | 584 | 286 | 870
Label 26 | 590 | 300 | 890
Label 27 | 425 | 213 | 638
Label 28 | 24 | 12 | 36
Total | 7933 | 3965 | 11898
Lower jaw | Label 38 | 31 | 16 | 47
Label 37 | 458 | 224 | 682
Label 36 | 586 | 296 | 882
Label 35 | 585 | 293 | 878
Label 34 | 589 | 292 | 881
Label 33 | 588 | 295 | 883
Label 32 | 600 | 300 | 900
Label 31 | 598 | 299 | 897
Label 41 | 598 | 300 | 898
Label 42 | 598 | 300 | 898
Label 43 | 589 | 297 | 886
Label 44 | 594 | 297 | 891
Label 45 | 581 | 289 | 870
Label 46 | 589 | 292 | 881
Label 47 | 456 | 225 | 681
Label 48 | 31 | 15 | 46
Total | 8071 | 4030 | 12101

|
---|---
(a) | (b)
Figure 5: Upper (a) and lower (b) statistics regarding number of teeth per
jaw.

## Code availability

We provide the code related for data manipulation and validation metrics under

https://github.com/abenhamadou/3DTeethSeg22_challenge.git

## Acknowledgments

The authors would like to thank Udini SA for helping with clinical data
collection as well as our clinical experts for thoroughly validating the
annotated data.

## Author contributions statement

A.B.H, A.R., O.S., H.C.C.: conception and design of the work, analysis and
interpretation of data, creation of new software used in the work, drafting of
the manuscript. A.B.H, H.C.C, S.P., E.B.: discussion and interpretation of
results, substantial revision of the manuscript. J.S., A.T., H.S., C.T, E.L.:
data acquisition and processing.J.S., A.T., H.S.: Data annotation validation.
All authors reviewed the manuscript.

## Competing interests

The authors declare no competing interests.

##  3 References

## References

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  * [2] Xu, X., Liu, C. & Zheng, Y.  3D Tooth Segmentation and Labeling Using Deep Convolutional Neural Networks.  _IEEE Transactions on Visualization and Computer Graphics_ 25, 2336–2348 (2018).
  * [3] Sun, D. _et al._ Automatic tooth segmentation and dense correspondence of 3d dental model.  In _International Conference on Medical Image Computing and Computer-Assisted Intervention_ , 703–712 (Springer, 2020).
  * [4] Zhao, Y. _et al._ 3D Dental model segmentation with graph attentional convolution network.  _Pattern Recognition Letters_ 152, 79–85 (2021).
  * [5] Ma, T., Yang, Y., Li, Y., Li, Z. & Li, Y.  An Efficient Method of Tooth Segmentation Under Massive Medical Data.  _Journal of Database Management (JDM)_ 33, 1–22 (2022).
  * [6] Zhao, Y. _et al._ Two-Stream Graph Convolutional Network for Intra-oral Scanner Image Segmentation.  _IEEE Transactions on Medical Imaging_ 41, 826–835 (2022).
  * [7] Kumar, Y., Janardan, R., Larson, B. & Moon, J.  Improved segmentation of teeth in dental models.  _Computer-Aided Design and Applications_ 8, 211–224 (2011).
  * [8] Yaqi, M. & Zhongke, L.  Computer aided orthodontics treatment by virtual segmentation and adjustment.  In _IEEE International Conference on Image Analysis and Signal Processing (ICISP)_ , 336–339 (2010).
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# GEAR-Up: Generative AI and External Knowledge-based Retrieval
Upgrading Scholarly Article Searches for Systematic Reviews

Kaushik Roy1, Vedant Khandelwal1, Harshul Surana1, Valerie Vera2, Amit Sheth1,
Heather Heckman2

###### Abstract

Systematic reviews (SRs) - the librarian-assisted literature survey of
scholarly articles takes time and requires significant human resources. Given
the ever-increasing volume of published studies, applying existing computing
and informatics technology can decrease this time and resource burden. Due to
the revolutionary advances in (1) Generative AI such as ChatGPT, and (2)
External knowledge-augmented information extraction efforts such as Retrieval-
Augmented Generation, In this work, we explore the use of techniques from (1)
and (2) for SR. We demonstrate a system that takes user queries, performs
query expansion to obtain enriched context (includes additional terms and
definitions by querying language models and knowledge graphs), and uses this
context to search for articles on scholarly databases to retrieve articles. We
perform qualitative evaluations of our system through comparison against
sentinel (ground truth) articles provided by an in-house librarian. The demo
can be found at: https://youtu.be/zMdP56GJ9mU.

##  1 Introduction

The proliferation of artificial intelligence (AI) technologies, e.g.,
Microsoft’s recent integration of ChatGPT into its Bing search architecture,
showcases AI’s immense potential for shaping information search and discovery
for educational purposes. For example, researchers at higher education
institutions often need to review various subjects and topics systematically.
For this, the researchers consult expert librarians trained in finding and
evaluating the information in university libraries. AI systems have the
potential to assist librarians through the systematic review process.
Moreover, if developed responsibly and with input from librarians, such
systems could help alleviate significant employee availability concerns (e.g.,
time and bandwidth limitations) (Borah et al. 2017; Bullers et al. 2018). We
demonstrate a pipeline to assist librarians with structured, systematic review
search processes. Our method is modular and can be described as follows:

(1) Query Expansion Module \- processes queries in natural language and
attaches additional context by querying external knowledge graphs and
pretrained language models (Kawintiranon and Singh 2021).

(2) Additional Related Query Generation Module \- Our system then uses this
expanded query to prompt ChatGPT, generating queries related to the original
input query (Lewis et al. 2020).

(3) Article Search and Retrieval Module With this list of queries, we first
obtain a list of articles using PubMed searches and implement a FAISS-powered
retriever that narrows the search down to the most relevant articles (Title,
abstracts, and relevant passages) (Komeili, Shuster, and Weston 2021).

Figure 1:  (a) shows all the steps in the systematic review process. First,
the research question is formulated in the ”Identify the issue and determine
the question” phase. Second, the review protocol is determined, i.e., what are
the related articles to include based on query concepts and their relation to
other concepts. This protocol is used to obtain a targeted search query.
Lastly, the targeted search query is executed, the relevant data are
extracted, the quality is assessed, and a systematic review is compiled and
disseminated. Our proposed system seeks to automate the first two steps of
issue identification and review protocol-based targeted query formulation. (b)
(1) We use natural language processing tools to obtain seed concepts from the
input query. In the figure example, the seed concept is Hepatitis A. (2) We
query KGs (e.g., PubMed) using the seed concepts in the input query to obtain
additional context. The figure shows subgraphs of concepts connected to the
seed concept Hepatitis A and the relationships that connect them. We also
query pretrained masked language models to obtain additional context terms.
The figure shows the relationships and concepts obtained for the seed concept
of Hepatitis A as causes, diagnoses, affects, associated with, complicates,
and Acetaminophen. Steps (1) and (2) form the Query Expansion Module from
Section 1. (3) The concepts and relationships from the previous steps are fed
into ChatGPT with an appropriate prompt to obtain a set of reformulated
queries. For example, the prompt in the figure is ”Formulate five prompt
queries with the keywords: causes, diagnoses, affects, associated with,
complicates, Acetaminophen”. The figure also shows the reformulated queries
that ChatGPT generates, e.g., “What are the causes of Hepatitis A and how is
it diagnosed?” Step (3) forms the Additional Related Query Generation Module
in Section 1. In Step (4), With this list of queries, we first obtain a list
of articles using PubMed searches and implement a FAISS-powered retriever that
narrows the search to the most relevant articles, including the article
titles, abstracts, and relevant passages. This forms the Article Search and
Retrieval Module in Section 1. Finally, the list of retrieved outputs is
presented to the librarian for feedback-based refinements to the overall
system.

##  2 The Systematic Review Process

The review process involves the following steps (Koffel 2015):

(i) Defining the research question: Formulating a clear, well-defined research
question of appropriate scope. Often, a researcher needs help to define a
research problem precisely and interacts with the expert librarian for help
with this effort. (ii) Developing a review protocol/criteria: This step is
often carried out in parallel with the first step and results in defining the
terminology and topics that inform the development of the research question.
(iii) Developing inclusion and exclusion criteria: The student needs to
understand and determine whether the review will include a particular study.
For this, they provide well-defined inclusion-exclusion criteria.

Steps (i), (ii), and (iii) correspond to; identifying the issue, determining
the question, and writing a plan for the review (protocol) in Figure 1 (a).
This functionality is carried out by modules (1) and (2) introduced in Section
1. The remaining steps involve searching a database and using existing machine
learning tools to help with the later stages, including article screening,
data extraction, and the risk of bias assessment. This is carried out by
module (3) in Section 1.

##  3 Details of Our Implementation and Evaluation

Due to space concerns, we ask the reader to refer to the caption of Figure 1
(b) for details and illustration of our system and its submodules (introduced
in Section 1)

### What does the Librarian Review?

The librarians’ review can be incorporated at several points in the system’s
execution. The librarian’s suggestions can be used to refine the Additional
Related Query Generation Module to extract more contextual and relevant
responses, without which ChatGPT might generate irrelevant and incoherent
queries. The librarian may also analyze the safety of the generated queries.
For example, the external knowledge contains information about how
acetaminophen could be misused. The system may then incorporate controls (via
KG paths) to avoid showing information due to sensitive content. Similar
controls can be placed to extend safety, including the relevant ethics and
bias issues. Note that safety is context-sensitive. For example, it may be
appropriate for addiction researchers to learn how a drug is abused (e.g.,
through higher doses, snorting, etc.). These aspects can be incorporated in
the Query Expansion Module.

##  4 Conclusion and Future Work

We demonstrate a system for assisting librarians in the SR process. It inputs
natural language queries and leverages external knowledge to return a set of
relevant research articles relevant to the review. We evaluated the retrieved
articles with an in-house librarian. Our system shows favorable reviews for
reducing the librarian burden by providing high-quality articles similar to a
human librarian. Our work currently stands at the implementation of the three
modules introduced in Section 1. Future steps involve exploring external
knowledge from unstructured (e.g., documents), semi-structured (e.g., web
URLs), and structured (e.g., knowledge graphs) before invoking the generative
model. Furthermore, we are working on tracing back outputs to the
corresponding knowledge sources to provide evidence for the appropriate parts
of the system output.

## Acknowledgements

This research was built upon prior work in (Roy et al. 2021, 2022; Roy and
Rawte 2022; Gupta et al. 2022; Roy et al. 2023), supported in part by NSF
Award 2335967 ”EAGER: Knowledge-guided neurosymbolic AI” with guardrails for
safe virtual health assistants”. Opinions are those of the authors and do not
reflect the opinions of the sponsor (Sheth et al. 2021, 2022; Sheth, Roy, and
Gaur 2023).

## References

  * Borah et al. (2017) Borah, R.; Brown, A. W.; Capers, P. L.; and Kaiser, K. A. 2017.  Analysis of the time and workers needed to conduct systematic reviews of medical interventions using data from the PROSPERO registry.  _BMJ open_ , 7(2): e012545.
  * Bullers et al. (2018) Bullers, K.; Howard, A. M.; Hanson, A.; Kearns, W. D.; Orriola, J. J.; Polo, R. L.; and Sakmar, K. A. 2018.  It takes longer than you think: librarian time spent on systematic review tasks.  _Journal of the Medical Library Association: JMLA_ , 106(2): 198.
  * Gupta et al. (2022) Gupta, S.; Agarwal, A.; Gaur, M.; Roy, K.; Narayanan, V.; Kumaraguru, P.; and Sheth, A. 2022.  Learning to Automate Follow-up Question Generation using Process Knowledge for Depression Triage on Reddit Posts.  In _Proceedings of the Eighth Workshop on Computational Linguistics and Clinical Psychology_ , 137–147.
  * Kawintiranon and Singh (2021) Kawintiranon, K.; and Singh, L. 2021.  Knowledge enhanced masked language model for stance detection.  In _Proceedings of the 2021 conference of the north american chapter of the association for computational linguistics: human language technologies_ , 4725–4735.
  * Koffel (2015) Koffel, J. B. 2015.  Use of recommended search strategies in systematic reviews and the impact of librarian involvement: a cross-sectional survey of recent authors.  _PloS one_ , 10(5): e0125931.
  * Komeili, Shuster, and Weston (2021) Komeili, M.; Shuster, K.; and Weston, J. 2021.  Internet-augmented dialogue generation.  _arXiv preprint arXiv:2107.07566_.
  * Lewis et al. (2020) Lewis, P.; Perez, E.; Piktus, A.; Petroni, F.; Karpukhin, V.; Goyal, N.; Küttler, H.; Lewis, M.; Yih, W.-t.; Rocktäschel, T.; et al. 2020.  Retrieval-augmented generation for knowledge-intensive nlp tasks.  _Advances in Neural Information Processing Systems_ , 33: 9459–9474.
  * Roy et al. (2023) Roy, K.; Gaur, M.; Soltani, M.; Rawte, V.; Kalyan, A.; and Sheth, A. 2023.  Proknow: Process knowledge for safety constrained and explainable question generation for mental health diagnostic assistance.  _Frontiers in big Data_ , 5: 1056728.
  * Roy et al. (2022) Roy, K.; Lokala, U.; Gaur, M.; and Sheth, A. P. 2022.  Tutorial: Neuro-symbolic AI for Mental Healthcare.  In _Proceedings of the Second International Conference on AI-ML Systems_ , 1–3.
  * Roy and Rawte (2022) Roy, K.; and Rawte, V. 2022.  TDLR: Top Semantic-Down Syntactic Language Representation.  In _NeurIPS’22 Workshop on All Things Attention: Bridging Different Perspectives on Attention_.
  * Roy et al. (2021) Roy, K.; Zhang, Q.; Gaur, M.; and Sheth, A. 2021.  Knowledge infused policy gradients with upper confidence bound for relational bandits.  In _Machine Learning and Knowledge Discovery in Databases. Research Track: European Conference, ECML PKDD 2021, Bilbao, Spain, September 13–17, 2021, Proceedings, Part I 21_ , 35–50. Springer.
  * Sheth et al. (2021) Sheth, A.; Gaur, M.; Roy, K.; and Faldu, K. 2021.  Knowledge-intensive language understanding for explainable ai.  _IEEE Internet Computing_ , 25(5): 19–24.
  * Sheth et al. (2022) Sheth, A.; Gaur, M.; Roy, K.; Venkataraman, R.; and Khandelwal, V. 2022.  Process knowledge-infused ai: Toward user-level explainability, interpretability, and safety.  _IEEE Internet Computing_ , 26(5): 76–84.
  * Sheth, Roy, and Gaur (2023) Sheth, A.; Roy, K.; and Gaur, M. 2023.  Neurosymbolic Artificial Intelligence (Why, What, and How).  _IEEE Intelligent Systems_ , 38(3): 56–62.

##  Appendix A Results, Librarian Review and Evaluation

An in-house librarian evaluates the retrieved articles compared to sentinel,
i.e., ground-truth articles from the librarian’s experience with similar
queries. Figure 2 shows an example review. More results are provided in the
supplementary.

Figure 2: Example of the in-house librarian review that provides detailed
comments about positives and negatives about the retrieved articles for a
given query.