formula = mhchem, greek = chemgreek, modules = thermodynamics, modules =
redox, modules = reactions supplemental-kinNOX

# Reactivity of Ru oxides with air radiolysis products investigated by
theoretical calculations

Faoulat Miradji  Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
PSN-RES, Cadarache, St Paul Lez Durance, 13115, France  Univ. Lille, CNRS, UMR
8522 - PC2A - Physicochimie des Processus de Combustion et de l’Atmosphère,
F-59000 Lille, France  Laboratoire de Recherche Commun IRSN-CNRS-Lille1
Cinétique Chimique, Combustion, Réactivité ($\mathrm{C^{3}R}$), Cadarache,
Saint Paul Lez Durance,13115, France  Univ. Lille, CNRS, UMR 8523 - PhLAM -
Physique des Lasers Atomes et Molécules, F-59000 Lille, France  Sidi M. O.
Souvi  Institut de Radioprotection et de Sûreté Nucléaire (IRSN) PSN-RES,
Cadarache, St Paul Lez Durance, 13115, France  Laboratoire de Recherche Commun
IRSN-CNRS-Lille1 Cinétique Chimique, Combustion, Réactivité
($\mathrm{C^{3}R}$), Cadarache, Saint Paul Lez Durance,13115, France  Laurent
Cantrel  Institut de Radioprotection et de Sûreté Nucléaire (IRSN) PSN-RES,
Cadarache, St Paul Lez Durance, 13115, France  Laboratoire de Recherche Commun
IRSN-CNRS-Lille1 Cinétique Chimique, Combustion, Réactivité
($\mathrm{C^{3}R}$), Cadarache, Saint Paul Lez Durance,13115, France  Florent
Louis  Univ. Lille, CNRS, UMR 8522 - PC2A - Physicochimie des Processus de
Combustion et de l’Atmosphère, F-59000 Lille, France  Laboratoire de Recherche
Commun IRSN-CNRS-Lille1 Cinétique Chimique, Combustion, Réactivité
($\mathrm{C^{3}R}$), Cadarache, Saint Paul Lez Durance,13115, France  Valérie
Vallet  Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et
Molécules, F-59000 Lille, France

(Received: )

###### Abstract

Quantitative predictions of the release of volatile radiocontaminants of
ruthenium (Ru) in the environment from either nuclear power plants (NPP) or
fuel recycling accidents present significant uncertainties while estimated by
severe accidents nuclear analysis codes. Observations of Ru from either
experimental or modeling works suggest that the main limitations relate to the
poor evaluation of the kinetics of gaseous Ru in the form of RuO3 and RuO4.
This work presents relativistic correlated quantum chemical calculations
performed to determine the possible reactions pathways leading to the
formation of gaseous Ru oxides under NPP severe accident conditions, as a
result of reactions of RuO2 gaseous with air radiolysis products, namely
nitrous and nitrogen oxides. The geometries of the relevant species were
optimized with the TPSSh-5%HF functional of the density, while the total
electronic energies were computed at the CCSD(T) level with extrapolations to
the complete basis set CBS limit. The reaction pathways were fully
characterized by localizing the transition states and all intermediate
structures using the internal coordinate reaction algorithm (IRC). The rate
constants were determined over the temperature range
$2502500\text{\,}\mathrm{K}$. It is revealed that the less kinetically
limiting pathway to form Ru gaseous fraction is the oxidation of Ru by
nitrogen oxide, corroborating experimental observations.

Severe accident; Ruthenium transport; Reactor cooling system; Kinetics;
Quantum chemistry

##  I Introduction

The prevention of the radiological consequences of ruthenium release in the
environment, implying the evaluation of its source term, is crucial for
nuclear safety, as ruthenium-containing compounds present severe sanitary
issues due to ^103Ru and ^106Ru isotopes, considered as short and medium radio
contaminants like ^131I and ^137Cs [1]. Such a release may occur mostly in the
event of a nuclear power plant (NPP) severe accident (SA) like the Three Mile
Island or the Chernobyl ones [2, 3], but sometimes from nuclear fuel recycling
plant as observed lately through the Ural accident provoking a release of
ruthenium ^106Ru over European countries [4, 5]. Literature review on Ru
transport studies reported that Ru volatilization can be influenced by
humidity, temperature, and air flow rate in the Reactor Coolant System (RCS)
[6, 7] during a severe accident. The interactions with other elements released
from the fuel may also impact the chemical composition and possibly the
quantity of transported Ru [8]. The mechanisms involved in the ruthenium
release are still not well characterized and implemented in SA analysis codes
[9]. The volatile form of Ru is ruthenium tetroxide that can exist in
oxidizing atmosphere and which is not easy to trap by usual filters [10] but
can be thermally reduced into non-volatile RuO2 form. Chemical reactivity of
gaseous RuO4 has to be modeled in order to better assess potential releases in
the frame of a nuclear accident. In a previous theoretical work, we have used
relativistic correlated quantum chemical methods to consolidate and extend Ru
thermodynamics database [11, 12]. It was revealed that thermodynamic
properties of Ru compounds in SA databases agree with our theoretical
calculations. Thence, a possible explanation for the observed discrepancies
between the simulated and experimental amounts of Ru transported fractions,
might be related to kinetic limitations in the formation of gaseous ruthenium
molecules [13].

Thus, several research programs are currently led to improve knowledge on Ru
transport schemes [14, 15, 6, 16, 17]. Among them, the Technical Research
Centre of Finland (Teknologian tutkimuskeskus, VTT) program studied ruthenium
transport in humid atmosphere with air radiolysis products [6, 16, 17]. The
radiation of the atmosphere in the reactor vessel is thought to occur under an
NPP SA leading in particular to the formation of air radiolysis products like
nitrogen and/or nitrous oxides [18, 19]. The results of the VTT program
underlined that the major part of Ru released from the crucible was deposited
inside the apparatus. The transported Ru fractions were in condensed and
gaseous forms. The aerosols were identified as RuO2 and the gaseous form was
identified as RuO4, according to instrumental neutron activation analysis. As
it was found that air radiolysis products enhance the fraction of gaseous Ru
at the outlet of the experimental set-up, we decided to launch quantum
chemical calculations to determine reaction pathways and their kinetic
parameters that lead to the formation of the gaseous fraction of ruthenium
(RuO3 and RuO4 compounds, likely to be formed under experimental conditions
[12]), with air radiolysis products N2O and NO2, according to the following
chemical reactions:

##  II Computational methodology

###  II.1 Structural properties and energetics

The geometries of all stationary points for the relevant chemical reactions
were optimized using the TPSSh-5%HF density functional [20], validated in our
previous works to obtain thermodynamic properties of Ruthenium oxides and
oxyhydroxides [11, 12]. In our calculations, the N, O, and H atoms are
described with augmented correlation consistent polarized triple zeta aug-cc-
pVTZ (noted aVTZ) basis sets [21]. The ruthenium atom is described by the aug-
cc-pVTZ-PP basis set of Peterson et al. [22], which incorporates a
relativistic pseudo-potential that accounts for scalar relativistic effects in
the Ru atom. Vibrational frequencies and zero-point energies (ZPE) were
determined at the same level of theory as the geometries. When a transition
state structure has been located on the potential energy surface, intrinsic
reaction coordinates calculations (IRC) have been performed using the
algorithm implemented in the Gaussian09 RevC.01 software [23] to find the
associated molecular complexes on the reactant (MCR) and product (MCP) sides.

In a second step, to obtain accurate potential energies of all stationary
points, single and double coupled cluster with inclusion of a perturbative
estimation for triple excitation (CCSD(T)) [24, 25] calculations were
performed with the MOLPRO quantum chemistry package Version 2015.1 [26, 27].
The full valence (oxygen 2s and 2p and ruthenium 5s and 4d) orbitals of Ru
compounds were correlated in the CCSD(T) calculations. The total energies
computed with triple-$\zeta$ ($n=3$), and quadruple-$\zeta$ ($n=4$) basis set
qualities were extrapolated to the complete basis set (CBS) limit using a two-
fold scheme to extrapolate Hartree-Fock energies [28, 29] and correlation
energies [30], as described in our previous works [11, 12]. The use of DFT
optimized geometries combined with CCSD(T) single point energy calculations
was portrayed in a recent work by Fang et al. [31] to study small Ru clusters
with water, enhancing the appropriateness of such methodology to evaluate Ru
related compounds thermochemistry.

Regarding spin-orbit (SO) coupling, it was found in our previous investigation
[11] that SO contributions amounted to
$16100.75\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ for Ru, RuO, and
RuO2 compounds, respectively. In this study, we don’t expect SO contributions
to exceed that found for the Ru atom, and as the ground state wave functions
have low spin contamination, we can safely assume that SO corrections cancel
when considering reaction and activation energies.

###  II.2 Rate constants

The rate constants of the reactions were calculated using the direct
transition state approach, as applied in our previous work [32]. The direct
mechanism considers the reaction from the reactants to the products, and the
formation of the pre-reactive complex (MCR) is disregarded. The canonical
Transition State Theory (TST) [33, 34, 35, 36, 37, 38, 39] was applied to
calculate the temperature dependence of the rate constant for the direct
mechanism, $k_{direct}$, as follows:

$\displaystyle k_{direct}(T)=$
$\displaystyle\Gamma(T)\times\frac{k_{B}T}{h}\times\frac{Q_{\ce{TS}}(T)}{Q_{\ce{A}}(T)Q_{\ce{B}}(T)}$
$\displaystyle\times\exp{\left(-\frac{E_{\ce{TS}}-E_{\ce{A}}-E_{\ce{B}}}{k_{B}T}\right)}$
(1)

where $\Gamma(T)$ represents the transmission coefficient used for the
tunneling correction at temperature $T$, and $k_{B}$ and $h$ are the Boltzmann
and Planck constants, respectively. $Q_{\ce{A}}(T)$, $Q_{\ce{B}}(T)$, and
$Q_{\ce{TS}}(T)$ are the total partition functions of A, B, and the TS at the
temperature $T$, respectively. $E_{\ce{A}}$, $E_{\ce{B}}$, and $E_{\ce{TS}}$
are the total energies at $0\text{\,}\mathrm{K}$ including the zero-point
energies.

The GPOP program [40] was used to extract information from the Gaussian output
files to estimate the Eckart tunneling corrections and to perform the rate
constant calculations over the temperature range of interest,
$2502500\text{\,}\mathrm{K}$. The structural properties, energetics and
kinetic parameters of selected reactions pathways are discussed in the next
subsections.

##  III Results and discussion

###  III.1 Reaction coordinates with N2O

The reaction coordinates involving oxidation of RuO2 by N2O are displayed in
Fig. III.1 for the formation of RuO3 and Fig. III.1 for the formation of RuO4.
The corresponding geometrical parameters and ZPE corrections are listed in
Tables 1, and 2, respectively.

Table 1:  Structural parameters (bond lengths $r$ in $\mathrm{\SIUnitSymbolAngstrom}$), imaginary vibrational frequency (${\mathrm{cm}}^{-1}$), and ZPE ($\mathrm{kJ~{}mol^{-1}}$), for the transition state and molecular complexes calculated at the TPSSh-5%HF/aVTZ level of theory, involved in the reaction RuO2 + N2O -> RuO3 +N2 Parameters | MCR(LABEL:eqru-n2a) | TS(LABEL:eqru-n2a) | MCP(LABEL:eqru-n2a)
---|---|---|---
$r(\ce{N-N})$ | 1.124 | 1.128 | 1.097
$r(\ce{N-O})$ | 1.222 | 1.351 |
$r(\ce{Ru-O_{N_{2}O}})$ | 2.126 | 1.934 |
$r(\ce{Ru-O})$ | 1.680 | 1.676 | 1.685
$r(\ce{Ru-N_{N_{2}}})$ |  |  | 4.527
$\theta(\ce{N-N-O})$ | 173.4 | 148.8 |
$\theta(\ce{O-Ru-O_{N_{2}O}})$ | 109.8 | 113.9 |
$\theta(\ce{O-Ru-O})$ | 140.5 | 133.9 | 120.0
$\nu_{im}$ |  | 590i |
ZPE | 43.94 | 49.96 | 36.20
Table 2: Structural parameters (bond lengths r in $\mathrm{\SIUnitSymbolAngstrom}$) imaginary vibrational frequency (${\mathrm{cm}}^{-1}$), and ZPE ($\mathrm{kJ~{}mol^{-1}}$), for the transition state and molecular complexes calculated at the TPSSh-5%HF/aVTZ level of theory, involved in the reaction RuO3 + N2O -> RuO4 +N2 Parameter | MCR(LABEL:eqru-n2b) | TS(LABEL:eqru-n2b) | MCP(LABEL:eqru-n2b)
---|---|---|---
$r(\ce{N-N})$ | 1.130 | 1.121 | 1.098
$r(\ce{N-O})$ | 1.187 | 1.262 |
$r(\ce{Ru-O_{N_{2}O}})$ | 4.986 | 2.103 |
$r(\ce{Ru-O})$ | 1\. 684 | 1.762-1.688 | 1.684
$r(\ce{Ru-N})$ |  |  | 4.020
$\theta(\ce{N-N-O})$ | 180 | 159.4 |
$\theta(\ce{O-Ru-O_{N_{2}O}})$ | 118.8 | 113.1-118.1 |
$\theta(\ce{O-Ru-O})$ | 120.0 | 108.1 | 109.3-109.5
$\nu_{im}$ |  | 572i |
ZPE | 50.73 | 49.96 | 48.62
Figure 1: Reaction coordinate at $0\text{\,}\mathrm{K}$ of the RuO2 + N2O ->
RuO3 + N2 reaction, including ZPE, calculated at the
CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory, displayed along with schematic
representations of the intermediate species involved. Figure 2: Reaction
coordinate at $0\text{\,}\mathrm{K}$ of the RuO3 + N2O -> RuO4 + N2 reaction,
including ZPE, calculated at the CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory,
displayed along with schematic representations of the intermediate species
involved.

The TS(LABEL:eqru-n2a) structure corresponding to the formation of RuO3
features a one-step mechanism with the breaking of the N-O bond, stretched up
to $1.351\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ from its equilibrium value
in N2O, to form the third Ru-O bond, equal to
$1.934\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. This bond length is typical of
ionic bonding, as observed between hydroxyl ligands and Ru oxides in our
previous work [12]. The value of the RuO2 bond angle decreases to favor a
pyramidal structure leading to the formation of RuO3.

In the TS(LABEL:eqru-n2b) structure leading to the formation of RuO4, the
elongation of N-O bond distance is only
$0.075\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, much closer to the equilibrium
reactant structure than in the previous TS. The bond angles and bond distances
shrink from their equilibrium values, to form the tetrahedral RuO4 structure.
This reaction involves the creation of the fourth Ru-O bond with a length of
$2.101\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, sharing fewer electrons
between Ru and O${}_{\ce{N2O}}$ atoms compared to its counterpart in the
previous TS. A bridge between O${}_{\ce{RuO3}}$ and N${}_{\ce{N2O}}$ is also
observed, measuring $2.258\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, indicating
that the formation of RuO4 originates from a large orbital mixing between the
reactants.

The connections between TS(LABEL:eqru-n2b) and both the RuO2…N2O reactant
complex (MCR(LABEL:eqru-n2a)) and RuO3…N2 product complex
(MCP(LABEL:eqru-n2a)) have been established in both forward and backward
directions via IRC calculations at the TPSSh-5%HF/aVTZ level of theory. The
ionic interaction ($2.126\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) between
$\ce{O_{N_{2}O}}$ and the Ru atom stabilizes the RuO2 and N2O reactants to
form the MCR(LABEL:eqru-n2a) complex. In reaction LABEL:eqru-n2b, the
structure of the MCR involves a very weak interaction of the Van der Waals
type ($4.986\text{\,}\mathrm{\SIUnitSymbolAngstrom}$), leaving the bond angles
and bond distances similar to those in RuO3 and N2O reactant species. Such
interactions are also observed in MCP systems for both reactions, where the
Ru-N bond length is equal to
$4.5274.020\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, for RuO3…N2 and RuO4…N2
complexes, respectively. The relative enthalpies at $0\text{\,}\mathrm{K}$ in
the reaction coordinate curve reveal that the reaction between N2O and RuO2
has to overcome a barrier of about
$14\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ to form the N2 and RuO3
products. The MCR(LABEL:eqru-n2a) is stabilized by $\sim$
$43\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ with respect to the
reactants. The MCP is similar to the products, and lies only
$0.6\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ below the product energy
limit.

For the reaction LABEL:eqru-n2b (See Fig. III.1), the transition state is
located above reactants with an important vibrationally adiabatic barrier of
about 113.9 $\mathrm{kJ~{}mol^{-1}}$ by comparison to the one found for
reaction 1a (13.9 $\mathrm{kJ~{}mol^{-1}}$).The pro- and post-reactive
complexes are similar to the reactants and products, respectively, differing
only by $\sim$ $4\text{\,}~{}$$\mathrm{kJ~{}mol^{-1}}$.

###  III.2 Reaction coordinates with NO2

We now turn to presenting the reaction coordinates corresponding to NO2
oxidation. The optimized geometry parameters for NO
($r(\ce{N-O})\sim$$1.154\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) and NO2
($r(\ce{N-O})\sim$$1.199\text{\,}\mathrm{\SIUnitSymbolAngstrom}$;
$\theta$(O-N-O)$\sim$$134.2\text{\,}\mathrm{\SIUnitSymbolDegree}$) are in good
agreement with their experimental counterparts
($r(\ce{N-O}$)$\sim$$1.514\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ for NO
[41]; r(N-O)$\sim$$1.193\text{\,}\mathrm{\SIUnitSymbolAngstrom}$;
$\theta$(O-N-O)$\sim$$134.1\text{\,}\mathrm{\SIUnitSymbolDegree}$ for NO2
[42]).

The structures of intermediate species involved in the formation of RuO3 in
reaction LABEL:eqru-noa and relative enthalpies at $0\text{\,}\mathrm{K}$ are
shown in Fig. 3. For the formation of RuO4, two reaction mechanisms, noted
paths 1 and 2, were explored and are illustrated in Fig. 4 and Fig. 5,
respectively. Path 1 showcases nitrogen oxide forming a bond with one of
ruthenium trioxide. Path 2 investigates Ru element forming a bond directly
with the oxygen of nitrogen oxide. The corresponding geometrical parameters
are reported in Tables 3, 4, and 5.

Table 3: Structural parameters (bond lengths $r$ in $\mathrm{\SIUnitSymbolAngstrom}$ ) imaginary vibrational frequency (${\mathrm{cm}}^{-1}$), and ZPE ($\mathrm{kJ~{}mol^{-1}}$), for the transition state and molecular complexes calculated at the TPSSh-5%HF/aVTZ level of theory, involved in the reaction RuO2 + NO2 -> RuO3 +NO Parameters | MCR(LABEL:eqru-noa) | TS(LABEL:eqru-noa) | MCP(LABEL:eqru-noa)
---|---|---|---
$r(\ce{N-O})$ | 1.191 | 1.175 | 1.145
$r(\ce{Ru-O_{NO_{2}}})$ | 1.316 | $1.8661.988$ |
$r(\ce{Ru-O_{NO}})$ |  |  | 1.693
$r(\ce{Ru-O})$ | 1.648 | 1.661 | $1.6731.847$
$\theta(\ce{O-N-O})$ | 124.8 | 124.7 | 110.8
$\theta(\ce{O-Ru-O_{NO_{2}}})$ | 93.0 | 72.9 |
$\theta(\ce{O-Ru-O_{NO}})$ |  |  | 114.8
$\theta(\ce{O-Ru-O})$ |  | 139.7 | 128.8
$\nu_{im}$ |  | 477i |
ZPE | 46.8 | 39.8 | 38.2
Table 4: Structural parameters (bond lengths $r$ in $\mathrm{\SIUnitSymbolAngstrom}$), imaginary vibrational frequency (${\mathrm{cm}}^{-1}$), and ZPE ($\mathrm{kJ~{}mol^{-1}}$), for the transition state and molecular complexes calculated at the TPSSh-5%HF/aVTZ level of theory, involved in path 1 for the reaction RuO3 + NO2 -> RuO4 +NO Parameters | MCR(LABEL:eqru-nob-P1) | TS1(LABEL:eqru-nob-P1) |  RuO2NO3 | TS2(LABEL:eqru-nob-P1) | MCP(LABEL:eqru-nob-P1)
---|---|---|---|---|---
$r(\ce{N-O})$ | $1.1971.200$ | $1.1841.188$ | 1.184 | 1.183 | 1.125
$r(\ce{Ru-O_{NO_{2}}})$ | 4.008 | 3.523 | 2.109 | 1.910 |
$r(\ce{Ru-O})$ | 1.687 | 1.686 -1.727 | 1.689 | 1.693 | $1.6941.735$
$r(\ce{N-O_{RuO_{3}}})$ | 2.893 | 2.13 | 1.134 | $1.4021.483$ |
$r(\ce{N-O_{RuO_{4}}})$ |  |  |  |  | 2.198
$\theta(\ce{O-N-O})$ | 134.7 | 137.6 | 124.2 | 125.3 |
$\theta(\ce{O-Ru-O_{NO_{2}}})$ | 104.0 | 103.8 | 62.3 | 70.9 |
$\theta(\ce{O_{RuO_{4}}-N-O_{RuO_{4}}})$ |  |  |  |  | 71.7
$\theta(\ce{O-Ru-O})$ | $119.8120.3$ | $117.9123.4$ | $102.6124.8$ | $109.7120.9$ | $95.7115.7$
$\nu_{im}$ |  | 150i |  | 662i |
ZPE | 44.6 | 47.2 | 54.2 | 48.0 |
Table 5: Structural parameters (bond lengths r are $\mathrm{\SIUnitSymbolAngstrom}$) imaginary vibrational frequency (${\mathrm{cm}}^{-1}$), and ZPE ($\mathrm{kJ~{}mol^{-1}}$), for the transition states and molecular complexes calculated at the TPSSh-5%HF/aVTZ level of theory, involved in path 2 for the reaction RuO3 + NO2 -> RuO4 +NO Parameters | MCR(LABEL:eqru-nob-P2) | TS1(LABEL:eqru-nob-P2) |  RuO3NO2 | TS2(LABEL:eqru-nob-P2) | MCP(LABEL:eqru-nob-P2)
---|---|---|---|---|---
$r(\ce{N-O})$ | 1.178-1.421 | 1.204-1.313 | 1.133 | 1.126 | 1.137
$r(\ce{Ru-O_{NO_{2}}})$ | 1.931 | 2.028 | 1.843 |  |
$r(\ce{O_{RuO_{4}}-N_{NO}})$ |  |  | 1.668 | 1.796 | 2.358
$r(\ce{Ru-O})$ | 1.688-1.725 | 1.685-1.723 | 1.692-1.733 | 1.693-1.728 | 1.696-1.711
$\theta(\ce{O-N-O})$ | 114.8 | 114.5 | 115.0 |  |
$\theta(\ce{O-Ru-O_{NO_{2}}})$ | 109.3 | 115.9 | 100.6 |  |
$\theta(\ce{Ru-O-N_{NO}})$ |  |  | 123.9 | 119.7 | 114.9
$\theta(\ce{O-Ru-O})$ | 109.7-121.5 | 108.9-120.9 | 108.0-120.1 | 107.7-116.7 | 106.7-110.7
$\nu_{im}$ |  | 209i |  | 229i |
ZPE | 47.1 | 47.5 | 47.4 | 45.6 | 46.2
Figure 3: Reaction coordinate at $0\text{\,}\mathrm{K}$ calculated at the
CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory for reaction RuO2 + NO2 -> RuO3 +
NO with schematic representations of the intermediate species involved. Figure
4: Reaction coordinate at $0\text{\,}\mathrm{K}$ calculated at the
CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory for path 1 in reaction RuO3 + NO2
-> RuO4 + NO, with schematic representations of the intermediate species
involved. Figure 5: Reaction coordinate at $0\text{\,}\mathrm{K}$ calculated
at the CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory for path 2 in reaction
RuO3 + NO2 -> RuO4 + NO, with schematic representations of the intermediate
species involved.

The investigation of reaction LABEL:eqru-noa pathway was conducted by
approaching NO2 species to RuO2 oxide. The most stable potential energy led to
an MCR(LABEL:eqru-noa) complex adopting a ring-like structure in which RuO2
and NO2 interact through two symmetric covalent bonds
($1.316\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) between
$\ce{O_{RuO_{2}}-N_{NO_{2}}}$, and $\ce{Ru-O_{NO_{2}}}$, forming a terminal
nitrate bidentate like structure. However, the N-O bond distance,
$1.191\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ remains similar to its
counterparts in nitrogen dioxide
($1.199\text{\,}\mathrm{\SIUnitSymbolAngstrom}$). Such observation is
consistent with our previous work [11] which underlined competitive effects
between an increase of oxide bond lengths and increase of oxide charges (in
this case on O atom) which kept the oxide bonds similar. In addition, the
analysis of spin density of MCR(LABEL:eqru-noa) (Fig. LABEL:fig:spin_3_mcr of
the ESI) compound shows that the spin density of NO2 is transferred to Ru
oxide, acknowledging a chemisorbed like structure, consistent within Lee et
al. work [43], who observed chemisorbed-like structures for group IV (MO2)_n,
M=Ti, Zr, Hf dioxides nanoclusters from DFT and CCSD(T) calculations. The bond
angle $\theta$(O-N-O) decreases by ca.
$9\text{\,}\mathrm{\SIUnitSymbolDegree}$. These results suggest that the RuO2
electrons are the ones mostly involved in these two symmetric bonds in this
complex; this is confirmed by the fact that the Ru-O bond lengths are shorter,
$1.648\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, and the $\theta(\ce{O-Ru-O})$
bond angle is more acute, $140.2\text{\,}\mathrm{\SIUnitSymbolDegree}$, than
in the RuO2 molecule.

The MCP associated with the formation of RuO3 presents a Ru-O bond lengths
lying between $1.6921.847\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, and a
$\theta$(O-Ru-O) bond angle of $128.8\text{\,}\mathrm{\SIUnitSymbolDegree}$,
slightly larger than those found in RuO3 product. On the contrary, the N-O
bond length $0.368\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ shorter than the NO
equilibrium distance. These geometrical changes are induced by the highly
covalent bond between $\ce{O_{RuO_{3}}}$ and N atoms with a length of
$1.693\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, that stabilizes RuO3 and NO
within MCP species. The analysis of the spin density reflected a chemisorbed
like structure (Fig.LABEL:fig:spin_3_mcp of the ESI), within a monodentate NO2
terminal, similar to the formed (MO2)NO2 chemisorbed species in Lee et al.’s
work [43].

The TS(LABEL:eqru-noa) connecting the MCR and MCP was found with an imaginary
frequency of 477i ${\mathrm{cm}}^{-1}$, within a terminal nitrate bidentate
like structure. The pro and post-reactants are found energetically more stable
than the associated reactants and products, as shown in Fig. 3: the MCR
complex lies $\sim$ $48\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ below
the reactants, while the MCP one is $\sim$
$17\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ below the products. This
confirms that the identified TS(LABEL:eqru-noa) is the transient species
leading to the formation of RuO3 and NO species from the reaction between RuO2
and NO2 compounds. However, the TS barrier is larger by about
$20\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ than the one in reaction
LABEL:eqru-n2a, with N2O species. This implies that this reaction will be
energetically less favorable at $0\text{\,}\mathrm{K}$. This finding is
comforted by $\ce{(N-O)_{N_{2}O}}$ and $\ce{(N-O)_{NO_{2}}}$ binding energies
of $-167.63-306.3\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$,
respectively, obtained using $\Delta_{r}E(0~{}K)$ of NO2= NO + O and N2O = N2
+ O, respectively, computed from the NIST standard values [41].

For the formation of RuO4 in reaction LABEL:eqru-nob, the two reactions paths
explored both involve two-step mechanisms. In the reaction path 1, the
connection of MCR(LABEL:eqru-nob-P1) to intermediate RuO2NO3 species by
TS1(LABEL:eqru-nob-P1) corresponds to the formation of a ring-like structure
between N, O_NO2, Ru, and O_RuO3 atoms. The molecular complex RuO2NO3, which
involves a nitrogen trioxide combined with a ruthenium dioxide, reveals
geometric parameters for N-O bond length
($1.198\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) and O-N-O bond angle
($132.2\text{\,}\mathrm{\SIUnitSymbolDegree}$), smaller than their
counterparts in NO3 ($1.238\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$120\text{\,}\mathrm{\SIUnitSymbolDegree}$, respectively [42]), and closer to
those featured in NO2. The analysis of the MCR(LABEL:eqru-nob-P1) spin density
reveals a physisorbed-like structure (See Fig.LABEL:fig:spin_4_p1_mcr of the
ESI), with the spin density localized on NO2, unlike the intermediate species
RuO2NO3 (See Fig LABEL:fig:spin_4_p1_interm of the ESI) in which the NO2
transfers its spin density to the Ru-oxide and binds to it in a monodentate
fashion. A similar result was found for adsorbed NO2 species onto MO3 trioxide
clusters, with M=Cr and Mo [43]. Although the MCP(LABEL:eqru-nob-P1) portrayed
a physisorbed like structure, within a terminal monodentate NO2 structure
(Fig.LABEL:fig:spin_4_p2_mcp), and a spin density localized onto the Ru metal
oxide.

In reaction path 2, the TS1(LABEL:eqru-nob-P2) ensures the bonding between
O_NO2 and the Ru metallic center of RuO3, to form the intermediate species
RuO3NO2. The latter complex exhibits Ru-O and N-O bond lengths slightly longer
to those computed in RuO3 and NO2. In MCR(LABEL:eqru-nob-P2), the spin density
(See Fig. LABEL:fig:spin_4_p2_mcr of the ESI) is localized on the Ru-O unit,
differing from the physisorbed molecular reactant species of path-1. This
chemisorbed character could explain that this reactive molecular complex
species lies $58.5\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ below the
reactant fragments, as well as the TS1(LABEL:eqru-nob-P2) barrier, which is
the highest barrier in reaction path 2, but above the MCR(LABEL:eqru-nob-P2)
by $19.3\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$. This transition
state leads to the formation of the intermediate chemisorbed species RuO3NO2
(Fig.LABEL:fig:spin_4_p2_interm), within a terminal monodentate NO2 structure,
slightly higher in energy than the MCR(LABEL:eqru-nob-P2).

For the second step of the reaction mechanism, the breaking of the symmetric
bonds between O_RuO3-N, and Ru-O_NO2, the shrinkage of Ru-O bonds, and finally
the elongation of Ru-N bond distance, is ensured by TS2(LABEL:eqru-nob-P2), to
form the RuO4…NO product complex. This MCP species portrayed a physisorbed
like shape, as the spin density is localized on NO2 (See Fig.
LABEL:fig:spin_4_p2_mcp of the ESI). In addition, the MCP(LABEL:eqru-nob-P2)
species has $\theta$(O-Ru-O
)($\sim$$108.7\text{\,}\mathrm{\SIUnitSymbolDegree}$) and
$r(\ce{Ru-O})$($\sim$$1.702\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) values
close to those of the RuO4 product. This MCP is geometrically different from
the one identified for the path 1 (MCP(LABEL:eqru-nob-P1)), which had larger
$\theta$(O-Ru-O)($\sim$$105.7\text{\,}\mathrm{\SIUnitSymbolDegree}$) and
r(Ru-O)($\sim$$1.714\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) values. These
geometrical characteristics are corroborated by the computed relative energies
at $0\text{\,}\mathrm{K}$ of the MCPs, that lie
$377.1\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ above the products for
MCP(LABEL:eqru-nob-P1) and MCP(LABEL:eqru-nob-P2), respectively. It should be
noticed that the MCP(LABEL:eqru-nob-P2) relative energy of -72.4
$\mathrm{kJ~{}mol^{-1}}$ is in the range of calculated adsorption enthalpies
from Lee et al.’s work [43] for group VI metal trioxide nanoclusters (from
-206.8 $\mathrm{kJ~{}mol^{-1}}$ ((CriO3)NO2, terminal bidentate nitrate like
structure) to -70.3 $\mathrm{kJ~{}mol^{-1}}$((CriO3)NO2, terminal bidentate
NO2 like structure), comforting the appropriateness of proposed reaction
pathway. In addition, the highest TS2(LABEL:eqru-nob-P1) barrier has a
relative energy with respect to the reactants equal to
$48.1\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$, twice as small as
those determined in reaction (LABEL:eqru-n2b).

In conclusion, the reaction (LABEL:eqru-nob) path 2 is the most energetically
favorable one to form RuO4, in contrast to the thermodynamic calculations of
the reaction Gibbs free energies [13], which suggested that the reaction with
nitrous oxide should be more spontaneous than the one with nitrogen oxide. The
kinetic parameters of these reaction pathways are investigated in following
section.

###  III.3 Kinetic Parameters

The calculations of the temperature dependence of the rate constants have been
performed at the CCSD(T)/CBS//TPSSh-5%HF/aVTZ for the reactions with N2O and
NO2, whose values are reported in Table 6. For the formation of RuO4 by NO2
oxidation of RuO3, we considered that the formation of the molecular complex
reactant will be the most limiting step, especially with increasing
temperature. However, in our temperature range of interest it is likely that
the MCR will be formed thus we approximate RuO4 as a fast reaction. The rate
constants for N2O and NO2 oxidation processes were fitted with the Arrhenius
equation:

$\displaystyle k(T)=B\times T^{n}\exp(-E_{a}/RT),$ (58)

where $R$ is the gas constant and $T$ is the temperature. The Arrhenius
parameters are the activation energy $E_{a}$, the pre-exponential factor, $B$,
and unit less $n$. The Arrhenius parameters adjusted to eq. 58 are given in
Table 7.

Table 6: Rate constants in
${\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$,
calculated at the CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory.

Reactions | Temperature ($\mathrm{K}$)
---|---
| 250 | 300 | 400 | 600 | 800 | 1000 | 1300 | 1500
Formation of RuO3 |  |  |  |  |  |  |  |
RuO2 + N2O -> RuO3 + N2 | $3.50\text{\times}{10}^{-16}$ | $1.08\text{\times}{10}^{-15}$ | $5.30\text{\times}{10}^{-15}$ | $3.75\text{\times}{10}^{-14}$ | $1.29\text{\times}{10}^{-13}$ | $3.12\text{\times}{10}^{-13}$ | $8.28\text{\times}{10}^{-13}$ | $1.37\text{\times}{10}^{-12}$
RuO2 + NO2 -> RuO3 + NO | $2.22\text{\times}{10}^{-22}$ | $3.53\text{\times}{10}^{-21}$ | $6.20\text{\times}{10}^{-20}$ | $6.79\text{\times}{10}^{-18}$ | $6.40\text{\times}{10}^{-17}$ | $2.88\text{\times}{10}^{-16}$ | $1.38\text{\times}{10}^{-15}$ | $3.00\text{\times}{10}^{-15}$
Formation of RuO4 |  |  |  |  |  |  |  |
RuO3 + N2O -> RuO4 + N2 | $1.07\text{\times}{10}^{-37}$ | $8.86\text{\times}{10}^{-34}$ | $8.16\text{\times}{10}^{-29}$ | $1.05\text{\times}{10}^{-23}$ | $4.77\text{\times}{10}^{-21}$ | $2.16\text{\times}{10}^{-19}$ | $8.48\text{\times}{10}^{-18}$ | $4.65\text{\times}{10}^{-17}$

The computed rate constants related to the formation of RuO3 through the
oxidation of RuO2 by N2O, range from $1\text{\times}{10}^{-16}$ at
$250\text{\,}\mathrm{K}$ to
$1\text{\times}{10}^{-12}\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$
at $1500\text{\,}\mathrm{K}$. The oxidation of RuO2 by NO2 shows a similar
temperature behavior, with values varying from $1\text{\times}{10}^{-22}$ to
$1\text{\times}{10}^{-15}\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$.
These two sets of results indicated that the mechanism involving the nitrogen
dioxide is slightly slower than the one with the nitrous oxide, confirming the
reactions coordinates curves depicted in Fig. 3, reflecting the fact that the
TS barrier is larger by
$\sim$$20\text{\,}\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$ in reaction
LABEL:eqru-noa than in reaction LABEL:eqru-n2a.

Table 7: Arrhenius parameters calculated over the temperature range $2502500\text{\,}\mathrm{K}$ from energy profiles calculated at the CCSD(T)/CBS//TPSSh-5%HF/aVTZ level of theory. | B | $n$ | $E_{a}$ | $k($298\text{\,}\mathrm{K}$)$
---|---|---|---|---
| (${\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$) |  | ($\mathrm{kJ}\text{\,}{\mathrm{mol}}^{-1}$) | (${\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$)
Formation of RuO3
RuO2 + N2O -> RuO3 + N2 | $2.21\text{\times}{10}^{-21}$ | $2.85$ | $8.0$ | $9.79\text{\times}{10}^{-16}$
RuO2 + NO2 -> RuO3 + NO | $4.01\text{\times}{10}^{-24}$ | $3.09$ | $27.1$ | $3.22\text{\times}{10}^{-21}$
Formation of RuO4
RuO3 + N2O -> RuO4 + N2 | $5.23\text{\times}{10}^{-22}$ | $2.72$ | $106.4$ | $6.14\text{\times}{10}^{-34}$

The reaction process involving the oxidation of RuO3 by N2O (reaction
LABEL:eqru-n2b) appears quite slow at our temperature scale, with rate
constant values varying from $1\text{\times}{10}^{-37}$ at
$250\text{\,}\mathrm{K}$ to
$1\text{\times}{10}^{-17}\text{\,}{\mathrm{cm}}^{3}\text{\,}{\mathrm{molecule}}^{-1}\text{\,}{\mathrm{s}}^{-1}$
at $1500\text{\,}\mathrm{K}$. These values are consistent with the TS barrier
displayed in Fig. III.1, and emphasizing the fact that the reaction
LABEL:eqru-nob involving nitrous oxide, path 2, is the more likely pathway to
form RuO4, the kinetically limiting step might only reside from the MCR
complex to overcome the TS1 barrier, as the MCR complex lies energetically
below the reactants at 0K.

###  III.4 Theoretical Results Compared to Experimental Tests

We can now discuss our theoretical results in the light of experimental data.
In the framework of the VTT program [44, 17], previously described in the
introduction, the ruthenium transport under humid atmospheres, and humid
atmospheres with air radiolysis products precursors, with different
temperature gradients was studied. Table 1 summarizes the results reported in
Kajan’s thesis [17].

Table 8: Measurement of transported Ru fraction in function of carrier gas and
temperature in VTT tests [17]. The model primary circuit is made of either
stainless steel tube or alumina tube samples. The temperature gradients range
from $130015001700\text{\,}\mathrm{K}$ down to ca. $300\text{\,}\mathrm{K}$
11footnotemark: 1

measured for $T$ = $1570\text{\,}\mathrm{K}$

With an atmosphere containing 50 ppmV of NO2, the transport of ruthenium
tetroxide increased by 92% at $1300\text{\,}\mathrm{K}$ and 42% at
$1500\text{\,}\mathrm{K}$, by comparison to humid air atmospheres. The
increase of RuO4 fractions was attributed to the reaction between NO2 and
RuO3, as expressed:

$\ce{RuO3+NO2->RuO4+NO}.$ (87)

The equilibrium constants Keq calculated by Kajan et al. [17] were derived
using HSC 5.11 chemistry software [45], equal to $28.5516.8511.3$ at
$130015001700\text{\,}\mathrm{K}$, respectively.

Our equilibrium constants obtained from the kinetic reactions rate constants
calculations appeared in good agreement with the ones derived from Kajan
work’s, though they come out slightly lower, $23.649.374.66$ at
$130015001700\text{\,}\mathrm{K}$, respectively. These differences could be
explained by the small deviations at higher temperatures of our derived
thermodynamic properties for Ru oxides, as discussed in our previous work
[12]. The decreasing amount of detected gaseous fraction of Ru as temperature
increases can be attributed to the decomposition of NO2 with temperature [46,
47]. This is fully supported by the free-energy calculations obtained for the
formation of RuO4 through nitrogen oxidation that shows higher values when
temperature increases. At this stage, it is not clear how the decrease of
aerosol formation is linked to the reaction of nitrogen oxide to form RuO4.
Such aspects are investigated through the study of the nucleation process of
Ru dimer in a parallel work [48].

With an atmosphere containing 50 ppmV of N2O, the experimental tests showcased
a similar production of RuO4 gaseous fraction in comparison to pure humid air
atmosphere, along with a slight increase as the temperatures rise. These
observations are also consistent with our quantum chemical data, as the
reaction barrier in the oxidation process of RuO3 by N2O to form RuO4 is
large.

Altogether, this discussion leads us to conclude that the calculated kinetic
rates for the formation of RuO4 in air radiolysis products atmospheres are
fully consistent with experimental observations, even if some other phenomena
can play a role like surface interactions.

##  IV Conclusions

The mechanisms and kinetics of the chemical reactions leading to the formation
of RuO3 and RuO4 gaseous species under severe accident (SA) conditions of a
nuclear power plant (NPP) were elucidated by state-of-the art quantum chemical
approaches. An in-depth investigation of the reaction pathways involving two
air radiolysis products N2O and NO2 to form RuO4 and RuO3, following
experimental observations, was conducted. The coupled-cluster theory was then
employed to compute the potential energies. The transition states obtained for
the formation of RuO4 from NO2 oxidation appeared energetically lower than the
reactants.

The derivation of the related kinetic rates to form RuO4 through the nitroxide
species revealed that nitrogen oxide process is a faster mechanism than the
one involving nitrous oxide, thus contrasting the thermodynamic predictions.
These results are consistent with the experimental observations and
measurements acquired by the VTT program, which concluded to an increase of
transported Ru gaseous fraction in humid atmospheres with air radiolysis
precursors.

## Acknowledgements

The computer time for part of the theoretical calculations was kindly provided
by the Centre Régional Informatique et d’Applications Numériques de Normandie
(CRIANN) of the University of Lille, and the HPC resources from GENCI-cines
(grant 2015-project number x2015086731). This work has been supported by the
French government through the Program "Investissement d’avenir" (LABEX CaPPA /
ANR-11-LABX-0005-01 and I-SITE ULNE / ANR-16-IDEX-0004 ULNE), as well as by
the Ministry of Higher Education and Research, Hauts de France council and
European Regional Development Fund (ERDF) through the Contrat de Projets État-
Région (CPER CLIMIBIO). The authors declare no competing financial interest.

## Author contributions

Dr. Faoulat Miradji: conceptualization, methodology, quantum chemical
calculations, kinetics calculations, data analysis, data validation, writing
(original draft), writing (review & editing), visualization. Dr. Sidi M. O.
Souvi: conceptualization, methodology, data analysis, data validation, writing
(review & editing). Dr. Laurent Cantrel: conceptualization, methodology, data
analysis, data validation writing (review & editing). Dr. Florent Louis:
conceptualization, methodology, data analysis, data validation, writing
(review & editing). Dr. Valérie Vallet: conceptualization, methodology,
quantum chemical calculations, data analysis, data validation, writing
(original draft), writing (review & editing).

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of supplemental-kinNOX.pdf See pages 7, of supplemental-kinNOX.pdf


# SEMv2: Table Separation Line Detection Based on Conditional Convolution

Zhenrong Zhang111Work done during an internship at iFLYTEK AI
Research.$~{}^{1,2}$, Pengfei Hu$~{}^{1}$, Jiefeng Ma$~{}^{1}$, Jun
Du222Correspondence Author. 1,
Jianshu Zhang2, Huihui Zhu2, Baocai Yin2, Bing Yin2, Cong Liu2
1 University of Science and Technology of China
2 iFLYTEK AI Research

###### Abstract

Table structure recognition is an indispensable element for enabling machines
to comprehend tables. Its primary purpose is to identify the internal
structure of a table. Nevertheless, due to the complexity and diversity of
their structure and style, it is highly challenging to parse the tabular data
into a structured format that machines can comprehend. In this work, we adhere
to the principle of the split-and-merge based methods and propose an accurate
table structure recognizer, termed SEMv2 (SEM: Split, Embed and Merge). Unlike
the previous works in the “split” stage, we aim to address the table
separation line instance-level discrimination problem and introduce a table
separation line detection strategy based on conditional convolution.
Specifically, we design the “split” in a top-down manner that detects the
table separation line instance first and then dynamically predicts the table
separation line mask for each instance. The final table separation line shape
can be accurately obtained by processing the table separation line mask in a
row-wise/column-wise manner. To comprehensively evaluate the SEMv2, we also
present a more challenging dataset for table structure recognition, dubbed
iFLYTAB, which encompasses multiple style tables in various scenarios such as
photos, scanned documents, etc. Extensive experiments on publicly available
datasets (e.g. SciTSR, PubTabNet and iFLYTAB) demonstrate the efficacy of our
proposed approach. The code and iFLYTAB dataset will be made publicly
available upon acceptance of this paper.

##  1 Introduction

Figure 1: Some table samples in the iFLYTAB dataset. (a)-(b) are wired tables.
(c)-(e) are wireless tables.

In this era of knowledge and information, document is a significant source of
information for numerous cognitive processes such as knowledge database
creation, optical character recognition (OCR), document retrieval, etc. As a
particular entity, the tabular structure is very commonly encountered in
documents. These tabular structures convey important information in a concise
form. They are highly prevalent in domains such as finance, administration,
research, and even archival documents. Table structure recognition (TSR) aims
to recognize the table internal structure to the machine readable data mainly
presented in two formats: logical structure and physical structure [33]. More
precisely, logical structure only contains every cell’s row and column
spanning information, while the physical one additionally contains bounding
box coordinates of cells. Therefore, TSR as a precursor to contextual table
understanding will be beneficial in a wide range of applications [27, 26].

Limited by the training datasets [7, 2, 37, 36] used for TSR, most previous
works [28, 24, 35, 26] focus on document images that are obtained from digital
documents (e.g., PDF files). In such a scenario, the table images are cropped
under optimal imaging conditions and are often horizontally (or vertically)
aligned with a clean background and distinct table structures. However, in
some real-world applications, document images may be captured by mobile
cameras. Many camera-captured document images are of poor image quality, and
tables contained in them may be distorted (even curved) or contain noises,
which makes TSR even more challenging. Although the WTW dataset proposed
recently [17] contains table images from natural scenes, it only focuses on
wired tables. Parsing wireless tables is a relatively more difficult task due
to the lack of visual cues to delimit cells, columns and rows. To
comprehensively evaluate the performance of TSR, we present a large-scale
dataset in this paper, dubbed iFLYTAB. As shown in Figure 1, the table images
in the iFLYTAB dataset are collected from various scenarios, and contain both
wired and wireless tables.

Considering that a table is composed of a set of table cells and each table
cell is composed of one or more basic table grids, the recently proposed
split-and-merge based methods [28, 35, 20] consider table grids as the
fundamental processing units. These methods recognize the table structure as
the following pipeline: 1) split table into basic table grid pattern 2) merge
grid elements to recover table cells that span multiple rows or columns. When
the TSR is performed in this way, once the “split” stage predicts erroneous
results, it is difficult for the “merge” stage to rectify them. Therefore, it
is essential to make the model detect table grids more accurately. The
previous methods [28, 35, 20] complete the first stage in a bottom-up manner.
Specifically, they first apply semantic segmentation [16] to predict table
row/column separation lines, and then represent the intersection of detected
row/column separation lines as table grids. However, segmenting table
row/column separation lines in a pixel-wise manner is imprecise due to the
limited receptive field. In addition, it necessitates complex mask-to-line
algorithms to extract the table separation lines from the predicted
segmentation results.

In this work, we follow the split-and-merge based method SEM [35], and
introduce an accurate table structure recognizer, termed SEMv2. Distinct from
previous segmentation-based methods [35, 26, 28, 20] in the “split” stage, we
aim to distinguish each table separation line and formulate table separation
line detection as an instance segmentation task. Specifically, the table
separation line mask generation is decoupled into a mask kernel prediction and
a mask feature learning, which are responsible for generating convolution
kernels and the feature maps to be convolved with respectively. Accurate table
row/column separation lines can be easily obtained by processing table
row/column separation line masks in a column-wise/row-wise manner. Moreover,
compared to the sequence decoder in the “merge” stage in [35], we propose a
parallel decoder based on conditional convolution to process the merging of
basic table grids, which increases the decoding speed. To comprehensively
evaluate the SEMv2, we also introduce a new large-scale TSR dataset iFLYTAB,
which contains multiple style tables in several scenes like photos, scanned
documents, etc.

The main contributions of this paper are as follows:

  * •

Following the split-and-merge based methods, we propose the SEMv2, which
introduces a novel instance segmentation framework for the table separation
line detection in the “split” stage, making the “split” more robust in various
scenes.

  * •

We release the iFLYTAB dataset, which is collected from various scenarios and
manually annotated carefully, to the community for advancing related research.

  * •

Based on our proposed method, we achieve state-of-the-art performance on
publicly available datasets SciTSR, PubTabNet and iFLYTAB.

##  2 Related Work

###  2.1 Existing Datasets

The first dataset for addressing TSR is ICDAR-2013 [7], but its data size is
limited (96 tables for training and 156 tables for testing). To meet the
requirement of data-driven approaches for TSR, large-scale datasets such as
TableBank [11] and PubTabNet [37] are proposed, but incomplete annotations
still impede their development. Recently, FinTabNet [36] and SciTSR [2] add
the cell coordinates and row-column information to become relatively
comprehensive datasets for TSR. Although dataset scale has been significantly
increased, these datasets solely focus on digital documents (e.g., PDF files).
Recently, a new dataset WTW [17], which contains tables in multiple real
scenes, is introduced. However, it only focuses on wired tables, ignoring the
more challenging wireless ones. To comprehensively evaluate the TSR
performance, we present a new large-scale dataset iFLYTAB. Different from WTW,
tables in iFLYTAB encompass both wired and wireless tables in various
scenarios.

###  2.2 Table Structure Recognition

Due to the rapid development of deep learning in documents, many deep
learning-based TSR approaches [37, 3, 35, 25] have been presented. These
methods can be roughly divided into three categories: bottom-up methods,
image-to-markup based methods and split-and-merge based methods.

One group of bottom-up methods [3, 23, 32] treat words or cell contents as
nodes in a graph and use graph neural networks to predict whether each sampled
node pair is in the same cell, row, or column. These methods rely on an
assumption that the bounding boxes of words or cell contents are available as
additional inputs, which are not easy to obtain from table images directly. To
eliminate this assumption, another group of methods [25, 24] proposed to
detect the bounding boxes of table cells directly. After cell detection, they
designed some rules to cluster cells into rows and columns. However, these
methods fail to handle distorted tables and tables containing a large number
of empty cells.

The image-to-markup based methods [37, 6, 21] treat table structure
recognition as a task similar to image-to-markup generation and directly
generate the markup tags that define the structure of the table through an
attention-based structure decoder. These methods rely on a large amount of
training data and are inefficient as the number of table cells increases.

The split-and-merge based methods [28, 35, 20] first split a table into the
basic table grid pattern, and then merge grid elements to recover table cells.
Previous methods utilize semantic segmentation [16] for identifying rows,
columns within tables in the “split” stage. However, segmenting table
row/column separation lines in a pixel-wise manner is inaccurate due to the
limited receptive field. In our work, we formulate the table separation line
detection as the instance segmentation task.

###  2.3 Instance Segmentation

Instance segmentation is a challenging task, as it necessitates instance-level
and pixel-level predictions simultaneously. The dominant framework for
instance segmentation is Mask R-CNN [8], which first detects the bounding
boxes of objects and then segments the object in the box. Many works [15, 1,
10] with top performance are built on Mask R-CNN. Due to the slender shape of
table separation lines, this widely utilized box-anchor based instance
segmentation methods cannot be employed directly. Another approach to instance
segmentation is based on dynamic filter network [4]. For example, SOLOv2 [31]
and CondInst [29] learn instance-dependent convolutional kernels, which are
applied to generate instance masks. Inspired by CondInst, we aim to resolve
the table row/column instance-level discrimination problem, and propose the
conditional table separation line detection strategy.

##  3 iFLYTAB

iFLYTAB collects table images of various styles from different scenarios.
Specifically, as shown in Figure 2, we collect both wired and wireless tables
from digital documents, and camera-captured photos. As shown in Table 1, the
table images of existing datasets (e.g. SciTSR, PubTabNet, etc.) are mainly
derived from digital PDF files. However, iFLYTAB includes table images
captured by cameras, which contain complex image backgrounds and non-rigid
image deformation. Although WTW provides table images in the photographic
scenario, it ignores the more challenging wireless tables. In terms of data
labeling, we provide full annotation for each table image including physical
coordinates and row/column information. We randomly select approximately 70%
of the table images as the training set, and the rest data samples are used
for testing. Finally, our iFLYTAB dataset has 12,104 training samples and
5,187 testing ones. Please refer to the Appendix for more details about the
proposed dataset.

Figure 2: Statistics of the iFLYTAB datasets. Table 1: Comparsion with other existing datasets. Dataset | Digital | Camera-captured
---|---|---
Wired | Wireless | Wired | Wireless
ICDAR-2013 [7] | ✓ | ✓ | ✗ | ✗
SciTSR [2] | ✓ | ✓ | ✗ | ✗
PubTabNet [37] | ✓ | ✓ | ✗ | ✗
WTW [18] | ✓ | ✗ | ✓ | ✗
iFLYTAB | ✓ | ✓ | ✓ | ✓

Figure 3: The overall architecture of SEMv2. $\boldsymbol{F}$ is the feature
map generated by fusing the FPN feature maps ($P$2 to $P$5). The Splitter
module consists of Kernel Branch and Feature Branch, and predicts table
separation lines between different columns or rows, which can be further
processed to obtain the Table Grid Structure. The Merger module predicts the
table cell to which each table grid belongs. We omit the Embedder module for
simplicity.

##  4 Method

The schematic of our approach is depicted in Figure 3. SEMv2 adheres to the
split-and-merge based methodology of its predecessor, SEM, and is primarily
comprised of three components: the splitter, the embedder, and the merger. The
splitter takes the table image as input and predicts the fine grid structure
of the table. The embedder extracts the grid-level feature representation of
each basic table grid. The merger predicts which grids should be merged to
recover the whole table structure. Subsequently, we will elucidate each
component.

###  4.1 Splitter

Given an input table image $\boldsymbol{I}\in\mathbb{R}^{H\times W\times 3}$,
as illustrated in Figure 3, the objective of the splitter is to predict the
table grid structure with a set of grid bounding boxes
$\boldsymbol{B}\in\mathbb{R}^{M\times N\times 4}$, where $M$, $N$ are the
number of rows and columns occupied by the table grid structure respectively.
Previous split-and-merge based methods apply the semantic segmentation to
predict all table row/column separation lines in one mask and subsequently
represent the intersection of detected row/column separation lines as grid
bounding boxes $\boldsymbol{B}$. In contrast to prior methods, we formulate
table separation line detection as an instance segmentation task and endeavor
to predict an individual mask for each table row/column separation line.

The overall architecture of our splitter is depicted in Figure 3. The
ResNet-34 [9] with FPN [13] is utilized to generate a feature pyramid with
four feature maps
$\\{\boldsymbol{P}_{2},\boldsymbol{P}_{3},\boldsymbol{P}_{4},\boldsymbol{P}_{5}\\}$,
whose scales are 1/4, 1/8, 1/16, 1/32 respectively. To amalgamate the
information from all levels of the FPN pyramid into a single output
$\boldsymbol{F}$, we also propose a straightforward fuse operation as follows:

$\displaystyle\boldsymbol{F}=\boldsymbol{P}_{2}+\text{Up}_{1\times}\left(\boldsymbol{P}_{3}\right)+\text{Up}_{2\times}\left(\boldsymbol{P}_{4}\right)+\text{Up}_{3\times}\left(\boldsymbol{P}_{5}\right)$
(1)

where $\text{Up}_{\text{n}\times}$ denotes the n times bilinear upsample
operation. $\boldsymbol{F}\in\mathbb{R}^{\frac{H}{4}\times\frac{W}{4}\times
C}$, where $C$ denotes the number of feature channels.

Inspired by CondInst [29], we decouple the table separation line mask
generation into a feature branch and a kernel branch. The feature branch
contains two $1\times 1$ convolution layers for generating
$\boldsymbol{F}^{\text{col}}$/$\boldsymbol{F}^{\text{row}}$, which will be
convoluted with convolution kernels from kernel branches to predict separation
line masks. Since the table separation lines are usually slender and traverse
the entire table image, it is necessary to design a kernel branch that has a
broader receptive field. To address this issue, we propose the Gather module
to capture the horizontal/vertical visual clues as shown in Figure 4.

Taking the Column Gather as an example, we first conduct three repeated down-
sampling operations on $\boldsymbol{F}$, and each operation is composed of a
sequence of a $2\times 1$ max-pooling layer, a $3\times 3$ convolutional layer
and a ReLU activation function. The down-sampled feature map
$\widetilde{\boldsymbol{F}}^{\text{col}}\in\mathbb{R}^{\frac{H}{32}\times\frac{W}{4}\times
C}$ will be taken as the input of two following spatial CNN modules [22]. The
first spatial CNN module divides the feature map into ${H}/{32}$ slices, which
are denoted as
$\boldsymbol{S}^{\text{td}}=\left\\{\left.\boldsymbol{s}_{i}^{\text{td}}\in\mathbb{R}^{1\times\frac{W}{4}\times
C}\right|i=1,2,...,\frac{H}{32}\right\\}$. Specifically, the topmost slice
$\boldsymbol{s}^{\text{td}}_{1}$ is convolved by a $1\times 5$ convolution
layer, and its output feature map is merged with the next slice
$\boldsymbol{s}^{\text{td}}_{2}$ by element-wise addition. This procedure is
done iteratively so that the information can be propagated from the topmost to
the bottommost effectively. The second spatial CNN module transmits
information in a reversed direction. In this way, each pixel in the output
feature map can leverage the structural information from both sides to enhance
its feature representation ability.
$\boldsymbol{G}^{\text{col}}\in\mathbb{R}^{1\times\frac{W}{4}\times C}$ is
obtained by taking the row mean of the enhanced feature map. We add a linear
transformation following the $\boldsymbol{G}^{\text{col}}$ to predict
$C$-dimensional output
$\boldsymbol{\theta}^{\text{col}}\in\mathbb{R}^{1\times\frac{W}{4}\times C}$.
$\boldsymbol{\theta}^{\text{col}}$ will be used as the weights of a $1\times
1$ convolution layer to predict table column separation line masks. We also
detect table column separation line instance by predicting
$\boldsymbol{\hat{p}}^{\text{col}}\in\mathbb{R}^{1\times\frac{W}{4}\times 1}$
through a linear transformation. The loss function on
$\boldsymbol{\hat{p}}^{\text{col}}$ is formulated as follows:

$\mathscr{L}_{inst}^{\text{col}}=\sum_{i=1}^{W/4}{\frac{L_{bce}\left(\hat{p}_{i}^{\text{col}},\tilde{p}_{i}^{\text{col}}\right)}{W/4}}$
(2)

Figure 4: Illustration of the Gather architecture. The upper part is the
Column Gather. The lower part is the Row Gather.

where $L_{bce}$ is the binary cross-entropy loss,
$\tilde{\boldsymbol{p}}^{\text{col}}$ denotes the ground-truth distribution of
starting points of table column separation lines on the x-axis.
$\tilde{p}^{\text{col}}_{i}$ is 1 if the start point of a table column
separation line is located in the i-th column, otherwise 0. To eliminate the
duplicated predictions of the starting point of a table column separation line
in $\tilde{\boldsymbol{p}}^{\text{col}}$, as shown in Figure 5(a), we perform
non-maximum suppression as follows: 1) binarize the
$\hat{\boldsymbol{p}}^{\text{col}}$ into $\boldsymbol{p}^{\text{col}}$, 2) for
the continuous pixels whose value equals $1$ in $\boldsymbol{p}^{\text{col}}$,
the pixel with maximum score in $\boldsymbol{\hat{p}}^{\text{col}}$ will be
selected to represent a table column separation line instance.

Figure 5: The illustration of Post-processing.

According to the detected table separation line instance, we select
convolution kernels from $\boldsymbol{\theta}^{\text{col}}$ to conduct dynamic
convolution with $\boldsymbol{F}^{\text{col}}$ to predict table column
separation line masks
$\boldsymbol{\hat{F}}^{\text{col}}\in\mathbb{R}^{\frac{H}{4}\times\frac{W}{4}\times
N^{\text{col}}}$, where $N^{\text{col}}$ represents the number of detected
table column separation line instances. The loss function on
$\boldsymbol{\hat{F}}^{\text{col}}$ is defined as follow:

$\mathscr{L}_{s}^{\text{col}}=\frac{1}{N^{\text{col}}}\sum_{k=1}^{N^{\text{col}}}{\sum_{i=1}^{H}{\sum_{j=1}^{W}{\frac{L_{fl}\left(\hat{F}_{i,j,k}^{\text{col}},\tilde{{F}}_{i,j,k}^{\text{col}}\right)}{\sum_{i=1}^{H}{\sum_{j=1}^{W}{\tilde{{F}}_{i,j,k}^{\text{col}}}}}}}}$
(3)

in which

$\displaystyle
L_{fl}\left(x,y\right)=\left\\{\begin{array}[]{c}\alpha\left(1-\sigma\left(x\right)\right)^{\gamma}\log\left(\frac{1}{\sigma\left(x\right)}\right),if\
y=1\\\
\left(1-\alpha\right)\sigma\left(x\right)^{\gamma}\log\left(\frac{1}{1-\sigma\left(x\right)}\right),if\
y=0\\\ \end{array}\right.$ (6)

where $\boldsymbol{\tilde{F}}^{\text{col}}$ denotes the ground-truth of table
column separation line masks. ${\tilde{{F}}}_{i,j,k}^{\text{col}}$ is $1$ if
the pixel in $i^{th}$ row, $j^{th}$ column and $k^{th}$ channel belongs to
$k^{th}$ table column line, otherwise 0. The function $L_{fl}$ is actually the
sigmoid focal loss [12] and the $\sigma$ is the sigmoid function.

Considering the table column separation lines are typically spread through
vertical direction, we process $\boldsymbol{\hat{F}}^{\text{col}}$ in a row-
wise manner to obtain the final table column separation line. Specifically, as
shown in Figure 5(b), given a table column separation line mask, we first find
the maximum score of each row, which is presented as a set of red dots as
shown in Figure 5(b). The table column separation line can be obtained by
connecting these red dots together. The grid bounding boxes $\boldsymbol{B}$
can be derived from the intersection of table row/column separation lines.

###  4.2 Embedder

The embedder aims to extract the grid-level feature representations
$\boldsymbol{E}\in\mathbb{R}^{M\times N\times D}$, where $D$ is the number of
feature channels. We take the image-level feature map $\boldsymbol{F}$ and the
well-divided table grids $\boldsymbol{B}$ obtained from the splitter as input,
and apply the RoIAlign [8] to extract a fixed size $R\times R$ feature map
$\boldsymbol{\hat{e}}_{i,j}\in\mathbb{R}^{R\times R\times C}$ for each grid.

$\displaystyle\boldsymbol{\hat{e}}_{i,j}=\text{RoIAlign}_{R\times
R}\left(\boldsymbol{F,b}_{i,j}\right)$ (7)

Then two liner transformations with a ReLU function are conducted on
$\boldsymbol{\hat{e}}_{i,j}$ to obtain the $D$-dimension output:

$\displaystyle\boldsymbol{e}_{i,j}=\max\left(0,\boldsymbol{\hat{e}}_{i,j}\boldsymbol{W}_{1}+\boldsymbol{b}_{1}\right)\boldsymbol{W}_{2}+\boldsymbol{b}_{2}$
(8)

where $\boldsymbol{W}_{1}$ and $\boldsymbol{W}_{2}$ are learned projection
matrices, $\boldsymbol{b}_{1}$ and $\boldsymbol{b}_{2}$ are learned biases. So
far, the features of each basic table grid are still independent of each
other. Therefore, we introduce the transformer [30] to capture long-range
dependencies on table grid elements and utilize its output as the final grid-
level features $\boldsymbol{E}$.

Table 2: Comparisons of different designed systems from T1 to T6 on diﬀerent
datasets. “InstSeg” means the Instance Segmentation method which is the
proposed splitter in this paper. “SemaSeg” means the Semantics Segmentation
method which follows the splitter in SEM [35]. “ParaDec” means the Parallel
Decoder which is the proposed merger in this paper. “SeqDec” means the
Sequence Decoder which follows the merger in SEM [35].

System | Splitter | Gather | Merger | SciTSR | iFLYTAB
---|---|---|---|---|---
InstSeg | SemaSeg | ParaDec | SeqDec | P | R | F1 | FPS | P | R | F1 | TEDS-Struct
T1 | ✓ | ✗ | ✓ | ✓ | ✗ | 99.3 | 99.2 | 99.3 | 7.3 | 93.8 | 93.3 | 93.5 | 92.0
T2 | ✗ | ✓ | ✓ | ✓ | ✗ | 99.1 | 98.5 | 98.8 | - | 81.9 | 72.7 | 77.0 | 75.8
T3 | ✓ | ✗ | ✗ | ✓ | ✗ | - | - | - | - | 91.1 | 89.8 | 90.4 | 89.3
T4 | ✓ | ✗ | ✓ | ✗ | ✗ | 99.1 | 97.4 | 98.2 | 8.9 | - | - | - | -
T5 | ✓ | ✗ | ✓ | ✗ | ✓ | 99.3 | 99.2 | 99.2 | 2.9 | - | - | - | -

###  4.3 Merger

The merger takes the grid-level features $\boldsymbol{E}$ as input and yields
a set of merged maps
$\boldsymbol{M}=\left\\{\boldsymbol{m}_{1,1},\cdots,\boldsymbol{m}_{M,N}\right\\},\boldsymbol{m}_{i,j}\in\left\\{0,1\right\\}^{M\times
N},i\in\left\\{1,\cdots,M\right\\},j\in\left\\{1,\cdots,N\right\\}$. Following
the approach of the splitter, as illustrated in Figure 3, we use a feature
branch and a kernel branch to predict $\boldsymbol{M}$ jointly. Each branch
contains only one $1\times 1$ convolution layer to generate feature maps
$\boldsymbol{E}^{f}\in\mathbb{R}^{M\times N\times D}$ and kernel parameters
$\boldsymbol{E}^{k}\in\mathbb{R}^{M\times N\times D}$. We first convolute the
feature map $\boldsymbol{E}^{f}$ with kernel parameter
$\boldsymbol{e}^{k}_{i,j}$, which is utilized as the weights of a $1\times 1$
convolution layer, to predict the merged map
$\boldsymbol{\hat{m}}_{i,j}\in\left[0,1\right]^{M\times N}$. The loss function
is formulated as follows:

$\mathscr{L}_{m}=\frac{1}{M\times
N}\sum_{i=1}^{M}{\sum_{j=1}^{N}{\frac{L_{fl}\left(\boldsymbol{\hat{m}}_{i,j},\boldsymbol{\tilde{m}}_{i,j}\right)}{\lVert\boldsymbol{\tilde{m}}_{i,j}\rVert_{1}}}}$
(9)

where $\lVert\cdot\rVert_{1}$ is the L1 norm, the function $L_{fl}$ has been
defined in Eq.6, $\tilde{\boldsymbol{m}}_{i,j}\in\left\\{0,1\right\\}^{M\times
N}$ denotes the merged map ground-truth of the $i^{th}$ row, $j^{th}$ column
table grid. If the value of $\tilde{\boldsymbol{m}}_{i,j}$ is equal to $1$,
then it indicates that the corresponding grid is associated with the identical
table cell; otherwise, 0. The final merged map $\boldsymbol{m}_{i,j}$ can be
obtained by binarizing $\boldsymbol{\hat{m}_{i,j}}$.

##  5 Experiment

In this section, we perform extensive experiments on the SciTSR, PubTabNet and
the proposed iFLYTAB dataset to verify the effectiveness of SEMv2. We first
introduce the relevant datasets and metrics, and then demonstrate the
implementation details of our method. We also conduct ablation studies to
analyze the effectiveness of our proposed splitter, gather and merger. Our
model is compared with state-of-the-art methods on public benchmark datasets.

###  5.1 Datasets

SciTSR comprises of 12,000 training samples and 3,000 testing samples of axis-
aligned tables extracted from the scientific literature. Furthermore, it also
selects all the 716 complex tables from the test set as a more challenging
test subset, called SciTSR-COMP.

PubTabNet contains 500,777 training samples and 9,115 validating samples. All
tables are also axis-aligned and collected from scientific articles.

iFLYTAB contains 12,103 training samples and 5,188 testing samples. In
addition to the axis-aligned digital documents, the collected table images
also include images taken by cameras, which are more challenging due to the
complicated background and non-rigid image deformation.

###  5.2 Metric

The F1-Measure and the Tree-Edit-Distance-based Similarity (TEDS) metric are
used to evaluate the performance of our model. The F1-Measure measures the
percentage of correctly detected pairs of adjacent cells, where both cells are
detected correctly and identified as neighbors. TEDS [37] measures the
similarity of the tree structure of tables. Since taking OCR errors into
account may lead to an unfair comparison due to the different OCR models used
by various TSR methods. We employ a modified version of TEDS, called TEDS-
Struct, which only evaluates table structure recognition accuracy while
disregarding OCR results.

###  5.3 Implementation Details

The ResNet-34 as our backbone is pre-trained on ImageNet [5]. The number of
feature channels $C$ and $D$ is set to 256 and 512 respectively. The pool size
$R\times R$ of RoIAlign in the embedder is set to $3\times 3$. The
hyperparameters $\alpha$ and $\gamma$ of sigmoid focal loss $L_{fl}$ are set
to 0.25 and 2. The threshold for binarization operations is set to 0.5.

The training objective of our model is to minimize the table row/column
separation line segmentation loss
($\mathscr{L}_{s}^{\text{row}}$/$\mathscr{L}_{s}^{\text{col}}$), the table
row/column separation line instance classification loss
($\mathscr{L}_{inst}^{\text{row}}$/$\mathscr{L}_{inst}^{\text{col}}$), and the
cell merge loss ($\mathscr{L}_{m}$). The objective function for optimization
is shown as follows:

$O=\lambda_{1}\mathscr{L}_{s}^{\text{row}}+\lambda_{1}\mathscr{L}_{s}^{\text{col}}+\lambda_{2}\mathscr{L}_{inst}^{\text{row}}+\lambda_{2}\mathscr{L}_{inst}^{\text{col}}+\lambda_{3}\mathscr{L}_{m}$
(10)

In our experiments, we set $\lambda_{1}=\lambda_{2}=\lambda_{3}=1$. We employ
the ADADELTA [34] for optimization, with the following hyperparameters:
$\beta_{1}=0.9$, $\beta_{2}=0.999$ and $\varepsilon=10^{-9}$. We set the
learning rate using the cosine annealing schedule [19] with the following
hyper parameters: $\eta_{min}=10^{-6}$ and $\eta_{max}=10^{-4}$. We use the
Nvidia Telsa V100 GPU with 32GB RAM memory for our experiments. The whole
framework is implemented using PyTorch.

Figure 6: The segmentation results from the splitters of the designed systems
T1 and T2. (a) and (b) correspond to images extracted from digital documents
and camera-captured documents, respectively. Table 3: Comparsion with state-
of-the-art methods. Bold indicates the SOTA and underline indicates the second
best.

Method | SciTSR | SciTSR-COMP | PubTabNet | iFLYTAB
---|---|---|---|---
P | R | F1 | P | R | F1 | TEDS | TEDS-Struct | P | R | F1 | TEDS-Struct
EDD [37] | - | - | - | - | - | - | 88.3 | - | - | - | - | -
TabStructNet [25] | 92.7 | 91.3 | 92.0 | 90.9 | 88.2 | 89.5 | - | 90.1 | - | - | - | -
GraphTSR [2] | 95.9 | 94.8 | 95.3 | 96.4 | 94.5 | 95.5 | - | - | - | - | - | -
SEM [35] | 97.7 | 96.5 | 97.1 | 96.8 | 94.7 | 95.7 | 93.7 | - | 81.7 | 74.5 | 78.0 | 75.9
LGPMA [24] | 98.2 | 99.3 | 98.8 | 97.3 | 98.7 | 98.0 | 94.6 | 96.7 | - | - | - | -
RobusTabNet [20] | 99.4 | 99.1 | 99.3 | 99.0 | 98.4 | 98.7 | - | 97.0 | - | - | - | -
TSRFormer [14] | 99.5 | 99.4 | 99.4 | 99.1 | 98.7 | 98.9 | - | 97.5 | - | - | - | -
SEMv2 | 99.3 | 99.2 | 99.3 | 98.7 | 98.6 | 98.7 | - | 97.5 | 93.8 | 93.3 | 93.5 | 92.0

###  5.4 Ablation Study

In order to investigate the effect of each component, we conduct ablation
experiments through several designed systems as shown in Table 2. The model is
not modified except for the component being tested.

The effectiveness of the splitter. In contrast to the majority of previous
“split-and-merge” based methods, we formulate table separation line detection
in the “split” stage as an instance segmentation task rather than a semantic
segmentation. To evaluate the efficacy of our proposed splitter, we devised
the systems T1 and T2 as shown in Table 2. Specifically, T1 represents our
proposed SEMv2, whereas T2 replaces the splitter with the one used in the
previous state-of-the-art method, SEM[35]. Although the performance of T1 is
only marginally better than T2 on datasets comprising axis-aligned scanned PDF
documents (e.g., SciTSR), T1 exhibits a significantly superior performance on
the iFLYTAB dataset. This is because the iFLYTAB dataset features camera-
captured images with severe deformation, bending, or occlusions. Additionally,
we present the segmentation results from splitters of both T1 and T2 in Figure
6. It can be seen that both T1 and T2 can get high-quality masks on the
digital document, but on the camera-captured document, the prediction result
of T2 is relatively lower. It’s very hard for the mask-to-line post-processing
module to handle such low-quality masks well. In contrast, our instance
segmentation based method can easily obtain the shape of the table separation
line in a row-wise or column-wise manner, which is more robust to such
challenging tables.

The effectiveness of the Gather. To illustrate the effectiveness of the Gather
module, as shown in Table 2, we designed a system T3, which eliminates
RowGather/ColGather, and obtains
$\boldsymbol{G}^{\text{row}}$/$\boldsymbol{G}^{\text{col}}$ by calculating the
column/row mean value of $\boldsymbol{F}$. T1 outperforms T3 by a large
margin, which demonstrates the effectiveness of the Gather module for
capturing horizontal/vertical visual clues.

The efficiency of the merger. As shown in Table 2, we design the systems T1,
T4 and T5 that employ different mergers. T4 eliminates the merger, while T5
substitutes it with the one utilized in SEM[35]. Though T4 exhibits slightly
higher Frames Per Second (FPS) than T1, its performance deteriorates
significantly as it disregards table cells that span multiple rows or columns.
The comparison between T1 and T4 also illustrates the indispensability of the
merger. The merger in SEM predicts the merging of grids in a step-by-step
manner. As the number of table cells increases, the decoding stages of T5
rise, causing the FPS of T5 to be much lower than T1 and T4.

Figure 7: Some structure recognition results of SEMv2. a* refer to SciTSR, b*
refer to PubTabNet, c* refer to iFLYTAB. c(1) refers to the digital wired
table, c(2)$\sim$c(3) refer to camera-captured wired tables, c(4) refers to
the digital wireless table, c(5)$\sim$c(6) refer to camera-captured wireless
tables.

###  5.5 Comparison with State-of-the-art Methods

We compare our method with other state-of-the-art methods on three TSR
datasets, including SciTSR, PubTabNet and iFLYTAB. The results are shown in
Table 3. Furthermore, we visualize the prediction results of our method as
shown in Figure 7.

SciTSR and PubTabNet As shown in Table 3, our method achieves competitive
performance compared to state-of-the-art methods. It is worth noting that the
LGPMA emerged as the winner of the ICDAR 2021 Competition on Scientific
Literature Parsing, Task B.

Figure 8: The Performance of SEMv2 on a series of iFLYTAB subsets.

iFLYTAB The iFLYTAB dataset is distinct from SciTSR and PubTabNet in that it
comprises table images with intricate backgrounds and non-rigid deformations.
It is worth noting that detection-based methods (e.g. TabStructNet, LGPMA) are
subject to the constraints that tables are free of visual rotation or
perspective transformation. This condition is difficult to satisfy when table
images are camera-captured. Therefore, as shown in Table 3, we re-implement
the closest method, SEM [35], for a fair comparison on the iFLYTAB dataset. It
can be seen that SEMv2 outperforms SEM by a large margin. As depicted in
Figure 8, we also evaluate the performance of SEMv2 on different subsets of
the iFLYTAB dataset. Notably, the model’s performance is comparatively lower
in the camera-captured scenarios due to the suboptimal image qualities.
Furthermore, the model’s performance is less satisfactory on wireless tables
than on wired ones, as the former lack crucial visual information.

##  6 Conclusion

In this paper, we propose a novel method for tackling the problem of table
structure recognition, SEMv2. It mainly contains three components including
splitter, embedder and merger. Distinct from previous methods in the “split”
stage, SEMv2 aims to distinguish each table line and formulate the table line
detection as an instance segmentation task. Moreover, we propose a parallel
decoder based on conditional convolution for the merger, which significantly
boosting the model’s efficiency. To comprehensively evaluate the SEMv2, we
also present a more challenging dataset for table structure recognition, named
iFLYTAB. We collect and annotate 17291 tables (both wired and wireless type
tables) in various scenarios such as camera-captured photos, scanned
documents, etc. Some table images in iFLYTAB have intricate backgrounds and
non-rigid deformations. The comprehensive experiments on the publicly
available datasets and the iFLYTAB dataset illustrate that SEMv2 achieves a
new state-of-the-art for table structure recognition. We hope our proposed
iFLYTAB dataset can further advance future research on table structure
recognition.

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