Roman Bertoni

Marco Cammarata

Maciej Lorenc

Samir F Matar

Jean-François Létard

Henrik T Lemke

Eric Collet

Ultrafast Light-Induced Spin-State Trapping Photophysics Investigated in Fe(phen) 2 (NCS) 2 Spin-Crossover Crystal

Few photo-active molecules undergo a complete transformation of physical properties (magnetism, optical absorption ...) when irradiated with light. Such phenomena can happen on the time scale of fundamental atomic motions leading to an entirely new state within less than one picosecond following light absorption. Spin crossover (SCO) molecules are prototype systems having the ability to switch between low spin (LS) and high spin (HS) molecular states both at thermal equilibrium or after light irradiation. In the case of a FeII (3d6) complexes in nearly octahedral ligand field, the two possible electronic distributions among the 3d split orbitals are S = 0 for the LS diamagnetic state and S = 2 for the HS paramagnetic state. In crystals, such photo-excited states can be long-lived at low temperature, as it is the case for the photoinduced HS state of the [Fe(phen)2(NCS)2] SCO compound investigated here. We first show how such bistability between the diamagnetic and paramagnetic states can be characterized at thermal equilibrium or after light irradiation at low temperature. Complementary techniques provide invaluable insights into relationship between changes of electronic states and structural reorganization. But the development of such light-active materials requires the understanding of the basic mechanism following light excitation of molecules, responsible for trapping them into new electronic and structural states. We therefore discuss how we can observe a photomagnetic molecule during switching and catch on the fly electronic and structural molecular changes with ultra-fast x-ray and optical absorption spectroscopies. In addition, there is a long debate regarding the mechanism behind the efficiency of such a light-induced process. Recent theoretical works suggest that such speed and efficiency are possible thanks to the instantaneous coupling with the phonons of the final state.

We discuss here the first experimental proof of that statement as we observe the instantaneous activation of one key phonon mode precluding any recurrence towards the initial state. Our studies show that the structural molecular reorganization trapping the photoinduced electronic state occurs in two sequential steps: the molecule elongates first (within 170 femtosecond) and bends afterwards. This dynamics is caught via the coherent vibrational energy transfer of the two main structural modes. We discuss the transformation pathway connecting the initial photo-excited state to the final state, which involves several key reaction coordinates. These results shows the need for replacing the classical single coordinate picture employed so far by a more complex multi-dimensional energy surface.

I. Introduction

The response of matter to light on ultrafast (i.e., picosecond and femtosecond) time scales represents a relatively new area in Materials Science. Electronic and/or structural changes are at the origin of light-activated functions in molecular [START_REF] Zewail | Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers[END_REF], biophysical [START_REF] Polli | Conical intersection dynamics of the primary photoisomerization event in vision[END_REF] or solid [START_REF] Nasu | Photoinduced Phase transitions[END_REF] materials. The past two decades saw remarkable technological advances in ultrafast laser systems and ultrafast science, making it possible to watch the dynamics and to understand the mechanisms of lightinduced transformations.

Spin CrossOver (SCO) molecules [START_REF] Halcrow | Spin-Crossover Materials: Properties and Applications[END_REF] are of particular interest because of their ability to switch between low spin (LS) and high spin (HS) molecular states not only under light excitation, but also at thermal equilibrium. In the case of a Fe II (3d 6 ) complexes, such as [Fe(phen) 2 (NCS) 2 ] investigated here, two possible electronic distributions among the 3d split orbitals in a nearly octahedral ligand field correspond to the LS (S=0) or HS (S=2) states (Fig. 1). The switching from LS to HS after light irradiation is referred to as the Light Induced Excited-Spin State

Trapping phenomenon (LIESST). It was thoroughly investigated in crystals; under continuous light irradiation at low temperature where a complete photo-conversion can be easily reached [5,[START_REF] Marchivie | D Structural Characterization of a Photoinduced Molecular Switch[END_REF][START_REF] Collet | Aperiodic Spin State Ordering of Bistable Molecules and Its Photoinduced Erasing[END_REF][START_REF] Buron-Le Cointe | Intermolecular control of thermoswitching and photoswitching phenomena in two spincrossover polymorphs[END_REF], or after pulsed irradiation at high temperature [START_REF] Cobo | Single-Laser-Shot-Induced Complete Bidirectional Spin Transition at Room Temperature in Single Crystals of (FeII(pyrazine)(Pt(CN)4))[END_REF][START_REF] Lorenc | Successive Dynamical Steps of Photoinduced Switching of a Molecular Fe(III) Spin-Crossover Material by Time-Resolved X-Ray Diffraction[END_REF][START_REF] Bertoni | Femtosecond photoswitching dynamics and microsecond thermal conversion driven by laser heating in FeIII spin-crossover solids[END_REF]. Light-induced SCO dynamics was also studied for molecules in solution, by the groups of McCusker, McGarvey, Hendrickson, Chergui, Mathies, Schoenlein. The use of ultrafast optical, X-ray or Raman spectroscopies gave a comprehensive dynamical description of the changes of electronic states and the structural reorganization [START_REF] Smeigh | Femtosecond Time-Resolved Optical and Raman Spectroscopy of Photoinduced Spin Crossover: Temporal Resolution of Low-to-High Spin Optical Switching[END_REF][START_REF] Cannizzo | Light-induced spin crossover in Fe(II)-based complexes: The full photocycle unraveled by ultrafast optical and X-ray spectroscopies[END_REF][START_REF] Mcgarvey | Spin-state relaxation dynamics in iron(II) complexes: solvent on the activation and reaction and volumes for the 1 A 5 T interconversion[END_REF][START_REF] Khalil | Picosecond Xray Absorption Spectroscopy of a Photoinduced Iron(II) Spin Crossover Reaction in Solution[END_REF][START_REF] Wolf | Sub-picosecond time resolved infrared spectroscopy of high-spin state formation in Fe(II) spin crossover complexes[END_REF][START_REF] Gawelda | Ultrafast Nonadiabatic Dynamics of [FeII(bpy) 3 ] 2+ in Solution[END_REF][START_REF] Brady | Spin-crossover in Transition Metal Compounds[END_REF][START_REF] Consani | Vibrational Coherences and Relaxation in the High-Spin State of Aqueous [Fe II (bpy) 3 ] 2+[END_REF][START_REF] Huse | Femtosecond Soft X-ray Spectroscopy of Solvated Transition-Metal Complexes: Deciphering the Interplay of Electronic and Structural Dynamics[END_REF][START_REF] Lemke | Femtosecond X-ray Absorption Spectroscopy at a Hard X-ray Free Electron Laser: Application to Spin Crossover Dynamics[END_REF][START_REF] Bressler | Femtosecond XANES Study of the Light-Induced Spin Crossover Dynamics in an Iron(II) Complex[END_REF][START_REF] Juban | Ultrafast dynamics of ligand-field excited states[END_REF][START_REF] Huse | Photo-Induced Spin-State Conversion in Solvated Transition Metal Complexes Probed via Time-Resolved Soft X-ray Spectroscopy[END_REF][START_REF] Chergui | Spin-crossover Materials[END_REF]. Our studies of LIESST in Fe III and Fe II SCO crystals [START_REF] Bertoni | Femtosecond Spin-State Photoswitching of Molecular Nanocrystals Evidenced by Optical Spectroscopy[END_REF][START_REF] Lorenc | Cascading photoinduced, elastic, and thermal switching of spin states triggered by a femtosecond laser pulse in an Fe(III) molecular crystal[END_REF][START_REF] Collet | Picosecond Diffraction Catches Structural Transients of Laser-Pulse Triggered Switching in a Spin-Crossover Crystal[END_REF][START_REF] Collet | Ultrafast spin-state photoswitching in a crystal and slower consecutive processes investigated by femtosecond optical spectroscopy and picosecond X-ray diffraction[END_REF][START_REF] Collet | Polymorphism in the spin-crossover ferric complexes [(TPA)Fe III (TCC)]PF 6[END_REF][START_REF] Marino | Femtosecond optical pump-probe reflectivity studies of spin-state photo-switching in the spin-crossover molecular crystals[END_REF], as well as reverse-LIESST [START_REF] Marino | The Role of Ligand-Field States in the Ultrafast Photophysical Cycle of the Prototypical Iron(II) Spin-Crossover Compound [Fe(ptz) 6 ](BF 4 ) 2[END_REF], indicated a photoswitching dynamics at the molecular level in nano-or micro-crystals [START_REF] Bertoni | Femtosecond photoswitching dynamics and microsecond thermal conversion driven by laser heating in FeIII spin-crossover solids[END_REF] similar to solution. After introducing how to investigate LIESST effect, we discuss its dynamics, including the coherent structural response recently revealed in [Fe(phen) 2 (NCS) 2 ] [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF]. . The value of the  M T product ( M being the molar magnetic susceptibility and T the temperature) approaching 3.3 cm 3 .K.mol -1 is characteristic of the paramagnetic HS (S=2) state above 180 K, while below this temperature it corresponds to the diamagnetic LS (S=0) state. Below 60 K, cw light-excitation at 650 nm completely transforms the system to the HS state [START_REF] Létard | A Guideline to the design of molecular-based materials with long-lived photomagnetic lifetimes[END_REF]. The change of electronic state also modifies optical properties (Fig 1b). At 650 nm, the higher absorption (lower reflectivity) in the LS state is due to the Metal to Ligand Charge Transfer (MLCT) band of the LS state. The electronic redistribution between the LS and HS states is accompanied by an increase of absorption below 620 nm and above 720 nm [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF].

Density Functional Theory [START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF][START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF] calculations (Fig. 2) performed with Gaussian 09 package [41] show that in the LS state the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbitals (LUMO) on both sides of the energy gap are respectively of t 2g -and e g -like character. The t 2g -e g energy gap is around 1.8 eV in LS state and 1.6 eV (775 nm) in the HS state. The LUMO lying  1.9 eV above the t 2g -like LS HOMO has electron density on the ligand phenanthroline groups only. The LS excitation at 650 nm corresponds then to a MLCT (green arrow in Fig. 2). -the distortion Σ of the FeN 6 octahedron, determined by the sum of the deviation from 90° of the 12 N-Fe-N cis angles in the coordination sphere:

     12 1 90 i i  changes from  LS  35° to  HS  65°.
These structural parameters (Fig 3b) are related to the spin state, and the photoinduced state generated at low temperature is very similar to the HS one [START_REF] Halcrow | Spin-Crossover Materials: Properties and Applications[END_REF][START_REF] Cannizzo | Light-induced spin crossover in Fe(II)-based complexes: The full photocycle unraveled by ultrafast optical and X-ray spectroscopies[END_REF][START_REF] Khalil | Picosecond Xray Absorption Spectroscopy of a Photoinduced Iron(II) Spin Crossover Reaction in Solution[END_REF][START_REF] Huse | Femtosecond Soft X-ray Spectroscopy of Solvated Transition-Metal Complexes: Deciphering the Interplay of Electronic and Structural Dynamics[END_REF][START_REF] Lemke | Femtosecond X-ray Absorption Spectroscopy at a Hard X-ray Free Electron Laser: Application to Spin Crossover Dynamics[END_REF][START_REF] Bressler | Femtosecond XANES Study of the Light-Induced Spin Crossover Dynamics in an Iron(II) Complex[END_REF][START_REF] Huse | Photo-Induced Spin-State Conversion in Solvated Transition Metal Complexes Probed via Time-Resolved Soft X-ray Spectroscopy[END_REF]. The <Fe-N> elongation in the HS state is associated with the electronic population of less bonding e g orbitals.

The increase of  due to N-Fe-N bending, was underlined as essential for stabilizing the photoinduced HS state at higher T(LIESST) [START_REF] Marchivie | D Structural Characterization of a Photoinduced Molecular Switch[END_REF]. Consequently, the equilibrium position in the HS potential is moved away from that of LS [START_REF] Buron-Le Cointe | Intermolecular control of thermoswitching and photoswitching phenomena in two spincrossover polymorphs[END_REF]. This electronic conversion accompanied by deformations of the Fe-N 6 octahedron, result in important changes of the XANES (x-ray absorption near edge structure) spectrum around the Fe K-edge (Fig. 3c). 2). The LS state is optically silent at 760nm since the lowest t 2g -like HOMO and e glike LUMO is at higher energy (Fig. 2). The absorption of the HS state at 1.6 eV results therefore from the d-d gap narrowing [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF]. Data at 760 nm show that this change occurs within  gap = 140 [START_REF] Huse | Femtosecond Soft X-ray Spectroscopy of Solvated Transition-Metal Complexes: Deciphering the Interplay of Electronic and Structural Dynamics[END_REF] fs. Since this ligand field weakening is related to the elongation of the <Fe-N> bond length,  gap correlates well with  <Fe-N>= 170 [START_REF] Huse | Femtosecond Soft X-ray Spectroscopy of Solvated Transition-Metal Complexes: Deciphering the Interplay of Electronic and Structural Dynamics[END_REF] fs measured by XANES. Our results demonstrate that by probing a transition sensitive to the ligand field, by means of optical spectroscopy, it is possible to gain some insight into structural dynamics of the Fe-N 6 octahedron. The electronic peak observed at 850 and 900nm, corresponds to the photoexcited singlet 1 MLCT state (t 2g 5 e g 0 L 1 ). It decays within less than 50 fs and cannot be well resolved with 100 fs time resolution [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF]. Other intermediate (INT) states can be involved in the inter-system crossing (ISC) and the 1,3 MLCT→ 3 T→HS sequence dominates [START_REF] Zhang | Tracking Excited-State Charge and Spin Dynamics in Iron Coordination Complexes[END_REF].

The optical kinetic traces shown in Fig. 6 also exhibit oscillating components both in reflectivity and transmission geometries. They are the signatures of molecular vibrations accompanying the LIESST and similar oscillations were observed first in Fe(bpy) 3 by Chergui et al [START_REF] Consani | Vibrational Coherences and Relaxation in the High-Spin State of Aqueous [Fe II (bpy) 3 ] 2+[END_REF]. The oscillating components shown in Fig. 7 were extracted from the fit of the data shown in Fig. 6 [33]. The time-dependent fast Fourier transform trace at 760 nm reveals a main mode at around 113cm -1 , which is only observed during the first picosecond. Other reflectivity traces reveal another oscillation around 85cm -1 , in-phase for all the probing wavelengths and observed both in transmission and reflectivity.

Different wavelengths are sensitive to different degrees of freedom. The response at 760 nm isas discussed abovemostly sensitive to the Fe-N core expansion, while the signal at 900 nm is mostly sensitive to the bending of the molecules (This remarkable difference is rationalized by using time dependent DFT calculations as discussed below). The exponential fits of optical reflectivity at these wavelengths show significantly different time scales thus suggesting a nonsimultaneous expansion and distortion of the molecule as depicted in Figure 7h where the two exponential time constants (from OR 760 nm and OR 900 nm) are used to reconstruct the average evolution of the two structural parameters. To test this hypothesis even further we have modeled a simple coupled-oscillator whereby the initial elongation of the Fe-N core induces the octahedral distortion. This model discussed in detail in reference 33 can reproduce fairly well the oscillating part of the experimental data as shown in Fig. 7, panels b and c.

To further this investigation, we present in Fig. 8 new measurements at 760 nm with probe light polarized parallel or perpendicular to the crystal axis b, while keeping all other experimental parameters identical. The data for the parallel configuration reproduces well the ones already published in ref 33 (Fig. 7), indicating the activation and damping of a mode around 113 cm -1 during the first ps. However, the data for the polarization perpendicular to b, show a different behavior as the frequency of the observed mode is 85 cm -1 .

III.2 Discussion

Recent theoretical studies by van Veenendaal discuss the mechanism behind the extremely fast and efficient ISC during LIESST in terms of dephasing of the photoexcited state into the HS phonon states [START_REF] Van Veenendaal | Model of Ultrafast Intersystem Crossing in Photoexcited Transition-Metal Organic Compounds[END_REF][START_REF] Chuang | Ultrafast cascading theory of intersystem crossings in transitionmetal complexes[END_REF]. The change from LS to HS states, which strongly differ in both electronic configuration and molecular structure (metal-ligand distance), is mediated by the spin-orbit coupling. The ultrafast ISC is displacive as the <Fe-N> bond elongation drives the system into the HS potential. Its strong damping is associated with the efficient self-trapping of the photoinduced HS state, as schematically shown in figure 9a. Our results shown in Fig. 6 and7 strongly support this mechanism. The 113 cm -1 mode is activated just after light excitation, as Fe-N elongates, and corresponds to the molecular breathing mode: a totally symmetric Fe-N stretching with respect to the 2-fold molecular axis [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF][START_REF] Baranovic | Vibrational study of the Fe(phen)2(NCS)2 spin-crossover complex by densityfunctional calculations[END_REF][START_REF] Ronayne | Vibrational spectrum of the spin crossover complex [Fe(phen) 2 (NCS) 2 ] studied by IR and Raman spectroscopy, nuclear inelastic scattering and DFT calculations[END_REF]. This eigenvector of symmetry A in the C 2 point group of the complex is hereafter referred to as the breathing coordinate D. Fig. 6b and6c also revealed the activation of a second mode at 85 cm -1 , corresponding to the butterfly mode [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF][START_REF] Baranovic | Vibrational study of the Fe(phen)2(NCS)2 spin-crossover complex by densityfunctional calculations[END_REF][START_REF] Ronayne | Vibrational spectrum of the spin crossover complex [Fe(phen) 2 (NCS) 2 ] studied by IR and Raman spectroscopy, nuclear inelastic scattering and DFT calculations[END_REF], which bends the ligand and the N-Fe-N angles without significantly changing Fe-N distances. We will refer to this mode as a bending coordinate . Unlike the breathing mode, activated instantaneously, the bending mode with 390 fs period appears only after 500fs and has a maximal amplitude around 1200fs (Figures 78). Such delayed activation of other modes results from the fact that the HS potential is reached with excess energy. Then the nonequilibrium vibrational energy relaxation in the product HS state activates other modes. For understanding why the observation of specific vibrational modes depends on the probe energy and/or polarization, an accurate description of excited states is needed. The time dependent DFT (TD-DFT) approach has proved an excellent tool used in quantum chemistry [47]. The results obtained within TD-DFT lead to the so-called 'natural transition orbitals' NTO through an account for hole-particle pairs which are then used to interpret the excited states corresponding to the absorption of the probe light. TD-DFT as implemented in the Gaussian 09 package [41] was applied for obtaining the NTO of HS [Fe(phen) 2 (NCS) 2 ] starting from geometry optimized molecule with UB3LYP/6-31g(d,p) functional-basis set. Fig. 10a shows the NTO corresponding to the hole-particle transition state around 760 nm for polarization parallel to the b axis. The strong weight of the particle orbital on the Fe-N bonds explains its sensitivity to the breathing mode, for which the Fe-N elongation is the main characteristic. Fig. 10b shows the transition state around 760 nm for polarization perpendicular to the b axis, Fig. 10c and10d shows the transition state around 550 and 900 nm respectively for polarization parallel to the b axis. For these last three cases, the sensitivity to the bending mode observed in Fig. 6b is explained by the weight of the particle orbital mainly located on the ligand (not on the Fe-N bonds). This selectivity in terms of light polarization, which can be used in the solid state, opens interesting opportunities for disentangling complex transformation dynamics where different degrees of freedom are involved.

III.3 Curved trajectory on the potential energy surface

We can now summarize all these results in a global picture for describing the photophysics of

LIESST. An ultrafast ISC from the MLCT state (50fs) occurs and the less bonding HS potential is rapidly reached, defining a new equilibrium Fe-N bond length. Intermediate states serving as mediators appear in the process but are difficult to identify here. Å,  LS =35°) and the one of the HS state at (D HS 2.16 Å,  HS =65°) (Figure 3b). The analysis of XANES, OT and OR data [START_REF] Cammarata | Sequential Activation of Molecular Breathing and Bending during Spin-Crossover Photoswitching Revealed by Femtosecond Optical and X-Ray Absorption Spectroscopy[END_REF] gave an average elongation D mean (t) with a 170 fs time constant, whereas the average torsion  mean (t) occurs with a 250 fs time constant (Fig. 7h). The system therefore follows a curved trajectory in the (D,) coordinate space of the PES, with a sequential activation of the key modes. This process involves a very fast energy transfer: the breathing mode is damped on a timescale of 160 fs (Fig. 7g). This strong damping hinders recurrence to the initial state and explains why the structural trapping is so efficient.

IV Conclusion

This comprehensive study allows drawing an elaborate scenario explaining the speed and efficiency of LIESST, underlying the importance of structural dynamics and energy dissipations.

The curved trajectory on PES, involving coherent structural dynamics, reveals the basic dynamical transformation mechanism associated with a deterministic process.

In order to understand the physical processes allowing functionalization with light, probes sensitive to specific degrees of freedom are mandatory. Ultrafast techniques allow now to follow and disentangle the dynamical changes of electronic and structural degrees of freedom. Such multi-probe ultrafast studies will become routine in the field of light-functionalized materials and the present results pave the way for investigating more complex phenomenon. As it is now possible to reach a time resolution better than elementary molecular motions, processes driven by coherent structural dynamics can be deeply investigated. It will represent an important topic in light-activated functions, as this mechanism allows to reach the shortest time-scale for the structural trapping, corresponding to the elementary molecular deformations.

Figure 1 .

 1 Figure 1. a) Thermal evolution of the  m T product of [Fe(phen) 2 (NCS) 2 ] showing a change of spin state around 180 K. The value above 180 K ( m T 3.3 cm 3 .K.mol -1 ) is typical of paramagnetic Fe II HS state, whereas the very small value below 180 K is typical of LS diamagnetic state. Below 60 K, the HS state is reached by cw light excitation of the LS state at 650 nm. b) Evolution of the diffuse reflectivity signal recorded at 650 nm and generating LIESST below 60 K.

Figure 2 .

 2 Figure 2. Schematic energy diagram and molecular orbitals obtained from DFT calculations. The MLCT process in the LS state with the pump at 650 nm promotes electrons from t 2g -like to ligand orbitals (L), whereas the probe at 760 nm corresponds to HS t 2g -like to e g -like d-d transition. The Fe atom is in the center, N atoms are blue, C atoms are grey, S atoms are yellow, H atoms are white.

Figure 3 .

 3 Figure 3. (a) LS (140 K, blue) and HS (200 K, red) structures of [Fe(phen) 2 (NCS) 2 ]. (b) Temperature dependence of Fe-N bonds and  parameter, showing the first-order phase transition around 180 K between LS and HS states. Tthe parameters obtained after cw irradiation at 650 nm are identical to those of the HS state at high temperature. (c) XANES spectra and variation XANES measured between the HS (200K) and LS (140K) states. Adapted with permission from ref. 33. Copyright (2014) American Physical Society.

Figure 4 .

 4 Figure 4. Schematic representation of the single crystals of [Fe(phen) 2 (NCS) 2 ] with the

Figure 5 .

 5 Figure 5. Time resolved change of X-ray absorption at 7125eV and 7148eV. Red lines are fit to single exponential rise with time constant  <Fe-N> =170(20)fs. Adapted with permission from ref. 33. Copyright (2014) American Physical Society.

Fig. 6

 6 Fig.6shows optical changes observed on single-crystals, when the probe polarization is parallel to the b axis. At the energy of 1.6 eV (760nm) both transmission and reflectivity show a decreasing signal related to the absorption of the HS state, which corresponds to d-d transitions (see part III.2). The LS state is optically silent at 760nm since the lowest t 2g -like HOMO and e g -

Figure 6 .

 6 Figure 6. a) Time resolved traces of optical transmission (OT) and reflectivity (OR) at 760nm, b) 900 nm and 550 nm, c) and 850nm with probe polarization parallel to b axis. All traces were fitted (red lines) with a single exponential function accounting for the fast dynamic and a fifth order polynomial to take into account for slower processes such as vibrational cooling. Adapted with permission from ref. 33. Copyright (2014) American Physical Society.

Figure7.

  Figure7. (a-c), oscillating component of OR at 760 nm, OR at 900 nm and OT at 850 nm. (d-f),

Figure 8 .

 8 Figure 8. Time resolved change of reflectivity at 760nm (1.6eV) for probe polarization parallel

Fig. 7 &

 7 8 show a spectral weight transfer from breathing to bending. The structural stabilization occurs over two steps with a sequential activation of breathing then bending via coherent energy transfer.

Figure 9 .

 9 Figure 9. (a) Schematic representation of the elongation and damping of the breathing mode

Figure 10 .

 10 Figure 10. NTO of hole and particle for different light polarization indicated in figure, with respect to the 2-fold molecular symmetry axis, around 760 nm calculated at 1.668 eV (a), around 760 nm and calculated at 1.667 eV (b), around 550 nm and calculated at 2.2 eV (c) and around 900 nm and calculated at 1.32 eV (d).

Funding Sources

This work was supported by the Institut Universitaire de France, Rennes Métropole, Région Bretagne (CREATE 4146), ANR (ANR-13-BS04-0002), CNRS (PEPS SASLELX) and Europe (FEDER). Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Stanford University.


M Yahiaoui
email: malik.yahiaoui@enit.fr

J-Y Paris

J Denape
email: cjean.denape@enit.fr

Correlation between acoustic emission signals and friction behavior under different sliding configurations and materials pairs

Keywords: Acoustic emission, friction, contact temperature, wear, speed camera, tungsten carbide, alumina, thermoplastic polyurethane

This work focuses on the acoustic emission signals related to three different tribological systems: a rotary sliding contact between WC-Co pins against alumina flat counterfaces, a fretting contact between alumina pins against alumina flat counterfaces and a reciprocating sliding flat on flat contact between thermoplastic polyurethanes (TPU) and a steel counterface. This document relates dependences observed between tribological behaviors and variations of acoustic emission signals. Therefore, a third body approach is used to explain these correlations and to highlight the aspect of nature and associated energy of acoustic emission sources.

Introduction

Tribological systems are studied using acquisition systems associated to several kinds of sensors. For example, load and torque sensors are performed to measure the friction coefficient, thermocouples to evaluate the contact temperature, vision systems to follow the evolution of the contact morphology, etc. However, the optical observation of the active surfaces during sliding friction is impossible in most of the tribological systems. In this way, the study of acoustic emission (AE) signals emitted by the closed sliding contact is an interesting solution.

Acoustic emission defines mechanical waves produced by the release of elastic stress energy from a localized source. Baranov et al. [START_REF] Baranov | Acoustic emission in friction[END_REF] identified different sources of acoustic emissions (e.g. cracks propagation and debris formation) and their associated range of energy and of frequency (e.g. 106 to 108 aJ for the microcracks formation) in the sliding contacts. They also specified a list of material physicochemical and mechanical properties and friction conditions influencing the acoustic emission amplitude. For example, a rough relief, a high hardness and an abrasive wear are factors of increase in amplitude. Conversely, fine grains, slow sliding velocity and adhesive wear are factors of decreasing amplitude of the acoustic emission signals.

This work focuses on the acoustic emission signals related to three different tribological systems:

• A rotary sliding contact between a WC-Co pin against an alumina flat counterface [START_REF] Yahiaoui | Comportement tribologique de diamants polycristallins et de carbures cémentés WC-Co avec traitements de graduation -application aux inserts et taillants d'outils pour le forage de formations rocheuses fortement abrasives[END_REF];

• A reciprocating sliding flat on flat contact between a thermoplastic polyurethane (TPU) and a steel counterface [START_REF] Martínez | Analysis of wear mechanism in TPU-steel contact pair by means of long stroke tribometer tests[END_REF];

• A fretting contact between an alumina pin against alumina flat counterface [START_REF]Performances en de composites alumine-métal avec ou sans nanotubes de carbone : identification des conditions de grippage et des mécanismes d'usure[END_REF]. This study gathers several test campaigns dealing with effects of contact parameters, as load and velocity, on acoustic emission. Moreover, the studied contacts highlighted the dependence of acoustic emission signals towards material physicochemical properties in relation to the contact thermomechanical responses. More generally, these experiments showed the links that can be revealed between the overall tribological system consideration and the acoustic emission.

Acoustic Emission Device

Acquisition Setup. Acoustic emission acquisitions are performed using a filter of vibrational phenomena which are unrelated to friction (e.g. movement of mechanical parts of the tribometer).

Hence, before each experiment, a threshold of mechanical noises must be set. In addition, the large band piezoelectric sensors (references Micro-80 and Pico of the company Euro Physical Acoustics) used in this study have an optimum sensibility between ultrasonic frequencies of 0.1 MHz and 1 MHz. The sensor fixation near the sliding contact is a crucial step in the acquisition setup called the coupling. This coupling was performed by a water-based adhesive containing styrene acrylic copolymer. This adhesive allows a good transmission of acoustic signals, dries in few seconds and the sensors are easily detached after the experiments. Hsu-Nielsen sources were created to test the coupling quality (standard NF EN 1330). This procedure consists in the breaking of standard pencil leads (hardness 2H and 0.5 mm in diameter) near the future sliding zone. The Hsu-Nielsen sources generate repeatable acoustic emission signals (i.e. standard hits). Finally, the coupling is achieved when the acoustic signal transmission leads to acquisition amplitude over 90 dB and ideally 100 dB.

Signals Processing. The recorded acoustic emission signals need to be pre-processed to avoid a too high storage of data and laborious post-processing operations. Therefore, the signals are not continuously recorded but are cut in hits. These hits correspond to events generating acoustic emission signals in the contact with amplitudes overpassing the fixed threshold. This threshold depends on the noise created by the mechanical parts surrounding the contact. The signals coming from the sensor are also pre-amplified before being treated by the acquisition card of the computer. A moving window of acquisition needs to be defined to obtain entire hits waveform without missing a part of them or to avoid echoes. This window is characterized by the parameters of sample rate, pre-trigger, peak definition time (PDT), hit definition time (HDT) and hit lockout time (HLT). These parameters depend on the tribological system and on the propagation of the acoustic emissions in the considered materials. In this study, only the energy of the acoustic emission signals is considered. More particularly, the absolute energy E a is calculated by the integration of the squared signal s(t), translation of the mechanical pulses in electrical tension, over the period of a hit and normalized by the resistance Re of the acoustic emission device (Eq. 1).

dt t s R E T e a ⋅ = ∫ ) ( 1 2 (1)
Experimental Procedures WC-Co / Alumina Sliding Contact. The wear mechanisms of cemented carbide samples were studied at the LGP laboratory with a rotary tribometer (Fig. 1a). During experiments, a pin-on-disk contact is realized. The samples have a spherical tip with a radius of 4.37 mm and slides against a flat alumina counterface. The wear of these samples was carried out at various normal loads FN between 0 and 300 N with velocities v between 0.1 and 1 m•s-1 with a test time t of one hour. Nominal conditions were also set at 264 N and 0.5 m•s-1 always during one hour. The normal load and the torque were measured to calculate the friction coefficient µ. The acoustic emission sensor was coupled on the upper shaft at 120 mm from the fixed insert to obtain optimum signals without saturation (Fig. 1b). Three different WC-Co samples were considered with the references P8, P12 and P16 from the company Varel Europe. These references respectively correspond to cobalt contents of 8 ± 1, 12 ± 2 and 15 ± 1 wt.%. In addition, others physicochemical and mechanical parameters have been measured for these samples (Table 1). Simply, as indicated by the cemented carbide manufacturers, when the cobalt content or the WC grains size increases, the hardness decreases and the fracture toughness increases. Wear experiments on TPU against a steel counterface were performed on a reciprocating long stroke tribometer at the ITA laboratory (Zaragoza, Spain) (Fig. 2). The selected TPU material has a density of 1.23 ± 0.02 g•cm -3 , a non-significant mineral charge content of 0.05 wt.% and an hardness of 54 ± 1 Sh(D). A flat-on-flat contact was set between a rectangular TPU sample (25 mm × 15 mm × 10 mm) and a steel countermaterial (2000 mm × 37 mm × 9 mm). Three experimental campaigns were carried out to study the effects of load (from 166 N to 401 N), velocity (at 0.32 m•s -1 and 0.5 m•s -1 ) and temperature (from 21 °C to 75 °C) to establish the TPU material tribological behavior against a heated steel counterface. The Pico EA sensor was fixed near the contact on the mobile part. Alumina / Alumina Fretting Contact. Friction experiments of alumina pins against a flat pure alumina were carried out with a fretting device at the LGP laboratory (Fig. 3). The alumina pins are hemispherical with a radius of 20 mm. The experiments were performed with progressive normal loads F N form 6 N with a step of 2 N each 5 min. A tangential force F T is generated by an inputted driving force. This force oscillates between -20 and 20 N (± 1 N). The pins of alumina at 99.7 % were manufactured by sintering under pressure and referenced as A99. The counterfaces of alumina at 99.7 % were realized by spark plasma sintering (SPS) and referenced A99S. The SPS process acts by significantly reducing the alumina mean grains size ( Table 2). This process also enhances the mechanical properties of the alumina. 3). The other parameters (e.g. PDT and HLT) were selected in order to obtain the shortest but complete hits wave form. For the other experiments, the threshold and the pre-amplification were respectively set at 30 dB and 40 dB.

Results and Correlations

AE and Mechanical Energy. For all the configurations, the amount of mechanical energy W transmitted through the sliding contact is equal to the product of the transverse force F T by the travel distance L or by the velocity v multiplied by the time t (Eq. 2).

t v F L F W ⋅ ⋅ = ⋅ = Τ Τ (2)
Most of this energy is converted to heat during friction and only a small part is transformed in elastic waves. In this way, the energy E a of the acoustic emission signals should increase with the overall mechanical energy W. This dependence clearly appears in the experiments studied here:

• For example, on the rotary tribometer with the WC-Co samples, E a globally increases from 0 to 7•10 10 aJ when the sliding velocity increases from 0.1 to 1 m•s -1 and vice versa (Fig. 4a); • During fretting experiments at progressive load with the alumina A99S, the work W decreases with time meanly because of a reduction of the stroke and the travel distance (Fig. 4b) and so as the absolute energy E a ; • With the reciprocating tribometer and the TPU samples, the work is approximately constant as a result of the imposed travel distance and the slightly increasing friction force. Again, the absolute E a follows the variation of the overall mechanical energy W (Fig. 4c).

( More precisely, the absolute energy E a tends to follow the friction coefficient changes. Indeed, even with a non-linear evolution of the friction coefficient, the acoustic absolute energy exhibits the same variations (Fig. 4a). These observations indicate an affine relationship between the friction and the acoustic emission energy.

Effect of Material Properties. Even if the energy E a follows the friction coefficient changes, its amplitude depends on the nature of the AE sources. In this way, the mean friction coefficient of the WC-Co samples decreases with the cobalt content (i.e. in order from P8, P12 to P16) but the AE absolute energy appears to be the highest on average for the P12 (Fig. 5). Observations of the P12 samples worn surfaces display a great proportion of transgranular cracks.

Further study on these cemented carbides showed that the transgranular cracking mode was associated to the P12 sample coarse WC grains. The P8 and P16 samples, with finer microstructures, show predominantly intergranular cracks during wear. This difference of crack mode explains that the P12 sample generates more energetic acoustic emission signals. Indeed, the energy dissipation induces by transgranular crack propagation is greater than the one induces by intergranular mechanism. This observation is also reflected by the fracture toughness K IC measured on the samples (Table 1).

Another example of the influence of materials and the importance of the nature of AE sources is brought by the experiments on the TPU polymer. During these experiments, it was shown that a stick-slip phenomenon appear in the contact after a threshold of load (around 270 N). The stick-slip produces a higher discrepancy on forces but friction meanly verifies an Amontons-Coulomb law (Fig. 6a). Concerning the absolute energy, before this threshold, E a increases because increasing load generates a higher mechanical energy in the contact (Fig. 6b). After this threshold, the stickslip mechanisms modify the nature of the AE sources by a change of sliding mode in the contact and a drop of absolute energy is then observed.

Discussions

Tribological behaviors can be described using a third body approach by considering the speed accommodation mechanisms in the contact [START_REF] Berthier | editeurs, The third body concept interpretation of tribological phenomena[END_REF][START_REF] Denape | Fundamentals of tribology and bridging the gap between the macro-and micro/nanoscales, chapitre Wear particle life in sliding contact under dry conditions: third body approach[END_REF]. In this way, acoustic emission sources can be localized at the accommodation sites S i and their nature can be associated to an accommodation mode M j (Fig. 7).

Fig. 7: Mechanisms of speed accommodation in the tribological system (after [START_REF] Denape | Fundamentals of tribology and bridging the gap between the macro-and micro/nanoscales, chapitre Wear particle life in sliding contact under dry conditions: third body approach[END_REF]).

With this approach, friction depends on the accommodation mechanisms acting at the interface through the third body. A poor third body action could provoke more direct interactions of the first bodies and more energetic modes (i.e. elastic, plastic and fracture) located on the samples surface. An active third body separates the first bodies and implies low energetic modes (i.e. shearing and rolling) inside the third body itself. Accordingly, the increase of the friction coefficient is associated to the increase of sites density and then of acoustic emission sources density. However, the amount of energy dissipated by these sources depends on the mode of accommodation. For example, concerning the stick-slip mechanism for the TPU/steel contact, the drop of acoustic emission energy can be related to less energetic mechanisms occurring during the stick periods. Indeed, during stick periods, the TPU polymer is elastically or plastically deformed (S 1 M 0 or S 1 M 1 ). Otherwise, during slip periods, the TPU slides against the steel counterpart, it wears (S 1 M 2 ) and rolls are formed (S 1 M 4 ). In addition, the third body shears (S 3 M 3 ) and rolling accommodations (S 3 M 4 ) are performed at the interface.

Conclusion

Three experimental devices were studied here: a rotary tribometer with a WC-Co / alumina contact, a reciprocating tribometer with a TPU / steel contact and a fretting tribometer with a alumina / alumina contact. In one hand, these experiments showed that the calculated acoustic emission energy follows the friction coefficient changes. In other hand, they also point out that material properties affect the level of energy of the acoustic emission signals. Eventually, a third body approach gathers these aspects. The friction coefficient and acoustic emission signals are related by the accommodation sites activated during friction. The acoustic emission energy dissipated by the sliding contact is function of the nature of acoustic emission sources associated to the modes of accommodation.

Fig. 1 :

 1 Fig. 1: Rotary tribometer and AE device configuration (LGP laboratory): a -general view of the rotary tribometer; b -view of the Micro-80 sensor coupled near the contact.

Fig. 2 :

 2 Fig. 2: Reciprocating long stoke tribometer and AE device configuration (ITA laboratory).

Fig. 3 :

 3 Fig. 3: Fretting device configuration and AE device configuration (at the LGP laboratory): aphotography of the device; b -detailed sketch of the device.

Fig. 4 :

 4 Fig. 4: Work, Friction coefficient and absolute energy results: a -experiment at progressive velocities (from 0.1 to 1 m•s -1 and from 1 to 0.1 m•s -1 ) on the rotary tribometer with the P8 WC-Co sample; b -fretting experiments at progressive load (from 6 to 48 N) with A99S counterface; cresults at constant a load of 248 N on the reciprocating tribometer with a TPU sample.

Fig. 5 :

 5 Fig. 5: Results of experiments with the WC-Co samples at constant load of 264 N over three repeatability tests: a -average of friction coefficients (box and whiskers chart); b -average of absolute energy.

Fig. 6 :

 6 Fig. 6: Effect of the stick-slip phenomenon: a -Amontons-Coulomb law tangential force vs. normal force; b -absolute energy vs. normal force.

Table 1 :

 1 Physicochemical and mechanical properties of WC-Co samples P8, P12 and P16.

	WC-Co samples	P8	P12	P16
	Cobalt content [wt. %]	8 ± 1	12 ± 2	15 ± 1
	Mean grain size [µm]	3 ± 0.1	7 ± 3	5 ± 1
	Hardness [HV 2 kg/10 s]	1326 ± 31 1095 ± 29 1061 ± 3
	Fracture toughness [MPa•m1/2] 11.0 ± 0.4 19.5 ± 0.8 18.2 ± 0.2

TPU / Steel Reciprocating Sliding Contact.

Table 2 :

 2 Physical and mechanical properties of alumina materials (CIRIMAT laboratory data[START_REF]Performances en de composites alumine-métal avec ou sans nanotubes de carbone : identification des conditions de grippage et des mécanismes d'usure[END_REF]).

	Alumina samples	A99	A99S
	Density [g•cm -3 ]	3.92 ± 0.05 3.98 ± 0.05
	Mean grain size [µm]	8 ± 0.2	2.5 ± 0.2
	Hardness [HV 1 kg/10 s]	1570 ± 70 2010 ± 110
	Ultimate strength [MPa]	320 ± 5	650 ± 10
	Fracture toughness [MPa•m 1/2 ]	5 ± 0.1	5 ± 0.2

AE

Device Parameters. The wear experiments with the WC-Co samples generated intense acoustic emission signals and the threshold was then set at 40 dB with the lowest pre-amplification of 20 dB (Table

Table 3 :

 3 Acoustic emission acquisition parameters of the various tribometer.

	AE parameters	Rotary tribometer	Reciprocating long stoke tribometer	Fretting tribometer
	Threshold [dB]	40	35	27
	Pre-amplification [dB]	20	40	40
	Sample rate [kHz]	5000	1000	5000
	Pre-trigger [µs]	50	256	50
	PDT [µs]	1000	200	200
	HDT [µs]	2000	800	500
	HLT [µs]	20000	1000	1000


Maroua Mehri
email: maroua.mehri@univ-lr.fr

Petra Gomez-Krämer

Pierre Héroux
email: pierre.heroux@univ-rouen.fr

Alain Boucher
email: alain.boucher@univ-lr.fr

Rémy Mullot
email: remy.mullot@univ-lr.fr

A Pixel Labeling Framework for Comparing Texture Features: Application to Digitized Ancient Books

Keywords: Ancient digitized books, Pixel labeling, Texture, Multiresolution, Consensus clustering, Clustering and classification accuracy metrics

In this article, a complete framework for the comparative analysis of texture features is presented and evaluated for the segmentation and characterization of ancient book pages. Firstly, the content of an entire book is characterized by extracting the texture attributes of each page. The extraction of the texture features is based on a multiresolution analysis. Secondly, a clustering approach is performed in order to classify automatically the homogeneous regions of book pages. Namely, two approaches are compared based on two different statistical categories of texture features, autocorrelation and co-occurrence, in order to segment the content of ancient book pages and find homogeneous regions with little a priori knowledge. By computing several clustering and classification accuracy measures, the results of the comparison show the effectiveness of the proposed framework. Tests on different book contents (text vs. graphics, manuscript vs. printed) show that those texture features are more suitable to distinguish textual regions from graphical ones, than to distinguish text fonts.

INTRODUCTION

In order to provide a wider access to libraries collections which need to be protected from too frequent handling, numerous projects have been established. For instance, Google has conducted large digitization programs "Google Books Library Project" of cultural heritage with the help of several libraries. Therefore, automatic processing of ancient digitized documents has undergone tremendous growth over the last few years. Thereby, reliable ancient document interpretation systems have been the topics of major interest of many libraries and historians and the prime issue of research in document analysis community. There has been a great challenge in the refinement of the wellknown approaches based on strong a priori knowledge. Many methods have been presented in the literature [START_REF] Mao | Document structure analysis algorithms: a literature survey[END_REF][START_REF] Mullot | Les documents écrits : De la numérisation à l'indexation par le contenu[END_REF] to perform this task. However, such algorithms rely on a priori knowledge in order to properly segment and characterize the document image content.

The problematic of this paper concerns the segmentation and characterization of ancient digitized book content with little a priori knowledge. Specifically, in the context of the DIGIDOC project (Document Image diGitisation with Interactive DescriptiOn Capability) 1 , we aim to propose new ways of interacting with scanners as well as new tools for analyzing documents during the whole acquisition process from scanning the document to knowledge representation and management of the ancient digitized document content. LeBourgeois et al. [START_REF] Bourgeois | Digital libraries and document image analysis[END_REF] highlight an essential necessity to conceive "intelligent" digitizers which can limit manual intervention and realize easy and high quality digitization of image documents. Thus, the main goal of our work is to develop a mapping between the scanned image and its content and subsequently use through a set of descriptors extracted and computed on it. Those descriptors will help representing a book page by a hierarchy of homogeneous regions without any hypothesis on the document structure, neither on the document model nor the typographical parameters. In such conditions, a texture analysis technique is a logical choice for solving our problem as it gives several features characterizing the textural properties of a region without using information on the document structure such as the document model and the typographical parameters [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF].

Among the most widely used texture feature extraction and analysis methods are those derived from statistical, geometrical, model-based, and signal processing primitives [START_REF] Chen | Texture analysis in the handbook of pattern recognition and computer vision[END_REF]. Several statistical texture-based segmentation methods have been presented, e.g. the autocorrelation function [START_REF] Petrou | Image processing: dealing with texture[END_REF] and GLCM (Grey Level Co-occurrence Matrix) [START_REF] Haralick | Textural features for image classification[END_REF][START_REF] Busch | Texture for script identification[END_REF]. The extracted texture features are mainly investigated and analyzed separately in independent experiments for document analysis [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF]. Some works deal with the whole ancient document image [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF] and others are applied to graphic images such as drop caps [START_REF] Uttama | Segmentation and retrieval of ancient graphic documents[END_REF][START_REF] Coustaty | Towards historical document indexing: extraction of drop cap letters[END_REF]. There have been few comparative studies on gradient, multiple channel Gabor filters, and co-occurrence features [START_REF] Payne | Document segmentation using texture analysis[END_REF][START_REF] Said | Personal identification based on handwriting[END_REF][START_REF] Liu | Gabor feature extraction for character recognition: comparison with gradient feature[END_REF][START_REF] Ding | A comparative study of Gabor feature and gradient feature for handwritten chinese character recognition[END_REF][START_REF] Zhu | Font recognition based on global texture analysis[END_REF] for document segmentation, character recognition, and script and language identification.

In (Mehri et al., 2013a), a texture-based framework for segmentation of digitized historical books is proposed. Nevertheless, the authors present only some preliminary study of texture feature comparison (autocorrelation, co-occurrence, and Gabor) using only texture feature extraction and pixel classification tasks on simplified document images. Moreover, in (Mehri et al., 2013c), the authors present a pixel labeling approach for historical digitized books based on two non-parametric tools: the autocorrelation function and multiresolution analysis. We propose in this paper a complete book pixel labeling framework for comparing texture features based on (Mehri et al., 2013a;Mehri et al., 2013c) including the automatic estimation of the number of homogeneous and similar content regions of book pages and the pixel labeling steps. The framework is evaluated on a large corpus of historical books using the autocorrelation and GLCM texture features in order to find the homogeneous regions defined by similar texture indices from the whole book instead of processing each page individually. We compare clustering and classification performance with selectivity to the book content, i.e. text vs. graphics and also book characteristics, such as manuscript vs. printed, in order to summarize the pros and cons of each texture-based method for each book category.

The remainder of this paper is structured as follows.

In Section 2, we describe the proposed framework of pixel labeling and characterization of the content of an entire book (Mehri et al., 2013a). The texture primitives, autocorrelation and co-occurrence, chosen for the validation and evaluation of the framework are detailed in Section 3. In Section 4, we propose a comparative analysis of the performance of the chosen texture features. Our conclusions and future work are presented in Section 5.

FRAMEWORK

A texture-based framework for segmentation of digitized historical books is proposed in (Mehri et al., 2013a). It is depicted in Figure 1. The proposed framework is pixel-based and does not require a priori knowledge on the document structure, neither about the document model, nor about the typographical parameters. Thus, it is adapted to all kinds of books. It is independent of the document layout, the typeface, the font size, the page orientation, the digitizing resolution, etc. as a texture analysis technique is introduced. The goal of the framework is to determine regions or groups of pixels which share similar properties or characteristics. These characteristics may be based on the pixel location, their surroundings, color, intensity or texture. In this work, we focus only on textural characteristics. The use of an texture-based approach has been shown to work effectively with skewed and degraded images [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF].

By selecting randomly a number of foreground pixels from a few pages of the same book, their textural features are computed firstly. Then, an estimated number of homogeneous and similar content regions is computed in the analyzed book by applying the Consensus Clustering method (CC) [START_REF] Simpson | Merged consensus clustering to assess and improve class discovery with microarray data[END_REF] on the extracted texture attributes (block 2 in Figure 1). Then, for each analyzed book page its texture features are extracted which are then used in a clustering approach by taking into consideration the estimation of the number of clusters given before by the CC method (block 1 in Figure 1) in order to automatically label content pixels with the same cluster identifier with respect to the book content.

Figure 1 illustrates diagrammatically the four main tasks of our proposed framework. The block 2 on Figure 1 ensures the estimation of the number of homogeneous and similar content regions from the extracted textural features on the whole analyzed book. The block 1 on Figure 1 integrates an unsupervised task enabling to automatically label content pixels with the same cluster identifier regarding to the book content in order to determine and characterize the homogeneous regions in the digitized book (block 3 on Figure 1).

The proposed framework is described by the following four tasks:

1) The texture feature extraction (Section 2.1), 2) The estimation of the number of homogeneous and similar content regions (Section 2.2), 3) The pixel clustering (Section 2.3), 4) The pixel labeling (Section 2.4).

Texture feature extraction

Texture feature extraction aims at representing the document image content by a set of descriptive features computed or extracted on it. Several studies [START_REF] Uttama | Segmentation and retrieval of ancient graphic documents[END_REF][START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF] proposed to characterize and index images of ancient documents by their content by exploring textural analysis based on statistical and spectral properties of texture. The authors of [START_REF] Uttama | Segmentation and retrieval of ancient graphic documents[END_REF] introduce a segmentation method of drop caps based on a combination of different texture analysis approaches such as the GLCM [START_REF] Haralick | Textural features for image classification[END_REF] and the autocorrelation function [START_REF] Petrou | Image processing: dealing with texture[END_REF]. In [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF], the authors propose an extraction algorithm of texture features that is devoted to the analysis of historical documents. The computed texture features are based on frequencies and the autocorrelation function. This method gives good information on the principal orientations and periodicities of the texture allowing characterizing the content of images without assumption on the image structure or properties.

In this paper, two statistical primitives are investigated: the autocorrelation function [START_REF] Petrou | Image processing: dealing with texture[END_REF] and GLCM [START_REF] Haralick | Textural features for image classification[END_REF]. The extraction of textural descriptors is performed on foreground pixels of gray-level images. The texture features are performed at various sizes of analysis windows in order to adopt a multiscale approach. A multiscale approach has been proposed by selecting concentric analysis windows with distinct sizes in order to characterize the images [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF][START_REF] Kricha | Exploring textural analysis for historical documents characterization[END_REF]. The optimal sizes of the sliding windows, respecting a constructive compromise between the computation time and segmentation quality, have been determined experimentally. The extraction of textural descriptors is performed from only the foreground pixels of the gray-level document images at four different sizes of sliding windows: (16 × 16), (32 × 32), (64 × 64), and (128 × 128). In order to avoid side effects, a border replication step is introduced allowing computing texture features on the whole image.

Estimation of the number of homogeneous and similar content regions

Since the goal of the proposed framework is to find homogeneous regions defined by similar texture features, a clustering approach is required in order to partition the analyzed page into regions which have similar properties with respect to the extracted features. However, the number of clusters must be known a priori especially for the conventional clustering techniques [START_REF] Lance | A general theory of classificatory sorting strategies 1. Hierarchical systems[END_REF][START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF][START_REF] Kaufman | Finding groups in data: an introduction to cluster analysis[END_REF].

Previous work has identified a number of approaches [START_REF] Ketchen | The application of cluster analysis in strategic management research: an analysis and critique[END_REF] for determining the correct number of clusters in a dataset. [START_REF] Simpson | Merged consensus clustering to assess and improve class discovery with microarray data[END_REF] have recently proposed an effective method, known as the Consensus Clustering (CC), to estimate the optimal number of clusters in biological data. The idea of CC consists in performing a consensus matrix by iterating multiple runs of clustering algorithms with random and re-sampled clustering options [START_REF] Monti | Consensus Clustering: a resampling-based method for class discovery and visualization of gene expression microarray data[END_REF]. Therefore, the consensus matrix analyzes the consistency of clustering results from five different clustering algorithms: AGglomerative NESting (AGNES), DIvisive ANAlysis clustering (DIANA), Partitioning Around Medoids (PAM), k-means clustering (k-means), and Hierarchical Ascendant Classification (HAC). Therefore, by weighting the different clustering methods in order to mitigate extremes in consensus values that can be created by the sensitivity of some algorithms, a merge consensus matrix is performed.

Thus, the estimation of the number of homogeneous and similar content regions is performed by using the merged CC approach. Although, to perform this task on all pages of the analyzed book is not possible in the case of huge amount of document images, because it needs a high computational time and memory. Hence, the number of clusters is estimated by using the merged CC method in a set of randomly selected foreground pixels from few random selected pages of a book. Due to the memory constraints and the high computational time of the merged CC method, a set of 1000 randomly selected pixels of 10 pages selected randomly from the same book is firstly proposed.

Pixel clustering

Since the optimal number of clusters k opt is estimated, a clustering method is required in order to characterize the content of an entire book and find the k opt homogeneous regions defined by similar texture indices on the whole book. The work presented in [START_REF] Nguyen | Stroke feature extraction for lettrine indexing[END_REF] has shown interesting results in classifying the strokes of initial letters by using the HAC algorithm. Due to the high requirement of a too large amount of memory to perform the merged CC method on all pixels from each analyzed document image, the HAC algorithm is performed on the extracted textural features without taking into account the spatial coordinates and by setting the maximum number of clusters to the estimated one, k opt , with the merged CC method. According to a hierarchical structure grouping of clusters based on the criteria of the minimum increased intra-clusters inertia, the HAC is applied on the texture features of the selected pixels of book pages. This stage of processing gives k opt clusters for the randomly selected samples.

Pixel labeling

This phase deals with labeling clusters or group of pixels with respect to the results of the pixel classification phase. The idea of this task is to assign a label to each cluster of pixels which share similar textural characteristics with respect to the obtained cluster of the selected samples of the analyzed book. Thus, the pixel labeling aims at determining and assigning the same cluster identifier for each similar cluster extracted from the digitized book.

Journet et al. [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF] propose to perform the clustering stage by using CLustering LARge Applications (CLARA) [START_REF] Kaufman | Finding groups in data: an introduction to cluster analysis[END_REF], which is known to be adapted to large scale databases, in the extracted texture features computed from six pages of the same book. Then, if two pixels of two different document images have the same cluster label, they belong to the same class. However, this technique is characterized by a high computation time and memory complexity.

In [START_REF] Mehri | Old document image segmentation using the autocorrelation function and multiresolution analysis[END_REF], a clustering approach without taking into account the characterization step, i.e. the pixel labeling step. In (Mehri et al., 2013a), an unsupervised task is proposed enabling to automatically label content pixels with the same cluster identifier regarding to the book content. For the same book, each cluster (represented by a given color) represents a similar or homogeneous region. Thus, by applying HAC, the homogeneous regions are defined by similar texture indices. Then, the Nearest Neighbor Search algorithm (NNS) [START_REF] Knuth | The art of computer programming[END_REF] is performed in order to assign the same label for each similar cluster extracted from the digitized book. NNS is used between each texture feature vector of each digitized page of the same book and the k opt clusters of the selected samples of a book in order to find the closest texture features vector to the cluster of the selected samples of a book, i.e. by selecting the minimum distance.

Finally, the NNS [START_REF] Knuth | The art of computer programming[END_REF] with the Mahalanobis distance [START_REF] Mahalanobis | On the generalised distance in statistics[END_REF] is applied in order to assign the same label for each similar cluster extracted from the digitized book. The NNS is used between each texture feature vector of each digitized page of the same book and the k opt clusters of the selected samples of a book in order to find the closest cluster to the one of the selected samples of a book. The Mahalanobis distance takes into account the dataset correlations and is particularly suited to arbitrarily shaped clusters, i.e. the minimum of the intra-cluster and inter-cluster distance is taken into consideration.

COMPARISON OF AUTOCORRELATION AND CO-OCCURRENCE FEATURES

In order to validate and evaluate the proposed framework of segmentation and characterization of ancient digitized books, two texture primitives are computed: the autocorrelation and co-occurrence features that are outlined below. The different texture descriptors used in this paper are reported in (Mehri et al., 2013a). Autocorrelation and co-occurrence features are extracted for several reasons: Firstly, we have made a comparative study about choosing the texture feature category, which ensures the best and constructive trade-off between best performance and lowest computation time.

Secondly, the pertinence of the segmentation experiments [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF] that are based on the autocorrelation function applied on document image leads us to work with the autocorrelation features in order to reach the objectives of determining homogeneous regions from the analyzed document without hypothesis on the document structure, neither on the document model nor the typographical parameters. Finally, the extraction of the these two texture features needs less parameter settings compared to the descriptors computed from Gabor filters [START_REF] Jain | Page segmentation using texture analysis[END_REF] for instance. A 2D Gabor filter is a linear selective band-pass filter, dependent on two parameters: spatial frequency and orientation. Moreover, Tamura features depend on the value of coarseness [START_REF] Howarth | Evaluation of texture features for content-based image retrieval[END_REF]. Indeed, without hypothesis on the document structure, neither on the document layout nor the typographical parameters, the choice of appropriate thresholds and parameters is a very difficult task.

Autocorrelation features

In this paper, we evaluate firstly the autocorrelation descriptors. The autocorrelation function [START_REF] Petrou | Image processing: dealing with texture[END_REF] is used to determine periodic patterns and can characterize similarity patterns through a number of extracted autocorrelation features. A number of autocorrelation features have been proposed in [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF][START_REF] Ouji | Chromatic / achromatic separation in noisy document images[END_REF][START_REF] Mehri | Old document image segmentation using the autocorrelation function and multiresolution analysis[END_REF]Mehri et al., 2013a) for segmenting ancient and contemporary documents images. In [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF], the authors use the directional rose [START_REF] Bres | Contributions à la quantification des critères de transparence et d'anisotropie par une approche globale: application au contrôle de qualité de matériaux composites[END_REF], a derivative of the autocorrelation function. The directional rose identifies significant texture orientations in the analyzed block image.

The extracted autocorrelation descriptors provide interesting information on the principal texture orientations and periodicities. Five autocorrelation features are computed, which have been reported in [START_REF] Mehri | Old document image segmentation using the autocorrelation function and multiresolution analysis[END_REF]: the main orientation of the directional rose, the intensity of the autocorrelation function for the main orientation, the variance of the intensities of the directional rose, and the mean stroke width and height estimated accurately along the axis of the main angle of the directional rose [START_REF] Journet | Document image characterization using a multiresolution analysis of the texture: application to old documents[END_REF][START_REF] Ouji | Chromatic / achromatic separation in noisy document images[END_REF][START_REF] Mehri | Old document image segmentation using the autocorrelation function and multiresolution analysis[END_REF].

Extracting these autocorrelation indices using a sliding window gives a total of 20 features (5 autocorrelation indices × 4 sliding window sizes for multiresolution). Therefore, to every selected foreground pixel from the digitized document image is assigned a vector which corresponds to the extracted autocorrelation indices.

Co-occurrence features

The co-occurrence attributes [START_REF] Haralick | Textural features for image classification[END_REF] are the second features tested in this paper, extracted from the GLCM. The GLCM determines the probability of occurrence of pixel pairs according to their gray levels and distance by considering the spatial relationship of pixels in the image. A GLCM element is the probability of the gray level pairs defined in a specified direction θ and separated by a particular distance of d units. By applying multi-distance and multi-direction approaches, a large number of co-occurrence descriptors can be extracted. Fourteen textural features extracted of the GLCM have been initially introduced by [START_REF] Haralick | Textural features for image classification[END_REF] for texture discrimination of natural and satellite images. A number of co-occurrence feature extraction and analysis methods [START_REF] Mikkilineni | Printer identification based on graylevel co-occurrence features for security and forensic applications[END_REF][START_REF] Lin | A texture-based method for document segmentation and classification[END_REF][START_REF] Payne | Document segmentation using texture analysis[END_REF][START_REF] Peake | Script and language identification from document images[END_REF][START_REF] Busch | Texture for script identification[END_REF] have been proposed in order to segment and classify the content of document images, and to identify script and language from document images. Briefly, the GLCM matrices are obtained for a small range of distance values d = 1, 2 and typically for the directions θ = {0 • , 45 • , 90 • , 135 • } [START_REF] Busch | Texture for script identification[END_REF].

Six co-occurrence features are extracted from the GLCM matrices: the maximum entry in the GLCM or the maximum probability, the correlation metric, the energy or the angular second moment, the entropy, the inertia or the contrast, and the local homogeneity for two distances {d = 1, 2} [START_REF] Mikkilineni | Printer identification based on graylevel co-occurrence features for security and forensic applications[END_REF][START_REF] Busch | Texture for script identification[END_REF]. In addition to the twelve cooccurrence features (six for each distance), two other descriptors are computed: the mean value and the standard deviation of the energy for the two distances combined [START_REF] Lin | A texture-based method for document segmentation and classification[END_REF].

Extracting these co-occurrence indices using a sliding window gives a total of 56 numeric values (14 co-occurrence indices × 4 sliding window sizes for multiresolution). Therefore, to every selected foreground pixel from the digitized document image a vector is assigned which corresponds to the extracted co-occurrence indices.

EVALUATION AND RESULTS

In the experiment, 316 pages extracted from 13 different books are considered. Our corpus is divided into two categories: 7 printed monographs and 6 manuscripts that encompass six centuries (1200-1900) of French history. For each category, we select three types of page content: 110 pages containing only two fonts, 100 pages containing graphics and single font texts, and 106 pages containing graphics and text with two different fonts. Evaluation of segmentation and region classification requires a ground truth which is performed by defining manually our ground truth with the Ground-truthing Environment for Document Images (GEDI)2 , a public domain document image annotation tool. Our corpus is composed of grayscale pages which were digitized with 300/400 dpi. The time required to process a page (1982*2750 pixels) using the autocorrelation approach is six minutes while using the co-occurrence descriptors is reduced to only one minute.

Figure 3 shows the real coherent separating power of the extracted texture features in the context of historical digitized book with little a priori knowledge. For the same book, each cluster (represented by a given color) represents a similar or homogeneous region. Because the process is unsupervised, the color attributed to text or graphics may differ from one book to another. The proposed framework (cf. Figure 1) is providing satisfying results particularly in distinguishing the textual regions from the graphical ones when comparing visually the segmentation results for both the autocorrelation and co-occurrence approaches. We note that in the case of the manuscript document category (one font and graphics), the segmentation result by the autocorrelation approach (cf. Figure 3(a)) is better than those performed by co-occurrence features (cf. Figure 3(b)), i.e. the graphic regions (blue) 3(a) are more homogeneous. Moreover, we show for the manuscript document category (two fonts and graphics) better results of discrimination text/graphics obtained by the autocorrelation approach (cf. Figure 3(e)) (graphic regions (red), textual regions (blue)) than those performed by the co-occurrence approach (cf. Figure 3(f)) (graphic regions (blue), textual regions (red)). In the case of the printed document category (one font and graphics), the segmentation results by the autocorrelation approach (cf. Figure 3(c)) show that the textural characteristics of each small letter in the beginning of each text line is different from the other text content while the clustering results by the co-occurrence approach consider them as text regions (cf. Figure 3(d)). This may be explained by the fact that the autocorrelation features give better information on the major orientation and periodicities of the textual texture than the co-occurrence ones. In general, the results for the two approaches are relatively similar for the documents containing only two fonts when we use the autocorrelation and co-occurrence descriptors, i.e. we distinguish two fonts: the normal (green) and uppercase (blue) fonts for the co-occurrence approach in Figure 3(i) and the normal (red) and uppercase (green) fonts for the co-occurrence approach in Figure 3(j). We also note that in Figure 3(g), we descriminate the normal (red) and uppercase (blue) fonts for the documents containing two fonts and graphics with the help of the autocorrelation primitives. Nevertheless, the co-occurrence approach offers important advantages such as a reduced processing time and the ease of implementation.

Indeed, this method of evaluating the performance of a segmentation method is inherently a subjective evaluation and we need to assess the effectiveness using an appropriate quantitative metric. For this reason, we perform firstly three external, or supervised cluster-ing, evaluation indices: Jaccard coefficient (J) [START_REF] Saxena | The effect of cluster size, dimensionality, and number of clusters on recovery of true cluster structure through Chernofftype faces[END_REF], Fowlkes and Mallows index (FM) [START_REF] Fowlkes | A method for comparing two hierarchical clusterings[END_REF], and purity per block (PPB) [START_REF] Mehri | Old document image segmentation using the autocorrelation function and multiresolution analysis[END_REF]. Then, three classification accuracy metrics: precision (P), recall (R), and classification accuracy (CA) [START_REF] Makhoul | Performance measures for information extraction[END_REF] are computed.

In Figure 2, it can be seen that the results obtained by the numerous clustering evaluation measures are coherent with the different classification accuracy ones for the two approaches. We obtain 85%, 70%, 70%, and 79% of mean purity per block accuracy, precision, recall, and classification accuracy respectively for the autocorrelation approach without taking into account the topographical relationships of the selected pixels with respect of 87%, 70%, 79%, and 83% respectively for the co-occurrence approach. We note also that the best segmentation results are obtained by extracting the autocorrelation features for manuscript documents containing one font and graphics. One assumption can be that the manuscript documents contain graphic regions that are more compact and homogeneous than the printed documents and the autocorrelation features are more suitable to discriminate compact graphical regions from textual ones. Whereas, the analysis of quantitative performance noted by using the co-occurrence approach provides different results according to the computed accuracy. Nevertheless, the best performance is obtained for documents containing graphics and text by extracting the co-occurrence features. Concerning the slight variability of the ranking of clustering performance by using the clustering and classification accuracy measures can be explained by the specificity of each clustering accuracy measure. We see that the best classification result of the precision metric (P) is obtained for the manuscript document category (one font and graphics) by using both the autocorrelation and cooccurrence approaches. Precision (P), recall (R), and classification accuracy (CA) show that the lowest values are obtained for printed documents (only two fonts) by using both the autocorrelation and co-occurrence approaches. Therefore, the obtained qualitative results are confirmed, i.e. the extracted autocorrelation and co-occurrence descriptors are more suitable to distinguish the textual regions from the graphical ones. We conclude that the overall results are quite satisfying since we do not integrate the topographical or spatial relationships.

CONCLUSIONS AND FURTHER WORK

This article presents and evaluates a framework for the comparative analysis of texture features for the segmentation and characterization of ancient book pages. The proposed framework is used to extract and compare automatically texture features. Then, a nonparametric clustering method is performed in order to determine the homogeneous regions from different pages of the same book. To validate the proposed method, we evaluate two approaches based on two different statistical categories of texture features: the autocorrelation function and the co-occurrence matrices. Our study demonstrates that the two kinds of texture features give different results according to the book content, i.e. text vs. graphics and also book characteristics, such as manuscript vs. printed. It shows that these texture features are more suitable to distinguish textual regions from graphical ones, than to distinguish text fonts. However, when the numerical complexity is taken into account, the co-occurrence approach would be the better choice. The first aspect of future work will be to test the framework with other texture descriptors such as the Tamura texture features, the local binary patterns, the multiple channel Gabor filters, and the wavelets. Further work also needs to be done in combining various texture descriptors in order to construct an optimal texture feature set and to provide a qualitative measure of which features are most appropriate for this task.

Figure 1 :

 1 Figure 1: Stages of our pixel labeling framework of historical digitized book content.

Figure 2 :

 2 Figure2: Evaluation of the pixel labeling framework of historical digitized book content by clustering and classification accuracy measures: three clustering accuracy metrics: Jaccard coefficient (J), Fowlkes and Mallows index (FM), and purity per block (PPB), and three classification accuracy measures: precision (P), recall (R), and classification accuracy (CA). The higher the values are, the better the results.

  Co-occurrence Figure3: Result examples the pixel labeling framework of historical digitized book content. For the same book, each cluster (represented by a given color) represents a similar or homogeneous region. Because the process is unsupervised, the colors attributed to text or graphics may differ from one book to another.

http://gedigroundtruth.sourceforge.net/

The DIGIDOC project is referenced under ANR-10-CORD-0020.