Philippe Cuvillier

Time-coherency of Bayesian priors on transient semi-Markov chains for audio-to-score alignment

Keywords: Bayesian inference, sequential estimation, hidden semi-Markov models, semi-Markov chains

This paper proposes a novel insight to the problem of real-time alignment with Bayesian inference. When a prior knowledge about the duration of events is available, Semi-Markov models allow the setting of individual duration distributions but give no clue about their choice. We propose a criterion of temporal coherency for such applications and show it might be obtained with the right choice of estimation method. Theoretical insights are obtained through the study of the prior state probability of transient semi-Markov chains.

INTRODUCTION

Many signals are structured as time-contiguous events which generate specific observations, e.g. music, speech or text. In music, basic events may be notes (pitched sounds) and silences. To recognize the sequence of events that generates an observed signal, probabilistic models [START_REF] Murphy | Dynamic Bayesian Networks: Representation, Inference and Learning[END_REF] are relevant when statistical relationships between observation and events are known. In particular, the Hidden Markov Models (HMM) [START_REF] Rabiner | Proc. of the IEEE[END_REF] assume that the signal is stationary on time-intervals and identify them with the occupancy of a hidden state. Once the state-space and the statistical priors are specified, Bayesian inference can be readily computed to recognize the state-sequence.

Score alignment [START_REF] Cont | [END_REF] is a Music Information Retrieval (MIR) task consisting of synchronizing a musical performance with its score, i.e. the sequence of notes. Since ordering of events is known, recognition boils down to alignment. Among the numerous applications of HMM, music has an outstanding property: a music score assigns to each event its nominal duration, i.e. a prior information on their likely duration.

A crucial and undermined question is about the modeling of nominal duration. This investigation is built on the framework of hidden semi-Markov models (HSMM) as it provides explicit choice of the prior duration model. In section 2 we detail this motivation and briefly introduce HSMM. This generalization of HMM involves many Bayesian priors whose tuning is a major issue. To this aim, most probabilistic models rely on learning with training datasets. This paper presents an alternative based on a theoretical study of prior probability distributions of semi-Markov processes.

In section 3, we state our condition of time-coherency, and explain how the Viterbi estimation does not fulfill it. In section 4, we investigate how the Forward estimation may fulfill it or not depending on several distribution properties of the Bayesian priors.

BACKGROUND & MOTIVATION

Semi-Markov models for alignment

Hidden semi-Markov models were introduced in [4] as a generalization of HMM. Both are defined with two stochastic processes [START_REF] Rabiner | Proc. of the IEEE[END_REF]. The process (S t ) t∈N * is a discretetime homogeneous Markov chain on a discrete state-space E def = {1, 2, . . . , J}, finite or not (J = ∞). Since its realizations (s t ) t∈N * are not known, they are called hidden states. The observation (o t ) t∈N * , e.g. the audio signal, is considered as a realization of the second process (O t ) t∈N * . We denote

N def = {0, 1, . . .}, N * def = {1, 2, . . .} and S t+u t def = (S t , S t+1 , . . . , S t+u ).
In such probabilistic models, the duration spent on a state j is a time-homogeneous random variable. Its law is called the occupancy distribution d j (u)

def = P(S t+u+1 = j, S t+u t+2 = j | S t+1 = j, S t = j) for u ∈ N * .
For a Markov state with self-transition p, d j would implicitly be a geometric law d j (u) = (1p)p u-1 . Assuming that (S t ) t is a semi-Markov chain allows choosing each Bayesian prior d j as any probabilistic mass function (pmf) on N * .

A semi-Markov chain consists of two additional choices per state j: the initial probability π( j) def = P(S 1 = j), and the transition probabilities p i j def = P(S t+1 = j | S t+1 = i, S t = i) with p ii = 0. In alignment tasks, left-to-right topologies of transition probabilities conveniently model the prior information of ordering. This study exclusively deals with the simplest topology, the linear semi-Markov chains: ∀i, j, p i j = δ i,i+1 and π j = δ 1, j (see figure 3

Modeling prior information of duration with HSMMs

Inference with semi-Markov models requires a careful design of the prior distributions d j for each state. Usual approaches rely on statistical learning. The Baum-Welch algorithm, i.e. the HMM version of Expectation-Maximization (EM), has been adapted to semi-Markov models [5]. But this non-parametric algorithm requires huge training datasets. Consequently, most implementations prefer a parametric EM [START_REF] Mitchell | Modeling duration in a hidden Markov model with the exponential family[END_REF] to learn the occupancy distributions over a parametric family of probabilities, e.g. Gamma, Poisson, log-normal, Negative Binomial laws.

This study aims at elaborating a criterion so as to justify or disqualify such choices. It is built on an interesting property of our application: musical events are associated with a reference duration. Indeed a music score provides the prior tempo and prior durations for all notes.

We denote this quantity the nominal duration l j . Although a few music alignment systems like [START_REF] Joder | An Improved Hierarchical Approach for Music-to-symbolic Score Alignment[END_REF] willingly discard this prior information, this work considers duration as an explicit element of modeling and makes the following assumption: two events with identical nominal duration should get identical occupancy distributions. So the duration model consists of a set of durations L ⊂ R + and a duration-indexed family of pmfs (d l ) l∈L such that for all state j, l j ∈ L and d j = d l j . This framework sharpens the problematic: are there coherent mappings from nominal durations l to distributions d l ?

CRITERION OF COHERENCY FOR PRIORS OF DURATION Hypothesis of non-discriminative observation

Ideal behavior with non-discriminative observation

We state our criterion of time-coherency. Its rationale is simple: if the observation probabilities do not discriminate states, then the inference should respect the states ordering and their nominal durations as these are the only available information. Time-coherency criterion 1. On a linear chain with non-discriminative observation, the inference successively decodes states 1, 2, 3, . . . at time steps 1, 1 + l 1 , 1 + l 1 + l 2 , . . . and assigns to each state j a duration which is equal to its nominal duration l j .

The hypothesis of non-discriminative observations makes the posterior probabilities equal to the prior probabilities:

∀t ∈ N * , P(S 1 , . . . , S t | O 1 , . . . , O t ) = P(S 1 , . . . , S t ).
Indeed, the Markovian assumption implies that

P(O t 1 | S t 1 ) = ∏ t u=1 P(O u | S u ) = ∏ t u=1 b S u (O u ). Assuming that b S u = b gives P(O t 1 | S t 1 ) = ∏ t u=1 b(O u ) = P(O t 1 )
, so (S t ) and (O t ) are independent. Thus, the inferred quantities become independent of the observations. Whether the criterion is fulfilled only depends on the underlying semi-Markov chain (S t ) t and the estimation method.

Offline alignments estimate the most likely sequence s T 1 at final time T , using the so-called Viterbi algorithm. But online alignments make sequential estimations. At each time t = 1 . . . T , they could either estimate the partial sequence s t 1 or the most likely current state ŝt . The Viterbi alignment is defined as ŝt such that ŝt

1 def = arg max s 1 ,...,s t ∈E t P(S t 1 = s t 1 | O t 1 = o t 1 )
. The Forward alignment is defined as ŝt = arg max s t ∈E P(S t = s t | O t 1 = o t 1 ). These quantities are obtained using the recursive equations detailed in [5]. Our first claim is that the Viterbi alignment fails to be time-coherent. Let us illustrate it with the example in figure 2: a linear Markov chain with identical first two states.

Failure of the Viterbi estimation

Let S = (S 1 , . . . , S t+1 ) be an admissible (i.e. non-decreasing) path. If S ends at S t+1 = 1, then P(S) = p t . If S t+1 = 2, then P(S) = (1p)p t-1 . So, if p > 1/2 then state 1 is more likely than state 2 at all times for the Viterbi estimation, whereas if p < 1/2 state 2 is more likely than state 1 at all times t > 1.

This simplistic example could be extended to semi-Markov chains for a wide class of occupancy distributions, but it is enough to reveal the lack of coherency of Viterbi alignments: the parameters cannot be tuned to take into account the nominal duration l 1 .

COHERENCY OF THE FORWARD ESTIMATION

Our second claim is that the Forward alignment may be time-coherent. This section introduces sufficient conditions on occupancy distributions that imply criterion 1.

Recall that under non-discriminative observation, F j (t) = P(S t = j). Let

F(t) def = (F 1 (t), F 2 (
∀t ∈ N * , M[F t ] = j ⇔ 1 ≤ t -(l 1 + . . . + l j ) ≤ l j+1
On linear chains, the prior state probabilities are given by successive convolutions. Using the recursive equations detailed in [5, Section 3.2], a simple induction over states j proves that where D j (t) = ∑ u≥t d j (u) is the survivor distribution associated to d j , and

F j (t) = 1 K(t) • d 1 * d 2 * . . . * d j-1 * D j (t) if j > 1 D 1 (t) else 1 d 1 (.)
K(t) = D 1 (t) + d 1 * D 2 (t) + d 1 * d 2 * D 3 (t) + . . . is an unimportant normalization constant.

The case of first two states

Since state 1 is the most likely one at first time step t =1, we begin with a comparison between states 1 and 2 by studying the evolution of the probability ratio F 1 (t) F 2 (t) . The Forward estimation respects the criterion 1 for these two states if and only if

∀ j ∈ E, F 2 (t) F 1 (t) ≤ 1 if t ≤ l 1 > 1 if t > l 1 . Proposition 1. Let us denote m[d 1 ] def = max{t | D 1 (t) ≥ 1/2} the median of d 1 . Then for any distribution d 2 , t ≤ m[d 1 ] ⇒ F 1 (t) ≥ F 2 (t).
Reciprocally there exists a distribution

d 2 such that t > m[d 1 ] ⇒ F 1 (t) < F 2 (t). Proof. Since D 2 (t) ≤ 1 for all t, ∑ t-1 u=1 d 1 (u)D 2 (t -u) ≤ ∑ t-1 u=1 d 1 (u) so F 2 (t) ≤ 1 -D 1 (t) and F 2 (t)-F 1 (t) ≤ 1-2D 1 (t). Since D 1 is non-increasing, if t ≤ m[d 1 ] then D 1 (t) ≥ 1/2 and 1 -2D 1 (t) ≤ 0.
For the necessary condition one may consider the trivial distribution

d 2 (t) = δ m[d 1 ] (t).
Last proposition tells that the median of d 1 is a lower bound for the duration assigned to state 1. Thus it prescribes choosing every distribution d l such that its median is ⌊l⌋. But even if this result provides the first half of the criterion 1, the other half may not be fulfilled in the general case.

Uncoherency of heavy-tailed distributions

First, we give a negative example of distributions that never fulfill the criterion. An important feature of probability distributions is their asymptotic speed of decay. This Convolutions of heavy-tailed distributions have been thoroughly studied. We borrow the following non-trivial result from [9].

Proposition 2. If d 1 is an heavy-tailed pmf, then lim inf t→∞ ∑ t-1 u=0 d 1 (u)D 1 (t -u) D 1 (t) = 1
If the two states have the same heavy-tailed occupancy distribution, then state 1 is decoded an infinite number of time. So, the criterion is never fulfilled. This fact discards using such pmfs as Bayesian priors.

Coherency of IHR distributions

Nevertheless, using light-tailed distributions does not guarantee neither the criterion. But another notion of tail analysis helps checking whether the criterion hold or not.

Definition 2. A distribution d is Increasing Hazard Rate (IHR) if its hazard rate h(n) def = d(n) D(n) is non-decreasing. Proposition 3. Let d 1 be an IHR pmf. For all distribution d 2 , d 1 * D 2 D 1 (t) is a non- decreasing function of t.
Proof. The proof uses simple algebraic computations. Let us define the functions

f u (t) def = 0 if t ≥ u d 1 (t-u) D 1 (t) D 2 (u) if 0 < t < u .
With this definition we have

d 1 * D 2 D 1 (t) = ∑ t-1 u=1 d 1 (t-u) D 1 (t) = ∑ u∈N * f u (t).
Let h be the hazard rate of d 1 , and u be in

N * . By definition of h, d 1 (t-u) D 1 (t) = d 1 (t-u) D 1 (t-u) D 1 (t-u) D 1 (t) = h(t -u) 1 ∏ u v=1 (1-h(t-v)) . Since the function x → 1 1-
x is positive and increasing on [0, 1[, if h is non-decreasing, then t → f u (t) is non-decreasing as a product of positive and non-decreasing functions. Consequently, t →

d 1 * D 2 D 1 (t) is non- decreasing.
Monotony is a stronger but very interesting requirement: if the ratio is non-decreasing then the estimation never come back to state 1 after having decode state 2.

Extension to N states

The previous arguments cannot be directly generalized to more than two states without further assumptions. Our next argument extends the idea of monotony that proposition 3 highlights. This approach turns out to be related to the notions of stochastic orderings introduced by [ This straightforward lemma is interesting: if the state probabilities of the semi-Markov chain (F(t)) t∈N * ) constitute an increasing family, then states are decoded with respect to their ordering -although some states might be skipped. Moreover, checking numerically the criterion on a given chain becomes very easy: it holds if and only if F j (1 + l 1 + . . . + l j ) > 1 for all j. So, to finish with, next proposition gives a sufficient condition to obtain an increasing process.

F j+1 F j (l 1 + . . . + l j ) ≤ 1 and
Definition 4. A discrete distribution d is log-concave if for all n in N, d(n) 2 ≥ d(n - 1)d(n + 1). This is equivalent to d(.) ≤ lr d(. + u) for all u ∈ N.
It is noteworthy that all log-concave distributions are IHR. The main point is that log-concavity "preserve" stochastic ordering, as the following lemma explains. See the reference for its proof, that is an application of the Binet-Cauchy formula. Proposition 4. If the semi-Markov chain is linear and all occupancy distributions d j are log-concave, then the process (F(t)) t∈N * is locally increasing.

Proof. Let j be in N * . Since d j-1 is log-concave, it is also IHR and D j-1

lr d j-1 * D j . If j > 1, let us consider F j+1 F j = d 1 * ... * d j-1 * d j * D j+1 d 1 * ... * d j-1 * D j
The class of log-concave distributions is stable by convolution [10], so d 1 * . . . * d j-1 is log-concave. Then, lemma 2 implies that t → F j+1 (t) F j (t) is increasing. The monotony of Markov processes has been largely studied -see [11] for a survey. Proposition 4 is a first step towards its extension to semi-Markov processes. Moreover, in locally increasing Markov chains, first-time passages T j def = inf{t | X t+1 ≥ j, X 1 = 1} have log-concave pmfs [START_REF] Karlin | Total positivity[END_REF]. Proposition 4 looks like a "reverse" counterpart of this result for linear semi-Markov chains, since the pmf of T j+1 is d 1 * . . . * d j for such chains.

As a conclusion, log-concavity seems to be the most desirable property for prior distributions of duration. While log-concavity plays an important role in many fields of statistics, it has been scarcely studied on HSMMs. It is highlighted by [START_REF] Tweed | Efficient Hidden Semi-Markov Model Inference for Structured Video Sequences[END_REF] for improving computational efficiency of the Viterbi algorithm. Proposition 4 shows it also provides theoretical coherency to the Forward estimation. Furthermore, experiments show that taking into account these prescriptions do improve the performances of realtime alignment. A comparative test with results and video files can be found on http: //repmus.ircam.fr/mutant/mlsp14.

CONCLUSION & PERSPECTIVES

This paper introduces a criterion of time-coherent modeling in semi-Markov models for alignment. This criterion is about estimation coherency under non-discriminative observation. We show that coherency cannot be obtained with Viterbi estimation but can be obtained with is the Forward estimation if the chosen probability distributions have some precise properties. This short study calls for further theoretical and experimental developments. More necessary and sufficient conditions related to the criterion can be derived. The framework can be extended to other estimators such as the Forwardbackward algorithms. Moreover the proposed prescriptions lead to constraints on the learning parameter space; adding these constraints in HSMM training algorithms would be an interesting issue.

FIGURE 1 .

 1 FIGURE 1. Music score of the Mazurka Op. 7 No. 5 by F. Chopin. It begins with a long sequence of repeated events, i.e. states with identical observation probabilities.Our definition of time-coherency emerges from the following fact: music scores might be composed of very long sequences of "repeated events" such that the one in figure1. What would happen if all states j ∈ E share the same observation probabilities? We call non-discriminative observation such a model where b 1 = b 2 = . . . def = b. Note that this assumption may model other realistic situations of Bayesian inference such as missing observations [8].

FIGURE 2 .

 2 FIGURE 2. Example of a linear Markov chain with identical first two states: p 11 = p 22 = p.

FIGURE 3 .

 3 FIGURE 3. Example of a linear semi-Markov chain.

  feature is related to the radius of convergence R d ∈ [1, +∞] of the probability generating function of d, denoted Z[d](z) def = ∑ n∈N d(n) z n . Definition 1. A discrete distribution d is said to be heavy-tailed if R d = 1, and lighttailed if not.

Lemma 2 (

 2 [10, Theorem 2.1]). Let f , g, h be three distributions. If f is log-concave, then glr h ⇒ f * g lr f * h.

  10]. Definition 3. Let p 1 , p 2 be two distributions. p 1 is said to be locally smaller that p 2 , denoted p 1 ≤ lr p 2 , if n → p 1 (n)/p 2 (n) is non-decreasing on supp[p 2 ]. A family (p t ) t∈I of pmfs indexed by I ⊂ R is said to be locally increasing if ∀t 1 ,t 2 ∈ I, t 1 ≤ t 2 ⇒ p t 1 ≤ Lemma 1. If (p t ) t∈I is an increasing family, then the mode M[p t ] of p t is a nondecreasing function of t.

	lr	p t 2 .


Ali Erçin Ersundu
email: ersundu@gmail.com

Miray Çelikbilek

Mohamed Baazouzi

Mohamed Toufik Soltani

Johann Troles

Süheyla Aydin

Characterization of new Sb2O3-based multicomponent heavy metal oxide glasses

Keywords: Antimony oxide, Heavy metal oxide glasses, Thermal behavior, FTIR spectroscopy

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Until today, conventional glass formers such as SiO2, B2O3, GeO2 or P2O5 have been preferred in opto-electronic applications. However, due to their limited infrared transmission, high optical losses and low solubility of rare-earth ions in glass network, considerable attention has been focused on the investigation of new glass types which demonstrate better optical properties. In this respect, heavy metal oxide glasses have attracted much attention for new generation opto-electronic applications due to their broad transparency from visible to infrared region, high solubility of rare-earth ions and good non-linear optical properties [1][2][3][4][5][6][7][8][9][10][11].

Recently, antimony oxide-based glasses have emerged as one major family of heavy metal oxide glasses and appeared promising for potential applications in non-linear optical devices like ultra-fast optical switches and power limiters [2][3][4][5]12]. They also have potential for broad band optical amplifiers operating around 1.5 mm as antimony-silicate glass fibers and in the field of optical amplification in telecommunication C-band (1530 -1560 nm) [1,13].

Antimonite glasses possess low phonon energy (605 cm -1 ) and large optical non-linearity that is correlated to high refractive index, good mechanical properties and better chemical durability than that of fluoride or tellurite glasses [1][2][3][4][5][6]14,15].

The incorporation of Sb2O3 with conventional glass formers enhances vitrification behavior but also increases the phonon energy which leads to reduced infrared transmission. Numerous Sb2O3-based binary and multi-component glasses including conventional glass formers have been reported in the literature [1,[16][17][18][19][20][21]. Therefore, recently alkali antimonite glasses free of conventional glass formers have been the subject of some studies in different systems such as; Sb2O3-Na2O-ZnO, Sb2O3-M2O-MoO3 (where M = Li, K), Sb2O3-Li2O-GeO2, Sb2O3-Na2O-WO3-Bi2O3, Sb2O3-M2O-PbO (where M = Li, Na or K), Sb2O3-Na2O-WO3 and Sb2O3-Na2O-Al2O3 [1][2][3][4][5]14,15,[22][23][24][25].

The aim of this work is to study new quaternary antimonite glasses in the Sb2O3-Na2O-WO3-PbO system. PbO and WO3 have been introduced since they increase refractive index hence yield suitable glasses for non-linear applications.

In order to develop new glasses for opto-electronic applications, the knowledge of physical features of these glasses in combination with their thermal and structural properties seems to be a useful tool for understanding the glass structure. In this paper, to the best of our knowledge, we report for the first time on the glass formation behavior and thermal, physical and structural properties of glasses in the Sb2O3-Na2O-WO3-PbO glass system.

Experimental procedures

Glass synthesis

In order to prepare and characterize new antimony oxide-based multicomponent heavy metal oxide glasses, high purity chemicals of Sb2O3 (Acros, 99.99%), PbO (Aldrich, 99.9%), WO3 (Aldrich, 99.995%) and Na2CO3 (Aldrich, 99.99%) were used as starting materials in the Sb2O3-Na2O-WO3-PbO quaternary glassy system. The synthesis was carried out through conventional melt-quenching method in open silica glass crucibles with 15 mm in diameter.

After weighing and thoroughly mixing, batches of 5 g in weight were flame heated at a temperature close to 900 °C for 10 to 15 minutes in air. During the synthesis, the tube was shaken to homogenize the melt, while a release of CO2 was observed due to the decomposition of sodium carbonate to sodium oxide. Vitreous samples were obtained by pouring the melt onto brass molds. The samples were annealed near the glass transition temperature for 6 hours in order to erase their thermal history. Finally, the samples were cut and polished. For different physical measurements, a set of samples were prepared according to the following composition rule: xSb2O3-10Na2O-yWO3-zPbO, z varying between 10 and 40 (mol %), the ratio of x/y=6 is maintained constant and x+y+z=90. Compositions of the prepared glass samples are given in Table 1 with their sample ID's.

To assess the residual silicon (SiO2) arising from crucible contamination in the prepared glasses, semi quantitative analysis was performed using scanning electron microscopy / energy dispersive X-ray spectroscopy (SEM / EDS) techniques in JEOL Model JSM 6400 microscope linked with Oxford link ISIS energy dispersive X-ray spectrometer. The EDS measurements on glass samples were done at four different points for each glass composition.

The amorphous nature of the as-cast samples was checked by X-ray diffraction analysis (XRD) using Cu Kα radiation PANalytical/Philips X'pert MRD system, at 40KV and 40mA in the 2θ range from 10° to 90°.

Thermal investigations

Thermal properties of glasses was investigated by using differential scanning calorimetry analysis (DSC) in a Netzsch DSC 204 F1 (limit of detection: <0.1 μW, with an error estimate of ± 1 °C) using a constant sample weight of 25 ± 1 mg in aluminum pans, under flowing (25 ml/min) argon gas with a heating rate of 10 °C/min to determine the glass transition onset (Tg), first crystallization onset (Tc1) and first crystallization peak (Tp1) temperatures. The temperature difference between the glass transition onset (Tg) and the first exothermic peak onset (Tc1), T = Tc1 -Tg, indicating the value of glass stability against crystallization was calculated.

The activation energy of the glass transition reaction, Eg, was determined by running non-isothermal DSC scans of the glasses at different heating rates, β, (10, 20, 30 and 40 °C/min). The activation energy values were calculated from the slopes of the linear fits to the experimental data from a plot of ln(Tg 2 / β) versus 1/Tg by using the modified Kissinger equation [26]:

const RT E T g g g            2 ln ( 1
)
where Tg is the glass transition onset temperature for a given heating rate β, Eg is the glass transition activation energy and R is the gas constant.

The fragility parameter, m, of the glasses was calculated (with an error estimate of ± 1) using the following expression [27,28]:

         g g RT E m ( 2
)
where m is the fragility parameter, Eg is the activation energy for glass transition, Tg is the glass transition onset temperature and R is the gas constant.

Physical investigations

Physical properties of glasses were investigated by measuring the densities of glasses and calculating the molar volume, oxygen molar volume and oxygen packing density values.

Theoretical density values of glasses were determined by using the theoretical densities of the constituent oxides according to their appropriate concentrations. Densities, ρ, of the glasses were determined at room temperature by the Archimedes' method using ethanol as an immersion liquid and a digital balance of sensitivity 10 -4 g. Density values obtained by three repeated measurements showed an error of ± 0.1 %. Density values of glasses, ρglass, were calculated using the following relation:

) ( water air air glass W W W    (3)
where Wair and Wwater are the weight of the glass sample in air and in distilled water, respectively [29].

Molar volume of the glasses, VM, was calculated as a function of the molar fraction of each component, using the relation:

glass i i glass glass M M x M V      ( 4
)
where xi is the molar fraction of each component i, Mi is the molecular weight and ρ density of the glass sample [29].

Oxygen molar volume of the glasses, VO, was calculated using the following formula:

                   i i i i O n x M x V 1  ( 5
)
where xi is the molar fraction of each component i, Mi is the molecular weight and ρ density of the glass sample and ni is the number of oxygen atoms in each constituent oxide [29,30].

Oxygen packing density of the glasses, OPD, was calculated using the density and composition values by applying the following formula:

) / ( 1000 M C OPD   (6)
where C is the number of oxygen atoms per each composition, ρ is the density and M is the molecular weight of the glass sample [29,30].

The refractive index of glasses was measured using a Metricon M2010 at four different wavelengths (632.8, 825, 1060.7 and 1551 nm) with an accuracy of ± 1.10 -4 .

The transmittance spectra of glasses were measured onto polished samples by a Perkin Elmer Lambda 1050 UV-Vis-NIR spectrophotometer operating between 400 and 800 nm, with 2 nm resolution. The wavelength, λg, corresponding to the optical band gap, Eg, is given when the absorption of the glass reaches 10 cm -1 [5]. The absorption coefficient is calculated according to the following equation:

𝛼 = 1 𝑥 𝑙𝑛 ( 𝑇 𝑚𝑎𝑥 𝑇 ) (7)
where T and Tmax are the transmittance and maximum transmittance, respectively and x is the sample thickness. Then, Eg values (in eV) were calculated using the following equation:

𝐸 𝑔 = ℎ𝑐 𝜆 𝑔 (8)
where h represents the Planck constant and c is the speed of light.

Structural investigations

Quantitative analysis of thermal and physical properties of these glasses with structural parameters like average cross-link density, number of bonds per unit volume and Poisson's ratio were also studied.

Average cross-link density, c n , of the glasses was calculated using the subsequent relation:

   i i c i i i c i c i c N x N n x n ) ( ) ( ) ( ( 9
)
where xi is the molar fraction of each component, nc is the cross-link per cation and Nc is the number of cations per glass formula unit [29,31].

Number of bonds per unit volume of the glasses, nb, was calculated by applying the following formula:

  i i f M A b x n V N n ) ( ( 10
)
where NA is the Avogadro's number, VM molar volume of the glass sample, nf coordination number of the cations, x molar fraction of each component oxide and i represents the component oxide [29,31].

For Eq. 9 and 10, the cross-link per cation (nc) is calculated as follows, nc = nf -2, where nf is the coordination number of the cations, which equals 6 for WO3, 4 for Na2O and PbO and 3 for Sb2O3, respectively [31,32].

Poisson's ratio of the glasses, μcal, was calculated theoretically according to the following expressions:

t cal V 2 . 7 1 5 . 0    (11)   i i i t V x M V  (12) ) ( 3 4 3 3 O A A i mr nr N V    ( 13
)
where Vt is the packing density, ρ density and M molecular weight of the glass sample, Vi packing factor of the oxide AnOm, NA Avogadro's number, rA and rO are the ionic radius of cation A and anion O, respectively [29,31].

FTIR spectra of the glasses were collected at room temperature using CsI pellet technique in the range 1200 -250cm -1 with a resolution of 1 cm -1 using a Perkin Elmer Frontier FTIR spectrometer. For the FTIR experiments 0.005 g of glasses were weighed, mixed and ground with 0.5 g CsI, then the mixture was pressed at 15 tons for 1 minute to yield transparent disks suitable for mounting in the spectrometer.

Results and discussion

The samples prepared in the Sb2O3-Na2O-WO3-PbO system are amorphous as it was

proven by XRD analysis.

The EDS analysis realized to check the elemental analysis of glasses and to assess the residual silicon arising from crucible contamination. Concentrations of all different elements in glasses are expressed in cation % and are listed in Table 2. The Si introduction in glasses is less The heating/cooling rate dependence of the glass transition temperature is used to determine the activation energy of the transition from glassy to liquid state.

As can be seen from Fig. 2, using the modified Kissinger equation (Eq. ( 1)), activation energy of the glass transition, Eg, for Sb2O3-Na2O-WO3-PbO glasses were determined from the linear fits of ln(Tg 2 / β) versus 1000/Tg plots. As shown in Fig. 2, activation energy of the glass transition increased with increasing PbO concentration from 330 kJ/mol to 412 kJ/mol (see also Table 1). A rough estimate of deviation of activation energies were calculated applying R× SEslope; R being the ideal gas constant and SEslope being the standard deviation of the slope obtained from linear regression and it was found that activation energies of Sb2O3-Na2O-WO3-PbO glasses showed an error of 16.7, 32,6, 35.9 and 39.5 kj/mol with increasing PbO concentration, respectively. As it was reported in the literature, the bond energies of Sb-O, W-O and Pb-O are 372 kJ/mol, 378 kJ/mol and 653 kJ/mol respectively and the increase in Eg values in Sb2O3-Na2O-WO3-PbO glasses with increasing PbO concentration is attributed to the increase in coordination number [33][START_REF] Cottrell | The Strengths of Chemical Bonds[END_REF][START_REF] Benson | [END_REF][36][START_REF] Darwent | Bond Dissociation Energies in Simple Molecules[END_REF].

The values of fragility parameter, m, which is often used to determine the strong-fragile characters of glass forming liquids, are listed in Table 1. Fragility parameters, m, of Sb2O3-Na2O-WO3-PbO glasses were found to vary between 70 and 87 and showed an increase with increasing PbO concentration. It is known from the literature that there is no sharp limit to characterize strong-fragile characters of liquids on the basis of their fragility parameters.

However, it is mentioned that a fragility value less than 90 can be attributed for strong liquids, whereas a value greater than 135 is typical for fragile liquids [27]. By taking this into account, it can be concluded that Sb2O3-Na2O-WO3-PbO glasses have a strong character and increasing the PbO concentration leads a less strong character. Therefore, it can be stated that the viscosity and heat capacity values of these glasses show a small change in the glass transition region [27,28,33].

Physical properties of the glasses were investigated by measuring the density, ρ, molar volume VM, oxygen molar volume, VO and oxygen packing density, OPD values to throw light on the structural behavior of Sb2O3-Na2O-WO3-PbO glasses and the obtained values are given in Table 1.

Densities of Sb2O3-Na2O-WO3-PbO glasses varied between 5.31 and 5.68 g/cm 3 and showed an increase with increasing PbO concentration. Densities of glasses determined at room temperature were found to be consistent with their theoretical values. The increase in density with increasing PbO concentration is due to the higher density of PbO among other constituent oxides. Molar volume values were calculated by taking into account the measured densities and they were found to vary between 48.01 and 41.72 cm 3 /mol. Molar volume values exhibited a decrease with increasing PbO concentration. The decrease in molar volume values with increasing PbO concentration is due to the decrease in the percentage of oxygen atoms which have the highest ionic radius in the glass structure (O 2-: 0.14nm, Sb 3+ : 0.076nm, W 6+ : 0.065nm, Pb 2+ : 0.119nm) [29,[START_REF] Shannon | [END_REF]. Therefore, it can be stated that decreasing oxygen content in glass composition decreases the excess free volume by decreasing the molar volume. Fig. 3 demonstrates the variation of density and molar volume values with changing PbO molar concentration.

Oxygen molar volume values of Sb2O3-Na2O-WO3-PbO glasses showed a change between 31.55 and 31.92 cm 3 /mol and increased slightly with increasing PbO concentration.

On the other hand, oxygen packing density values varied between 54.16 and 47.94 mol/l and showed a decrease with increasing PbO concentration. Variation of oxygen molar volume and oxygen packing density values of Sb2O3-Na2O-WO3-PbO glasses is illustrated in Fig. 4. As it can be seen from Fig. 4, oxygen molar volume and oxygen packing density values show opposite behavior to each other. Therefore, it can be concluded that due to the substitution of higher field intensity constituent ions (Sb 3+ : 0.73, W 6+ : 1.47) with lower field intensity Pb 2+ ions (0.27) [29,39,40] a slight increase in oxygen molar volume and a decrease in oxygen packing density values were observed in Sb2O3-Na2O-WO3-PbO glasses which results less tightly packing of the glass network.

The measured refractive indices in the Sb2O3-Na2O-WO3-PbO system were found to vary between 2.0 and 2.1 depending on wavelength and composition (Table 3). For each glass sample the increase of the density implies the increase of the refractive index. Therefore, it was observed that the density, and together with it the refractive index, both show an increase with increasing concentration of lead oxide (Fig. 5).

The transmittance spectra of Sb2O3-Na2O-WO3-PbO glasses are illustrated in Fig. 6.

The short wavelength absorption edge is located at around 450 nm, hence the glasses have a light yellow color. The positions of the short wavelength absorption edge depend slightly on the glass composition with increasing PbO concentration and practically remained invariant.

As it can be seen from Table 1, Eg values initially showed a decrease from 2.979 to 2.972 eV by increasing the PbO concentration to 20 mol % and then linearly increased with further increase of PbO concentration.

In glasses, generally the addition of alkali oxides, alkaline earth oxides and many other divalent metal oxides like PbO causes depolymerization in the glass network by breaking chains to create non-bridging oxygens (NBOs). Consequently, any changes in the oxygen bonding in a glass network, such as the formation of NBOs will also result in changes in the absorption characteristics. The NBOs, which bound an excited electron less tightly than the bonded oxygens (BOs), are more polarizable than the BOs. Thus, creation of NBOs seems to be the In order to interpret thermal and physical properties of Sb2O3-Na2O-WO3-PbO glasses thoroughly, structural properties were investigated by calculating average cross-link density, c n , number of bonds per unit volume, nb, and Poisson's ratio, μcal, and the obtained results are given in Table 1.

Average cross-link density values decreased from 2.21 to 2.13 with increasing PbO concentration. The decrease in average cross-link density with increasing PbO concentration implies that the addition of PbO to antimonite glasses decrease the network connectivity by creating non-bridging oxygen sites.

Number of bonds per unit volume varied between 75.24 and 77.92 x 10 21 cm -3 and showed an increase with the increase in PbO concentration. The theoretically calculated

Poisson's ratio values varied between 0.174 and 0.158 and decreased with increasing PbO concentration. The increase in number of bonds per unit volume and decrease in calculated

Poisson's ratio with the increase in PbO concentration yields a rigid and more linked glass network.

FTIR spectra in the spectral range [1200-250cm -1 ] of Sb2O3-Na2O-WO3-PbO glasses for increasing PbO concentration are shown in Fig. 7. In general, FTIR spectra of glasses showed broad peaks and shoulders due to the disorder of the glass structure.

Sb2O3 exists in two crystalline forms: cubic senarmontite and orthorhombic valentinite.

Antimony oxide is a weak glass network former and does not form glass without the presence of modifiers with SbO3 triangular pyramids. Sb participates in the glass network with the oxygen at three corners and the lone pair of electrons of antimony at the fourth corner.

Crystalline Sb2O3 exhibits four fundamental absorption bands: symmetric stretching vibrations ν1 (925 cm -1 ), symmetric bending vibrations ν2 (600 cm -1 ), doubly degenerate stretching vibrations ν3 (710 cm -1 ) and doubly degenerate bending vibrations ν4 (485 cm -1 ). The network structure of the glass is found to be double chains consisting of four membered rings of SbO3 pyramids similar to the valentinite form [21,[41][42][START_REF] Som | Antimony oxide glasses and their nanocomposites for optical, photonic and nanophotonic applications[END_REF]. As reported in the literature, during synthesis of glasses at high temperatures, small part of Sb 3+ (in Sb2O3 used as the raw material) is expected to convert to Sb 5+ by accepting oxygen from air due to its multivalent characteristics. These Sb 5+ ions enter to the glass structure as singly positive [SbO4] 4- coordinated units [START_REF] Som | Antimony oxide glasses and their nanocomposites for optical, photonic and nanophotonic applications[END_REF].

The spectra for Sb2O3-Na2O-WO3-PbO glasses are dominated by four main bands centered at around 470, 594, 700 and 937 cm -1 in the fingerprint range of 400-1200 cm -1 . The IR bands at 470 and 594cm -1 correspond to the ν4 and ν3 vibration modes of SbO3 of the valentinite form of Sb2O3 as reported by Terashima et al. [42]. The band located at 700cm -1 can be assigned to the ν1 vibration mode and the band at 937cm -1 is due to the Si-O stretching vibration of SiO4 tetrahedra. These bands were due to the contamination from the silica crucible used for melting the glasses as confirmed by EDS analysis. The presence of bands related to Sb 5+ is not confirmed in these glasses.

According to the literature, PbO has the ability to form stable glasses due to its dual role in glass structure. When PbO introduced to the glass structure as a modifier, Pb-O binding has an ionic character and observed in the range 400-200 cm -1 , whereas as a glass former Pb-O binding is covalent and observed in the range 600-400 cm -1 . In the latter case, Pb ions create three-dimensional spatial network with [PbO4] or [PbO3] units. This fact is possible for glasses having high amounts of PbO (more than 50 mol %) [32]. Accordingly, as can be seen from Fig. 7, the band located in the far infrared spectra at 290 cm -1 can be assigned to the ionic bands of Pb-O. The intensity of this band decrease with increasing PbO concentration and for SNWP30 and SNWP40 glasses two new bands appear at 350 cm -1 and 450 cm -1 which can be assigned to the vibrational mode of covalent bonds in [PbO4] or [PbO3] units.

In our previous study [START_REF] Soltani | [END_REF], it was observed that the equimolar substitution of Sb2O3 with In summary, PbO enters the glass structure as a glass modifier and increasing the PbO concentration by keeping the Sb2O3/WO3 ratio constant leads to the formation of lead structural units and favors the former role at the expense of modifying role.

Conclusions

In this experimental work, thermal, physical and structural properties of new heavy metal oxide glasses in the Sb2O3-Na2O-WO3-PbO system were investigated. Thermal

FIGURE CAPTIONS

than 3 .

 3 22 cation % and increased in the range 0.09, 1.37, 2.51 and 3.22 cation % with increasing PbO concentration from x=10, 20, 30 to 40 mol % respectively. The increase in the Si ratio can be related firstly to the increase in melting time needed to homogenize the melt when the PbO concentration increases in the glass and secondly to the increase in the melting temperature of the melt when the PbO ratio increases. Considering that the melting temperature of individual antimony, tungsten, lead and sodium oxides are 656, 1473, 888 and 851°C respectively and the mean melting temperature of the glass batch varies between 850 and 880 °C, the used melting temperature of 900°C is sufficient to achieve the melting procedure. Chemical analysis of glass samples is in good agreement with the compositions determined from weighed starting batch materials. Volatilization during melting is limited and the deviation from the nominal composition is less than 1.5%.It should be noted that the concentration of Na2O in Sb2O3-Na2O-WO3-PbO glasses is maintained constant and equals to 10 mol %. However, in fact the ratio of Na2O in the glasses doesn't necessarily remain constant when the concentration of PbO increases from 10 to 40 mol %. A fourfold increase in the concentration of PbO at the same time leads to almost a twofold increase in the concentration of Na2O. It is determined that Na + concentration changes from 11.2 to 13.08 cation % in the nominal composition and from 8.63 to 11.93 cation % in the real composition of the prepared glasses. This small change in the concentration of sodium is expected to have a small influence on different physical properties of these glasses and therefore the main influence can be related to the change in PbO concentration.DSC analysis was performed to investigate the thermal properties of Sb2O3-Na2O-WO3-PbO glasses. Thermal analysis details of quaternary glasses are given in Table1. The DSC curves of SNWP10, SNWP20, SNWP30 and SNWP40 glasses scanned at a heating rate of 10 °C/min are shown in Fig.1. Each DSC scan exhibited a shallow endothermic change between 287 and 289 °C corresponding to the glass transition temperature (Tg) and large peaks between 375 and 500°C corresponding to the crystallization process. As can be seen from Table1, Tg values remain practically invariant with changing composition. However, first crystallization onset temperatures initially showed an increase by increasing PbO concentration to 20 mol% and then decreased with further increase of lead oxide concentration. The temperature difference between Tg and the first exothermic peak onset Tc1, ΔT, indicating the glass stability against crystallization was found to vary between 73 and 115 °C and the most stable glass composition with a maximum ∆T value was found as SNWP20 glass sample. It was observed that the change in ∆T with increasing PbO concentration showed a similar behavior to the change observed in first crystallization onset temperatures (see Fig.1).

  reason for the decrease in Eg values when PbO content increased from 10 to 20 mol %. In this case PbO plays the role of glass modifier by forming [PbO6] units to repair the balance charge of two NBOs induced by two alkali ions like Na + . The increase in Eg for PbO concentrations more than 20 mol% may indicate the decrease in the NBOs. In this case PbO is supposed to play a former role by forming [PbO3] or [PbO4] units.

  PbO reduces the elastic properties in ternary glasses (90-x)Sb2O3-10Na2O-xPbO (for x=10-40) by creating weak Sb-O-Pb bonds. These weak bonds can be the consequence of the presence of the band situated at 812 cm -1 (see Fig.7). Its intensity increases with increasing PbO concentration which excludes the possibility of assigning this band to W-O vibrations. In the same order, the remarkable shift of the asymmetric stretching vibration of [SbO3] units from 594 to 580 cm -1 can be caused by the presence of weak bonds corresponding to Sb-O-Pb linkages. The incorporation of WO3 in glasses generally induces the appearing of two shoulders at around 700-800 and 800-860 cm -1 which are attributed to W-O-W vibration modes and a well-defined band in the 905-930 cm -1 range corresponding to the vibration mode of W-O in the tetrahedral [WO4] or octahedral [WO6] units[39]. In the FTIR spectra given in Fig.7, a weak shoulder at 913 cm -1 confirmed the presence of tungstate units in Sb2O3-Na2O-WO3-PbO glasses. The decrease of WO3 concentration in the glass structure induces a shift of this band from 913 to 893 cm -1 . This shift was attributed to the change of tungsten coordination from [WO6] to [WO4] units which is in good agreement with the diminution of oxygen packing density of the glasses with increasing PbO concentration[45].

  investigations reveal that the glass transition values remained practically invariant with changing composition, while the first crystallization onset temperatures initially showed an increase with increasing PbO concentration and then decreased. Kinetic investigations of glass transition region showed that activation energy of glass transition values increased with increasing PbO concentration due to the increase in coordination number. Kinetically estimated fragility values show that Sb2O3-Na2O-WO3-PbO glasses have a strong character. Physical and structural investigations revealed that increasing PbO concentration in glass structure results a decrease in molar volume, oxygen packing density, average cross-link density and calculated Poisson's ratio values and on the contrary results an increase in the density, refractive index, oxygen molar volume and number of bonds per unit volume. Taking these into account, it can be concluded that increasing PbO concentration decreases the network connectivity of quaternary antimonite glasses by creating non-bridging oxygen sites which also results less tightly packing of the glass network. However, the FTIR results suggest the presence of both modifier and former role of PbO in these glasses.

Fig. 1 .

 1 Fig. 1. DSC curves of Sb2O3-Na2O-WO3-PbO glasses, scanned at a heating rate of 10 °C/min.

Fig. 2 .

 2 Fig. 2. The Kissinger plots for determining glass transition, Eg values of Sb2O3-Na2O-WO3-PbO glasses.

Fig. 3 .

 3 Fig. 3. Variation of density, ρ and molar volume, VM values of Sb2O3-Na2O-WO3-PbO glasses with PbO molar concentration.

Fig. 4 .

 4 Fig. 4. Variation of oxygen molar volume, VO and oxygen packing density, OPD values of Sb2O3-Na2O-WO3-PbO glasses with PbO molar concentration.

Fig. 5 .

 5 Fig. 5. Variation of refractive index of Sb2O3-Na2O-WO3-PbO glasses with PbO molar concentration at different wavelengths.

Fig. 6 .

 6 Fig. 6. Tranmittance spectra of Sb2O3-Na2O-WO3-PbO glasses.

Fig. 7 .

 7 Fig. 7. FTIR spectra of Sb2O3-Na2O-WO3-PbO glasses.

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .

 1234567 Fig. 1.

Table 3

 3 Refractive indices and band gap of Sb2O3-Na2O-WO3-PbO glasses.

	Sample ID	Refractive index (±1.10 -4 ) at 632.8 nm 825 nm 1060.7 nm 1551 nm	Eg (eV)
	SNWP10	2.0353	2.0180	2.0091	2.0033	2.979
	SNWP20	2.0799	2.0470	2.0310	2.0149	2.972
	SNWP30	2.0894	2.0560	2.0382	2.0221	2.975
	SNWP40	2.0953	2.0621	2.0431	2.0285	2.976

TABLES Table 1

Values of glass transition (Tg) and first crystallization onset and peak (Tc1/Tp1) temperatures, glass stability (∆T), glass transition activation energy (Eg), fragility parameter (m), density (ρ), molar volume (VM), oxygen molar volume (VO), oxygen packing density (OPD), average cross-link density ( c n ), number of bonds per unit volume (nb) and Poisson's ratio (µcal) of Sb2O3-Na2O-WO3-PbO glasses.


Marthe Lagarrigue

Florence Rossant

Alain Pierrot

Joël Gardes

Christophe Maldivi

Eric Petit

ASSESSING THE QUALITY OF DIGITAL RE-PUBLISHING OF TEXTUAL DOCUMENTS THROUGH THE FOLLOW-UP OF A CORRECTION PROTOCOL BY CROWDSOURCING

Keywords: digital edition, crowdsourcing, quality assessment, OCR, correction protocol, semantics, semiotics

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The preservation and the availability to the public of documents stored in libraries have become a very important issue. Gallica, a BnF1 (Bibliothèque nationale de France) library of digitized documents, has been created to this aim. Optical Character Recognition (OCR) software goal is to retrieve the textual information from images of documents, obtained through a digitization process. The output is then stored as ALTO 2 files, an electronic document format with the purpose of analysing the textual content of document images while storing the layout coordinates of textblocks. Yet, even if OCR algorithms reach nowadays high recognition rates for simple and well-printed documents, they still fail in specific cases, where document complexity, variability and quality are out of expectation. Such issues may come from the layout complexity, the quality of the original document, the typewriting itself, the digitization process, and so on. Hence, the OZALID project subscribes to the CIDRE [START_REF] Bapst | Integrated Multi-Agent Architecture for Assisted Document Recognition[END_REF] -Cooperative and Interactive Document Reverse Engineering -philosophy which aims at bringing humans in the loop, through a crowdsourcing process, admitting limits of OCR technologies. It is a cybernetics approach [START_REF] Bonin | Cybernetics or control and communication in the animal and the machine[END_REF] [START_REF] Wiener | Speech, langage and learning[END_REF]. Internet users are invited to spot content errors and interactively correct them through a User Interface (UI). One main and challenging issue is to determine automatically at which correction step a consensus is almost found; then the document can be sent to the chief editor, alleviating his checking task. User corrections may provide several text versions of a document. The main issue is then to follow up their quality and determine automatically when a satisfying version is obtained. The proposed solution consists in elaborating a protocol which assesses the quality of character identification by analysing the correction process evolution. The document structure recovery is not handled here. In short, the text quality is said "good enough" when a majority of correctors have no additional correction to propose. The role of the editor will be to check if the quality level is actually sufficient. The main contribution of the proposed study is the design of a quality assessment protocol, capable of processing huge amount of data without the need of any ground truth. Here is presented a feasibility study of the protocol with experimental results obtained with two data sets. This paper is organized as follows. First, we describe some related work (section 2). Secondly, we give a general description of the proposed protocol (Section 3). Experimental results are presented in the Section 4 before conclusion and perspective remarks.

RELATED WORKS

To the best of our knowledge, no automatic and general process has been proposed in the literature for assessing document reproduction quality, ensuring high-fidelity conformity of the electronic version to the original document.

Crowdsourcing is a very common method for correcting content of digitalized documents. For instance, the work of Garby et al. [START_REF] Grady | Crowdsourcing document relevance assessment with Mechanical Turk[END_REF] underlines the great impact of crowdsourcing with Mechanical Turk, and the one of Anh-Hoang et al. proposes a model and a tool to collect users' traces [START_REF] Anh-Hoang | Collecting Interaction Traces in Distributed Semantic Wikis[END_REF]. When it comes to comparing the quality of two text versions of a document, there are two standard methods. The first one compares the number of changes necessary to switch from one version to the other. This method, applied in several works is based on the Levenshtein distance (edit distance) [START_REF] Levenshtein | Binary codes capable of correcting deletion, insertions, reversals[END_REF] or some of its improved derivative [START_REF] Yujian | A normalized Levenshtein distance metric[END_REF]. The Levenshtein distance measures the similarity between strings by computing the minimal cost to align them through basic insertion, deletion and substitution operations. This kind of measure is very common in pattern recognition and error corrections [START_REF] Rice | The tird annual test of OCR accuracy[END_REF] [START_REF] Munyaradzi | Quality assessment in crowdsourced indigenous language transcription[END_REF]. Unfortunately, such method cannot decide which recognition result is the best one. A reference document, i.e. a ground truth, is needed to make a decision, see for example the work of Gardy et al. [START_REF] Grady | Crowdsourcing document relevance assessment with Mechanical Turk[END_REF] or Belaïd et al. [START_REF] Belaïd | A generic approach for OCR performance evaluation[END_REF]. This is a real drawback for systems working with big data sets. The second method for comparing two text versions aims at analysing the difference between quality indicators computed on each one. A lot of indicators have been proposed to describe a document and the identification of its characters. For example, Ben Salah's layout parameters [START_REF] Ben-Salah | Adaptative detection of missed text areas in OCR outputs: application to the automatic assessment of OCR quality in mass digitalization projects[END_REF] measure text areas in the document. OCR parameters, such as Word Confidence (WC), which measures the confidence on the character identification and Word Dictionary (WD), which states if a word exists in a dictionary or not, are also straightforward indicators. In this article, we propose a methodology which analyses the evolution of observables evaluated on every emended version provided by the crowdsourcing. Each observable quantifies the quality of the identification with respect to a specific criterion: based on image analysis features or referring to a dictionary. We assume that the quality level can no more be increased within the system when the proposed observables converge and remain stable, indicating that the correctors have reached a consensus.

PROTOCOL FRAMEWORK

The protocol aims at assessing the evolution of the text recognition during correction iterations performed by crowdsourcing. It takes place in two main phases: the document content correction by crowdsourcing and the measure of indicators on each corrected version.

Document corpus

Correction protocol: crowdsourcing simulation

We have experimented two crowdsourcing processes. In the first process (P1), the text is simultaneously and independently corrected by several correctors. Their corrections are merged. The merged version is then corrected, in the same way and the process is repeated several times (cf. Figure 2.a). In the second one (P2), the text is successively corrected by several correctors, one by one (cf. Volunteers in our study used a web interface developed by Orange Labs 3 for the corrections. Our experimentation involved eight volunteers with various profiles, whose one who sometimes makes intentional errors, and provided five corrections by crowdsourcing process.

Quality assessment protocol: indicators

We propose two complementary categories of observables. The first one gives priority to semiotics [START_REF] Gardes | Le document numérique : la complexité des formes et les formes de la complexité Systèmes et interfaces utilisant des descripteurs sémiotiques[END_REF], i.e., fidelity to the digitized image; observables of this category are therefore based on image analysis techniques. The second one favours semantics, i.e., conformity of the document; in this case, used tools are dictionary and statistical lexical analysis. Sometimes both are conflicting as in the following example, which can be interpreted either as pièces or pièees: In this case, we have to favour semantics tools and read pièces which exists in French dictionary. On the contrary, in the Lettre du petit Lily in Le château de ma mère of M. Pagnol, intentionally written with a lot of orthographic errors, the identification should rely mostly on the image. In our study, the proposed observables come from two software tools. The first one refers to image processing and clustering technics developed by Orange Labs, and the second one is the ABBYY Finereader5 OCR as used by i2S 4 , both labs collaborating to this work. Observables are measured on every corrected version of the text provided during the crowdsourcing process.

Characters confidence via image analysis techniques

A character confidence indicator, named CCF, has been proposed by Orange Labs in order to estimate the validity of the recognition and also control the users' correction process. Its principle relies on a consistency measure between a set of similar character shapes and their semantic values (i.e. their labels). Its calculus is based on the steps: Segmentation of the bounding box of the words (given in the ALTO file), in order to extract the character images on an entire page.

-Clustering analysis applied on the whole set of character images. For that, an agglomerative clustering algorithm has been implemented, based on a single-linkage criterion. -For each character shape s(i) of label l(i), belonging to the cluster C(i), counting of the number n(i) of shapes inside the cluster C(i) that are also labelled l(i). -The CCF is then given by ( ) ( ) ( )

i N i n i ccf =
, where N(i) is the total number of elements in the cluster C(i).

3 http://www.orange.com/fr/innovation 4 http://www.i2s.fr/ Hence, for any given shape, if all the other shapes of the same cluster have the same label than it, its CCF score is

( ) ( ) ( ) i N i N 1 -
. Thus, this score tends to 1 when the cluster size increases, meaning that consistency is maximum considering semiotic aspects. Conversely, if the CCF score is close to zero we are probably faced with either a misor a segmentation concern.

The OCR indicators OCR software usually computes two indicators, namely WC and WD. As we want to analyse the evolution of these scores, we have to guarantee that they are calculated in same conditions. However, the ones given by the initial recognition process cannot be reproduced since the first OCR is not known nor fixed (cf. section 3.2). For this reason, we propose to generate new images from every text version (including the first one), in known and constant conditions, and to apply a known and efficient OCR software to these new images. The OCR chosen in our study is ABBYY's FineReader 5 . WC and WD values provided by ABBYY for every version can then be compared. The image generator creates a synthetic bitmap from a text document (cf. [START_REF] Rabeux | Document perceptual quality groundtruth creation[END_REF] and [START_REF] Kieu | Semi-synthetic Document Image Generation Using Texture Mapping on Scanned 3D Document Shapes[END_REF]) given font, background and noise properties, it has been developed by the LaBRI lab 6 , partner of this work. The font is created from the original images of the document, whereas the text comes from the corrected version produced by crowdsourcing, which has to be evaluated.

Global protocol synthesis

Figure 4 synthesizes the quality assessment protocol that we propose for the evaluation of the text recognition quality, throughout each correction process performed by crowdsourcing. The clusters and CCF are calculated thanks to the original images as well as the current text version. In parallel, the observables WC and WD are calculated by the ABBYY OCR applied on images generated from the current text version.

Figure 4 Synthesis of the quality assessment protocol

The last step consists in analysing the evolution of these observables, based on statistics calculated on them. The results are presented in the following section.

RESULTS

The analysis focuses on the evolution of the indicator values; therefore, the shown graphics represent the evolution of indicators in %. An evolution tending to 0 means that the text identification converges to a stable and satisfying version according to the users. Our experiments are composed of four different flows since we consider two different crowdsourcing processes applied to two document extracts. The following indicators have been studied, describing:

-global statistics related to identification: the numbers of identified characters and strings; -semiotics aspect: mean and standard deviation of the CCF, number of element with CCF=1, WC; -semantics aspect: WD. We present one graphics by document with the evolution of all the indicators, expressed in %. ∆(t i ) describes the evolution in % of the score indicators between the i th and the i+1 th correction. Figure 5 emphasizes the evolution of indicators for the Hugo extract treated with the crowdsourcing process P2. Here are two important observations. First, there is a big variation between the first and the second correction steps mainly due to the great amount of artefacts considered as characters by the OCR and quickly corrected by users. Second, the variation of all studied indicators tends to 0 in a quite small number of iterations, which indicates, as expected, that correctors reach agreement. This tendency is very similar for the three other experimented flows.

Figure 5 Evolution of the indicators in a Hugo extract

In order to analyse more precisely the indicators evolution, we propose the following two tables. Table 1 which can be viewed as a very basic fusion rule of all criteria. These two tables show that all indicators tend to 0 for the four experimented flows. This means that for this set of correctors, we are near to obtain a stable state of the identification, i.e., the correction activity can stop. It is worth noting an increase of the global variation measure for Le Vampire processed with P1, between the 4 th and the 5 th corrections. Indeed, one corrector introduced intentional errors which were corrected during the 5 th iteration.

CONCLUSION AND PERSPECTIVES

This work is a preliminary study for assessing the quality of digital re-publishing of textual documents through the follow-up of a correction protocol by crowdsourcing. It is based on statistics, semantics and semiotics indicators. The experimental results presented above are very positive, since they show a convergence of the indicator variation measurements towards 0, meaning that a consensus has been reached between correctors. The protocol is being integrated on the OZALID platform and it will be tested on large databases during the next experiment. Further investigations will focus on two important points.

The first one will address the issue of indicators interpretation by implementing advanced fusion rules, especially when semantics and semiotics diverge. The second one will assess the establishment of a decision criterion notifying the end of the correction process, meaning that the current document version can be sent back to the editor.

  We tested our protocol on two book extracts. The first one comes from L'art d'être grand-père written by Victor Hugo, monograph of 1881, edition C. Levy; the second extract comes from Le vampire de Dusseldorf, 1932, edition Le Livre national (Paris).

Figure 1 :

 1 Figure 1: images and zooms extracted from our corpus

Figure 2 .Figure 2 :

 22 b). Both processes are very realistic, with cases of conflicts between simultaneous corrections (P1) and instabilities in corrections (P1, P2). The conflicts are resolved by majority vote during the merging process (P1). If the alternatives have the same cardinality, the original version is kept. The second process (P2) generally achieves a faster stabilization of the corrections, i.e. accordance between correctors. a) First process (P1) b) Second process (P2) Illustration of the two crowdsourcing processes

Figure 3 :

 3 Figure 3: Ambiguous case: semantics vs. semiotics

Table 2

 2

	presents the corresponding standard
	deviation.

Table 1 : Mean of the absolute value of indicator variation measures, expressed in %

 1

		∆1-0	∆3-1	∆3-2	∆4-3	∆5-4
	Hugo P1	1,27	3,62	0,92	0,90	0,56
	Vampire P1	3,97	1,09	0,11	0,10	0,19
	Hugo P2	10,76	0,30	0,31	0,25	0,19
	VampireP2	4,45	3,37	0,18	0,21	0,00

Table 2 : Standard deviation of the absolute value of indicator variation measures, expressed in %

 2

http://www.bnf.fr

http://www.loc.gov/standards/alto/v3/alto-3-0.xsd, http://www.abbyy-developers.eu/en:tech:features:alto

http://www.abbyyonline.com/

http://www.labri.fr/

Acknowledgements:

We would like to thank Nicolas Journet, Vincent Labreux and Kieu Van Cuong from the LaBRI lab for their kind and efficient collaboration to this work. We also thank Isabelle Josse and Sébastien Roux for their participation to the document correction and all the interesting discussions when elaborating this protocol. Finally, we are grateful to Jean-Luc Bloechle for his help brought to this article. This study was accredited by Cap Digital, and has been financed by BPI-France, Ile-de-France Region, General Council of Seine-Saint-Denis.