Amelia Carolina Sparavigna

Dunes changing their shape: The case of the dunes of the Laayoune-Sakia El Hamra region

Keywords: Sand dunes, Satellite images, Time series, Google Earth

Sand can create an endlessly moving collection of dunes, drifted by the prevailing winds. However, it can happen that, changing the winds, also the motion and the shape of the dunes change. Here we show an example in the dunes of the Laayoune-Sakia El Hamra region, in the west of Sahara. We can observe that the barchans assume a deformed shape in the satellite images of 2016, images that we can find in the time series of Google Earth. The origin of this deformation is in the change of the prevailing wind.

Dunes are made of sand interacting with the local wind and soil surface. By this complex interaction, the variety of shapes displayed by the dunes arise [START_REF] Sparavigna | A Study of Moving Sand Dunes by means of Satellite Images[END_REF][START_REF] Hersen | Relevant Length Scale of Barchan Dunes[END_REF]. Moreover, in the case that wind is blowing from a prevailing direction, the dunes migrate. The first studies on the migration rates of dunes were made by field measurements [START_REF] Beadnell | An Egyptian Oasis, and Account of the Oasis of Kharga in the Libyan Desert, with Special Reference to Its History, Physical Geography and Water-Supply[END_REF][START_REF] Bagnold | The Physics of Blown Sand and Desert Dunes[END_REF]. Today, controlled experiments and numerical simulations had been added to such measurements, to have a better comprehension of the mechanisms of formation and drift of sand dunes [START_REF] Beadnell | An Egyptian Oasis, and Account of the Oasis of Kharga in the Libyan Desert, with Special Reference to Its History, Physical Geography and Water-Supply[END_REF][START_REF] Bagnold | The Physics of Blown Sand and Desert Dunes[END_REF][START_REF] Pye | Aeolian Sand and Sand Dunes[END_REF][START_REF] Cooke | Desert Geomorphology[END_REF][START_REF] Dauchot | Barchan Dunes in the Lab[END_REF][START_REF] Andreotti | Selection of Dune Shapes and Velocities[END_REF][START_REF] Herrmann | Aeolian Transport and Dune Formation[END_REF][START_REF] Herrmann | The Shape of Dunes[END_REF][START_REF] Herrmann | The Morphology of Dunes[END_REF][START_REF] Sauermann | The Shape of the Barchans Dunes of Southern Morocco[END_REF][START_REF] Sauermann | Wind Velocity and Sand Transport on a Barchan Dune[END_REF]. As stressed in [START_REF] Thomas | Remobilization of Southern African Desert Dune Systems by Twenty-First Century Global Warming[END_REF][START_REF] Hiza Redsteer | Monitoring and Analysis of Sand Dune Movement and Growth on the Navajo Nation[END_REF], field measurements are fundamental to have information on the specific features of sand composition and environmental conditions. To estimate the migration rates of dunes, we need measurements made on large length and time scales [START_REF] Hersen | Relevant Length Scale of Barchan Dunes[END_REF], which are corresponding approximately to 100 m and 1 year. For this reason, in the study of the motion of dunes, we can have a great help from the use of the time series of satellite images, which allow an easy remote measure and control of dunes. Examples are given in [START_REF] Sparavigna | A Case Study of Moving Sand Dunes: The Barchans of the Kharga Oasis[END_REF][START_REF] Sparavigna | Peruvian transverse dunes in the Google Earth images[END_REF][START_REF] Sparavigna | Sedimentary Patterns of Moving Sand Dunes in Orinoca district, Bolivia[END_REF][START_REF] Sparavigna | Analysis of the Motion of Some Brazilian Coastal Dunes[END_REF][START_REF] Sparavigna | The GNU Image Manipulation Program applied to study the sand dunes[END_REF]: in these references we used the time series of Google Earth. In [START_REF] Sparavigna | The GNU Image Manipulation Program applied to study the sand dunes[END_REF], we investigated some dunes which were studies in [START_REF] Durán | The Dune Size Distribution and Scaling Relations of Barchan Dune Fields[END_REF]. The authors of [START_REF] Durán | The Dune Size Distribution and Scaling Relations of Barchan Dune Fields[END_REF] measured the width and position of more than 5,000 dunes corresponding to four dune field corridors of Morocco and Western Sahara, using the satellite images from Google Earth. Their aim was that of determining the size distribution and structure of the dune fields; therefore, in [START_REF] Durán | The Dune Size Distribution and Scaling Relations of Barchan Dune Fields[END_REF], the motion of the dunes was not discussed in details. However, Google Earth gives us the possibility to investigate their migration rate too: we considered some of these dunes (coordinates 27.387239,-12.607788), giving their motion as a function of their size (Figure 5 in [START_REF] Sparavigna | The GNU Image Manipulation Program applied to study the sand dunes[END_REF]). Of this location in Western Sahara we have not recent images provided by Google Earth (in [START_REF] Sparavigna | The GNU Image Manipulation Program applied to study the sand dunes[END_REF], we used those recorded in 2005, which are the only images given in the time series). But the dunes which are in northern locations, such as those in the Laayoune-Sakia El Hamra region, are shown in images of 2016. Therefore, here we consider some of the dunes of this region.

The dune field of the Laayoune-Sakia El Hamra region is very interesting, because the recent images of 2016 show that the dunes are changing their shape. This is clearly visible in the Figures 1234(the satellite images have been enhanced using GIMP Retinex; about this filter see [START_REF] Sparavigna | GIMP Retinex filter applied to arts: Gerrit van Honthorst and his Chiaroscuro[END_REF] and references therein). We can suppose that the dunes are changing their shape because of a change in the direction of prevailing wind. In the images of 2012 and 2013, according to the shape of the barchans, the direction of the wind was NNE, but in the images of 2016 the barchans appear deformed by ESE wind (see Figure 5 for the directions). Let us conclude stressing that the satellite images of 2016 are showing a quite interesting phenomenon, which requires further detailed researches, in particular concerning the direction of the wind. From the deformation of the barchans, it seems that this region of Sahara is subjected to a climate change.

Figure 1 :

 1 Figure1: Dunes in the Laayoune-Sakia El Hamra region. Use the black stars as reference points to compare the images. Note from the images of 2016 that the shape of the dunes changed. In the upper and middle images, the prevailing wind was NNE; in the lower image, we see that the prevailing wind changed.

Figure 2 :

 2 Figure 2: Two barchans in the Laayoune-Sakia El Hamra region. Use the black stars as reference points to compare the images and see the motion of the dunes. They have changed their shape. Note the faint "ghost" image of the previous position and shape of the dunes.

Figure 3 :

 3 Figure 3: Barchans changed their shapes (the red circle is the reference point). Note the faint "ghost" shapes (marked in red) of the previous position and shape of a dune.

Figure 4 :

 4 Figure 4: Other barchans (the red circle is the reference point). Here too we can see the faint "ghost" shapes in the image of the right panel.

Figure 5 :

 5 Figure 5: Barchans in 2016, deformed by ESE wind.


M R Kamsap

C Champenois

J Pedregosa-Gutierrez

S Mahler

M Houssin

M Knoop

Experimental demonstration of an efficient number diagnostic for long ion chains

Keywords: numbers: 64.70.kp Specific phase transition -Ionic crystals, 05.65.+b Self-organized systems, 03.67.Lx Quantum computation architectures and implementations

Very long, one-dimensional ion chains are the basis for many applications, in particular in quantum information processing, and reliable diagnostics are needed to quantify them. To that purpose, we have experimentally tested Dubin's model for very long ion chains [Phys. Rev. E 55, 4017 (1997)] which describes the equilibrium state of a one-dimensional correlated system. For chains larger than 100 ions, this diagnostic allows us to determine the number of trapped ions with a 8%-precision in a 95% confidence interval, without counting individual ions. This measurement is based on the experimental determination of the ion-ion distance of the innermost particles and of the trapping potential along the ion chain direction. The agreement of the model with experiments allows one to determine the degree of local homogeneity of the ion crystal in the center of the chain.

I. INTRODUCTION

Trapped one-dimensional ion chains encounter increasing interest in different areas of modern physics, as they constitute controllable model systems to test fundamental questions. They are among the most attractive candidates in quantum information [1][2][3], and they serve as model systems for the study of nano-friction [4][5][6], or investigations of the Kibble-Zurek mechanism [7][8][9].

Regarding trapped ions as support for quantum computation, the key challenge now is to increase the number of trapped ion qubits to a level where simulations that are intractable otherwise might become possible [10]. One strategy pursued for up-scaling is to operate with small linear ion chains and multiplex the system by shuttling ions between multiple chains, which requires a dedicated electrode structure and very precise control of ion trajectories [11]. Another approach is based on a long linear trap in order to store a single ion-chain containing more than a hundred ions [1]. One of the issues raised by this approach is the structural stability of the chain, which requires the aspect ratio of the trapping potential to fulfil a condition which depends on the number of trapped ions [12,13]. It then becomes mandatory to have an efficient diagnostic of the number of trapped ions, in a regime where simply counting them on a recorded image, like routinely done for up to 50 ions, may not be feasible anymore. Furthermore, it would be useful to have a global criterion linking the minimum number of ions to the local homogeneity at the chain center, opening the way for the implementation of dedicated quantum information protocols [1].

In this article, we propose an efficient diagnostic for the total number of ions in a chain in a harmonic potential, even if only the central part of the chain can be recorded. This diagnostic does not rely on the individual counting * caroline.champenois@univ-amu.fr of each ion but on the measurement of the average interion distance at the center of the chain. To that purpose, we experimentally test the model developed by Dubin in the 1990s [12,14], which allows the total number of ions in the trap to be deduced with an ultimate precision of a few percent. This measurement is also a diagnostic for the local homogeneity of the chain.

A one-dimensional chain of identical, charged particles can be experimentally created in a linear radiofrequency (rf) trap. In most linear rf traps, the trapping potential along the chain axis can be very well approximated by a harmonic potential and the equilibrium position of each particle along the trap axis results from the balance between the Coulomb interactions with all other particles and the restoring trapping force. In many experiments, the trapped ions are laser-cooled to temperatures below 10 mK and once crystallised in a stable structure, they make small oscillations around their equilibrium position. They are typically separated by a distance of several µm enabling individual detection of their fluorescence and/or individual addressing by a tightly focussed laser beam. The observation of ion positions for chains longer than a hundred particles allows one to experimentally study a correlated system where the correlation energy between particles is as important as the mean-field energy [14]. This situation is rarely met. For example, in a 3D-system, it takes a 1/r 3 interaction potential to fulfill this condition. The strong role of particle correlation in the equilibrium energy makes analytical calculations complicated. For a 1D-system, D.H.E. Dubin takes into account these correlations through the Local Density Approximation and is able to describe the dependency of the local density with the chain length and the total number of particles [12,14]. Once confirmed, these theoretical laws can be used as an efficient diagnostic for the particle number and local homogeneity for long ion chains, suppressing the need for individual counting of the ions.

To test these laws, we confront model predictions with precise experimental results. Our experiments are based on the imaging of the laser induced fluorescence of in-dividual ions on a intensified CCD camera. Long ion chains are routinely created in several groups and parts of ion chains have been observed and reported before (e.g. [8,15]) but they have been limited to ion numbers below 40, mostly because of the limits of the collecting optics set-up. Our experimental set-up allows the controlled translation of the imaging optics along the trap axis without destruction of the chain [16], in order to record pictures at various positions along the ion string which can be joined to build a picture of the complete string.

In this article, we present the above cited model for ion string structures, then describe the experimental realisation of very long ion chains, followed by a discussion of the uncertainty budget of the method.

II. SCALING LAWS FOR LONG COULOMB CHAINS

A very prolate potential shape is needed to force a sample of the order of 100 ions to organise as a chain. In a trapping potential which is harmonic in the three directions of space, the structural phase transitions of linear Coulomb crystals are controlled by the number N of trapped particles and by the trapping potential aspect ratio ρ, which reduces to the ratio of the axial over radial potential steepness ρ = ω 2 z /ω 2 r in the case of a linear trap with cylindrical symmetry [12,13,17,18]. In the following, we assume that the stability condition for a linear chain is satisfied. In [12,14], Dubin treats the N ion chain as a charged fluid at zero temperature with total charge N Q and shows that in the frame of this approximation the local density, or number of ions per unit length along the chain, can be chosen to be

1/a(z) = 3N 4L 1 - z 2 L 2 (1)
where a(z) is the distance between closest neighbours, z is the distance from the chain centre and 2L is the chain's total length. This equation reflects the increasing inter-ion distance for larger distance to the chain center, which is well confirmed by numerical simulations based on potential energy minimization [14,19] and experimental observations. According to Dubin, this trial function (Eq. 1) slightly overestimates the chain length but its simple form allows the comparison with experimental results. This is the main limit of the model and as an example, the overestimation reaches 12% for a 160 ion chain [14].

Taking into account correlations between ions, Dubin derived the half-length L in terms of the two-body equilibrium length scale l = (Q 2 /4π 0 mω 2 z ) 1/3 by

L = l(3N ) 1/3 (ln N + ln 6 + γ e -A) 1/3 (2)
with γ e ≈ 0.577 the Euler constant (m is the particle mass).

Describing the relevant physical parameters (length and reduced density) of a chain with a (ln N ) -1 power series, Dubin obtains a value for A = 7/2, by neglecting terms of the order of (ln N ) -2 [14], improving his earlier results [12]. Later work [18] confirmed the scaling law L l(3N ln N ) (1/3) for N 1. To be consistent, the power series description of Dubin also concerns the local density 1/a(z). If we combine the power series of the chain length and of the density, we obtain an expression for the smallest inter-ion distance a 0 D at the chain center,

a D 0 = 4l(3N ) -2/3 (ln N + ln 6 + γ e -A) -1/3 + B(ln N ) -4/3 -1 (3
) where A is 7/2 and B = -5/2 + 3 ln 2. This equation allows the number of ions in the chain to be deduced from the measurement of the smallest inter-ion distance a 0 and the characteristic length l, with an error of the order of (ln N ) -2 which is equivalent to ±4% for the largest chain we could observe.

III. EXPERIMENTAL SET-UP

Our experimental set-up for trapping long ion chains is based on a linear radio-frequency trap where the distance between the trap center and the rods polarised by rf-voltage is r 0 = 3.93 mm and the distance between the plane electrodes confining the ions along the trap z-axis is 96 mm, justifying that we neglect the role of image charges [14]. The V dc = 2000 V applied to the z-electrodes results in a harmonic potential of ω z /2π = 3.1 ± 0.15 kHz (95% confidence interval). Ions are created by isotope selective photo-ionisation of a neutral calcium beam and are then shuttled to the part of the trap where the long chain is formed [16] to avoid perturbation of the potential by any calcium deposit on the electrodes. Ions are laser-cooled by two collimated laser beams close to resonance with the [4S 1/2 -4P 1/2 ]transition, of equal power (397 nm, 2 mW on a 2 mm 1/e 2 diameter), counter-propagating along the trap axis. Once excited from the ground state, calcium ions can relax to a long-lived metastable state [3D 3/2 ] from which they have to be re-pumped to maintain efficient laser cooling. This re-pumping process is assured by a 866 nm laser beam [resonant with 3D 3/2 -4P 1/2 ] of approximately 2.5 mW and 4 mm 1/e 2 diameter which copropagates with one of the cooling lasers. The trapped ions are observed through their laser induced fluorescence on the cooling transition which is collected along a direction perpendicular to the trap symmetry axis, and projected onto a photomultipler (PM) and an intensified charge coupled device (CCD) camera. The camera screen is an array of 1024 × 1024 pixels with a pixel size of 13 µm. In order to obtain a sufficient spatial resolution to distinguish ions separated by a few µm, an optical magnification larger than 10 is required, which limits the number of observable ions to less than 100. These values are representative for many ion-trap experiments. In our The translation step of 1 mm is smaller than the camera sensor size in the object space. Some ions are then redundant and are recorded on two consecutive pictures. The average inter-ion distance is 22 pxl which is larger than the uncertainty associated to one translation (±5 pxl) and which results in 6 redundant ions for each translation (4 for the last one). These numbers are sufficient to check precisely the consistency of the superposition and deduce an exact number of 155 ions in the chain in

IV. DATA ANALYSIS

We have fitted these data with Eq. ( 1) fixing N to 155. The best fit finds a chain center z 0 located at the physical center of the chain and a chain length (2L f = 5420 ± 30 µm) which is more than 17% larger than the measured physical length 2L m . Like mentioned earlier, this overestimation is expected from the simple equation form given in Eq.( 1) and also includes experimental uncertainties. However, Dubin's model allows to be used in a form relating the inter-ion distance at the center of the chain a 0 to the ion number, without an explicit dependence on L, as given by Eq. (3). To demonstrate the relevance of using only the central pic-ture of the chain to deduce an ion number, we calculate a 0 based on the relative position of the 20 central ions. The result is then a 0 = 24.1 ± 1.0 µm (95% confidence). Assuming for l the value determined from the direct measurement ω z /2π = 3.1 ± 0.15 kHz, we can calculate the number N D of ions in the chain from Eq. ( 3). The result is N D = 151 ± 12 where the two major causes of uncertainty are, in order of importance, statistics and the uncertainty in the determination of ω z .

To reduce the experimental uncertainty of a 0 , and if the optical field of view allows for it, one can average a(z) for more central ions. The number N a of included ions can not be extended too far as there is a quadratic dispersion in inter-ion distance with the distance from the center. If we use Eq. ( 1) around the chain center, one can show that the dispersion in the distance to the next neighbours behaves like

δa a = 2N a 3N 2 . (4)
In practice, the gain of adding more ions is limited. For the above described ion chain, the minimum of the standard deviation is reached by averaging over N a = 80 ions, dividing the standard deviation not even by a factor of 2. The corresponding mean value a 0 is reduced by less than 1.5%, far less than one standard deviation.

The optical magnification is measured at the chain center, by translating the objective across the trap axis and keeping the detector fixed. 8 successive translations of the objective, perpendicular to the optical axis and to the chain axis, over a total range of 1 mm, by a translation stage with a 10 µm resolution screw result in an uncertainty which is an order of magnitude lower than the magnification shift induced by the translation of the objective along the trap axis. The tiny modification of the objective-to-image distance induces a change in the measured magnification of the order of 2 ppm, an order of magnitude lower than the statistical dispersion of the data around their mean.

Data analysis was carried out for several chains of different ion number ranging from 46 to 155. To confirm the relevance of Dubin's trial function, Fig. 3 plots the local density 1/a(z) for three of them together with the fit by Eq. ( 1). Although the parameter L extracted from the fits systematically overestimates the physical length of these chains, the local density profile is very well represented by Eq. ( 1). The differences between the calculated ion numbers and the directly counted ones lie within the above measured 8% uncertainty for chains larger than 100 ions. This difference increases for shorter chains, reaching values up to 15%. For these smallest chains, an alternative tool to study self-organization of ions in a 1D potential is potential energy minimization. In [19], James proposed an empirical law for the closest distance a J 0 fitting its numerical results for N ≤ 50 : For short ion strings, and even if the law deduced from Dubin's work is only relevant in the limit of large N , it systematically agrees to the experimental observations better than the prediction from Eq. ( 5) by a few percent.

a J 0 = 2.018lN -0.559 . (5)
In conclusion, we have experimentally tested the local description derived for long, one-dimensional Coulomb systems in a harmonic potential, an example of a strongly correlated system. The derived law is useful as a diagnostic to prepare chains with sufficient ions to have a minimum number of equidistant particles in its central part. The total number of ions can be derived without individually counting them, if the potential well along the chain direction is known.With the described ion chain, we were able to retrieve the ion number from a single picture with a uncertainty of ±8% due to fluctuations in ion positions and the uncertainty on the axial potential. Furthermore the simple form of (Eq. 1) can be used to describe the density at the center of the chain for the minimum energy state. Without any reference to the total length L, one can deduce from (Eq. 4) the minimum number of ions N required to have N a nearly equidistant ions within a chosen tolerance. Such a system could be the starting point for explorations of quantum information protocols as proposed in [1]. The validation of this straightforward number diagnostic which does not require fastidious counting of individual ions, makes these systems simpler to control, and therefore more attractive.

FIG. 1

 1 FIG. 1. a) Picture of an ion chain of 155 ions composed from 5 pictures taken with a translated objective and b) picture of the central part of the chain. Axes are in pixels whose size is 13 µm and the optical magnification is 11.58. The scale bar stands for 100 µm. The integration time is 1s.

Figure ( 1 )

 1 from counting the individual ion fluorescence images. The figure shows the global picture of the whole chain which can be composed by several images. The variation in the fluorescence signal may be due to spatially varying radial secular motion or micro-motion made possible by insufficient cooling of the radial motion by the two longitudinal laser beams. It may also be the signature of dark ions hopping along the chain. The total length of the chain is measured to be 2L m = 4620 ± 25 µm. The set of nearest neighbour distances a(z) is extracted from the data set obtained by vertical binning of the image, and multiple-Gaussian fit to the resulting fluorescence profile. The thus obtained a(z) are represented on Fig. (2).

FIG. 2 .

 2 FIG. 2. Red dots : distance between neighbouring ions a(z)vs their position in the chain, in µm, in a 155-ion chain. Blue line : best fit of the inverse of the distance by Eq. (1) where z is replaced by z -z0 and N is fixed to 155. The error bar stands for the ±5 pxls of the typical FWHM of individual ion picture.

FIG. 3 .

 3 FIG. 3.Local density 1/a(z) vs the ion position in the chain, in µm, measured for chains containing 134 ions(red circles), 95 ions(blue squares), 47 ions(green triangle). The lines are the best fit by Eq. (1) where z is replaced by z -z0 and N is fixed to the counted value.

ACKNOWLEDGEMENTS

Fruitful discussions with Dan Dubin, Jérôme Daligault and Dominique Escande are gratefully acknowledged. This experiment has been financially supported by ANR (ANR-08-JCJC-0053-01), CNES (contract 116279) and Région PACA. MRK acknowledges financial support from CNES and Région Provence-Alpes-Côte d'Azur.


Bernard Yannou

Yann Leroy

Toufic Zaraket

Activity-based simulation of households' energy and water consumptions

INTRODUCTION

The building stock accounts for between 16 and 50 percent of national energy consumption worldwide [START_REF] Saidur | An application of energy and exergy analysis in residential sector of Malaysia[END_REF][START_REF] Masoso | The dark side of occupants' behaviour on building energy use[END_REF][START_REF] Hoes | User behavior in whole building simulation[END_REF]. Governments around the world are thus rolling out energy directives, national regulations and energy-efficiency labels that set minimum requirements for buildings' performance [START_REF]Concerted Action | Energy Performance of Buildings Directive[END_REF], and promote the construction of green buildings [START_REF] Vierra | Green Building Standards and Certification Systems | Whole Building Design Guide[END_REF]. Buildings' stakeholders have thereby started dealing with buildings as products-with-services rather than just simple products. Services may for instance include energy monitoring or equipments' maintenance during a building's use-phase. Moreover, new market expectations such as the 'energy performance contracts' have started to emerge in a number of countries [START_REF] Cpe | Contrats de performance énergétique -Ministère du Développement durable[END_REF]. Such services and offers require thus a better control of performance's variability during a building's lifecycle. Consequently, a better comprehension and consideration of the key determinants of energy performance has become essential for the design and marketing processes of buildings. Occupant behavior is a substantial source of uncertainty in energy modeling since. It can impact energy consumption by as much as 100% for a given dwelling [START_REF] Masoso | The dark side of occupants' behaviour on building energy use[END_REF][START_REF] Page | A generalised stochastic model for the simulation of occupant presence[END_REF][START_REF] Yu | A systematic procedure to study the influence of occupant behavior on building energy consumption[END_REF][START_REF] Pachauri | An analysis of cross-sectional variations in total household energy requirements in India using micro survey data[END_REF][START_REF] Fabi | Occupants' window opening behaviour: A literature review of factors influencing occupant behaviour and models[END_REF][START_REF] Swan | Modeling of end-use energy consumption in the residential sector: A review of modeling techniques[END_REF][START_REF] Clevenger | The impact of the building occupant on energy modeling simulations[END_REF][START_REF] Seryak | Occupancy and behavioral affects on residential energy use[END_REF][START_REF] Emery | A long term study of residential home heating consumption and the effect of occupant behavior on homes in the Pacific Northwest constructed according to improved thermal standards[END_REF]. Industrial energy simulation tools such as Energy Plus and eQUEST propose some simplifications regarding occupants' behavior (among other simplifications), which may lead to unrealistic energy estimates, and may eventually be one of the reasons behind high discrepancies between predicted and real energy consumption values [START_REF] Malavazos | Energy and behavioural modelling and simulation for ee-buildings design[END_REF][START_REF] Kashif | Simulating the dynamics of occupant behaviour for power management in residential buildings[END_REF][START_REF] Bourgeois | Adding advanced behavioural models in whole building energy simulation: a study on the total energy impact of manual and automated lighting control[END_REF][START_REF] Chiou | Deriving US household energy consumption profiles from american time use survey data a bootstrap approach[END_REF]. Nowadays, such performance discrepancies are no longer toleratedespecially in the case of green (energy-efficient) buildings. More precise methods are therefore needed to model occupants' influence on buildings' energy performance. Such models should result in more accurate energy estimations, and hence improve building designs and marketing offers. The authors have proposed an activity-based model of residential energy demand (SABEC, standing for Stochastic Activity Based Energy Consumption) in a doctoral dissertation [START_REF] Zaraket | Stochastic Activity-based Approach of Occupant-related Energy Consumption in Residential Buildings[END_REF] . The present paper is not intended to detail the model, but it briefly recalls the adopted modeling methodology. The main focus here is to show how a user-focused model, which accounts for occupants' energy-related needs and activities, can be used within the engineering design, energy management processes, and marketing offers of residential buildings.

A literature review is first presented followed by a brief recall of the proposed modeling methodology and a sample of simulation results. The possible integration of the proposed model into the design and energy management processes of residential buildings is then demonstrated through a number of use cases.

BACKGROUND AND RELATED WORK

Occupants' Behaviour and Energy Use Trends in Residential Buildings

According to Ellegård and Palm [START_REF] Ellegård | Visualizing energy consumption activities as a tool for making everyday life more sustainable[END_REF], energy use is embedded in most aspects of households' daily life. People use energy and water to satisfy their daily living needs and activities such as preparing food and supplying heat and light [START_REF] Pennavaire | Comprehensive modeling of energy use in households. An Agent Based case study on potential behavioural and technicalmeasures towards an energy neutral urban environment[END_REF][START_REF] Kashif | Agent based framework to simulate inhabitants' behaviour in domestic settings for energy management[END_REF]. Scientific literature points out the major end-use groups of energy such as space heating, space cooling, domestic hot water, appliances and lighting [START_REF] Hoes | User behavior in whole building simulation[END_REF][START_REF] Swan | Modeling of end-use energy consumption in the residential sector: A review of modeling techniques[END_REF][START_REF] Yao | A method of formulating energy load profile for domestic buildings in the UK[END_REF]. This energy consumption is highly dependent on the behavior of occupants [START_REF] Masoso | The dark side of occupants' behaviour on building energy use[END_REF][START_REF] Emery | A long term study of residential home heating consumption and the effect of occupant behavior on homes in the Pacific Northwest constructed according to improved thermal standards[END_REF][START_REF] Yun | Behavioural, physical and socio-economic factors in household cooling energy consumption[END_REF]. Past experience shows that energy usage can vary dramatically from one household to another [START_REF] Clevenger | The impact of the building occupant on energy modeling simulations[END_REF][START_REF] Seryak | Occupancy and behavioral affects on residential energy use[END_REF][START_REF] Paauw | Energy Pattern Generator; Understanding the effect of user behaviour on energy systems[END_REF]. This variation reflects the heterogeneity in occupants' needs and preferences. Literature confirms the presence of high correlations between household attributes on the one hand, and domestic appliances ownership levels, their energy rating, and their use patterns on the other [START_REF] Yun | Behavioural, physical and socio-economic factors in household cooling energy consumption[END_REF][START_REF] Weber | Modelling lifestyle effects on energy demand and related emissions[END_REF][START_REF] Mansouri | Energy consumption in UK households: Impact of domestic electrical appliances[END_REF][START_REF] Lutzenhiser | The 'Average American' Unmasked: Social Structure and Differences in Household Energy Use and Carbon Emissions[END_REF][START_REF] Guerin | Occupant predictors of household energy behavior and consumption change as found in energy studies since 1975[END_REF][START_REF] Nugroho | DEVELOPMENT OF A HOUSEHOLD ENERGY CONSUMPTION MODEL FOR MEGACITIES IN ASIA[END_REF][START_REF] Yun | Thermal performance of a naturally ventilated building using a combined algorithm of probabilistic occupant behaviour and deterministic heat and mass balance models[END_REF][START_REF] Mcloughlin | Characterising domestic electricity consumption patterns by dwelling and occupant socio-economic variables: An Irish case study[END_REF]. This would explain why general assumptions about occupants' behavior imply ambiguities and inevitably lead to significant uncertainties in energy predictions. Therefore, a better modeling of occupant-related energy consumption must merge from a better understanding of their needs, preferences and usage-contexts, and, thus from a better representation of their socio-economic and demographic attributes that influence their energy consumption trends.

Existing modelling approaches

Literature reveals the existence of a number of different scientific techniques for modeling energy consumption in residential buildings [START_REF] Swan | Modeling of end-use energy consumption in the residential sector: A review of modeling techniques[END_REF]. Some authors, such as Seryak & Kissock [START_REF] Seryak | Occupancy and behavioral affects on residential energy use[END_REF] and Yohanis et al. [START_REF] Yohanis | Real-life energy use in the UK: How occupancy and dwelling characteristics affect domestic electricity use[END_REF], use real sub-metering data in order to derive representational loads (so-called "diversity profiles") of occupants energy use, and thus deduce estimates of buildings' total energy consumption. Other modeling methods are those aiming at simulating occupancy patterns and various energy-load schedules by using stochastic approaches (e.g. Monte Carlo Markov Chains) that are based on national time use surveys (TUS) [START_REF] Chiou | Deriving US household energy consumption profiles from american time use survey data a bootstrap approach[END_REF]. Authors such as Tanimoto [START_REF] Tanimoto | Validation of probabilistic methodology for generating actual inhabitants' behavior schedules for accurate prediction of maximum energy requirements[END_REF] , Richardson et al. [START_REF] Richardson | Domestic lighting: A high-resolution energy demand model[END_REF][START_REF] Richardson | Domestic electricity use: A highresolution energy demand model[END_REF], Widén and Wäckelgård [START_REF] Widén | A high-resolution stochastic model of domestic activity patterns and electricity demand[END_REF] , Muratori [START_REF] Muratori | A Highly Resolved Modeling Technique to Simulate Residential Power demand[END_REF] and Subbiah [START_REF] Subbiah | An Activity-Based Energy Demand Modeling Framework for Buildings: A Bottom-Up Approach[END_REF] adopted such type of approaches. These modeling approaches yet still have some drawbacks. First, even though they correlate occupancy schedules to appliance use-patterns and consumption, yet to the authors' knowledge, neither of the existing approaches establishes the link between occupants' daily living needs (Maslow's pyramid) and their related energy consumption. Second, they do not generate energy demand profiles based on the activities performed in each household and more particularly by each household member. Therefore, they lack the capability to depict use-situations such as the sharing phenomena of appliances and activities (e.g. Watching TV). Third, the existing models are not exhaustive in representing household attributes (such as the income, age, etc.), where in most cases, the main variable considered for representing households is the number of occupants. Consequently, such models cannot assess energy consumption variability between different population segments and household profiles.

Based on these conclusions, we believe that a user-focused statistically-derived approach which correlates occupants' profiles (socio-economic and demographic) on the one hand, to activities, appliance ownership and use trends, and usage contexts on the other hand, can be very useful for the design process of buildings.

The benefits of such a model may not be limited to energy consumption predictions, but it can go further to be used for adapting building design solutions and for energy monitoring and management during the use-phase of buildings for instance.

THE SABEC MODEL

Ontology and principles

SABEC model is developed in the scope of forecasting occupant-related energy consumption in residential buildings, while accounting for variability in consumption patterns due to heterogeneity in occupants' socio-economic and demographic profiles [START_REF] Zaraket | Stochastic Activity-based Approach of Occupant-related Energy Consumption in Residential Buildings[END_REF]. The model accounts mainly for energy consumption related to domestic activities such as watching TV, washing dishes, and doing laundry. The structure of the proposed Activity-Based Energy Consumption SABEC model is presented in Figure , whereas its different objects are very briefly introduced in this section. Occupants' behavior is characterized through a needactivity-action paradigm. We consider that occupants satisfy their daily living needs (e.g. house-caring) by performing a set of daily activities (e.g. washing dishes), which in turn are conducted through a set of actions (e.g. wash dishes by machine, wash dishes by hand). Exhaustive inventories of energy-use needs, activities, actions and appliances are established in accordance with existing literature and related theories (e.g. Maslow's pyramid, activity theory) [START_REF] Zaraket | Stochastic Activity-based Approach of Occupant-related Energy Consumption in Residential Buildings[END_REF]. An Activity-based model entails that energy consumption of a household is estimated by summing up the energy use of different activities performed (such as cooking, washing clothes, etc.). The model is of a stochastic nature due to the twofold probabilistic mapping (conditional probabilities) established between household attributes (household type, number of occupants, socio-professional category, etc.), as well as the corresponding appliance ownership rates, appliance characteristics and power ratings, and activity quantities. A household model with an exhaustive representation of occupants' attributes is proposed. Domestic activities are classified according to their nature (shared, additive), and a quantification unit is attributed for each of them (service unit). For a given activity (a given need), the service unit is coupled with appliance's energy rating in order to estimate the resulting energy and water consumption. The proposed model can thus quantify energy consumption per domestic activity at the level of a specific individual or household. We highlight here that the technical and computational aspects of the model are not presented in this paper. For more details, the reader may refer to [START_REF] Zaraket | Stochastic Activity-based Approach of Occupant-related Energy Consumption in Residential Buildings[END_REF] and [START_REF] Zaraket | A usage model-driven approach for forecasting occupant-related energy consumption in residential buildings[END_REF][START_REF] Zaraket | A Stochastic activity-based approach for forecasting occupant-related energy consumption in residential buildings[END_REF].

Deterministic simulation of energy and water consumptions

This SABEC model has been used for stochastic simulations in [START_REF] Zaraket | An occupant-based energy consumption model for user-focused design of residential buildings[END_REF] of households' energy and water consumptions. The detailed work can be found in [START_REF] Zaraket | Stochastic Activity-based Approach of Occupant-related Energy Consumption in Residential Buildings[END_REF] (Downloadable here: https://hal.archives-ouvertes.fr/tel-01087894).

In the following, the authors present the deterministic energy and water consumption simulation of a household's whole set of domestic activities. For summary, it has been proposed a parametric modelling principle of the energy envelope of an activity of a family of occupants according to their characteristics (number, age, sex, occupation and sociological characteristics of family members) by:  Considering the amount of this activity,  Correlating the quality and eco-efficiency of equipment brought by the family  Calculating the consumption by additive summation of individual consumptions and heuristic estimation of the activity sharing  Fitting of consumption patterns (electricity and water) related to an activity based on national statistical data of consumption. In total, 28 domestic energy and water consuming activities have been modeled (see the list in Figure 2). These consumption models are expressed with about twenty parameters featuring the household composition.

Figure 2: The 28 activities of energy and water consumption

Each activity has been modeled in an Excel spreadsheet by: a subset of influencing households variables, a causal graph of influence starting from these households variables and ending with activity quantities passing through a number of quantitative intermediate variables (e.g. occupation rate, number of weekly meals, laundry weight…), modeling assumptions used, incoming data from statistical databases or national consumptions, and procedures used for model fitting to national consumption data. Figure 3 represents such a data streaming for assessing the final electrical consumption for "Watching TV" activity.

Figure 3: Watching TV electrical consumption model

The household simulation of energy and water consumption is monitored through a dedicated Excel spreadsheet allowing the definition of the household features and of some building physical features (see Figure 4). Some graphical outputs of simulations are provided in Figure 5: for a given dwelling and different households considered: Figure 5.a provides a comparison of both energy and water consumptions, Figure 5.b provides such a comparison under each of the 28 activities. the frame (e.g. effectiveness or no of pre-installed washing machines)  to obtain heat gain estimates by activities that are useful inputs for further more accurate dynamic thermal simulations (DTSs). The originality of our work is the decomposition of electro-domestic consumption by activities. This is of the utmost importance since occupants can and know how to regulate their activities. This model could be central to the development of a connected building approach, to the Internet of Things at the service of information and regulation of consumption. Although to date, we still do not have adequate technical resources for allocating consumption by activities, we can get ahead by calculating consumption by reference activities from the cloud data "for comparable family", develop visualization interfaces and offer occupants means to voluntarily de-consume (incentives, emulation by social network, diagnostic and support to action plan ...).

BIBLIOGRAPHY

Figure 1 :

 1 Figure 1: Architecture of SABEC model

Figure 4 :Figure 5 :

 45 Figure 4: The SABEC simulation energy and water consumption dashboard for a given household


domain: info scco spi.auto

text:
Arnaud Ahouandjinou
email: ahouandjinou@lisic.univ-littoral.fr

Eugène C Ezin

Kokou Assogba

Cina Motamed

Mikael A Mousse

Bethel C A R K Atohoun

Robust Facial Expression Recognition Using Evidential Hidden Markov Model Applied to medical videos sequences analysis

Keywords: Face Detection, Facial Expression Information Extraction, Facial Expression Recognition, Hidden Markov Model, Transferable Belief Model Framework (TB¨M) MOTS-CLÉS : Détection de face, Extraction d'information d

A great challenge of practical significance in a recent research topic is to develop computer vision system which can automatically recognize a variety of facial expressions. Such an automated system enables to detect faces, analyzes and interprets facial expressions in a scene although the accomplishment of this task is rather strenuous. There are several related problems: detection of an image segment as a face, extraction of the facial expression information, classification of the expression (e.g., in emotion categories) and their recognition. In this paper, we proposed system that performs facial expression recognition using an Evidential Hidden Markov (Ev-HMM) model in order to manage efficiently the constraints related to facial expression recognition problem. An application of this method as part of improving the monitoring system in medical intensive care units is carried out through to analysis and interpretation of the patient face behavior. The experimental results are very exciting and have shown a promise of our automatic recognition system.

Introduction

Facial Expression Recognition (FER) in video scenes is an important topic in computer vision, impacting important applications in areas such as video conferencing, forensics, biomedical applications such as pre or post surgical path planning or clinical improvement prediction, machine vision [START_REF] Punitha | HMM Based Real Time Facial Expression Recognition[END_REF]. The most expressive way humans display emotions is through facial expressions and this latter provides cues about facial behavior. The aim of facial expression recognition methods is to build a system for the classification of facial expressions from continuous video input automatically. Furthermore, development of an automated system that recognizes facial expression is rather a difficult task. There are three main related problems for facial recognition system: detection of an image segment as a face, extraction of the facial expression information, classification of the expression (e.g., in emotion categories) and facial expression recognition. In this paper, we propose a system that detects the face while analyzing and interpreting the behavior of the face of a human in a medical video. Indeed, this system contributed significantly to the recognition of interest's events (critical health) that can improve the quality of the patient monitoring system in ICU [START_REF] Ahouandjinou | Activity Recognition Based on Temporal HMM for Visual Medical Monitoring Using a Multi camera System[END_REF]. An original application is proposed in order to assess the impact of the proposed method for patient monitoring in medical ICUS in cardiology section. Three main contributions can be noted in this work: i) the first deals with the efficiency of facial expression recognition system based on robust approach by using an evidential HMM. This extension of the HMM allows to take into account at the same time several constraints of the system like physiognomic variability of the human, environment situation-dependent, timing of facial expressions that is a critical factor in the interpretation of expressions. The power of the proposed model lies in the ability and the potential of what the reasoning framework as transferable belief model. ii) The second contribution is related to the combination of facial expression information that uses the maximum intensity of the mouth on the one hand and on the other the maximum intensity of the eyes. iii) Finally, the field of applications is the originality of this work. For this, analysis and understanding of the scene in a video was not done in medical environment. In addition to this, a scenario such as "fields the pain" and "anxious" in a patient had never been studied.

The paper is organized as follows. In the first section, we describe our proposed method for facial expressions recognition in images sequences. To this end, we present at first, the face detection technique in image and then we explain how the facial expressions features are extracted. Finally, the last part of this section is to expose our robust and flexible algorithm for facial expressions recognition. Thus, after a briefly overview on Transferable Belief Model (TBM) framework [START_REF] Smets | The transferable belief model[END_REF], the main steps of evidential hidden Markov model for facial expressions recognition are presented. Section 3 is devoted for applying our approach to recognize facial expressions in medical video. The performance analysis of our method is done by comparing some experimental results with a baseline algorithm applied to various databases in section 4.

Proposed Method for facial expression recognition

Detailed review of existing methods on facial expression is seen in [START_REF] Fasel | Automatic facial expression analysis: a survey[END_REF][START_REF] Pantic | Automatic analysis of facial expressions: the state of the art[END_REF]. A thorough study of the state of the art of existing methods on facial expression is proposed by Maja Pantic in IEEE transactions on pattern analysis and machine intelligence [panticPAMI00], and is also seen in [START_REF] Pantic | Automatic analysis of facial expressions: the state of the art[END_REF]. Since the mid-1970s, many methods have been proposed for facial expression analysis and their recognition from either static facial images or image sequences. Among these, we have the approaches based on active contours, robust appearance filter, probabilistic tracking, adaptive active appearance model and active appearance model [START_REF] Punitha | HMM Based Real Time Facial Expression Recognition[END_REF]. The aim of this section is to explore the issues in design and implementation of a system that could perform automated facial expression analysis. In general, three main steps can be distinguished for solving this problem. First step, before the analysis of facial expression, the face must be detected in a scene. The next step is to devise mechanisms for extracting the facial expression information from the observed facial image or image sequence. The final step is to define some sets of categories, which will be used for facial expression classification and/or facial expression interpretation, and to devise the mechanism of categorization. To this end, most facial expression recognition systems focus on only six basic expressions (i.e., joy, surprise, anger, sadness, fear, and disgust) proposed in the work of Darwin at the beginning [START_REF] Ekman | Strong evidence for universals in facial expressions: A reply to Russell's mistaken critique[END_REF] and more recently Ekman [START_REF] Ekman | Strong evidence for universals in facial expressions: A reply to Russell's mistaken critique[END_REF]. In everyday life, however, these six basic expressions occur relatively infrequently, and emotion or intent is more often communicated by subtle changes in one or two discrete features, such as tightening of the lips which may communicate anger. Facial expression recognition or human emotion analysis remains a very daunting task.

Face Regions Detection

In response to real-time system development and the homogenous processing system for facial expression recognition, we used Hidden Markov Model (HMM) to detect face in video sequence. HMM consists of two interrelated processes: (1) an underlying, unobservable Markov chain with a finite number of states, a state transition probability matrix and an initial state probability distribution and (2) a set of probability density functions associated with each state [START_REF] Rabiner | A Tutorial on HMMs and Select Applications in Speech Recognition[END_REF]. The used approach is based on the technique proposed by A. Nefian and Monsson Hayes III in [START_REF] Nefian | Hidden markov model for Face Recognition[END_REF]. This technique involves the extraction of the face features in order to detect it. Each face image of width W and height H is divided into overlapping blocks of height L and width W. The amount of overlap between consecutive blocks is P. T is the number of observations which denotes the number of blocks extracted from each face. T is generated using equation 1: Particular facial regions such as: hair, forehead, eyes, nose and mouth come in a natural order from top to bottom, even if the images are taken under small rotations in the image plane. Each of these facial regions is assigned to a state from the left to the right topology of HMM. Note that, the state structure of the face model and the non-zero transitions probabilities are shown in Figure 2.

1 + - - = P L L H T (1)
( ) ( ) ( ) ( ) n t n t O P Max O P λ λ = k (2)
After the face detection, the facial expression recognition system performs the mouth and the eye region feature extraction using the pixel intensity code value to recognize facial expression in images sequences.

Feature Extraction Process from Eye and Mouth Region

This work exploits the temporal intensity change of expressions in videos for facial expression recognition through the HMM. Considering the intensity scale of the different facial expressions, each person has his/her own maximal intensity of displaying a particular facial action. We combine the Mouth region intensity Code Value namely MICV [START_REF] Punitha | HMM Based Real Time Facial Expression Recognition[END_REF] and the Eye region Intensity Code Value namely EICV as features for facial expression recognition.

In this section, we describe how we compute the eye and the mouth region intensity coded value (EICV/MICV). The E/MICV for eye and the mouth region which characterizes the intensity variations between blocks that corresponds respectively to the eye and the mouth region in a video frame is computed using a simple procedure that divides a mouth region into blocks and creates a code called EICV and MICV which represents the intensity difference between blocks in a frame. Eq. ( 3) illustrates the generation of proposed MICV feature [START_REF] Punitha | HMM Based Real Time Facial Expression Recognition[END_REF]. i and j represent the ith and jth blocks in a frame. MICV is generated using Equation 3 [START_REF] Lien | Automatic recognition of facial expressions using hidden Markov models and estimation of expression intensity[END_REF]:

( ) ( ) ( )    > =       + + - Otherwise 0 i x if 1 2 1) i(i - j 25 1 j x i y j i and 25 2 , 25 1 < ≤ ≤ ≤ ≤ j i (3)
Where x(i), x(j) are the average intensities of the ith and jth blocks respectively. To generate the MICV, for example, the frame is divided into 5 x 5 blocks to generate the feature vector. Figure 3 shows the detected mouth region and the 5 x 5 representation of mouth region. To generate the MICV [START_REF] Punitha | HMM Based Real Time Facial Expression Recognition[END_REF], for example, the frame is divided into 5 x 5 blocks to generate the feature vector. Fig. 3a and3b show the detected eye and mouth region with both their representation. Each block in a frame is compared with every other block to generate EICV and MICV using "Eq. (4)". For example, if the image is divided into 5 x 5 blocks, then "Eq. ( 4)" generates 300 dimensional feature vectors. First element in the feature vector compares the intensity of 1st and 2nd block; second element compares the intensity of 1st and 3rd block and so on. The distance or error between the two comparison codes and can be calculated using equation 4:

( )

∑ = ⊕ = n k k k q p d 1 (4)

Robust and Flexible Facial Expression Recognition

The proposed system for facial expressions recognition is using an evidential Hidden Markov Model (EvHMM) developed by E. Ramasso in [START_REF] Ramasso | Contribution of belief functions to Hidden Markov Models[END_REF] and first introduced by [START_REF] Ekman | Strong evidence for universals in facial expressions: A reply to Russell's mistaken critique[END_REF]. This version of HMM is based on an extension of probabilistic reasoning framework to the evidential. This new reasoning framework is very generic and powerful to develop tools to support any type of application with better management of uncertainty and imperfect data. In addition, it is possible to combine information with the careful fusion rules and operators. In this work, we proposed a new and robust approach for event recognition in videos sequences. A substantial benefit of belief functions is their versatility and efficiency in the information fusion process. Transferable Belief Model is a very suitable tool for information combination as it takes into account the nature and quality of sources to provide noisy information [START_REF] Smets | Decision making in the TBM : The necessity of the pignistic transformation[END_REF]. Another advantage of the reasoning part also lies in its ability to manage the imperfections of the data in order to estimate the best accuracy recognition system. In the related work, we noted that facial expression recognition from still image has less precision with respect to video sequence because a single image offers much less information than a sequence of images for expression recognition processing. ) n q q q q q ,........, , ,

=

Feature classification is performed in the last stage of our automatic facial expression analysis system. Hidden Markov Models (HMMs) have been widely used to model the temporal behaviors of facial expressions from image sequences. This work exploits HMM to recognize facial expression. Three basic facial actions are defined (neutral, smile, eyes closed and raised eyebrows) and five emotional or facial expressions (neutral, happy, anxious, painful, and disgusted) can be recognized by the system. For each facial expression, we use an Evidential HMM for training the model and afterwards to recognize its. We define five HMMs to recognize the facial expression which are "neutral", ''happy", "disgust", "pain" , and "anxious". Facial expressions features such as EICV and MICV are computed in probabilistic quantity. And then, we have combined in the belief mass two main information estimated on the eye region features named (Eye Intensity Probability Value: EIPV) and the mouth region features called (Mouth intensity Probability Value: MIPV). The result of EIPV and MIPV combination design Facial Expression Code Value (FECV) is given as input to estimate Ev-HMM parameter from the learning step. The remainder of this section describes the HMM learning process and the recognition of facial expressions through two steps. These steps are implemented using the beliefs parameter input in probabilistic HTK toolkit for the expression recognition.

TBM tools overview

Transferable Belief Model (TBM) is a generic formal framework [START_REF] Smets | The transferable belief model[END_REF] for the knowledge representation and information combination. This framework provides powerful tools for managing data uncertainty and imprecision. In this work, TBM is used to combine the mouth/eye features parameter of facial expression recognition in single parameter named Facial Expression Code Value (FECV). Our models use the belief mass for estimate the sensor confidence and we transform it in the Communality function before combining information. This section succinctly reviews some TBM basic notions [START_REF] Smets | Decision making in the TBM : The necessity of the pignistic transformation[END_REF].

Indeed, TBM framework provides powerful tools for managing data uncertainty and imprecision. In our work the TBM is used to propagate uncertainty of low level information over the scenario recognition process. This section succinctly reviews some TBM basic notions [START_REF] Kanade | Comprehensive database for facial expression analysis[END_REF]. Several functions which are the belief masses, the Credibility (bel : Belief) , the Plausibility (pl) and the Communality (q) are defined in the TBM. The belief of an agent in subsets of the frame of discernment can be represented by a basic belief assignment (BBA), also called belief mass assignment (equation 8):

MAX (O/P) Expression

Recognized facial expression

t Ω [ ] 1 0 :→ Ω t m ( ) B m B t Ω a Such as ( ) ( ) ( ) 0 m and 1 t = = Ω Ω ∈ Ω ∑ φ P B B m t (8)
The mass noted t m Ω is the part of belief the information source at t time. Moreover, the use of communalities functions makes them less cumbersome and time consuming calculations while providing near those probabilistic expressions. Accordingly, the use of this belief function is a main advantage of computational complexity for proposed recognition algorithm. In equation ( 9), this function is defined as:

( ) ( ) t B , Ω ⊆ ∀ = ∑ ⊇ Ω Ω B m B q B C t t (9)

Step 1: Evidential HMM training

For HMM training, FECV is computed after the EPIV and MIPV are extracted using respectively eye and mouth region intensity from each frame in the video sequence and is given as input to estimate the parameters of Ev-HMM. Learning of model parameters consists in defining a technique for estimating and automatic adjustment of parameter by exploiting the features of training data. We propose to use a Credal version of HMM algorithm proposed in my previous paper in order to handle the spatial and temporal variability and also the uncertainty existing over the machine learning task. To this end, regrouping components into states is made automatically by maximizing likelihood, and a relevant regrouping implies a better recognition of states. Given observations sets how to adjust the HMM parameters to maximize the training set likelihood? For this, we have used three levels for Ev-HMM learning step. Nevertheless, it should be noted that the complexity of the Baum-Welch algorithm in its credal version that we present in [START_REF] Ahouandjinou | Credal Human Activity Recognition Based-HMM by Combining Hierarchical and Temporal Reasoning[END_REF]. This is due to the beliefs functions that do not have the same mathematical properties those probabilities and over, beliefs functions are defined on large space discernment. Three parameters are usually learned during the Ev-HHMM training step. Indeed, two key levels passing by an initialization phase helps to describe Baum-Welch in credal version used for learning:

1. Initialization level: Ev-HInit does initialization. It computes an initial set of parameter values using Viterbi alignment to segment the training observations and then recomputed the parameters by pooling the vectors in each segment.

Level 1:

To determine the parameters of Ev-HMM, the output of Ev-HInit is fed as input &into Ev-HRest. The models are re-estimated using Baum-Welch re-estimation.

Level 2:

Testing the data against the model built.

The HMM classification scheme used in the present approach is shown in Fig. 4. Initially, separate HMMs are used for each expression. FECV is fed as input to the Ev-HMM. Finally, the maximum output obtained is considered as the output expression.

2,3.3. Step 2: Facial Expressions Recognition by Ev-HMM

This step concerns the test of the data against the model built. The Ev-HMM classification scheme used in thiq approach is shown in Fig. 4. Initially, separate Ev-HMMs are used for each expression. FECV is fed as input into the Ev-HMM. Finally, the maximum output obtained is considered as the output expression. Upon completion of learning step, the properly so called recognition stage is carried out. For this purpose, we use credal forward and backward propagation [START_REF] Ahouandjinou | Credal Human Activity Recognition Based-HMM by Combining Hierarchical and Temporal Reasoning[END_REF]. The propagations processes follow the same traditional patterns as those existing in the probabilistic framework [START_REF] Ahouandjinou | Credal Human Activity Recognition Based-HMM by Combining Hierarchical and Temporal Reasoning[END_REF][START_REF] Ahouandjinou | A temporal belief-based hidden markov model for human action recognition in medical videos[END_REF]. In the case of credal forward propagation, it is done in three steps which are: initialization, induction and end step. Moreover, Credal Backward propagation makes the complete estimation of HMM parameters requires the computation of three auxiliary variables which are: the backward variable β and the smoothing variables γ and ξ . In fact, a similar process can be used in Ev-HMM [21] for the backward propagation to generate a backward variable ( )

j S q t Ω β
in the prediction and melting process which is estimated with equation 5:

( ) [ ] ( )( ) [ ]( ) j j j t b i S S q S O m m S q t t t t Ω Ω Ω Ω × = ∑ α β β (5) ( ) [ ] ( )( ) [ ]( ) j j j t b i S S q S O m m S q t t t t Ω Ω Ω Ω × = ∑ α β β (6) ( ) [ ] ( )( ) [ ]( ) j j j t b i t i S S q S O m m S q S t t t t Ω Ω Ω Ω × = Ω ⊆ ∀ ∑ α β β , in induction phase (7)

Applying Method to Recognize Facial Expression in Medical Video

In this section, we present on one hand, an appliance of evidential Markov model for facial expression recognition and on the other hand, the experimental results on realworld facial expression dataset. In addition, we described the used datasets and presented the experimental results of even the performance analysis of the proposed approach compared it to other existing methods. An experimental study conducted in two datasets (Cohn-Kanade [START_REF] Kanade | Comprehensive database for facial expression analysis[END_REF] AU code facial expression database and our database) shows good performance of our proposed method in term of recognition rate precision and its accuracy. Our Algorithms have been implemented using Matlab, C/C++ using OpenCV library).

Tested Data Setup

In order to test the algorithms described in the previous sections we use two different databases, a database collected by us and the Cohn-Kanade [START_REF] Kanade | Comprehensive database for facial expression analysis[END_REF] AU code facial expression database. The first used benchmark (FACS) which is Cohn-Kanade AU-Coded Facial Expression Database is for research in automatic facial image analysis, synthesis and for perceptual studies. We used the second version of the Cohn-Kanade to test our algorithm. Facial behavior of 210 adults was recorded using two hardware synchronized Panasonic AG-7500 cameras. Participants were 18 to 50 years of age, 69% female, 81%, Euro-American, 13% Afro-American, and 6% other groups. Image sequences for frontal views and 30-degree views were digitized into either 640x490 or 640x480 pixel arrays with 8-bit gray-scale or 24-bit color values. Full details of this database are given in [START_REF] Kanade | Comprehensive database for facial expression analysis[END_REF]. The second test database is ours. The data collection method is described in detail in [START_REF] Ahouandjinou | Activity Recognition Based on Temporal HMM for Visual Medical Monitoring Using a Multi camera System[END_REF], our database has been collected from the experimental video-surveillance system that we installed in the cardiology department at the hospital (have collected roughly 47 videos sequences for three activities with 1500 frames/sequences. An observation sequence is recorded every one and a half second from the 25fps video. The duration of the video sequences is 300 seconds with an average length of circa 90 seconds. In this database, we have the subjects that were instructed to display facial expressions corresponding to the five types of emotions such as "neutral", ''happy", " disgust", "pain" , and "anxious". Four basic actions (neutral, smile, eyes closed and raised eyebrows) detected over the face feature extraction step are used through like input data of the Evidential HMM to recognize these facial expressions.

Experiments Results 1: Using Cohn-Kanade AU database

All the tests of the algorithms are performed on a set of five persons, each one displaying five sequences of each of the five emotions, and always coming back or not to a neutral state between each emotion sequence. The sampling rate of the video sequence was 30 Hz, and a typical emotion sequence is about 150 samples long (5s). Figure 5, shows one frame of each emotion for each subject. We used the sequences from a set as test sequences and the remaining sequences were used as training sequences. In this case, we performed person dependent experiments, in which part of the data for each subject was used as training data, and another part as test data. Table 1 show the recognition rate of the test for each HMM version. Note that the results obtained with this database are much better than the ones obtained with our database. This is because in this case we have more training data. Furthermore, it is observed that among the five expressions "happy" expression is well (98% recognition rate) recognized than the others (between 70% and 85% recognition rate). It can also be seen that the evidential HMM with temporal constraints, achieves the best recognition rate (and improves it in some cases) compared to the other used version HMM, even though the input is segmented as continuous video. The other expressions are greatly confused with one another other. See below an illustration results in Table I.

See in following Figure 5, the examples of images from the video sequences used in the experiment.

Experiments Results 2: Using Medical videos database

Our experimental data were collected in an open recording scenario, where the patient was asked to display the expression corresponding to the emotion being induced: This is a simulation process for generating facial expressions in medical context. Although we are aware that this assumption does not take into account all the constraints related to the real conditions of facial expressions data collection, we think that, the experimental result achieved shows involved significantly the technological progress. For complex and highly sensitive applications such as patient monitoring in medical UCIs, power, robustness and efficiency of the proposed model stands out and improves very significant way the performance of the expressions recognition system facial. The specific facial expressions recognition rate to the medical context such as feel the pain and the patient is in anxious condition depends on the performance of the facial feature extraction system for the detection of facial expressions basic such as smile, eyes closed, eyebrows raised and finally neutral. In average, the best results of facial expression recognition were obtained using Ev-HMM. The temporal layer assumption gives a significant improvement in recognition rate comparing with standard probabilistic HMM. Find in Table 2 & 3, the results reporting the facial expression recognition rate reached depending on the various kinds of HMM we tested. In this used case of Ev-HMM, "Happy" was detected with over 96% accuracy and Disgust with over 83% accuracy. Whereas, the patient's behavior like fells the pain and anxious state are recognized at respectively 78 % and 70%. See in following Figure 6, the examples of images from the medical video sequences used in the experiment.

Conclusion

We have developed in this work, a computer vision system that automatically recognizes a series of complex facial expressions. Our recognition system applied to psychological research in medical field. In the first instance, the proposed approach has been tested on a generic [AUBd] database of facial expression to assess the system is performance and efficiency .More specifically, the proposed system was used to recognize the patient's specific behaviors closely linked to his facial expressions and emotions (resentment pain and mental state of anguish) in cardiological ICUs. A Robust and powerful approach for automatic facial recognition expression using HMM in belief The patient feels pain 54,00 55,00 55,00 78,00

The patient Anxiety 50,00 52,00 55,00 70,00

Happy Surpprise

Feel Pain Anxious Neutral framework is presented. The proposed work is able to detect human faces over extracting face features using HMM tool by segmenting face from the real time video. Among the facials expressions, happy and disgust expressions has been recognized with an accuracy of 96% but expressions neutral and disgust cannot be distinguished well. Thank to our method, because it provides better rate recognition with complex expressions in a medical environment such as the issue of pain and patient anxious are not easy to recognize. Nevertheless, our system has allowed us to recognize these two expressions with a rate of about 83% on average. Hence the future work aims to apply the feature extracted in this work to the forehead and noise region and also considering more number of expressions. In addition, we think to take into account a generic maximal intensity for all people because that is the lack in current model, each person has his/her own maximal intensity of displaying a particular facial action. This work is just another step on the way toward achieving the goal of building more effective medical computers-assisted that can help us better analyzing physiological states such as heart beat and skin conductivity of patient in critical care.

Figure 1

 1 Figure 1 is an illustration of face image parameterization and blocks extractions.

Figure 2 :

 2 Figure 2: Left to right HMM for face recognition [5].

Figure 3 :

 3 Figure 3: (a) representation of mouth region and (b) the same for eye region

Figure 4 :

 4 Figure 4: An illustration for Ev-HMM architecture to recognize facial expressions

Figure 5 :

 5 Figure 5: Used data of Cohn-Kanade AU database

Figure 6 :

 6 Figure 6: Our used data gathered from experiment video surveillance system in UCIs.

Facial

Table I :

 I Facial Expression recognition rate for Cohn-Kanade AU database (average in %)

Table II :

 II Facial Expression recognition rate for our test database (average in %)

Table III :

 III Facial Expression recognition rate for our test database (average in %)

Acknowledgments

The authors would like to thank Professor Hippolyte AGBOTON who is in charge of the cardiology section research team. We also acknowledge each individual (Fréjus Laleye, Akpaka Ulrich and Arcadius Abraham) appearing in our face database.