Karmel De

Oliveira Lima

Rogéria Rocha Gonçalves

Domitille Giaume

Alban Ferrier
email: alban.ferrier@chimie-paristech.fr

Philippe Goldner
email: philippe.goldner@chimie-paristech.fr

Influence of Defects on Sub-Å Optical Linewidths in Eu 3+ :Y 2 O 3 Particles

Rare earth doped nanocrystals have been recently suggested as useful materials for applications in quantum information processing. To reach optical properties closer to bulk crystals ones, it is still necessary to reduce the defects that can arise in nanoscale structures. Here, we probe the defects level by monitoring the inhomogeneous broadening of the 7 F 0  5 D 0 transition in particles of 0.3% Eu 3+ :Y 2 O 3 . We find that lines as narrow as 14 GHz (0.015 nm), a value comparable to single crystals, can be obtained in 150 nm particles calcinated at 1200°C. The additional broadening observed for particles calcinated at lower temperature is attributed to defects inside crystallites and not to surface effects. A linear correlation is also observed between optical and Raman linewidths, suggesting that both processes are sensitive to the same defects. 5 D 0 excited state lifetimes are well described by a model based on an effective refractive index and we conclude that the defects causing the inhomogeneous broadening have no effect on the excited state population.

INTRODUCTION

Rare earth (RE) doped particles are actively investigated as efficient light emitters for various applications in biology, imaging, lighting or display [1][2][3][4][5][6]. Recently it was shown that RE nanocrystals could also be useful in quantum information processing (QIP) [7][8][9] and extend the promising results already obtained in bulk single crystals [START_REF] Goldner | Handbook on the Physics and Chemistry of Rare Earths[END_REF], especially in the field of quantum memories [START_REF] Bussières | [END_REF][12][13][14][15]. QIP relies on superposition states with long lifetime, corresponding to the so-called coherence lifetime (T 2 ). In Eu 3+ :Y 2 O 3 nanocrystals, photon echo measurements showed that T 2 can be as long as 3.7 µs at 1.3 K [7] suggesting that these materials could offer new functionalities like coupling to other quantum systems or optical control of single ions [8,16]. To achieve this, materials still need to be significantly improved, as T 2 in RE particles is still several orders of magnitude lower than in the best bulk crystals [7,8]. In particular, defects that may arise at the nanoscale should be reduced. This has been widely studied in fluoride and oxide particles for luminescence based applications [1]. Especially significant improvements in emission and excitation efficiencies have been obtained in RE doped Y 2 O 3 particles e.g. by postsynthesis treatments, core-shell structures, co-doping or varying particle and crystallite sizes [17][18][19][20].

Superposition states are much more sensitive to perturbations, and their lifetime T 2 can strongly change in materials with similar excited state lifetimes (T 1 ) [21]. Low temperature and high resolution optical spectroscopy is a convenient technique to probe defects at low concentrations, as they cause optical lines to broaden through the variation in the local electric field felt by the optical centers [22]. These defects include impurities, dopants, and vacancies (point defects) as well as various types of dislocations (extended defects). Because of the random nature of defects, each optical center sits in a different environment, resulting in differing optical frequencies. The consequence is the so-called inhomogeneous broadening (Γ inh ) of the transition.

In this paper, we report on the inhomogeneous linewidths of the 7 F 0 -5 D 0 transition of sub-micron Eu 3+ :Y 2 O 3 particles in the 10-40 GHz range (0.01-0.04 nm). By independently varying particle and crystallite sizes, we show that defects contributing to Γ inh can be partially removed at high calcination temperatures. These defects are also likely to cause Raman line broadening, as a nearly linear correlation between Raman and optical linewidths is observed. Finally, the variation of 5 D 0 excited state lifetimes as a function of particle size is well described by local field and photon density of states effects. This suggests that the defects have no influence on the relaxation dynamics of the excited state.

EXPERIMENTAL SECTION

Synthesis of Eu 3+ :Y 2 O 3 particles

We have used Y(NO 3 ) 3 • 6H 2 O (99.9% pure, Alfa Aesar) and Eu(NO 3 ) 3 • 6H 2 O (99.99% pure, Reacton) as yttrium and europium sources. The Eu 3+ concentration used for all samples was 0.3 at. %. In a typical synthesis [23,24], an appropriate amount of urea (CO(NH 2 ) 2 > 99% pure, Sigma) was dissolved in a mixed Eu/Y aqueous nitrate solution to make a total solution volume of 800 mL. The concentrations varied as 0.3, 0.5, 2.0 and 3.0 mol.L -1 for urea and 7.5 mmol.L -1 for metals (Eu 3+ and Y 3+ ). The mixed solutions were heated at 85°C for 24 h in a Teflon reactor. The final suspensions were then cooled to ambient conditions and the colloidal particles collected via centrifugation. The wet precipitates were washed with distilled water once to remove the byproducts, then rinsed twice with absolute ethanol, and dried at 80°C for 24 h to yield a white powder. The synthesis yield was 78 % in weight. The 0.3 at. % Eu 3+ :Y 2 O 3 samples were obtained by calcination of these original powders [Eu 3+ : Y(OH)CO 3 . n H 2 O] under air during 6 h at temperatures ranging from 900 to 1200°C, which were reached using a heating rate of 3 °C min -1 . The cooling rate was 5 °C min -1 .

Characterization Techniques

The morphology, size and dispersion of the original and calcinated particles were visualized by transmission electron microscopy (TEM) using a JEOL -JEM-100CXII apparatus at an accelerating voltage of 100 kV. For TEM measurements, a small amount of powder was dispersed into anhydrous ethanol, and a drop placed over a carbon coated microscope copper grid. TEM images were used to measure the particle size distributions of each sample, using about 300 particles. The crystalline phase of the annealed systems was determined by x-ray diffraction (XRD) analysis with a PANALYTICAL X`PERT PRO diffractometer using monochromatic CuKα1 radiation (wavelength at 154.060 pm) in the 2θ range between 12 and 150˚, with a 0.006˚ step size at room temperature. The crystallite sizes were determined by Rietveld refinement [25] using FullProf software [26]. The integral breadth of all diffractogram peaks between 12 and 150˚ were taken into account.

Micro-Raman spectra were recorded in the range 100-800 cm -1 using a Renishaw In-via Raman spectrometer with a He-Ne laser excitation (wavelength: 633 nm). For optical spectroscopy, the particles, in the form of a powder, were packed into a 2 mm diameter hole in a 0.5 mm thick copper plate and held in place by two glass windows. The assembly was put into a closed-cycle cryostat (Janis CTI-Cryogenics Model CCS-150) with the temperature monitored by a LakeShore model 330 controller. The inhomogeneous linewidths were probed by monitoring fluorescence intensity as a function of the frequency of a single mode dye laser (Coherent 899-21, 1 MHz linewidth). A low laser intensity (25 µW/cm 2 ) was used to avoid saturation of the transition and spectral hole burning. Fluorescence was collected by a 75 mm diameter lens and focused on a photomultiplier tube after suitable filtering to eliminate scattered laser light. Decay measurements were recorded using a tunable optical parametric oscillator pumped by a Nd:YAG Q-switched laser (Ekspla NT342B-SH) with 6 ns pulse length, a Jobin-Yvon HR250 monochromator and a photomultiplier tube. The detection time constant was 20 µs and data were recorded on a digital oscilloscope. [23,24]. In this reaction RE cations precipitate with anions such as CO 3 2-and OH -produced by the dissolution of urea and form an amorphous Y(OH)CO 3 • n H 2 O compound [27]. In order to change the size of these particles the concentration of urea was systematically varied from 0.3 to 3.0 M. Fig. 1 shows a series of histograms and TEM micrographs that illustrate the effect of urea concentration on particle size of Eu 3+ : Y(OH)CO growth processes [27,28]. At high urea concentration, the elevated amount of CO 3 2-and OH -groups promotes a higher degree of super-saturation before the beginning of precipitation. Thus, the larger nucleation density decreases the average particle sizes. The yttrium basic carbonate can be decomposed into Y 2 O 3 at temperatures higher than 600°C [23,27], and in order to obtain yttrium oxide particles, all synthesized systems with different particle sizes were calcinated at 900, 1000, 1100 and 1200°C during 6 h. The TEM images of systems prepared by using 0.3 and 3.0 M of urea, and calcinated at 900, 1000, 1100 and 1200°C over 6 h are presented in Fig. 2. The calcination process changes the morphology of the particles as evidenced by the appearance of crystalline planes on the particle surfaces (Fig. 2d and2h). Micrographs also show that Y 2 O 3 particles are generally formed by several crystallites that grow when the temperature of calcination is increased. However, single crystalline particles were observed after treatment at 1200°C (Fig. 2h) when using 3.0 M of urea. Average particle size as a function of calcination temperature for samples prepared using 0.3 and 3.0 M of urea are shown in Fig. 3.

RESULTS AND DISCUSSION

Optical Inhomogeneous Linewidths

Measurements were performed on Eu 3+ 7 F 0  5 D 0 transition at low temperatures (12 K) to reduce homogeneous broadening to negligible values [29]. Eu 3+ ions substitute for Y 3+ ones, which occupy two sites in the Y 2 O 3 cubic structure. We probed Eu 3+ ions in the C 2 symmetry site, as the absorption corresponding to the other site, of C 3i symmetry, is very weak because of inversion symmetry. Linewidths were recorded by monitoring the intensity of the strong 5 D 0 -7 F 2 emission at 611 nm, while scanning a single-mode laser centered at 580.88 nm (vacuum) through the 7 F 0  5 D 0 absorption. Fig. 6 shows the 7 F 0  5 D 0 lineshapes obtained for particles using 0.3 and 3.0 M of urea and calcinated at varying temperatures. As in all particles, the lines were centered at a wavelength of 580.88 +/-0.01 nm (vacuum), identical to that found in single crystals and transparent ceramics [30][31][32]. For both urea concentrations, the inhomogeneous linewidths  inh decrease from 35 GHz (0.04 nm) to about 12 GHz (0.013 nm) with increasing calcination temperature. At 1200 °C,  inh = 12

GHz for the 0.3 M particles of average size 540 nm, a value similar to the one found in a 0.3 % Eu 3+ :Y 2 O 3 single crystal fiber (11 GHz) [30]. Results obtained for other particles are gathered in Fig. 7 and are comparable to values reported for 0.05-0.5 % Eu 3+ :Y 2 O 3 bulk crystals (5-23 GHz) [30,31], 0.1 % Eu 3+ doped Y 2 O 3 ceramics (7.8 GHz) [32], and 0.86 at. % Eu 3+ doped Y 2 O 3 particles of 5 µm containing 60 nm nanocrystals (17 GHz) [7]. Inhomogeneous linewidths of this magnitude in rare earth doped crystals are generally due to strains produced by defects.

Lineshape analysis can differentiate between point and extended defects. In all particles, a Lorentzian lineshape was found, indicating that  inh is due to point defects with a low concentration (Fig. 6, inset) [7,22]. A first contribution to point defects comes from Eu 3+ ions themselves, partly because of the difference between their ionic radius compared to Y 3+ (IR (Eu 3+ , ) 0. 50 A, IR (Y 3+ , ) 0. 2 A [33]). We estimate this contribution to be about 6 GHz by comparing  inh for single crystals at 0.3 and 0.004 % Eu 3+ doping [30]. Fig. 7 shows that in all systems an additional broadening, due to other defects, is observed. This broadening clearly decreases with increasing calcination temperature, but show limited correlation with particle or crystallite size (Fig. 7). For example, 32 to 37 GHz linewidths are found for all particles calcinated at 900 °C, whereas particle and crystallite size vary by a factor 3.6 and 1.5 respectively. With the same size variations,  inh stays between 16 and 19 GHz for particles calcinated at 1100 °C. Moreover, for a fixed crystallite size of 60 nm,  inh can vary from 36 to 16 GHz. This suggests that the nature of the crystallites' surface and surface/volume ratio has little influence on the inhomogeneous broadening. In particular, for all particles calcinated at 1200 °C, linewidths comparable to those found in single crystal fibers can be obtained [30]. It should also be noted that no strong satellite lines were observed, meaning that most Eu 3+ sites are only slightly distorted compared to bulk samples. We therefore conclude that the major contribution to  inh besides Eu 3+ doping originates from low concentration defects internal to the crystallites. Oxygen vacancies could be one of theses defects. Indeed, they have been suggested as responsible for abnormal temperature variations of the homogeneous linewidths in Eu 3+ :Y 2 O 3 single crystals [30]. The same behavior was found in Eu 3+ :Y 2 O 3 nanocrystals and was also attributed to oxygen vacancies [7]. We also performed Raman spectroscopy as vibrational lines are also sensitive to strain, disorder and crystallite size [34,35].

Fig. 8 shows the Raman spectra of Eu 3+ :Y 2 O 3 particles synthesized using 3.0 M of urea and calcinated at different temperatures. As a reference, the spectrum obtained on a 0.5% Eu 3+ :Y 2 O 3 transparent ceramic (50 µm of crystallite size) is also presented. All lines could be assigned according to the cubic Y 2 O 3 space group, in agreement with previous reports [36,37]. Additional bands were assigned to Eu 3+ fluorescence [17] and are marked by asterisks in Figure 8. To compare different particles, we focused on the main line at 377 cm -1 . Although it showed no significant frequency shift, a clear decrease of its linewidth with increasing calcination temperature could be observed for particles of different sizes (Fig. 9). As the linewidth shows little correlation with crystallite size, we attribute it to the lattice defects [38], as in the case of the 7 F 0  5 D 0 linewidth. Fig. 10 shows that the correlation between the Raman and optical linewidths is nearly linear, except for the smallest particle calcinated at high temperature. This suggests that the same defects, e.g. oxygen vacancies [38], are broadening both Raman and optical lines.

Excited State Lifetime

The defects that broaden the 7 F 0  5 D 0 transition may also have dynamical effects by inducing non-radiative relaxations or changing radiative emission probabilities because of site distortion. To investigate this, we recorded the 5 D 0  7 F 2 emission decay at 611 nm after excitation of the 7 F 0  5 D 0 transition, at 12 K and room temperature. In the latter case, particles were in air in the form of a powder or dispersed in water. All decays could be well fitted by single exponentials and showed no evidence of energy transfers. This was expected as the 5 D 0 level is separated by 12000 cm -1 from the 7 F 6 one, making it largely insensitive to relaxations by radicals (e.g. OH -) that can be present at the particles surface. Moreover, the low doping concentration prevented strong resonant energy transfer between Eu 3+ ions. For all particles, room and low temperature decays were identical, which also suggests that the non-radiative relaxations from the 5 D 0 level are negligible. However, the lifetimes significantly varied as a function of particle size and temperature of calcination, as shown in Fig. 11. 5 D 0 lifetimes measured in air varied from 1.08 ms in the largest particles (540 nm) calcinated at 1200 °C, to 1.7 ms in the smallest ones (150 nm) treated at 900 °C. This effect could be solely due to changes in the photon density of states and local electric field in the particles. This has been reported in many rare earth doped systems [39][40][41][42]. When the particles are much smaller than the wavelength of light, radiative transitions probabilities are expressed as a function of an effective index, which is a weighted average between the surrounding medium and bulk crystal indices [39]. In our case, the largest particles have a size comparable to the emission wavelength (λ =611 nm), while the recorded lifetimes are still longer (1.08 ms) than those of a ceramic with 50 µm crystallites (934 µs). On the other hand, the smallest particles have a size of 150 nm which is about λ /4 and thus not negligibly small. Hence, models applying to size << λ [39,[43][44][45] do not apply directly and were indeed unable to reproduce our results. To explain our observations, we first make the assumption that each particle is spherical (radius R) and surrounded by the medium (air or water) and other identical particles. This is described by the socalled filling factor x, equal to the volume ratio between the particles and the medium [39]. We take x as independent of the particle size for a given calcination temperature. When calcination temperature increases, agglomeration, and therefore x, may increase. A particle is therefore surrounded by a medium of index n M = x n B +(1-x) n, where n B =1.91 is the Y 2 O 3 bulk refractive index and n=1 for air and 1.33 for water. In a given particle, each Eu 3+ ion is placed at the center of a sphere of influence (radius R i ) in which an average index n a is calculated by solving the equation [46,47]:

where is the dielectric permittivity corresponding to the refractive index n i . f M and f B =1-f M are the fractions (in volume) of the sphere of influence occupied by the surrounding medium (index n M ) and the particle (index n B ). They depend on R i , R and the distance of the ion from the center of the particle. For particles of diameter larger than R i , ions closer to the surface of the particle are therefore in regions of lower index than those at the center of the particle. This average index n a is then used to compute the lifetime τ of the emitter using the empty cavity model [43] ( )

where τ 0 is the emitter lifetime in vacuum. Finally lifetimes for all emitters in the particle are averaged to give a single value that can be compared to the experimental decay times. First, they were fitted by leaving R i and x free and we found that R i was nearly constant for all data. It was then fixed to R i = 203 nm and only x was adjustable to generate the curves shown in

CONCLUSIONS

Monodispersed particles of 0.3% Eu 3+ :Y 2 O 3 have been synthesized with sizes between 150 and 540 nm. Varying the calcination temperature of the amorphous precursor from 900 to 1200 °C allowed us to independently vary the crystallite size from 40-60 nm to 90-120 nm. The inhomogeneous linewidths of Eu 3+ 7 F 0  5 D 0 transition were measured by high-resolution laser spectroscopy and vary between 38 and 12 GHz, in the range of single crystals and transparent ceramics at the same Eu 3+ concentration. Whereas the particles calcinated at 1200 °C show an inhomogeneous broadening close to single crystals even for size as low as 150 nm, other particles exhibit an additional broadening independent on particle or crystallite size. We attribute it to point defects, like oxygen vacancies, the concentration of which is reduced by increasing calcination temperature. A nearly linear correlation was also observed in the particles between optical and Raman linewidths, suggesting a common origin. Finally, the influence of these defects on the 5 D 0 excited state lifetime was investigated. Although we observed a strong dependence of lifetimes as a function of particle size, experimental data could be reproduced by a model based on an effective refractive index. We conclude that these defects have a negligible effect on dynamical properties of 5 D o population. Further studies, based on photon echoes and time resolved spectra hole burning, are in progress to evaluate their effects on coherence lifetimes of the 7 F 0  5 D 0 transition.

FIGURE CAPTIONS

  3 . All systems exhibit spherical, well-dispersed particles with smooth surfaces. An increase in urea concentration decreases the average particle size from 729 ([urea]= 0.3 M), 633 ([urea]= 0.5 M), 289 ([urea]= 2.0 M) to 198 nm ([urea]= 3.0 M), with standard deviations of particle sizes around ± 73, ± 67, ± 39 and ± 38 nm, respectively, according to a log normal fit. The inverse relationship between urea concentration and the average particle size is due to the balance between nucleation and

Fig. 1 .

 1 Fig. 1. TEM images and histograms with log normal fit (red line) of 0.3 at. % Eu 3+ : Y(OH)CO 3 products obtained using urea concentrations from 0.3 to 3.0 M. The scale bars (1 µm) are identical in all images.

Fig. 2 .

 2 Fig. 2. TEM images of 0.3 at. % Eu 3+ : Y 2 O 3 particles obtained using 0.3 M of urea and calcinated at (a) 900, (b) 1000, (c) 1100, (d) 1200 °C, and using 3.0 M of urea and calcinated at (e) 900, (f) 1000, (g) 1100, (h) 1200°C during 6 h.

Fig. 3 .

 3 Fig. 3. Average particle size as a function of calcination temperature for 0.3 at. % Eu 3+ : Y 2 O 3 particles obtained by using 0.3 and 3.0 M of urea. The error bars are based on the standard deviation of size distributions.

Fig. 4 .

 4 Fig. 4. XRD patterns of 0.3 at. % Eu 3+ : Y 2 O 3 particles calcinated at 900, 1000, 1100 and 1200°C and synthesized using 0.5 M of urea.

Fig. 5 .

 5 Fig. 5. Crystallite size as a function of temperature of calcination for 0.3 at. % Eu 3+ : Y 2 O 3 particles synthesized with varying urea concentrations. Average particle sizes are indicated in the legend.

Fig. 6 .

 6 Fig. 6. 7 F 0  5 D 0 transition lineshapes obtained by monitoring 5 D 0 -7 F 2 emission at 12 K in 0.3 at. % Eu 3+ : Y 2 O 3 . Particles synthesized with (a) 0.3 and (b) 3.0 M of urea, and calcinated at temperatures from 900 to 1200°C. Maxima of all spectra are set at 0 frequency. Inset: Lorentzian fit (dashed line) of the spectrum of the 3.0 M particles calcinated at 1200 °C.

Fig. 7 .

 7 Fig. 7. Inhomogeneous linewidth  inh of the 7 F 0  5 D 0 transition as a function of crystallite size for Eu 3+ : Y 2 O 3 particles synthesized with varying urea concentrations. Dashed line:  inh in a 0.3% Eu 3+ :Y 2 O 3 single crystal fiber [30]. Average particle sizes are indicated in the legend.

Fig. 8 .

 8 Fig. 8. Raman spectra of 0.3 at. % Eu 3+ : Y 2 O 3 particles prepared using 3.0 M of urea and calcinated under different temperatures, and of a 0.5% Eu 3+ :Y 2 O 3 transparent ceramic. Asterisks: Eu 3+ fluorescence.

Fig. 9 .

 9 Fig. 9. Linewidth of the main Raman line at 377 nm as a function of calcination temperature of 0.3 at. % Eu 3+ : Y 2 O 3 particles synthesized using different urea concentrations. Dashed line: linewidth in a 0.5% Eu 3+ :Y 2 O 3 transparent ceramic. Average particle sizes are indicated in the legend.

Fig. 10 .

 10 Fig. 10. Linewidth of the main Raman line as a function of the 7 F 0  5 D 0 inhomogeneous linewidth in 0.3% Eu 3+ : Y 2 O 3 synthesized using varying urea concentrations and calcinated at different temperatures. Average particle sizes are indicated in the legend.

Fig. 11 .

 11 Fig. 11. Lifetimes of the 5 D 0 level measured in air (a) and water (b) as a function of particle size in 0.3% Eu 3+ : Y 2 O 3 synthesized using varying urea concentrations and calcinated at different temperatures. Solid lines: fit using an effective index based model; x: filling factor (see text).

Figure 11 (

 11 Figure 11 (each curve corresponds to a single value of x). A reasonable agreement is observed, both with absolute values and general shape of the experimental data variations. Only the lifetime measured in air for the 150 nm particles calcinated at 1200 °C does not follow the general trend. This could be due to an increased agglomeration. The value of R i is close to the one given in Ref.46 (R i =150 nm) and x ranges from 0.47 to 0.62, corresponding to moderate packing. As expected, x increases with calcination temperature and in air compared to water. This analysis shows that a simple model based on an effective refractive index can reproduce the experimental lifetime variations. Together with the single exponential fluorescence decays and their lack of temperature dependence, we conclude that the defects causing additional inhomogeneous broadening of the 7 F 0  5 D 0 transition in some particles have a negligible effect on the 5 D 0 level excited state dynamics.

Fig. 1 .

 1 Fig. 1. TEM images and histograms with log normal fit (red line) of 0.3 at. % Eu 3+ : Y(OH)CO 3 products obtained using urea concentrations from 0.3 to 3.0 M. The scale bars (1 µm) are identical in all images.

Fig. 2 .

 2 Fig. 2. TEM images of 0.3 at. % Eu 3+ : Y 2 O 3 particles obtained using 0.3 M of urea and calcinated at (a) 900, (b) 1000, (c) 1100, (d) 1200 °C, and using 3.0 M of urea and calcinated at (e) 900, (f) 1000, (g) 1100, (h) 1200°C during 6 h.

Fig. 3 .

 3 Fig. 3. Average particle size as a function of calcination temperature for 0.3 at. % Eu 3+ : Y 2 O 3 particles obtained by using 0.3 and 3.0 M of urea. The error bars are based on the standard deviation of size distributions.

Fig. 4 . 5 M

 45 Fig. 4. XRD patterns of 0.3 at. % Eu 3+ : Y 2 O 3 particles calcinated at 900, 1000, 1100 and 1200°C and synthesized using 0.5 M of urea.

Fig. 5 .

 5 Fig. 5. Crystallite size as a function of temperature of calcination for 0.3 at. % Eu 3+ : Y 2 O 3 particles synthesized with varying urea concentrations. Average particle sizes are indicated in the legend.

Fig. 6 .

 6 Fig. 6. 7 F 0  5 D 0 transition lineshapes obtained by monitoring 5 D 0 -7 F 2 emission at 12 K in 0.3 at. % Eu 3+ : Y 2 O 3 . Particles synthesized with (a) 0.3 and (b) 3.0 M of urea, and calcinated at temperatures from 900 to 1200°C. Maxima of all spectra are set at 0 frequency. Inset: Lorentzian fit (dashed line) of the spectrum of the 3.0 M particles calcinated at 1200 °C.

Fig. 7 .

 7 Fig. 7. Inhomogeneous linewidth  inh of the 7 F 0  5 D 0 transition as a function of crystallite size for Eu 3+ : Y 2 O 3 particles synthesized with varying urea concentrations. Dashed line:  inh in a 0.3% Eu 3+ :Y 2 O 3 single crystal fiber [30].

Fig. 8 .

 8 Fig. 8. Raman spectra of 0.3 at. % Eu 3+ : Y 2 O 3 particles prepared using 3.0 M of urea and calcinated under different temperatures, and of a 0.5% Eu 3+ :Y 2 O 3 transparent ceramic. Asterisks: Eu 3+ fluorescence.

Fig. 9 .

 9 Fig. 9. Linewidth of the main Raman line at 377 nm as a function of calcination temperature of 0.3 at. % Eu 3+ : Y 2 O 3 particles synthesized using different urea concentrations. Dashed line: linewidth in a 0.5% Eu 3+ :Y 2 O 3 transparent ceramic.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Linewidth of the main Raman line as a function of the 7 F 0  5 D 0 inhomogeneous linewidth in 0.3% Eu 3+ : Y 2 O 3 synthesized using varying urea concentrations and calcinated at different temperatures.

ACKNOWLEDGMENT

We thank Dr. John Bartholomew and Dr. Nathalie Kunkel for useful comments. The research leading to these results has received funding from the European Union's Seventh Framework Programme FP7/2007-2013/ under REA grant agreements No. 287252 (CIPRIS, People Programme-Marie Curie Actions) and ANR project RAMACO (12-BS08-0015-01).


Arnaud Lienhard

Patricia Ladret

Alice Caplier

How to predict the global instantaneous feeling induced by a facial picture ?

Keywords: Aesthetic Quality, Likability, Automatic Scoring, Portraits

Picture selection is a time-consuming task for humans and a real challenge for machines, which have to retrieve complex and subjective information from image pixels. An automated system that infers human feelings from digital portraits would be of great help for profile picture selection, photo album creation or photo editing. In this work, two models of facial pictures evaluation are defined. The first one predicts the overall aesthetic quality of a facial image, and the second one answers the question "Among a set of facial pictures of a given person, on which picture does the person look like the most friendly?". Aesthetic quality is evaluated by the computation of 15 features that encode low-level statistics in different image regions (face, eyes, mouth). Relevant features are automatically selected by a feature ranking technique, and the outputs of 4 learning algorithms are fused in order to make a robust and accurate prediction of the image quality. Results are compared with recent works and the proposed algorithm obtains the best performance. The same pipeline is considered to evaluate the likability of a facial picture, with the difference that the estimation is based on high-level attributes such as gender, age, smile. Performance of these attributes is compared with previous techniques that mostly rely on facial keypoints positions, and it is shown that it is possible to obtain likability predictions that are close to human perception. Finally, a combination of both models that selects a likable facial image of good quality for a given person is described.

INTRODUCTION

Context

Social psychological studies have shown that people form impressions from facial appearance very quickly [START_REF] Willis | Making Up Your Mind After a 100-Ms Exposure to a Face[END_REF]. With the widespread use of digital cameras and photo sharing applications, selecting the best picture of a particular person for a given application is a time-consuming task for humans. Thus, an automated system providing a feedback about facial images would be an interesting and useful tool. Sorting images automatically, editing images to enhance their visual aspect or selecting a few images among an entire collection would be simplified for home users. Generally, images with low aesthetic quality are manually rejected whereas appealing images are selected.

In the particular case of facial pictures, features have to be adapted to the considered use: profile pictures on social networks are different from pictures presented in a professional purpose (resumes, visiting cards). To this end, this work focuses both on predicting the overall aesthetic quality of a facial image and selecting images that infer a feeling of likability. Ideally, the models developed in this work should encode relevant information about the global image aesthetics adapted to facial pictures as well as information related to facial expressions and high-level attributes (smile, age, gender, etc.). Facial beauty is not considered at all: the main idea is to estimate the feeling induced by a given facial picture (especially in term of likability), which is not necessarily correlated with the reality.

Previous Work 1.2.1. Aesthetic Photo Quality Evaluation

Automated aesthetic evaluation of facial pictures is a challenging task that requires to understand subjective notions that are implicitly encoded in the image. To solve this problem, different approaches exist. In most of recent works, a large number of features describing the image aesthetics are extracted and machine learning algorithms are applied to fit the feature values to ground truth images obtained from human evaluation. Features can either be explored at pixel level (e.g. Fisher Vectors) [START_REF] Marchesotti | Assessing the Aesthetic Quality of Photographs Using Generic Image Gescriptors[END_REF] or by estimation of high-level attributes (smiles, eyes closeness) [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF][START_REF] Dhar | High Level Describable Attributes for Predicting Aesthetics and Interestingness[END_REF] that are closer to human interpretation. To encode both local and global information into the models, the main approach for evaluating portraits aesthetic quality is characterized by computing a set of features about the subject (face) and background (nonface) regions. Often, low-level image statistics such as contrast, sharpness or color distribution are computed in addition to features that describe subjectbackground relationship [START_REF] Jiang | Automatic Aesthetic Value Assessment in Photographic Images[END_REF][START_REF] Tang | Content-Based Photo Quality Assessment[END_REF].

To the best of our knowledge, few researches have been done on the particular case of pictures containing a unique and centered frontal face [START_REF] Males | Aesthetic Quality Assessment of Headshots[END_REF]. Plus, there are no publicly available datasets containing facial images and human aesthetic ratings, which makes comparison with previous models difficult. In previous work [START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF], we developed a method that segments precisely a portrait (hair, shoulders, skin, background) and computes features in each region. The main result of this previous work is that facial area is almost sufficient to describe efficiently the global aesthetic of the entire facial picture. This idea is exploited in the proposed work, where features are extracted in small and informative facial ares (eyes, mouth).

Likability Evaluation

The feeling induced by a facial picture depends on facial expression, face shape and other cues such as make-up or face adornments. However, stateof-the-art face evaluation systems do not consider many of these attributes. A first attempt to create a data-driven model of several evaluation traits is discussed in [START_REF] Todorov | Modeling Social Perception of Faces[END_REF], in which 300 faces are generated by the Facegen Modeller software (http://www.facegen.com) with different shape parameters. A subjective experiment is conducted, where participants evaluate each face with respect to a particular trait: aggressiveness, attractiveness, threat, etc. Finally, shape parameters are fitted to the ground truth scores provided by participants to build a regression model for each social judgment.

Besides, behavioral studies have shown that facial image quality estimation does not only rely in face shape and that reflectance (cues such as skin illumination and texture) also plays an important role in face perception [START_REF] Blanz | A Morphable Model for the Synthesis of 3D Faces[END_REF]. A more complete model including reflectance parameters is elaborated and validated in [START_REF] Todorov | Validation of Data-driven Computational Models of Social Perception of Faces[END_REF]. However, the faces considered in all their experiments are synthetic and without facial hair, make-up or accessories. Real 3-D scanned faces have been used in [START_REF] Walker | Portraits made to measure: Manipulating Social Judgments about Individuals with a Statistical Face Model[END_REF] to identify relevant shape and reflectance features. Even in recent attempts of automated face expression evaluation in videos [START_REF] Masip | Automated Prediction of Preferences Using Facial Expressions[END_REF], the use of facial keypoints is still predominant. The disadvantage of these models is that it only takes into account the position of facial keypoints and reflectance parameters. Plus, facial keypoints are heavily related to the face shape whereas our goal is to predict the most likable image of a given person which is not entirely defined by the face shape.

High-level attributes are defined as abstract and global concepts describing an image. They correspond to descriptors that cannot directly be obtained by extracting visual data due to the semantic gap between information contained in pixels and human analysis. Many attributes (age, gender, presence of glasses, beard, smile, etc.) have already been successfully used in various research domains such as face recognition or verification [START_REF] Kumar | Attribute and Simile Classifiers for Face Verification[END_REF] and portraiture aesthetics [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF]. A small set of such attributes provides more significant information than the relative positions of many facial keypoints.

Objectives

The main contribution of this paper is to propose the first model that combines both aesthetic quality assessment and likability estimation for frontal facial pictures, in order to perform automatic picture selection. For each criterion (aesthetic quality and likability), a model that outperforms stateof-the-art methods is presented, and the most relevant features are described.

Aesthetic quality of facial pictures is evaluated using the same feature set than in our recent work [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF]. The difference rely on the use of 4 learning algorithms that are combined to provide a more accurate and robust prediction, which outperforms our previous results. This work also focuses on demonstrating the advantages of using high-level attributes in order to build likability evaluation models. 3 tools are considered to compute the attributes: Betaface (http://betaface.com), SkyBiometry (http://skybiometry.com) and SHORE [START_REF] Ernst | A Modular Framework to Detect and Analyze Faces for Audience Measurement Systems[END_REF]. It is shown that for real images, these features are significantly more efficient to predict likability. This work is organized as follows. Section 2 describes the main steps of the proposed method, including feature computation and selection and learning algorithms. Section 3 demonstrates the relevance of the algorithm combination and compares the results with previous recent works. In Section 4, the same pipeline is applied to perform likability evaluation. The major difference between aesthetic quality and likability evaluation is the feature extraction process, which rely either on low-level statistics or on high-level attributes. Finally, both predictions are combined in Section 5 to perform automatic selection that retains automatically good quality images with friendly faces.

Proposed Method for Aesthetic Quality Estimation

In this work, headshots are defined as frontal portraits cropped to the extremes of the target's head and shoulders. A method predicting the aesthetic quality of headshots is described in this section. To the best of our knowledge, it reaches the best state-of-the-art results on headshots, and performs well on every dataset containing frontal portraits.

The proposed method consists in computing 15 low-level features in 4 image regions corresponding to the face and its facial attributes (Section 2.1). To eliminate non relevant features, a feature selection algorithm is presented. Then, automated aesthetic prediction is performed by using the learning algorithms that are described in Section 2.2. Prediction performance is evaluated by the metrics defined in 2.2.2 and a fusion technique is proposed in order to combine the advantages of each algorithm in 2.2.3.

Feature Computation 2.1.1. Facial Attributes Segmentation

Appealing headshots presents a clear architecture: a face located near the image center and well contrasted with respect to the background. Thus, in the proposed model, features of different regions are computed to encode the subject/background relationship. To locate the face area, bounding box detection is performed by using Viola-Jones algorithm [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF] and the OpenCV library. Inside the face region, observers are more likely to focus on eyes and mouth, which provide information about the subject: facial expressions, presence of make up, etc. The proposed method relies on the fact that decisive information about facial image aesthetic quality can be obtained by computing features in these small areas only [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] (eyes and mouth). Each image is finally decomposed into the 4 regions described in Figure 1: entire image R A , face area R B , eyes area R C and mouth area R D . Eyes and mouth areas are also detected by Viola-Jones algorithm and both eyes are considered to be part of the same region.

Features Extraction

State-of-the-art methods implement a lot of different low-level features (76 in [START_REF] Faria | Challenges of Finding Aesthetically Pleasing Images[END_REF], including brightness, contrast, color and sharpness information) in order to assess aesthetic quality of facial images. In this work, the 15 low-level features presented and tested in [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] are considered. They consist in image statistics that can be computed in each region: each face picture is described by a set of 60 values (15 features in each of the 4 regions). Features correspond to sharpness, illumination, contrast and color distribution measures. These categories have been chosen because they are close to human perception. Thus, it is possible to have feedback about relevant features, which can be helpful for photo editing and feature design. Features are grouped into the 4 categories described below.

Sharpness is evaluated by 3 different values: F 1 , F 2 , F 3 . The first sharpness measure F 1 is computed by using the blur estimation method described in [START_REF] Crete | The Blur Effect: Perception and Estimation with a New No-reference Perceptual Blur Metric[END_REF], which compares the difference between an original image I and its low-pass filtered version I b . More precisely, gradients are measured in I and in I b : the greater the gradient differences between both images, the sharper the original image I. Indeed, high differences mean that the original image has sharp edges, and loses a lot of its sharpness through the filtering process. On the contrary, blurry images do not change a lot after filtering. This method appeared to be very discriminant in our previous work [START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF].

Since a sharp facial picture contains high gradients located in the face region, the average gradient value F 2 is computed. The size of the bounding box containing 90% of the image gradients F 3 is calculated as described in [START_REF] Ke | The Design of High-level Features for Photo Quality Assessment[END_REF] in each region.

Illumination is characterized by 2 values, F 4 and F 5 , evaluated by the means of two channels: Value V and Luminance L * (respectively from HSV and L * a * b * color spaces). Both measures are considered in several articles [START_REF] Ke | The Design of High-level Features for Photo Quality Assessment[END_REF][START_REF] Datta | Studying Aesthetics in Photographic Images using a Computational Approach[END_REF][START_REF] Pogačnik | Evaluating Photo Aesthetics using Machine Learning, Data Mining and Data Warehouses[END_REF]. They provide information about the image global brightness if computed on the entire image, or local brightness if computed on facial regions. Even if these values are highly correlated, both are implemented because the less discriminant measure will automatically be removed by the feature selection process. Combination of local and global measures also gives some indications about the brightness difference between face and non face regions, which influences our perception of aesthetics [START_REF] Wong | Saliency-enhanced Image Aesthetics Class Prediction[END_REF][START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF]. This information is implicitly encoded through the learning process, where brightness values from different regions are fused.

Contrast is measured by 4 values, from F 6 to F 9 . Two of them correspond to the standard deviation of V and L * (respectively F 6 and F 7 ). Then, the width of the middle 90% mass of L * histogram F 8 [START_REF] Ke | The Design of High-level Features for Photo Quality Assessment[END_REF][START_REF] Wong | Saliency-enhanced Image Aesthetics Class Prediction[END_REF] and the Michelson contrast value F 9 [START_REF] Desnoyer | Aesthetic Image Classification for Autonomous Agents[END_REF] Color information is extracted with the measurement of 6 values, from F 10 to F 15 . The Dark Channel (DC), introduced to perform haze removal [START_REF] He | Single Image Haze Removal Using Dark Channel Prior[END_REF], provides information about sharpness and colors. High values are related with dull colors or blurry areas. DC corresponds to a minimal filter applied on the RGB color space. Each pixel p(i, j) of an image I is computed as follows: p(i, j) = min c∈R,G,B (min (i ,j )∈Ω(i,j) I c (i , j )) where I c is a channel of I and Ω(i, j) corresponds to the 5 × 5 neighborhood of p(i, j). It has been shown that DC evaluation helps to increase performance of image aesthetic assessment [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF]. Since faces are composed of area with low DC values (skin for example) and high DC values (eyes), the DC mean and its standard deviation are considered (respectively F 10 and F 11 ).

Hue H and Saturation S standard deviations (from HSV color space) are also computed (F 12 to F 13 ). The number of different hues F 14 in each area is an indicator of its complexity [START_REF] Ke | The Design of High-level Features for Photo Quality Assessment[END_REF][START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF]. Finally, the colorfulness measure F 15 described in [START_REF] Hasler | Measuring Colorfulness in Natural Images[END_REF] is implemented, providing information about the mean and standard deviation of the channels a * and b * of L * a * b * color space. In recent work [START_REF] Aydin | Automated Aesthetic Analysis of Photographic Images[END_REF], it is shown that F 15 is highly correlated to the human perception of colorfulness and that this measure is an indicator of the overall image aesthetic quality.

The features described above are represented by numerical values between 0 and 1.

Feature and Region Selection

Some of the considered features may be more relevant when computed in limited regions only. For instance, facial images often have blurred background and sharp edges in the face. Measuring each feature inside all the regions may also add noise in the data due to redundant or irrelevant values. Thus, selecting the most discriminant features for a given area can enhance the prediction performance, or at least reduce the number of features needed to obtain the optimal result.

In this work, the 60 feature couples (Feature, Region) are ranked using the Relief metric, implemented as described in [START_REF] Robnik-Šikonja | Theoretical and empirical analysis of ReliefF and RReliefF[END_REF]. This metric provides feedback about the ability of each couple to separate images with similar features but different subjective aesthetic quality scores. The Relief metric is preferred to other feature selection methods because it can be adapted to both classification and regression problems and can compute ranks for each feature couple simultaneously. Plus, it is possible to consider both discrete and continuous features. This will be helpful for likability evaluation in Section 4, for which both types of features are considered.

In case of classification, the Relief value of a given feature f , Relief (f ) Class , is computed as follows. First, an image i is randomly selected in the training set. For each class, the K closest images to i (measured by the euclidean distance in the feature space) are considered, and the value Relief (f, i) Class is computed:

Relief (f, i) Class = 1 N c -1 Nc c =c i K k=1 dF ikc D ikc K k=1 D ikc - K k=1 dF ikc i D ikc i K k=1 D ikc i (1)
where dF ik is the relative difference of feature f for images i and k. D ik is the Euclidean distance between images i and k in the feature space. c i is the class of image i and N c corresponds to the total number of classes. K is set to 10, as it has been advised in [START_REF] Robnik-Šikonja | Theoretical and empirical analysis of ReliefF and RReliefF[END_REF]. The contribution of each nearest neighbor k c is weighted with respect to the distance between i and k c . This process is repeated N t times, for several images in the training set. Due to the small number of images in the available datasets, in our implementation, the entire training set is considered. For classification, the Relief value is obtained by summing the contribution of each image:

Relief (f ) Class = Nt i=1 Relief (f, i) Class (2)
The sum of the first term of Equation 1) represents the probability that two close images (for the Euclidean distance in the feature space) belonging to different classes have close values of f , and the sum of the second term estimates the probability that two close images from the same class have close values of f . As a result, discriminant features are associated to high Relief values, while the value of noisy or irrelevant features are close to 0.

For regression models, it is not possible to consider images that belong to different classes, and the previous formula is adapted as described in [START_REF] Robnik-Šikonja | Theoretical and empirical analysis of ReliefF and RReliefF[END_REF]. Using the same notations as for Equation 1, the following values are defined:

P D F = 1 N t Nt i=1 K k=1 dF ik D ik K k=1 D ik (3)
P D S = 1 N t Nt i=1 K k=1 dS ik D ik K k=1 D ik (4) P D S ,D F = 1 N t Nt i=1 K k=1 dS ik dF ik D ik K k=1 D ik (5)
where dS ik is the relative score difference between images i and k. Equations 3, 4 and 5 represent respectively the estimation of the probabilities that two similar images have different values of f (high dF values), different scores (high dS values) and both different scores and different values of f . The expression of Relief (f ) Reg is finally:

Relief (f ) Reg = P D S ,D F P D S - (P D F -P D S ,D F ) 1 -P D S (6)
The first term of Equation 6 represents the probability of having similar images with different scores and different values of f , and the second term represents the probability of having similar images with close scores and close values of f . More information about the choice of parameters and implementation details is provided in [START_REF] Robnik-Šikonja | Theoretical and empirical analysis of ReliefF and RReliefF[END_REF].

Aesthetic Prediction 2.2.1. Description of the Learning Algorithms

In this work, 4 learning algorithms are considered. They have been chosen due to their ability to perform both classification (separation between low and high aesthetic quality images) and regression (aesthetic quality rating) tasks. These algorithms are implemented in the OpenCV library, and are described below. For each algorithm, OpenCV default parameters are considered, and no significant improvement have been observed by tuning the parameters. Support Vector Machine. SVM [START_REF] Chang | LIBSVM: A Library for Support Vector Machines[END_REF] is often used as a classifier in aesthetic prediction [START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF][START_REF] Pogačnik | Evaluating Photo Aesthetics using Machine Learning, Data Mining and Data Warehouses[END_REF][START_REF] Faria | Challenges of Finding Aesthetically Pleasing Images[END_REF][START_REF] Males | Aesthetic Quality Assessment of Headshots[END_REF][START_REF] Tang | Content-Based Photo Quality Assessment[END_REF][START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] and can also be considered for regression analysis [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF]. In this work, a Gaussian kernel are used.

Artificial Neural Networks. ANN [START_REF] Lecun | Efficient Backprop[END_REF] is a powerful and adaptable algorithm which can be designed for a particular problem by modifying the number of hidden layers and the number of neurons in each layer. In this work, neural networks are built using one hidden layer, containing N f /2 neurons, where N f is the number of features.

Random Forest. Like SVM, RF [START_REF] Breiman | Random Forests[END_REF] is frequently used as a learning algorithm in recent works on automatic aesthetic prediction [START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF][START_REF] Faria | Challenges of Finding Aesthetically Pleasing Images[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF]. It outputs the average of several decision trees (50 in default OpenCV implementation) built using randomly different subsets of the training features and samples. Such a statistical tree-based model makes RF robust to very noisy data, and able to deal with both discrete and continuous features.

Gradient Boosted Trees. GBT [START_REF] Friedman | Stochastic gradient boosting[END_REF] is a boosting algorithm using decision trees as weak learners. Thus, it combines the advantages of classical boosting algorithm like Adaboost, and the ability to learn from both discrete and continuous data due to its tree-based structure. OpenCV default parameters are considered: 200 × c trees are built during the learning process, where c is the number of considered classes (c = 1 for regression).

Performance Evaluation

In this work, for each experiment, 10-fold cross validation is performed by selecting randomly the testing and training images. This task is repeated 10 times to avoid sampling bias, and only average results are reported.

Classification performance is evaluated by the Cross-Category Error (CCE) and the Multi-Category Error (M CE). Let c i be the ground truth class and ĉi the predicted class of image i. CCE is a function of the error magnitude:

CCE(k) = 1 N t Nt n=1 χ(c i -ĉi = k) (7)
where N t is the number of test images, N c the number of classes and k is the difference between ground truth and prediction. χ is the function defined by χ(x) = 1 if x is true, χ(x) = 0 otherwise. The Multi-Category Error M CE is the weighted sum of the errors:

M CE = Nc-1 k=-(Nc-1) |k|CCE(k) M CE Rand (8)
M CE Rand is a normalization constant that is related to the number of classes and corresponds to the M CE value obtained by using a random classifier:

M CE Rand = N t N c N 2 c -1 3 (9)
The Good Classification Rate GCR = CCE(0)/N t is defined as the ratio between the number of images correctly classified CCE(0) and the number of test images N t . In the case of 2-class categorization, performance can also be measured by the Area Under the ROC Curve AU C. Ideally, GCR and AU C should be the highest (close to 1) and M CE the lowest possible (close to 0). Regression performance is computed by Pearson's correlation R. Let s i be the ground truth and ŝi the predicted score of picture i. R is calculated by the formula:

R = Nt n=1 (ŝ i -s) • (s i -s) Nt n=1 (ŝ i -s) 2 • Nt n=1 (s i -s) 2

Late Score Fusion

For each set of features and data, each learning algorithm will produce different performance. In the case of 2-class categorization, it is possible that one classifier predicts the erroneous class for a particular image, and the 3 other algorithms predicts the correct class. To improve the overall classification performance, the choice has been done to combine the outputs of each algorithm to obtained a fused prediction that corresponds to a weighted vote of each algorithm.

In the case of regression, the combined prediction P for an image i is defined as:

P(i) = 4 A=1 P A (i) • R p A 4 A=1 R p A ( 11
)
where A is the considered algorithm (SVM, ANN, RF, GBT). R A is the correlation obtained by cross validation of A on the training set, and P A (i) is the quality score predicted by algorithm A for image i.

p is a user-defined parameter that increases or decreases the weight of each algorithm: for p = 0, each algorithm will have the same weight and the final prediction corresponds to the mean of each prediction. For a large value of p (e.g. 100), only the algorithm with the highest Pearson's correlation will be considered. In practice, algorithms with low Pearson's values should not be considered, while two algorithms with high values should both be considered. Thus, in all the following experiments, we use p = 10 to both remove algorithms that are significantly worse than the best one and retain those producing almost the same performance.

In the case of classification, instead of Pearson's correlation, we consider the GCR and the M CE value to obtain information about the number of images that are correctly classified and the error magnitudes. Since a good classifier presents high GCR and low M CE values, the following formula is used:

P(i) = 4 A=1 P A (i) • ( GCR A M CE A ) p 4
A=1 ( GCR A M CE A ) p (12)
P A (i) is the class predicted by A, and P(i) is the final prediction. Since classes are designed by integer labels, the overall prediction corresponds to the nearest integer of P(i). In the following sections, this Late Score Fusion technique is referred as LSF .

Validation of the Proposed Method

Datasets

Experiments are made on 4 different datasets that have been considered for comparison with previous works. Most of state-of-the-art research present results on only one dataset, which can limit the ability of the method to be extended to other type of pictures.

CUHKPQ [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF] is a dataset containing 17673 images with manually labeled ground truth, downloaded from the DPChallenge website. Images are separated in seven categories corresponding to different subjects: human, landscape, architecture, etc. For each category, the top and bottom 10% images are labeled respectively as high and low quality images. In this work, only the human category is considered, and 335 high quality and 285 low quality headshots are automatically extracted. Due to the significant quality difference between both groups, recent works [START_REF] Marchesotti | Assessing the Aesthetic Quality of Photographs Using Generic Image Gescriptors[END_REF][START_REF] Tang | Content-Based Photo Quality Assessment[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] achieve classification performance above 90%. Since these images are associated to classes and not to scores, it is not possible to perform regression with this dataset.

HFS, for Human Face Scores [START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF], contains 250 portraits that have been gathered and manually cropped to fit our definition of headshots. More precisely, it contains a set of 7 different images for each of 20 different persons, and 110 additional portraits. Examples of images for 3 particular persons are given in Figure 2. Each image has been rated by 25 persons on a 1 to 6 scale (6 means the highest quality).

FAVA, for Face Aesthetic Visual Analysis, is a subset of the AVA database [START_REF] Murray | AVA: A Large-scale Database for Aesthetic Visual Analysis[END_REF] containing various images from which headshots are extracted. More precisely, each picture is scored from 1 to 10 by internet users (10 means the highest quality). This dataset is similar to the one used in [START_REF] Pogačnik | Evaluating Photo Aesthetics using Machine Learning, Data Mining and Data Warehouses[END_REF] and is used for comparison with previous works. Samples are shown in Figure 3.

Flickr is a website hosting a lot of pictures and portraits. [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF] created a dataset of 500 images gathered on this website and scored by the Amazon Mechanical Turk system. Each image is associated to a ground truth score between 0 and 10 (10 means high quality). Photos are either portraits or group portraits. In this work, only the biggest detected face is considered in each picture, while [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF] consider all the faces as well as the relationship between them (distances between faces, face pose and expressions). Images with extremes poses, occluded or very small faces (with a relative size below 1% of the entire image) are automatically removed and finally, 412 pictures are retained for our experiments.

The histograms presented in Figure 5 show that HFS presents a higher variance than FAVA, for which there is a lot of images with medium scores that makes the learning step more difficult. Thus, prediction performance is likely to be lower for FAVA than for HFS. Since Flickr does not contain only frontal and centered faces but also group portraits, the prediction performance may also be lower than for HFS.

Influence of the Feature Selection Process

15 features and 4 regions (R A , R B , R C , R D ) are a priori considered. Finding the most discriminant couples (Feature, Region) in the case of aesthetic quality estimation presents multiple advantages. First, it helps to design more efficient metrics, adapted to the considered problem. It also enables to compute fewer features, reducing the implementation and computational cost, and finally improving the overall accuracy of the prediction. In this section, the HFS dataset is considered because it contains only centered standardized facial portraits, so that there is no bias related to subject placement or image/face size. For more details about the relevance of each features and regions, refer to [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF].

The experimental procedure is the following. Features are computed and sorted using the Relief metric described above. Then, 2-class categorization and regression are performed using SVM on the couple (Feature, Region) with the highest rank. The process is repeated by adding the second most discriminant couple in the model, the third, etc. After the addition of the 60 features, Figure 6 is obtained. 2 observations can be made from this figure. First, less than half of the features are enough to obtain the same performance as the entire set(about 25 for both classification and regression). The second is that by retaining the 35 most relevant features, performance is optimal: GCR and R increase respectively from 86% to 87% and from 0.71 to 0.73. This can be explained by the fact that noisy or less relevant values are removed from the data. In our experiments, the couples with the highest Relief values are (F {1,2} , R {B,C,D} ): sharpness measures in the facial areas are the most discriminant values for aesthetic quality assessment. This observation is coherent with the model proposed in [START_REF] Aydin | Automated Aesthetic Analysis of Photographic Images[END_REF], where sharpness metrics are clearly presented as essential because the absence of sharp edges in the subject's area automatically results in low aesthetics ratings.

Influence of Algorithms

In this section, the entire feature and region sets are considered. 2-class categorization and regression are performed for each of the dataset previously presented. For categorization, datasets are separated in two equally distributed groups (except CUHKPQ which is already separated by labels), containing respectively the images with the lowest and highest aesthetic scores. If SVM generally outputs satisfying performance, in this section it is shown that sometimes it is better to consider different algorithms, and the optimal solution is to combine the algorithms as described in 2.2.3.

For classification, as shown in Table 1, LFS outputs the optimal performance. There are however large disparities among the datasets: CUHKPQ is easily separated (GCG = 95%) whereas FAVA is a difficult dataset (GCR < 70%). This is mostly explained by the fact that there are many average images in FAVA which can be classified in both categories (see Figure 5). Removing 50% of the images with average scores from FAVA leads to approximately 81% of good classification. Pearson correlations R for each dataset are summarized in Table 2. The same observation can be made: LSF enhances performance. CUHKPQ is not considered here since images are not associated to a ground truth score.

Comparison with Previous Works

To compare the proposed method with previous work, the experiments of [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF][START_REF] Pogačnik | Evaluating Photo Aesthetics using Machine Learning, Data Mining and Data Warehouses[END_REF][START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF][START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] are reproduced, using the same learning algorithms and databases with the proposed feature set. These works use images containing both group pictures and portraits [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF], only portraits [START_REF] Pogačnik | Evaluating Photo Aesthetics using Machine Learning, Data Mining and Data Warehouses[END_REF][START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF] or headshots [START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF][START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF]. The method is first compared with previous works performing image categorization, then with works performing score prediction.

Comparison with Previous Categorization Models

CUHKPQ has been considered in several recent works [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] to perform 2-class categorization, and performance is measured by the AU C. [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF] and [START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] obtain respectively an AU C of 0.974 (SVM) and 0.972 (RF). These results show that this dataset is not very challenging for state-of-the-art methods: only very low and very high quality images are considered, for which very discriminant features exist. Figure 7 presents two curves obtained with the proposed method and SVM classifiers. Without considering eyes and mouth (regions R C and R D are excluded from the model), performance is very close to [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF] and [START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] (second curve : AU C = 0.968). The first ROC curve is obtained with the entire feature set computed in each region: AU C = 0.989. This value is above the results of [START_REF] Tang | Content-Based Photo Quality Assessment[END_REF][START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF] and it shows, as demonstrated in [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF], that computing features in eyes/mouth regions adds significant information to the model in the case of frontal portrait evaluation.

[3] consider 500 images from the Flickr dataset, which are separated in 5 classes with respect to their ground truth aesthetic score. They perform 5-class categorization and measure accuracy within one cross-category error: (CCE(-1) + CCE(0) + CCE( 1))/N t = 0.68. Even if our method is not designed to evaluate group pictures, the same accuracy is obtained using the SVM classifier and by performing feature selection. LF S achieves 73% of accuracy as shown in Figure 8, which is above previous performance. This is due to the combination of SV M accuracy (GCR = 0.32) and the low error magnitudes obtained from the tree-based classifiers (M CE < 0.68 for RF and GBT, 0.71 for SVM). For other datasets, our recent work [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] showed that computing features in additional relevant face regions significantly outperforms methods that are designed to evaluate portraits but do not consider the particular case of headshots. The classification performance for each dataset is compared to state-of-the-art results in Table 3. In some cases, state-of-the-art is not outperformed. This happens when a classifier outputs results that are significantly above other classifiers, so that the combination does not improve the overall performance.

Comparison with Previous Regression Models

Among the 4 works previously cited, only [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF] and our previous work [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] performed aesthetic score prediction. [START_REF] Li | Towards aesthetics: A Photo Quality Assessment and Photo Selection System[END_REF] calculated the residual sum-of-squares error RSE to measure performance:

RSE = 1 N t -1 Nt i=1 ( Ŝi -S i ) 2 (13)
where N t is the number of test images, S i is the ground truth score and Ŝi the predicted score. They perform SVM regression to make score prediction.

Using the same dataset and learning algorithm, their features lead to RSE = 2.38 while the proposed features lead to RSE = 2.17, which is slightly better. RSE can be reduced to 2.12 by combining the algorithms.

Other regression results are directly compared with our previous work [START_REF] Lienhard | Low Level Features for Quality Assessment of Facial Images[END_REF] in Table 4, showing that most of our previous results are slightly outperformed with the late score fusion.

Discussion

The results obtained in this section reveal several crucial steps related to aesthetic quality estimation of facial portraits. First, feature extraction and selection are key parts of the process: reduced feature sets can perform equally or better than the entire feature set. By comparing the proposed results with the method developed in [START_REF] Lienhard | Photo Rating of Facial Pictures based on Image Segmentation[END_REF], it can be observed that it is not necessary to compute precise contours of the face. Simple regions, defined by the face, eyes and mouth bounding boxes add sufficient information to the model. This makes the model easily reproducible with a low computational cost: features can be computed in small regions that are detected in real time via the Viola-Jones algorithm.

If several learning algorithm produce satisfying performance, there is no optimal choice adapted to each feature and dataset. Thus, a trade-off that combines the advantages of the 4 algorithms has been proposed. This step enhances the robustness of the method and is a good alternative to timeconsuming parameter tuning that makes the model very dependant. Moreover, it enables to work with both continuous and discrete data, as it is shown in the next section.

Finally, the method described here can be applied to aesthetic quality estimation of other type of pictures, by replacing the face detection step by any other object detection or pyramidal decomposition of a picture. Learning models can also be added in the combination. The proposed method has been limited to the computation of low-level statistics and it is likely that the model would benefit from the addition of other specific features, such as the lighting templates considered in [START_REF] Khan | Evaluating Visual Aesthetics in Photographic Portraiture[END_REF], features that encode directly subject and background relationship [START_REF] Kim | Aesthetic Quality Classification via Subject Region Extraction[END_REF], or by combining the outputs of each of the feature categories (texture, illumination, contrast, color) as described in [START_REF] Zhang | Feature Correlation Hypergraph: Exploiting High-order Potentials for Multimodal Recognition[END_REF].

LIKABILITY ESTIMATION

The method proposed for facial picture aesthetic estimation is used with a different feature set in order to evaluate how much likable a person looks like on a given picture. Features considered for likability evaluation are highlevel descriptors (such as smile, eyes openness, eyebrow position) obtained from the 3 different face analyzers described in Section 4.2. Performance is measured on two types of dataset, involving either synthetic or natural faces. Experiments are made using the feature selection method and the algorithms proposed in Section 2. To the best of our knowledge, few works have explored the automatic evaluation of human traits (trustworthiness, dominance, threat) except for attractiveness due to its application in marketing and cosmetics. In this work, likability estimation is proposed because of its possible application in automatic picture selection for home users, but the same framework can be applied to any other trait.

Datasets 4.1.1. Synthetic Faces used for Validation

Few datasets containing facial pictures have been built and annotated with respect to likability. In this section, synthetic faces are considered, without any extra-facial cues such as hairstyle, beard, glasses or jewelry.

Using human-rated synthetic facial pictures, models of face evaluation are computed in [START_REF] Todorov | Modeling Social Perception of Faces[END_REF] with respect to the following traits: attractive, competent, dominant, extroverted, likable, threatening, trustworthy. For each model, a dataset of 25 distinct faces is created. These faces are manipulated along the respective traits to generate 7 variations corresponding to 7 different levels of the considered dimension, producing sets of 25 × 7 = 175 images. Subjective experiments [START_REF] Todorov | Validation of Data-driven Computational Models of Social Perception of Faces[END_REF] revealed that these synthetic faces are greatly correlated with the models built in [START_REF] Todorov | Modeling Social Perception of Faces[END_REF]. 7 variations of likability for a given face are presented in Fig. 9. Only the dataset corresponding to likability is considered, and it is used to verify that our evaluation is consistent and to prove that high-level attributes can be good likability descriptors. [START_REF] Todorov | Modeling Social Perception of Faces[END_REF]. From left to right: unlikable, neutral and very likable.

Human Study on Natural Images

To evaluate our model on natural images, the set of 140 frontal and centered pictures of 20 different persons (10 men and 10 women) from HFS dataset is considered (see Figure 2). To obtain ground truth scores, participants were asked to evaluate each image in the same viewing conditions, and to rate how likable the person on the image seems. Images were presented in a random order, after a preliminary learning process where participants had to rate images that are not part of the dataset. A discrete scale from 1 (not at all likable) to 6 (very likable) has been considered. Finally, 27 participants aged from 20 to 55 rated each image. Scores average and standard deviation are respectively 3.37 and 0.79.

High-Level Attributes for Face Evaluation

In this work, attributes extraction is performed by 3 tools provided "as is": the SHORE software [START_REF] Ernst | A Modular Framework to Detect and Analyze Faces for Audience Measurement Systems[END_REF] and two free cloud based applications: Betaface and SkyBiometry. Each tool T returns a total of N T distinct features. Values may either be discrete (is it a male or a female ?) or continuous (how much is the person smiling ?). Some features have both a discrete component ("yes" or "no") and a continuous component ("how much ?"): Does this person smile (yes or no) ? How much (from 0 to 1) ?

A total of 63 attributes is gathered: 37 from Betaface, 20 from SkyBiometry and 6 from Shore. A simplified list of these attributes is given in Tab. 5. Note that Betaface and SkyBiometry also return a list of facial keypoint positions (respectively 94 and 73 points); detection examples are given in Figure 10. Thus, it is possible to compare keypoints and high-level attributes. Performance of each distinct tool is not discussed in this work (see [START_REF] Lienhard | Fully Automated Facial Picture Evaluation Using High Level Features, Automatic Face and Gesture Recognition[END_REF] for more details) and attributes are fused so that each image is described by a vector containing 63 values.

Experiments 4.3.1. Validation on Synthetic Faces

In a first set of experiments, synthetic faces are considered to verify that face likability models can be built using the proposed set of high-level attributes. The dataset contains faces grouped in seven categories, corresponding to seven levels of likability (cf Figure 9). Since the faces are generated by keypoints distortion, models based on facial keypoints should provide high classification performance. Our first attempt in creating a likability model requires the facial keypoints provided by either Betaface or SkyBiometry. Applying each learning algorithm, the results presented in the first two lines of Table 6 are obtained.

The performance of a random classifier is approximately GCR = 14% and M CE = 1. Low M CE values reported in the table (between 0.28 and 0.52) and high GCR (between 30 and 50%) indicate that not only our classifier is able to classify correctly many faces (high GCR), but also makes only minor mistakes (low M CE). It is noticeable that SkyBiometry facial keypoints are slightly more efficient than Betaface's: the keypoints detected are not the same for both tools (see Figure 10). Finally, for this configuration of features and images, Neural Networks outperform any other learning algorithms. A possible explanation is that the synthetic faces are very similar, and the high number of keypoints enables the network to fit very well to the learning data. Further experiments on natural images in Section 4.3.2 show that this observation cannot be generalized.

The principal contribution of this article in the domain of automatic likability evaluation is the use of high-level attributes. Results are significantly above chance and close to the results obtained with keypoints, even on this particular case of synthetic faces based on keypoint manipulation. This validates the use of HL descriptors as a possible alternative to facial keypoints for likability evaluation. Like the low-level set of features proposed in Section 2, HL attributes provide concrete feedback and can be summarized by a very small number of values that corresponds to human analysis: is the subject smiling ? Is he/she happy ? In the following section, it is shown that in the case of natural images, it is more difficult to evaluate likability by using only facial keypoints.

Application on Natural Images

The dataset of natural images is used for an ultimate validation of the proposed model. Since each picture has a ground truth likability score, it is possible to build regression models. This section validates the use of highlevel attributes in the case of natural faces, and shows that facial keypoints are significantly less efficient. In the case of natural pictures, many facial cues play a role in face likability evaluation: hairs, beard, glasses, etc. This is confirmed by the experimental results presented in Table 7. Using attributes instead of keypoints enhances the performance: Pearson's correlation increases from about 20%. In this example, GBT and RF are the most efficient algorithms. ANN is outperformed by tree based algorithms that can efficiently work with features that contain both discrete and continuous data and missing attributes (e.g. eyes that cannot be seen behind sunglasses).

Table 7 shows the correlation between ground truth and predicted scores for the model based on attributes. In the case of natural images, some missing attributes in the feature space (background or reflectance cues are not considered) and errors during the feature extraction process may lead to erroneous predictions. This is discussed in the following section, which presents an example of a possible application of this method and its limits.

APPLICATION TO AUTOMATED PICTURE SELECTION

Automated picture selection of a given person is a practical application of the proposed method and its results. People may have hundreds of pictures from which they want to select a small set that is relevant for a given application. Since this work focuses on aesthetic quality and likability assessment, possible applications may relate to profile pictures for social networks or meetings websites. The objective is to combine both models (aesthetic and likability) and to sort the pictures with respect to these criteria. The problem is the lack of ground truth data that take both parameters in consideration. Subjective experiments are not a satisfying solution because participants would have to judge simultaneously aesthetic quality and likability. It is possible to ask participants the following question: "Among these images, which one would you choose for this particular application ?". However, this operation ranks the images but does not produce the ground truth scores that are needed for applied the proposed regression models. Thus, in this section, a combination of the aesthetic quality and likability ground truth scores is considered, even if there may be some bias due to the fact that both evaluations are completely different. Several combination are possible (e.g. a weighted linear combination of both ground truth) and the product of both ground is considered in the proposed experiments. Using the product instead of a linear combination ensures that both aesthetic quality and likability evaluations have to be satisfying in order to obtain a high score. The experimental procedure as well as the performance are described in details in Section 5.1. Discussion about the proposed method is given in Section 5.2.

Experiments

Since both likability and aesthetic ground truth scores are required, the only dataset that is considered in this section is the subset of HFS containing 7 images of 20 different persons. The objective is to classify pictures for a given person, therefore instead of performing 10-fold cross validation and random sampling, the model is learned using 19 persons and the prediction is made for the remaining 7 pictures of the last person. This task is performed for the 20 different persons, for both aesthetic and likability predictions. Performance is similar to the performance obtained by 10-fold cross validation in the previous sections: the Pearson's correlation for aesthetic quality and likability estimation are respectively 0.75 (0.74 in Section 3.4.2) and 0.85 (0.84 in Section 4.3.2). The small increase of correlation may be due to the use of 20-fold cross validation instead of 10-fold, and in the case of aesthetic quality assessment, only a subset of the entire HFS dataset is considered. Figure 11 presents the point clouds obtained by performing either likability or aesthetic quality estimation and by multiplying the values of both estimations for each picture. The combined prediction, that takes both aesthetic quality and likability estimation into account still presents a correlation of 0.83, implying that it is possible to select pictures that are both of good quality and showing a likable face.

Discussion

In this section are presented and discussed examples of image automatically selected. Using appropriate thresholds (see Figure 12, it is possible to retain automatically good quality images with likable faces (pictures above the green line). Threshold can either be user defined, implying more or fewer accepted images, or by selecting the number of pictures to be selected. This method presents the following drawbacks.

First, it is sensitive to the feature extraction process: it is possible that faces are not correctly detected, or that facial attributes present erroneous measurements. Figure 13 show examples of such mistakes. Face a) is overrated by the aesthetic predictor, which is likely due to the lack of information provided by the color channels. The system has been trained on colored images, as a result the evaluation of an image that does not present the 3 color channels is biased. Faces b) and c) have high likability ratings even if they present non smiling faces: facial expressions are not correctly evaluated for extreme emotions. Rating details are presented in Table 8. Pictures d) to f) are nicely predicted by the model. Note that the system considers closed eyes (picture d)) as satisfying pictures if the person is smiling. This particular case may be solved either by adapting the learning data (which currently does not include poorly rated images with closed eyes) or by performing an additional filtering step where images with closed eyes are removed.

To give more weight to one of the criteria (likability or aesthetics), it is possible to replace the combination function which is currently the product 8. of both predictions. It has to be noticed that the proposed dataset is very limited: only 140 images are considered. The accuracy of the model is both limited by the feature extraction step and the learning data. However, the point cloud presented in Figure 11 show promising applications.

CONCLUSION

In this paper, a framework for automated facial picture selection has been proposed. To assess aesthetic quality, features are extracted in different face regions (entire face, eyes, mouth) that contain the most relevant information about the portrait. Few pixel-level statistics are computed in each region and late fusion of several learning algorithms is performed to enhance the global prediction performance. Likability is evaluated by extracting different highlevel descriptors such as the presence of a smile, eyes closeness or eyebrow position. Then, the process of feature selection and algorithm combination is applied, and satisfying performance is obtained on the considered dataset. A method to combine both predictions is presented, and enables the user to select appealing images, facial images that look likable, or images that fit to both criteria. A major limitation of the proposed likability estimation is that it requires the use of tools that can extract automatically and evaluate correctly high-level attributes.

Results regarding aesthetic quality estimation are promising since recent works are outperformed. The same method is applied to likability evaluation, and our hypothesis is that the same selection and learning process can be applied to other type of images, by adapting the features and the selected regions. Another possible way to enhance the results would be to add classifiers to the model, and/or to optimize the parameters of the learning algorithms which are currently OpenCV default parameters. It is also possible to employ several times the same algorithm, using different parameters for each time (more trees in the tree based algorithms, different neuron numbers in ANN, etc.). Though, the proposed set of algorithms is quite robust and presents satisfying results.

The choice of the features in this article was motivated by their ability to provide directly feedback to users since they can be easily interpreted: blurry image, poor face enlightening, non smiling face, etc. Plus, the proposed framework can be directly applied for profile picture selection and can be easily applied for other applications, by adapting the learning data and/or the features. In future work, other state-of-the-art features will be added in the model in order to enhance the performance. Also, the feature selection process enables us to decrease the feature number, and by avoiding heavy feature combination it is possible to make the process usable in real-time. Finally, this work focused on likability evaluation, but the framework can be applied to evaluate other traits. For instance, competence evaluation may enable users to select images for professional purposes: resumes, visiting cards, etc. But competence evaluation requires the addition of attributes related to clothes (men in suits are often rated as competent) that are not considered in the proposed model.

Figure 1 :

 1 Figure 1: Example of an image and its 4 regions.

Figure 2 :

 2 Figure 2: 7 pictures of 3 persons from the HFS dataset.

Figure 3 :

 3 Figure 3: Samples from the FAVA dataset.

Figure 4 :

 4 Figure 4: Samples from the Flickr dataset.

Figure 5 :

 5 Figure 5: Histograms of ground truth scores for HFS (250 images rated from 1 to 6), FAVA and Flickr (respectively 636 and 500 images rated from 1 to 10).

Figure 6 :

 6 Figure 6: Influence of the number of most discriminant features retained in the model (according to the Relief metric), for 2-class categorization and regression.

Figure 7 :

 7 Figure 7: ROC curves obtained by using usual regions (entire image R A and face R B ) and the proposed regions, including eyes and mouth.

Figure 8 :

 8 Figure 8: Performance of [3] is compared to the Proposed Method (PM) using either SVM or the LSF.

Figure 9 :

 9 Figure9: Examples of synthetic faces manipulated for likability[START_REF] Todorov | Modeling Social Perception of Faces[END_REF]. From left to right: unlikable, neutral and very likable.

Figure 10 :

 10 Figure 10: Examples of facial keypoint positions for synthetic and natural images. a) and c) show Betaface points, b) and d) SkyBiometry points.

Figure 11 :

 11 Figure 11: Point clouds obtained from computing with the proposed method, from left to right: aesthetic quality estimation, likability estimation, the product of both evaluations. Ground truth scores of the third image are obtained by multiplying the aesthetic quality and likability ground truth scores.

Figure 12 :

 12 Figure 12: Examples of ground truth and prediction scores for several images of a given person. Images above the green line are selected and images below are rejected.

Figure 13 :

 13 Figure 13: Images a) to c) are erroneously rated by the system and images d) to f) present correct predictions. Details about prediction values are given in Table8.

Table 1 :

 1 GCR (%) of the classification algorithms for each dataset.

	Datasets SVM ANN RF GBT LSF
	CUHKPQ 93.9 93.0 90.7 91.4 94.8
	HFS	77.8 76.6 76.3 76.0 79.3
	FAVA	65.1 62.7 65.9 66.2 67.1
	Flickr	69.1 65.2 67.5 67.7 69.3

Table 2 :

 2 Correlation (R) of the regression algorithms for each dataset.

	Datasets SVM ANN RF GBT LSF
	CUHKPQ	/	/	/	/	/
	HFS	0.71 0.60 0.69 0.67 0.73
	FAVA	0.44 0.46 0.47 0.50 0.51
	Flickr	0.46 0.44 0.43 0.44 0.49

Table 3 :

 3 GCR (%) of State-of-the-Art (SotA) is compared with the Proposed Method (PM) for each dataset, using Late Score Fusion.

				Table 4: Correlation (R) of State-of-the-
				Art (SotA) is compared with the Pro-
				posed Method (PM) for each dataset, us-
				ing Late Score Fusion.
	Dataset	SotA	PM	Dataset	SotA	PM
	CUHKPQ 90.0 [6, 34] 94.8	CUHKPQ	/	/
	HFS	86.5 [15]	86.9	HFS	0.74 [15] 0.74
	Flickr	68.0 [3, 15] 73.2	Flickr	0.47 [15] 0.49
	FAVA	81.0 [15] 81.0	FAVA	0.46 [15] 0.51

Table 5 :

 5 Simplified list of high-level attribute categories computed by each tool. The number of values (discrete or continuous) describing each category is reported in each cell.

		Gender Age Smile Mood Beard Mustache Glasses Eyes Mouth Eyebrows Nose Skin Hair Shape
	Betaface	2	1	3	3	3	3	4	3	3	2	2	5	3
	SkyBiometry	2		2	8		4	2	2
	SHORE	1	1		1			2	1

Table 6 :

 6 Experimental results for 7-class categorization using either Betaface / SkyBiometry facial keypoints (KP) or high-level (HL) attributes.

	Algorithm	SVM	ANN	RF		GBT		LSF
	Criterium	GCR M CE GCR M CE GCR M CE GCR M CE GCR M CE
	KP Betaface	29.9	0.39	33.2	0.40	17.1	0.52	27.7	0.41	35.3	0.38
	KP SkyBiometry 34.5	0.33	43.3	0.28	22.5	0.41	33.0	0.35	43.3	0.33
	HL Attributes	24.9	0.42	43.8	0.28	22.5	0.41	35.9	0.32	44.3 0.28

Table 7 :

 7 Average correlation (R) for natural images, using either keypoints or combined attributes.

	Algorithm	SVM ANN RF GBT LSF
	KP Betaface	0.43 0.43 0.37 0.46 0.50
	KP SkyBiometry 0.36 0.27 0.25 0.18 0.39
	HL Attributes	0.74 0.72 0.81 0.82 0.84

Table 8 :

 8 Ground Truth (GT) and Prediction (P) results obtained by applying the proposed method on the images presented in Figure13. Aesthetics 2.52 2.58 1.72 2.00 1.36 2.63 3.72 3.76 2.64 2.77 3.12 2.58 Likability 1.59 2.75 2.11 3.38 2.63 3.14 3.67 3.62 2.85 2.72 3.26 3.92 Aes. x Lik. 4.01 7.10 3.63 6.79 3.57 8.26 13.6 13.6 7.52 7.55 10.2 10.1

	a)		b)		c)		d)		e)		f)
	GT	P	GT	P	GT	P	GT	P	GT	P	GT	P