Mokhtar Taffar
email: mokhtar.taffar@gmail.com

Serge Miguet
email: serge.miguet@univ-lyon2.fr

Face Class Modeling based on Local Appearance for Recognition

Keywords: Invariant Descriptors, Local Binary Patterns, Features Matching, Probabilistic Matching, Model Learning, Appearance Modeling, Object Class Recognition, Facial Detection

This work proposes a new formulation of the objects modeling combining geometry and appearance. The object local appearance location is referenced with respect to an invariant which is a geometric landmark. The appearance (shape and texture) is a combination of Harris-Laplace descriptor and local binary pattern (LBP), all is described by the invariant local appearance model (ILAM). We applied the model to describe and learn facial appearances and to recognize them. Given the extracted visual traits from a test image, ILAM model is performed to predict the most similar features to the facial appearance, first, by estimating the highest facial probability, then in terms of LBP Histogram-based measure. Finally, by a geometric computing the invariant allows to locate appearance in the image. We evaluate the model by testing it on different images databases. The experiments show that the model results in high accuracy of detection and provides an acceptable tolerance to the appearance variability.

INTRODUCTION

The facial image analysis remains an active domain of study [START_REF] Agarwal | Learning to detect objects in images via a sparse, part-based representation[END_REF][START_REF] Fei-Fe | A bayesian approach to unsupervised one-shot learning of object categories[END_REF] due to the difficulty to model and learn a wide range of intra-class appearance variability characterizing the face objects. The face detection is a subjacent problem to recognition where detect face can be considered as a two-class recognition problem in which a pattern is classified as being a face or non-facial appearance.

Thus, developing systems for facial detection has mainly two challenges: facial appearance modeling and probabilistic classifier design. The aim of facial modeling is to choice a set of the most discriminative local features extracted from face images and to construct a model, across these instances of facial features. The model should represent a large range of facial appearance by minimizing the intra-class variations and maximizing the extra-class ones. Obviously, if inadequate facial features are adopted, even the most performant classifiers will fail to accomplish the given recognition task of facial appearance (Hadid et al., 2004). Therefore, it is important to derive local features which should verify some properties like: prompt and easy extraction from images for an efficient processing, coding in a small size descriptor vector (low dimensionality of appearance space) to avoid a high computational cost of classifier, and a best classes discrimination with tolerance to withinclass variations. But, it is not obvious to find features which simultaneously meet all these criteria because of the large variability in appearances due to different factors such as scale, face pose, facial expressions, lighting conditions, etc.

The basic LBP (local binary patterns) [START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[END_REF] features have been performed very well in various applications, including texture classification and segmentation, image retrieval and surface inspection. By this work, we adapted a discriminative feature space which will be suitable to use for facial appearance recognition. The proposed approach based on the local descriptions consists of extracting a set of independent facial regions using Harris-Laplace detector. For each region, LBP feature histogram (representing texture contents within region) is computed and combined with the Harris-Laplace descriptor to build descriptor code of the region. That is this code that allows features matching and objects recognition in scene.

We present an invariant model based on local appearance, denoted ILAM, which is useful to detect/recognize faces in images. The learned model is based on similarity of appearances to recognize the facial patches, then it become possible to predict their presence on new image. The ILAM model is defined across instances of a face; it is a geometric referential that links features over appearance changes. We boosted our LBP representation by a convenient probabilistic formulation to learn appearance variations. By this manner, the model captures well the multimodal nature of facial appearances in the cases of illumination and viewpoint changes. With new features a classifier is trained to capture the facial appearance of any viewpoint (frontal, profile, ...) in cluttered images. The facial LBP-appearance approach proposed here is suitable for any resolution images and has a short feature vector necessary for fast processing.

Experimentation proves that the ILAM learned and boosted leads to accurate face localization even when the appearance variation and intra-class variability occur (i.e., beard, ethnicity, etc.). The developed appearance algorithm is simple and has acceptable cost. Experiments with detecting low-resolution faces from images are also carried out to demonstrate that the same facial modeling can be reliable and efficiently used for such tasks.

In the following, a summary is given on works related to object class appearance modeling and recognition based on local descriptors. Section 3 provides a presentation of the new objects appearance description based on local traits useful for both learning process described in section 4 and facial detection process presented in section 5. We give, in section 6, some experimental results obtained on facial appearance recognition. Finally, at section 7, a conclusion finishes this paper.

RELATED WORKS

Due to difficulties to capture the large appearance variability of objects through the local features, despite the invariance of the last ones to different variations such as illumination, viewpoint, partial occlusion, etc., many models [START_REF] Fergus | Object class recognition by unsupervised scale-invariant learning[END_REF][START_REF] Toews | Detection over viewpoint via the object class invariant[END_REF][START_REF] Taffar | Generic face invariant model for face detection[END_REF][START_REF] Lindeberg | Feature detection with automatic scale selection[END_REF] and features [START_REF] Lowe | Distinctive image features from scaleinvariant keypoints[END_REF][START_REF] Mikolajczyk | Scale and affine invariant interest point detectors[END_REF][START_REF] Kadir | Saliency, scale and image description[END_REF][START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[END_REF] have been proposed and applied to facial appearance analysis. For instance in face detecting, the normalized pixel values [START_REF] Heisele | Face detection in still gray images[END_REF][START_REF] Yang | Detecting faces in images: A survey[END_REF] and Haar-like features [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF] are the most considered ones. Heisele et al. [START_REF] Heisele | Face detection in still gray images[END_REF] reported that normalized pixel values perform better than the gradient and wavelet features. Viola and Jones [START_REF] Viola | Rapid object detection using a boosted cascade of simple features[END_REF] used Haar-like features to form integral image characteristics and boosted them by AdaBoost algorithm for fast learning, this results an efficient face detection system. Some features, such as those using PCA [START_REF] Turk | Eigenfaces for recognition[END_REF] and LDA [START_REF] Etemad | Discriminant analysis for recognition of human face images[END_REF] subspaces in face recognition, have also been considered. Such features are simple to compute, but their discriminative power is limited [START_REF] Phillips | The feret evaluation methodology for face recognition algorithms[END_REF]. To overcome the main limitation of the PCA representation, Local Feature Analysis (LFA) is developed in [START_REF] Penev | Local feature analysis: a general statistical theory for object representation[END_REF]. A good results have been obtained with Gabor wavelet features used in the elastic bunch graph matching algorithm (EBGM) [START_REF] Wiskott | Face recognition by elastic bunch graph matching[END_REF]. Unfortunately, the algorithm performs a complex analysis to extract a large set of Gabor wavelet coefficients. In [START_REF] Ahonen | Face recognition with local binary patterns[END_REF], authors have obtained good performances in face recognition using an LPB-based method in which the face image was divided into many small nonoverlapping blocks, but the representation cannot be used for small-sized face images common in many face detection and recognition problems. In [START_REF] Taffar | Viewpoint invariant face detection[END_REF] the authors present a model which combines SIFT [START_REF] Lowe | Distinctive image features from scaleinvariant keypoints[END_REF] local features and a face invariant used as a geometric landmark. The model have a detection performance highly invariant to face viewpoints.

In (Hadid and Pietikinen, 2004), authors introduced a representation which consists of dividing the face image into several (e.g. 49) non-overlapping blocks from which the local binary pattern histograms are computed (using the LBP u2 8,2 operator) and concatenating them into a single histogram. In such a representation, the texture of facial regions is encoded by the LBP while the shape of the face is recovered by the concatenation of different local histograms. However, this representation is more adequate for larger sized images (such as the FERET images) and leads to a relatively long feature vector typically containing thousands of elements. Therefore, to overcome this effect, they proposed in (Hadid et al., 2004) a new facial representation which is efficient for lowresolution images.

The emerging paradigm tries to model the objects as a collection of parts [START_REF] Pope | Probabilistic models of appearance for 3-d object recognition[END_REF][START_REF] Fergus | Object class recognition by unsupervised scale-invariant learning[END_REF][START_REF] Bart | View-invariant recognition using corresponding object fragments[END_REF]. Many contributions [START_REF] Nanni | Random interest regions for object recognition based on texture descriptors and bag of features[END_REF][START_REF] Déniz | Face recognition using histograms of oriented gradients[END_REF][START_REF] Yu | Feature integration analysis of bag-of-features model for image retrieval[END_REF] used a combination of features from local regions looking for growth the performance of the detectors and recognition systems. However, the difficulty lies in learning the parameters for the model because we do not want to explore a huge space to know which parts are best for recognition. We overcome this problem by designing a convenient appearance representation. The approach adopted learns simultaneously the facial LBP-appearance, its geometry and co-occurrence of features. The preselected facial features, through an histogram-based matching using a linear measure, are used in a probabilistic matching to predict facial appearance and to localize and recognize it with accuracy even in the presence of viewpoint changes and a rich multimodal appearance (i.e., expression, race, glasses).

LOCAL FACIAL APPEARANCE FORMULATION

In several LBP approaches of the literature, the representation of the whole face by dividing the face image (either or not by overlapping blocks) is effective and appropriate whether for images of high or low resolutions, but never for both. In addition, a LBP description computed over the whole face image encodes only the occurrences of the micro-patterns without any indication about their locations with respect to faces on images. The new appearance representation described here tries to overcome these limits. It will be suitable to deal with facial images of any sizes and where faces can be anywhere on image.

During learning, we compute a facial LBP-feature at each keypoint detected on face by using a scale and affine invariant detector, such Extended Harris-Laplacian detector [START_REF] Mikolajczyk | Scale and affine invariant interest point detectors[END_REF]. A scale and an affine invariant interest point detector combines the Harris detector with the Laplacianbased scale selection. The Harris-Laplace detector is then extended to deal with significant affine transformations.

In affine scale-space the second moment matrix µ, at a given point x, is defined by:

µ(x, S I , S D ) = det(S D )g(S I ) ⇤ ((-L )(x, S D )(-L )(x, S D ) T ) (1)
where S I and S D are the covariance matrices which determine the integration and differentiation Gaussian kernels. These interest keypoints have invariant properties and are reputed to be tolerant to affine transforms, inplane changes of scale and rotation. Each keypoint location corresponds to a central pixel of LBP region. By this manner, a geometric information enriches the structure of the local facial appearance with respect to an invariant. The keypoints detected on face are located anywhere in the image and computed on the 16 ⇥ 16 neighborhood. In this way, they can be at different locations, nearest or farest, from each other. In other terms, the LBP-blocks can be overlapped or not, as shown in Fig. 1. Thus, the representation which consists of dividing the face image into several overlapping blocks or not, and from which the local binary pattern histograms are computed then concatenated into a single histogram has been abandoned.

The proposed facial LBP-appearance representation consists to define two kinds of blocks (overlapping and non overlapping ones) around each detected keypoint from which the local binary pattern histograms are computed (using two LBP operators: LBP u2 8,2 and LBP 4,1 ) then concatenated into a single (two dimension) histogram. In such a representation, the texture of facial regions is encoded by the LBP while their shape is recovered by the concatenation of different local histograms. Therefore, we will propose here a general facial modeling which is not only efficient for low-resolution images, but also more adequate for larger sized images (such as FERET images). A strong point of this approach is that it requires no pretreatment of the face images (such standardization, background suppression, face mask extraction, etc.) and no geometric constraints (such as size of face and its location in image), so it is independent of the nature and size of the used image.

The first step uses the overlapping regions which are scrutinized by 8-neighborhood LBP operator (LBP 8,2 ), where the overlapping size is set to 2 pixels, this allows to avoid statistical unreliability due to long histograms computed over small regions. At each keypoint, in total 36 regions can be used to generate LBP code and construct histograms. The second process uses the non-overlapping blocks exploited by 4-neighborhood LBP operator (LBP 4,1 ) where the corresponding histogram is sampled in the same way as the LBP 8,2 operator. In total 25 regions are used to generate LBP code and construct histograms. Thus, each face is modeled by a set of local features. A local facial characteristic is defined by two LBP codes Finally, in the learning model, each local facial appearance is described by an Extended Harris-Laplace descriptor enhanced by a global LBP histogram computed over a 15 ⇥ 15 facial region around the keypoint by a concatenation of a set of local (LBP 4,1 and LBP 8,2 operators) LBP histograms. In addition, we assigned to each facial feature f i the geometric parameters which correspond to in-plan transformations of the facial region with respect to (wrt) the landmark located on the nose and schematized as an arrow, it represents the face invariant (FI), denoted inv, as shown in Fig. 2. By this manner, during detection process, from the learning model, it will be possible to deduce the presence of a new facial region from all LBP histograms computed over a combination of detected features that strongly match to some model traits belonging to different learning images. This approach is also very useful for recognition. Thus, the face invariant inv in the test image could be easily predicted and localized from the geometric parameters (e.g., position, scale, and orientation) of a detected facial region (which has similar facial appearance in the model) with respect to invariant in the learning model.

In our experiments, we considered 15 ⇥ 15 as the minimal standard resolution region around a detected keypoint and we derived the facial LBP-appearance representation as follows:

At first, we divide a 15 ⇥ 15 facial image region around the keypoint into 36 overlapping regions of 5 ⇥ 5 pixels (overlapping size=2 pixels). From each region, we compute a 256-bin histogram using the LBP 8,2 operator which is sampled into 16-bin histogram with a sampling step of 16. Then, we concatenate the results into a single 576-bin histogram. In the second step, we divide the same 15 ⇥ 15 face region around the same keypoint into 25 non-overlapping blocks of 3 ⇥ 3 pixels. From each region, we compute a 16-bin histogram using the LBP 4,1 operator and con-catenate the results into a single 400-bin histogram. Additionally, we apply LBP u2 8,1 to the whole 15 ⇥ 15 facial region and derive a 59-bin histogram which is added to the 976 bins previously computed. Thus, we obtain a (59 + 976 = 1, 035)-bin histogram as a local face representation at the detected point of interest (see Fig. 1). Finally, a face is defined by a set of independent local representation of facial appearance who is none other than a set of Extended Harris-Laplace descriptor and 1035-bin histogram. Thus, each facial feature, denoted

f i = { f p i , f g i , f a i },

LEARNING PROCESS

Given a set of N visual traits { f i } extracted from the training image, the model learns to detect if each f a i whether or not a facial appearance. In probability term, from a set of facial appearance { f a i } of the subwindows extracted from the training image, the model quantifies the likelihood term of each f a i = (D EHL f i , LBP f i ) feature which can be expressed as

p( f p=1 i | f a i ) = p( f p=1 i )p( f a i | f p=1 i ) p( f a i ) (2)
where p is the binary presence parameter of facial appearance, e.g., p = 0 for non face or background sample. LBP f i is the LBP facial representation of the training sample f i extracted around Extended Harris-Laplace keypoint described by D EHL f i appearance, D EHL f i and LBP f i parts of f a i are statistically independents. Thus, it is important to accomplish the learning model under the following assumptions:

• f g i and f a i are statistically independent given presence

f p i . • D EHL f i
and LBP f i are geometrically independents.

• f g i parameter is related to the geometry of D EHL f i appearance parameter of f i .

Depending on whether f i is a positive or negative sample (face or non-face), the model exhibits the quantity of the probability ratio R( f

a i ) = p( f p=1 i | f a i ) p( f p=0 i | f a i ) , e.g., f i is face if R( f a i ) > 1.

RECOGNITION PROCESS

In facial appearance recognition, given a set of visual observations { f i } extracted from test image, each f i is defined by its appearance values

f a i = (D EHL f i , LBP f i ) and geometric values f g i = { f g:(x,y) i , f g:s i , f g:q i }
of the extracted image feature f i . Thus, the learning model attempts to confirm if each f i is or not a facial appearance ( f a i , f p=1 i

). The classifier decides on the facial appearance of the subwindow according to the likelihood value of the following expression:

p( f a i | f p=1 i ) = p( f a i )p( f p=1 i | f a i ) p( f p=1 i ) (3) where p( f a i | f p=1 i
) is a posterior value to affirm the facial appearance of the feature, p( f a i ) is a prior over facial appearance in the learning model, p( f

p=1 i | f a i )
is the likelihood value of feature presence f i given its facial appearance, and p( f p=1 i

) is the evidence that the feature is facial in the learning model.

Thus, it is interesting to perform facial appearance recognition using the learning model under the assumptions that are: is the appearance part that matches to D EHL f j in the model. In addition, before to perform the EM classifier, a set of similarity measures is applied over the LBPhistograms (three different histograms-based metrics: Histogram Intersection, Log-Likelihood Statistic, Chi Square Statistic) in order to confirm the facial presence detections and remove the false ones. The threshold values are fixed empirically for each distance. For a given detected window, we count the number of recognitions by matching the histograms within a neighborhood of 15 ⇥ 15 pixels (each detected window is geometrically localized by its central trait). The detections are removed if no matching occurs at this region. Otherwise, we keep them, the regions for which the matching occurs have a high outcome of EM classification. The LBP traits extracted from new image are expected as facial features under different lightning and viewpoints variations. The idea is to find a cluster of features that have appearance agreement with a face. This set of data observations { f p=1 i } is formed by estimating appearance distance d( f a i , f a j | f b j ) result of a true face or background relatively to an appearance threshold G a .

• D EHL
For each feature f i , when appearance matching occurs, the facial appearance probability of f i , denoted p( f i | f p=1 i , f a j ), can be computed, where p is the presence parameter, e.g., p=0 for background or face appearance absence. Features with facial appearance are retained and they are reputed to belong to face, e.g., p(

f i | f p=1 i , f a j ) > p( f i | f p=0 i , f a k )
, where f j and f k are the features of best probabilistic matching with f i in facial and background spaces respectively. Moreover, we calculated the number of model features

v p=1 i (resp. v p=0 i
) that have voted for image feature f i as facial (resp. background). Thus, this appearance probabilistic classification of f i allows deciding one by one if the image features have facial appearance or not.

Furthermore, once all the facial features are known in the test image, a hierarchical clustering based on the geometrical classification algorithm is performed. This makes it possible to group them according to their geometrical positions in the image. Using a geometric clustering threshold G c , the algorithm provides one or more clusters of facial features. This allows to generate one invariant inv for each cluster. Each inv localizes a possible facial presence. Thus, a multiple facial appearance can be recognized in image. This procedure tries to confirm the appearance statistical dispersion on test image with respect to the appearance in the learning model.

EXPERIMENTATION

Data and Experimental Considerations

Because we assume that our appearance-based detection scheme captures very well the variability of Then, we increase the number of

f i = { f p i , f g i = ( f g:(x,y) i , f g:s i , f g:q i ), f a i = (D EHL f i , LBP f i )}
features in the learning model by adding a negative samples { f p=0 i } from some natural images from the net to obtain a set of 960 face and non-face appearances. Additionally, to enable the system to also detect faces from any viewpoint (in-plane rotation), we used a training set of face images of the CMU-Profile database. Fig. 3 shows the examples of face images and the different rotated face samples. Overall, we obtained a training set of 360 faces. The faces are divided into three categories of views: frontal, view angle 20 -70 , and profile.

To collect more consistent and reliable (face and nonface) appearances (patterns and shapes), we used the boostrap strategy in five iterations [15]. First, we randomly extracted 200 appearances from a set of MIT-CMU Profile database which contain faces and 100 appearances from a set of natural images which do not contain faces. Then, at each iteration we trained the system, run the face detector, and collected all those face (resp. nonface) appearances that were wrongly classified as nonfaces (resp. faces) and used them for training. Overall, we obtained 1080 + 132 facial appearances as positive training examples and 60 + 47 nonface as negative training examples. The learning model involved 1, 319 features (1, 212 facial features and 107 negatives); they are chosen well, deemed to be informative with respect to (wrt) invariant, and not redundant. Some parameters have been experimentally fixed by testing their impact on accurate localization of the face invariant. The appearance threshold G a is empirically set at different values for the corresponding histogram distances, this allows to preselect only features with coherent facial appearance.

To check the geometric agreement of predicted in-variants and a symmetric consistency of facial features, the value of threshold G g is set on 3-parameters that correspond to position, scale and rotation. The position parameter of threshold G g:(x,y) is a pixel distance that must be less than inverse of invariant scale.

The scale parameter of threshold G g:s is limited to a ratio of 5% in scale with respect to the scale variation in image, and orientation threshold G g:q enables 10 degrees of tolerance.

A clustering threshold G c allows aggregating the geometry of predicted invariants for accurate localization of the best cluster of invariants. An invariant is clustered if its minimal distance to any invariant (either clustered or not) is less than G c relative to the mean of scales.

Facial Recognition from Viewpoint

The performance of ILAM model is evaluated for different values of appearance threshold G a and for different histogram distances. Figure 4 plots the result of experiments which allow us to set the best G a value for each distance. For intersection and likelihood metrics the best detection rates (resp. 83.27% and 79.6%) are obtained for the values 0.4 and 0.9 of G a respectively but less than for Chi Square distance. For G a = 0.6, ILAM model gives a good precision result and the Chi Square distance is clearly best. The face detection grows quickly to reach the rate of 92.4% since the chosen threshold G a is cut as a precision factor to predict the facial appearance presence.

The Precision-Recall curves (PRC) in figure 5 drawn the performance comparison of ILAM model for different distances of similarity on the same protocol. It depicts that histogram distance of Chi Square provides an accuracy quality to the model than the Log-likelihood Statistic similarity. The Chi Squared distance is slightly better than the Histogram Intersection metric and no need to impose geometric or appearance constraints on faces in cluttered image before detection.

From the collected training sets, we extracted the proposed facial representations (as described in section 5). Then, we used these features as inputs to the classifier and trained the face detector. Thus, the system is run on several images from different sources in order to prove its acceptable performance of facial appearance recognition. Fig. 6 shows some detection examples. It can be seen that not only most of the upright frontal faces are detected but also the faces which present viewpoint changes and an appearance variability. For instance, Fig. 6.A shows perfect detections. In Fig. 6.D no face is missed and one face is detected by the system even when the severe occlu- sion occurs. A similar case is shown in Fig. 6.G in which the face is not missed despite a large in-plane rotation.

Since the system is trained to detect faces at any degree of in-plane rotation, from the face view to the profile view (i.e., up to ±90 ), it succeeded to find the strongly rotated faces in Fig. 6.G, 6.H and Fig. 6.I, and failed to detect slightly rotated ones (as those in Fig. 6.C) due to the large appearance variability. A false negative is shown in Fig. 6.J while a false positive is shown in Fig. 6.C, 6.G and 6.H but their numbers in the statistics detector are very low. Notice that this false positive is expected since the face is pose-angled from the range angle of 45 ± 5 worsened when the facial appearance variability is drastic and the detector performs well for the profil view. These examples summarize the main aspects of our detection system using images from different sources. The detected faces are marked by a rectangle encompassing or covering one or several facial regions each characterized by the detected facial LBP-appearance, as shown in Figure 7. In order to report quantitative results and compare them against those of the state-of-the-art algorithms, we considered the test images from the MIT-CMU sets (CMU-Database, 2009) that are used principally with the Bayesian Discriminating Features (BDF) method [START_REF] Liu | A bayesian discriminating features method for face detection[END_REF], Schneiderman-Kanade approach [START_REF] Schneiderman | Probabilistic modeling of local appearance and spatial relationships for object recognition[END_REF], Normalized Pixel features [START_REF] Heisele | Face detection in still gray images[END_REF], and LBP representation as in (Hadid et al., 2004). There are 80 images containing 227 faces. Some of these images are shown in Fig. 6.(A, D, E, G, H, andI).

Table 1 presents the performance of our facial appearance recognition system and those of other approaches like: BDF [START_REF] Liu | A bayesian discriminating features method for face detection[END_REF], [START_REF] Schneiderman | Probabilistic modeling of local appearance and spatial relationships for object recognition[END_REF], and LBPfeature used in (Hadid et al., 2004). We can see (from the 1st, 2nd, 5th and 6th rows of Table 1) that our approach has a performance slightly higher to the comparative approaches. The proposed ILAM detector using LBP-based approach (where LBP features are extracted around Extended Harris-Laplace keypoint) succeeded in detecting 225 faces with few false positives caused by the similar appearance of the detected objects to faces. Some missing faces are mainly due to severe facial appearance variability added to a large in-plane rotation (as shown an example in Fig. 6.C) and sometimes to occlusion. We notice that ILAM system has an high performance, moreover, it is more general and not only dedicated to frontal faces but also to faces in different poses and even when occlusion occurs.

Additionally, if the detected faces are to be fed to a recognition step, then, no raison to tolerate some false detections even if it is likely that these images will be rejected (therefore they will not be accepted as those of an individual). In such a context even if our face detector performs slightly better as it succeeded in detecting 225 faces among 227 (the system detected the tilted faces in Fig. 6.G despite the large in-plane rotation) it tolerates only 3 false detections. The 8th row of Table 1 presents this performance.

Analyzing the ILAM representations and investigating the usefulness of dividing the facial images into regions around detected keypoints, we noticed that calculating the LBP traits from these regions yielded a good result (see the 8th row in Table 1). This is expected since such a representation encodes only the occurrences of the micro-patterns without any indication about their locations. Combining both representations further enhances the detection performance. However, computing the LBP traits only from the whole images (59 bins) yields a low detection rate of 20.7% (see 5th row in Table 1).

In order to further investigate the discriminative power of facial appearance of ILAM model, we used a similar face detector combined with an EM classifier and using different features as inputs, then compared the results to those obtained using the proposed f i traits. We trained the system using the same training samples as described in Section 6. We chose, for experimental purpose, the HoG (histograms of oriented gradients) features [START_REF] Déniz | Face recognition using histograms of oriented gradients[END_REF], LBP/LTP representation [START_REF] Nanni | Random interest regions for object recognition based on texture descriptors and bag of features[END_REF], and ones based on patch-based SIFT-LBP integration [START_REF] Yu | Feature integration analysis of bag-of-features model for image retrieval[END_REF] as inputs, even if, it has been shown in [START_REF] Nanni | Random interest regions for object recognition based on texture descriptors and bag of features[END_REF] that such texture descriptors (LBP/LTP patterns and local phase quantization) for describing region and a bag-of-features approach for describing object performs comparably well to HoG and SIFT-LBP based ones when using a SVM classifier.

Table 2 (5th row) shows the performance of ILAM model based on LBP 4,1 + LBP 8,2 + LBP u2 8,1 traits computed over the local region. Although the results are quite good as 294 faces among 300 were detected, still the proposed approach using the f i visual features, where f a i = (D EHL f i , LBP f i ) is the facial appearance part of f i , computed over regions around keypoints

• performed better (comparison between the 5th row and 6th row in Table 2);

• used a combination of well know features which results on simple descriptor and histogram vectors and thus more faster to compute over the little regions;

• did not need to impose anyone constraint like histogram equalization; and

• principally needs a simple EM classifier to estimates the latent data, than using a series of SVM classifiers (Hadid et al., 2004;[START_REF] Vapnik | Statistical learning theory[END_REF].

CONCLUSION

The appearance representation of face class presented in this paper offers robust properties such as tolerance to geometric transforms and illumination changes. It captures well the viewpoints variations and especially intra-class variability. It has a geometric localization sufficiently accurate and its magnitude remains roughly constant with respect to size of object in image. The ILAM model based on combination of local appearance of Extended Harris-Laplace descriptor and texture of LBP feature provides a low degree of supervision. The experimentation reveals that the facial formulation is useful and has high capability to classify new face instances, of course this representation can be applied to another object class.

Figure 1 :

 1 Figure 1: Local representation of facial appearance: in addition to Extended Harris-Laplacian descriptor, a 15 ⇥ 15 facial region around the keypoint is described by a concatenation of a set of local (LBP 4,1 and LBP 8,2 operators) LBP histograms.

Figure 2 :

 2 Figure 2: Facial invariant, represented by a red arrow on nose, is a geometric landmark for the local representation of facial appearance represented by yellow squares on face. The double-headed arrow describes affine transformation of the appearance region f i to face invariant inv.

  appearance f a i . The model is based on the assumptions which are the presence parameter f p i follows a discrete binomial distribution in the presence space and the appearance parameter f a i = (D EHL f i , LBP f i ) modeled by Extended Harris-Laplacian descriptor (denoted D EHL f i ) and LBP f i representation of feature f i follows a normal distribution with mean µ a and covariance  a in the appearance space. The geometric parameter f g i of the feature when with him is determined with respect to face invariant inv in the image.

  depends on presence of the local facial appearance f a i in the image. From these hypothesis, given an appearance D EHL f i detected in the test image, it becomes easier to deduce multiple shapes and patterns of the facial appearance given by a combination of D EHL f j and LBP f k parts of different traits in the learning model, where f j and f k are the model traits, and D EHL f i

Figure 3 :

 3 Figure 3: Examples of face images from CMU-Profiles database (CMU-Database, 2009) where faces present pose changes.

Figure 4 :

 4 Figure 4: The evaluation results of facial appearance detection for different values of G a , on the protocol of 300 face images from the CMU-Profile database (CMU-Database, 2009), allows to set the best G a value for each distance. The results illustrate the rate of 92.4% of ILAM model to infer faces which present viewpoint changes.

Figure 5 :

 5 Figure 5: PRC curves of facial appearance model, on the protocol of 180 face images from the ORL database (AT&T-Database, 1994) for a face localization task, illustrates the rate of 95.6% of ILAM model to infer faces in images for threshold appearance G a = 0.6, since Chi Squared distance is proved the best in this context.

Figure 6 :

 6 Figure 6: Facial appearance recognition examples in several images from different databases. The images A, D, E, G, H and I are from the subset of MIT-CMU tests. They belong to the 120 images considered for comparison. The images B, C and F are from PIE database. We notice the excellent detections of upright faces in A, D, F and G; detections under slight in-plane rotation in G and H; even with glass occlusion a right detection in D, missed face and false detection in C because of high appearance variability, detected faces correctly in E, G, H and I even with a large in-plane rotation; no missing face in B caused by a profile view of face; and false detections in G and H due to similarity to facial appearance.

Figure 7 :

 7 Figure 7: The yellow englobing rectangles of detected faces include one or several facial LBP-appearance regions represented by white rectangles.

  1 and we perform the tests on 238 images containing 300 faces from the subset of CMU-Profile (CMU-Database, 2009), CMU-PIE (PIE-Database, 2009), and AT&T (AT&T-Database, 1994).

Table 1 :

 1 Comparative performance of ILAM facial detector based LBP-appearance representation with some detectors on 80 images containing 227 faces.

	Method	Face Det.	False Det.	Det. rates
	BDF Method	221	1	97.4%
	Schneiderman-Kanade(1.0, 1.0)	218	41	96.0%
	Normalized Pixel features	213	6	93.8%
	LBP feature LBP u2 8,1 (59 bins)	47	184	20.7%
	LBP feature LBP 4,1 (144 bins)	211	9	92.9%
	LBP 4,1 +LBP u2 8,1 trait(203 bins)	222	13	97.8%
	ILAM based f i trait	225	3	99.1%

Table 2 :

 2 Comparative performance of ILAM modeling combined with an EM classifier to different features used as inputs.

	Method	Face Det.	False Det.	Det. rates
	HOG features	293	8	97.6%
	LBP/LTP representation	294	6	98.1%
	Patch-based SIFT-LBP	296	6	98.6%
	LBP 4,1 + LBP 8,2 + LBP u2 8,1 trait f i = { f p i , f g i , f a i } trait	294 298	9 5	98.0% 99.3%


J Pierron

C Inguimbert

M Belhaj

M Raine

J Puech

Monte Carlo Simulations of Low Energy Electrons in Silicon

The electron transport in silicon at low and very low energy (10 eV -2 keV) is investigated with a Monte Carlo code. The elastic scattering with nuclei is described by Mott's model of partial waves, whereas the inelastic collisions with electrons are described by the complex dielectric function theory. The code has been validated by means of comparison with electron emission yields (EEY) and energy loss spectra experimentally measured in ultrahigh vacuum on an Ar-etched sample. Electron emission yields, practical ranges, and ionizing doses are presented for electrons in silicon down to 10 eV.

INTRODUCTION

he study of low energy electron transport in matter is of great interest for many fields of applications. For instance, in microelectronics, the shrinking of electronic devices has recently reached about 14 nm [1] and thus has created a need for more precise electron transport codes at very low energy to study the effects of ion and electron trackstructures on the sensitivity of electronic devices [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF]. At these scales, the radiation transport modeling shall be accurate over small distances of few nanometers and very low energies of few tens of eV. Some authors have worked to develop numerical methods adapted to the electron transport at low energy [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [3] [4] [START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energyrange validity up to 10 GeV/nucleon[END_REF] [6] [START_REF] Fitting | Attenuation and escape depths of low-energy electron emission[END_REF] [START_REF] Kuhr | Monte Carlo simulation of electron emission from solids[END_REF]. Recently, a new module dedicated to low energy electron transport has been implemented in Geant4. This electromagnetic model of Geant4 called MicroElec performs the electrons transport down to ~16 eV [START_REF] Raine | Improved simulation of ion track structures using new Geant4 models -Impact on the modeling of advanced technologies response[END_REF] [START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energyrange validity up to 10 GeV/nucleon[END_REF] [6]. It has been used to improve the modeling of heavy ion track structures below a radial distance of 10 nm [START_REF] Raine | Improved simulation of ion track structures using new Geant4 models -Impact on the modeling of advanced technologies response[END_REF]. The Geant4-MicroElec library extension [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] [4] [START_REF] Raine | Geant4 physics processes for silicon microdosimetry simulation: Improvements and extension of the energyrange validity up to 10 GeV/nucleon[END_REF] [6] has also been employed to investigate the sensitivity of advanced devices to incident electrons [START_REF] Inguimbert | Electron Induced SEUs: Microdosimetry in Nanometric Volumes[END_REF]. For now, the Geant4-MicroElec model is only valid down to ~16 eV for a single material (silicon). Some other codes have been implemented over the past years for silicon [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [START_REF] Fitting | Attenuation and escape depths of low-energy electron emission[END_REF]. ONERA in collaboration with CNES has developed its own code: OSMOSEE [10] [11]. In this code dedicated to low energy electron emission, the implemented physical models were initially specific to aluminum. On the other side, the Geant4-MicroElec library extension is based on the complex dielectric function theory and could be easily adapted to different materials. In a collaborative effort, this work proposes to extend the domain of validity of such kind of approaches to different materials and down to a few eV. At these low energies additional phenomena (not included in MicroElec), for example the crossing of the surface potential barrier or surface plasmon excitations, must be taken into account. Up to now, three materials (aluminum, silver and silicon) have been implemented in the code OSMOSEE for energies between 10 eV and 2 keV [START_REF] Pierron | Monte-Carlo lowenergy electron transport in metals for secondary emission applications[END_REF]. This enables to estimate some relevant parameters for new generation devices of small dimensions such as the range of electrons and the ionizing dose.

The validation of the model is performed by means of comparisons with experimental measurements obtained with a facility entirely dedicated and designed to electron emission [START_REF] Roupie | Contribution à l'étude de l'émission électronique sous impact d'électrons de basse énergie (<=1 keV) : application à l'aluminium[END_REF] [START_REF] Gineste | Investigation of the electron emission properties of silver: from exposed to ambient atmosphere Ag surface to ion-cleaned Ag surface[END_REF]. Electron Emission Yield (EEY) and energy loss spectra obtained in ultrahigh vacuum on an Ar-etched sample of silicon are compared with simulation results.

II. LOW ENERGY MONTE CARLO CODE

If electron transport in matter is well described at high energies, it is not the case at low (few tens of eV) and very low energy (a few eV) where most analytical models extrapolated from high energy fail [START_REF] Inguimbert | Monte Carlo simulation of the electron range/energy relationship in the sub-keV energy domain[END_REF]. In matter the trajectory of the electrons is driven by two main mechanisms: the elastic and the inelastic scatterings. At low energy, one has to take into account not only the inelastic scattering (i.e. collision with electrons), but also the elastic scattering (i.e. deflection by nuclei) that is predominant in these energy ranges. In the code OS-MOSEE, the elastic interactions are described by Mott's model (or partial waves) from the code ELSEPA [START_REF] Salvat | ELSEPA -Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules[END_REF]. The inelastic scattering is described by the complex dielectric function theory and optical data [3] [16]. The code takes into account surface plasmon excitations and the crossing of the surface potential barrier [START_REF] Roupie | Contribution à l'étude de l'émission électronique sous impact d'électrons de basse énergie (<=1 keV) : application à l'aluminium[END_REF] [START_REF] Roupie | The study of electron emission from aluminium in the very low primary energy range using Monte Carlo simulations[END_REF]. The MC procedure is a standard one. Random numbers are used to determine the type of interaction, the distance traveled between collisions, and the characteristics of the interaction (scattering angles, energy transfers). It has been described in previous papers [START_REF] Roupie | Contribution à l'étude de l'émission électronique sous impact d'électrons de basse énergie (<=1 keV) : application à l'aluminium[END_REF] [START_REF] Roupie | The study of electron emission from aluminium in the very low primary energy range using Monte Carlo simulations[END_REF]. Paths and energy losses are calculated until the electron is emitted out of the solid or until its energy falls under an energy threshold. This threshold equals eχ+E G +ΔV for semiconductors, with E G the energy bandgap, eχ the electron affinity, and ΔV the valence bandwidth.

First, the principle of the simulation method (complex dielectric function theory) is briefly described in section III. Next, simulation results (energy spectra, EEY, practical ranges, and T ionizing doses) performed with the code OSMOSEE in silicon targets are presented in sections IV, V, and VI.

III. INELASTIC MEAN FREE PATHS

In the complex dielectric function theory, the total inelastic cross section σ can be obtained using equation (1) where NZ is the electronic density of the solid, a 0 =0.529 Å the Bohr radius, T the kinetic energy of the incident electron, and 𝜀(ℏ𝜔, ℏ𝑞) the exact dielectric function of the solid with ℏ𝜔 and ℏ𝑞 the energy and momentum transferred to the electrons of the solid [2] [3].

𝑑 2 𝜎 𝑑ℏ𝜔𝑑ℏ𝑞 = 1 𝑁𝑍 1 𝜋𝑎 0 𝑇 ℑ𝑚 [ -1 𝜀(ℏ𝜔, ℏ𝑞) ] 1 ℏ𝑞 (1)
The first step of this method is to model the imaginary part of the inverse of the dielectric function (energy loss function) that contains all information on the electronic band structure of the solid. The energy loss function for ℏ𝑞 = 0 may be obtained from optical data [START_REF] Edwards | Handbooks of Optical Constants[END_REF]. Methods to extend this function to all momentums ℏ𝑞 have been described by different authors [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [3] [8] [17] [START_REF] Shinotsuka | Calculations of electron inelastic mean free paths. X. Data for 41 elemental solids over the 50 eV to 200 keV range with the relativistic full Penn algorithm[END_REF]. Consistency of the fitting is given by three sum-rules [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF]. We found a maximum discrepancy of 8 % for silicon.

To get the total inelastic mean free path, one has to integrate (1) over energy ℏ𝜔 and momentum ℏ𝑞 transfers. The boundaries in ℏ𝑞 are determined [3] [17] by the law of conservation of energy and momentum [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF].

𝑞 ∓ (𝑇, ℏ𝜔) = √2𝑚 ℏ [√𝑇 ∓ √𝑇 -ℏ𝜔] (2)
The boundaries in energy transfer ℏ𝜔 are obtained with respect to the Pauli principle [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] [8] [START_REF] Ganachaud | A Monte-Carlo calculation of the secondary electron emission of normal metals[END_REF]. In the MC code, the bottom of the valence band has been chosen as an energy reference for electrons in semiconductors. Equations ( 3) and (4) provide respectively the total inelastic mean free path λ and the stopping power SP, E being the total energy of the electron in the solid.

𝜆 -1 (𝐸) = 1 𝜋𝑎 0 (𝐸-𝐸 𝐺 -𝛥𝑉) × ∫ ∫ ℑ𝑚 [ -1 𝜀(ℏ𝜔, ℏ𝑞) ] 1 ℏ𝑞 𝑞 + (𝐸-𝐸 𝐺 ,ℏ𝜔) 𝑞 -(𝐸-𝐸 𝐺 ,ℏ𝜔) 𝐸-𝐸 𝐺 -𝛥𝑉 𝐸 𝐺 𝑑ℏ𝑞 𝑑ℏ𝜔 (3)
𝑆𝑃(𝐸) = ∫ ℏ𝜔 𝑑𝜆 -1 (ℏ𝜔) 𝑑ℏ𝜔 𝑑ℏ𝜔 𝐸+𝐸 𝐺 2 𝐸 𝐺 (4)
These calculations are presented on Fig. 1 and Fig. 2. As depicted on these figures, the calculated total inelastic mean free path and stopping power are in good agreement with data from the literature.

In the code OSMOSEE, the surface plasmon excitations are taken into account by replacing the energy loss function

ℑ𝑚 [ -1 𝜀(ℏ𝜔,ℏ𝑞) ] by ℑ𝑚 [ -1 𝜀(ℏ𝜔,ℏ𝑞)+1
] with 𝜀(ℏ𝜔, ℏ𝑞) + 1 = 0 the dispersion relation for collective excitations near the surface [START_REF] Ganachaud | A Monte-Carlo calculation of the secondary electron emission of normal metals[END_REF]. A dependence of the electron depth z (i.e. Begrenzung effect) is then added to the surface plasmon mean free path 𝜆 𝑠𝑝 [START_REF] Kuhr | Monte Carlo simulation of electron emission from solids[END_REF] [10] [START_REF] Roupie | The study of electron emission from aluminium in the very low primary energy range using Monte Carlo simulations[END_REF] with equation ( 5), 𝜆 𝑣𝑝 being the volume plasmon mean free path, and ℏ𝜔 𝑠 being the surface plasmon energy.

𝜆 𝑠𝑝 -1 = 𝜆 𝑣𝑝 -1 . [exp (- 𝑧 𝑧 0(ℏ𝜔 𝑠 ) )] (5)
𝑤ℎ𝑒𝑟𝑒 𝑧 0 (ℏ𝜔) ≈ 3.90 √𝑇 ℏ𝜔 (𝑖𝑛 Å)

According to this model, the surface plasmon excitations may occur only in the first atomic layers from the surface [START_REF] Kuhr | Monte Carlo simulation of electron emission from solids[END_REF]. As a result, the probability for exciting surface plasmons increases at very low energy. Fig. 1. Total inelastic mean free path for electrons in silicon. Full [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF], dashed [START_REF] Fitting | Attenuation and escape depths of low-energy electron emission[END_REF] and dotted [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] [18] lines represent calculations. Dots represent experimental data from references [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] [19] and therein, and crosses are used for calculations from [START_REF] Tung | Electron inelastic mean free paths and energy losses in solids II[END_REF] and therein. Fig. 2. Stopping power for electrons in silicon. Full [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF], dashed [START_REF] Kumagai | Energy dependence of electron stopping powers in elemental solids over the 100 eV to 30 keV energy range[END_REF] and dotted [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] lines represent calculations. Dots represent experimental data from [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] and therein.

E-E F (eV)

Valentin et al. [START_REF] Fitting | Attenuation and escape depths of low-energy electron emission[END_REF] Kumagai et al. [25] Akkerman et al. [6] Luo et al. [START_REF] Fitting | Attenuation and escape depths of low-energy electron emission[END_REF] and therein This work

[18] [3] [2] [7] [2] [3] [20] [3]
IV.

VALIDATION: ENERGY LOSS SPECTRA AND EEY

The code OSMOSEE has been validated by comparisons with the literature and experimental measurements of different physical quantities, such as the energy loss spectra and the Electron Emission Yield (EEY). Some backscattered electrons are primary electrons that have undergone inelastic energy losses. The electrons that have been backscattered after experiencing a single inelastic interaction will get out of the target material with a typical energy loss ℏω representative of the interaction. On an energy loss spectrum, that leads to a typical structure at the characteristic energy 𝐸 = 𝐸 0 -ℏ𝜔, with E 0 the incident electron beam energy. Usually for backscattered electrons, the spectra are given in function of the energy loss ℏ𝜔 = 𝐸 0 -𝐸.

The energy loss spectra measurements were performed in an ultrahigh vacuum facility on an Ar-etched sample of silicon. A full description of the experimental facility can be found in reference [START_REF] Gineste | Investigation of the electron emission properties of silver: from exposed to ambient atmosphere Ag surface to ion-cleaned Ag surface[END_REF] and therein. Fig. 3 shows that a good agreement is found between MC simulations and experimental measurements. The peaks corresponding to the volume plasmon excitation (vp) and its multiples appear clearly at ℏ𝜔 =16.8, 33.6 and 50.8 eV. The surface plasmon excitation (sp) corresponds to the shoulder at 11.6 eV. It is less noticeable than the volume plasmon excitations on both simulated and experimental spectra [START_REF] Cao | Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy[END_REF] (and therein). Fig. 3. Energy loss spectrum for backscattered electrons in silicon. Our experimental spectrum corresponds to E0=1990 eV whereas our MC spectrum (dashed line) and the experimental measurements of Cao et al. [START_REF] Cao | Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy[END_REF] are for E0=1000 eV. Fig. 4. Energy spectrum for the L2,3VV Auger transition in silicon. Full lines are MC simulation and experimental measurements of [START_REF] Cao | Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy[END_REF]. The dashed line is our MC simulation.

In addition to the backscattered electrons, the study of the Auger electrons is useful to validate a MC code. The Auger electrons are secondary electrons born from collisions with core electrons of the solid. They are emitted out of the solid with a typical energy that depends on the core levels involved in the interaction. Fig. 4 shows the MC results for the L 2,3 VV and L1L 2,3 V Auger transition in silicon. Our MC simulations are in fairly good agreement with the MC simulations and the experimental results of Cao et al. [START_REF] Cao | Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy[END_REF].

The EEY is defined as the ratio between the number of electrons emitted by a solid over the number of electrons initially impacting this solid. For silicon, as depicted in Fig. 5, MC simulated yields are in good agreement with Bronstein & Fraiman's experimental data [START_REF] Bronstein | Secondary electron emission[END_REF], and with the MC simulations of Kuhr & Fitting [START_REF] Kuhr | Monte Carlo simulation of electron emission from solids[END_REF]. Since our measurements are performed on bulk solids, for easily oxidized materials such as silicon, a capping layer of oxide may remain on the sample after Ar-etching. This may explain the discrepancy at very low energy between our data and Bronstein and Fraiman's. Fig. 5. Backscattered and secondary electron emission yields at low energy for silicon. Full lines are MC simulations [START_REF] Kuhr | Monte Carlo simulation of electron emission from solids[END_REF], circles are Bronstein & Fraiman's experimental data [START_REF] Bronstein | Secondary electron emission[END_REF], and square are our experimental measurements.

V. CSDA AND PRACTICAL RANGES

In a solid, the incident electrons are slowed down by successive inelastic scattering with some electrons of the solid atoms. Each electron has an individual trajectory. The path length of this trajectory is the total distance traveled until the electron comes to rest. The average path length is known as the 'range' of the electrons in the solid [START_REF] Inguimbert | Monte Carlo simulation of the electron range/energy relationship in the sub-keV energy domain[END_REF] [START_REF] Inguimbert | Extrapolated range expression for electrons down to ~10 eV[END_REF]. The range, in the Continuous-Slowing-Down Approximation (CSDA), can be estimated by integration of equation ( 4) over energy from a final to an initial value. Our simulations enable the estimation of the CSDA range down to a few eV as depicted in Fig. 6.

However, due to deflections by nuclei, most electrons do not reach a depth that equals their range. The depth they finally reach is called the penetration depth. For electrons, it is common to define the average penetration depth, a metric more representative than the CSDA range of the penetration distance that can be traveled by the electrons in a solid. The practical range is commonly defined [START_REF] Inguimbert | Monte Carlo simulation of the electron range/energy relationship in the sub-keV energy domain[END_REF] (see Fig. 7) as the point where the tangent at the steepest section of the transmission curve intersects with the thickness or depth axis (X-axis).

[22] Fig. 6. CSDA ranges for electrons in silicon. The data are from [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [3] and references therein. The practical range is plotted on Fig. 8. A good agreement is found with data from the literature at high energy, however as can be seen in Fig. 8, below 100 eV the practical range tends to stabilize to a value of a few nanometers [START_REF] Inguimbert | Extrapolated range expression for electrons down to ~10 eV[END_REF] instead of decreasing according to a power law as predicted by commonly used analytical models [START_REF] Inguimbert | Monte Carlo simulation of the electron range/energy relationship in the sub-keV energy domain[END_REF] [START_REF] Inguimbert | Extrapolated range expression for electrons down to ~10 eV[END_REF]. Fig. 8. Practical ranges for electrons in silicon. The data come from [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [3] and [START_REF] Kurniawan | Investigation of range-energy relationships for low-energy electron beams in silicon and gallium nitride[END_REF].

VI. IONIZING DOSE

The ionizing dose is the deposited energy by unit of mass of a target material subsequent to interactions with the electrons of the solid. The code OSMOSEE enables the calculation of dose profiles down to a few eV. Fig. 9 shows the ionizing doses profiles for 100 eV and 1 keV. As depicted in that figure, at 1 keV our MC simulation are in fairly good agreement with the MC simulation of Akkerman et al. [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF], and that of Valentin et al. [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF]. At 100 eV, there is a huge discrepancy with the results of Valentin et al. who use the Geant4-MicroElec library extension. This discrepancy may be explai-ned by the differences on the elastic and inelastic mean free paths, and on the energy cutoff at which the electrons come to rest in the solid. Fig. 9. Ionizing dose for electrons of energy E0=100 eV and E0=1 keV in silicon. The data come from [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] and [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF].

The probability of the elastic scattering is shown in Fig. 10 for the three codes. For an incident electron, the number of elastic scatterings is the result of a competition between the elastic and the inelastic mechanisms. Fig. 10 shows that the probability of the elastic scattering presents a huge discrepancy at low energy. As previously depicted on Fig. 1, the inelastic mean free path of the code OSMOSEE is much lower below 50 eV than those of Akkerman et al. and of Valentin et al. In the code OSMOSEE, the electrons tend to do more inelastic collisions at low energy. As a result, the electrons may go further in the solid and lose their energy faster. A discrepancy also exists for the elastic scattering. The code OSMOSEE uses the cross sections from the code ELSEPA of Salvat and coworkers [START_REF] Salvat | ELSEPA -Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules[END_REF] down to 10 eV. Valentin et al. employ the cross sections from the ICRU database [25] based on the code EL-SEPA but above 50 eV. Below 50 eV, the Mott's model (or partial waves) has been extrapolated down to 10 eV in the code OSMOSEE, whereas Akkerman et al. [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] and Valentin et al. [START_REF] Valentin | Geant4 physics processes for microdosimetry simulation: Very low energy electromagnetic models for electrons in silicon[END_REF] employ the cross sections for CS 2 from ab initio calculations by Bettega et al. [START_REF] Bettega | Electron collisions with CS2[END_REF]. Fig. 10. Probability of elastic scattering calculated from the elastic and inelastic mean free paths for electrons in silicon in [START_REF] Akkerman | Monte Carlo calculations of electron transport in silicon and related effects for energies of 0.02-200 keV[END_REF] [3] and in the code OS-MOSEE.

In the code OSMOSEE, the energy cutoff is of 𝑒𝜒 + 𝐸 𝐺 + Δ𝑉 with respect to the bottom of the valence band. This limit is equivalent to 𝑒𝜒 = 4.05 𝑒𝑉 in the vacuum. Fig. 11 presents the ionizing dose profiles calculated with the code OSMOSEE for electrons from 10 to 200 eV. Below 100 eV, as the electrons go slightly further into the solid, they mainly deposit their energy in the first few nanometers from the surface. As a result, the ionizing dose level increases near the surface. This behavior is in agreement with the practical range of electrons that shows a threshold below 100 eV (Fig. 8). At 200 eV, as the electrons go deeper in the solid, they deposit their energy further into the solid. As a result, the maximum level of the ionizing dose is located deeper. This behavior is also shown on Fig. 9

VII. CONCLUSION

The transport of electrons in silicon is investigated with a Monte Carlo code down to 10 eV. The MC code is based on the complex dielectric function theory and takes into account surface plasmon excitations. The code has been validated by comparisons with experimental measurements of electron energy loss spectra and electron emission yields performed in ultrahigh vacuum on an Ar-etched sample. Simulation results of practical ranges and ionization doses are in good agreement with the literature. The calculations of the ionizing dose profiles are given down to 10 eV. At low energy, the ionizing dose profiles show a correlation with the practical range. Below 100 eV, while the practical range of electrons stabilizes to a value of a few nanometers, the ionizing dose level increases near the surface. When increasing the energy of incidence, the electrons go further into the solid and the maximum ionizing dose level is located deeper.

Fig. 7 .

 7 Fig. 7. Definition of the practical range for electrons. The curve is shown for electrons of E0=800 eV in silicon.

  For the codes of Akkerman et al. and of Valentin et al., the energy cutoff is respectively of 5 eV and of 16.7 eV.

Fig. 11 .

 11 Fig. 11. Ionizing dose profiles for electrons of energy E0=10, 20, 50, 70, 100 and 200 eV.

Index terms -Electron emission yield, low energy electrons, Monte Carlo code, practical range.


est destinée au dépôt

Performing Arts and Governments in France Emmanuel Négrier

The aim of this paper rests on three aspects. The first is to assess the organization of the policies of support of performing arts in France. We shall examine strategies of 4 levels of government. The State historically plays a central role in cultural public support. Cities are also key actors for it. Departments occupy a peculiar and variable place. Regions are new poles, still minor, of the governmental support of performing arts. For all these actors, we shall analyse their mode of intervention, their level of financing, and the main choices they do according to areas (dance, theatre, music) and types of action. The second objective is to examine the kind of relationship between the main levels of public action. We shall show that the public action, in show, is mainly marked by multilevel partnerships. If the State is not predominant any more in terms of financial support, it remains crucial within the process of artistic recognition. The third objective is to analyse the two main changes that affect this different public policies today. The emergence of new territorial institutions, the Metropolitan Communities, affects the financial and space conditions of cultural democratization. The new practices of festivals allow to go beyond the traditional debate about the pertinence of such events in terms of innovation, employment, social and spatial access and territorial attractivity.

The performing arts have been one of the priority fields of the governmental action for several years. After a long period when its support depended very mainly on the central State, it depends today of multiple public financings and policies. The performing arts (601,5 million euros) account for 36% of the budget of the Ministry of Culture (2,8 billions € -a little less than 1% of the total budget of the State). The State intervention differs according to four key fields, in terms of modes of cultural financing. The first mode of intervention relates to the field which comes under its exclusive responsibility. They are in particular all the aspects of regulation of the sector. Here, it is the direct intervention that prevails. This type of intervention is, on the whole of the spectrum of action, relatively rare.

The second mode of intervention relates to the vast field of the Public establishments which are under supervision of the Ministry. Here, the nature of the intervention of the State is also very strong, but more indirect. These Public-owned establishments benefit from a financial autonomy and a proper legal identity, within the framework of a contract fixed by the State. This one names the managers of the Establishment, takes part in the Board of directors, finances the functioning of the structure and defines the priorities of its actions, in coherence with the priorities of the Ministry itself. The State has defined, for a few years, a contractual step aiming at influencing the policy of the establishments, by means of a "contract average objectives" which appeared not effective enough. Today, a new stage opens where the concept of performance appears. The "performance contracts", whose assessment is examined by the Parliament each year, are based on the evaluation of the Establishment's policy on the base of indicators concerning the public, the quality of cultural or artistic offers, financial standing… etc. This support and indirect management of Establishments under supervision represents a very significant part of the total of the State cultural funds. One traditionally distinguishes these Establishments according to their more or less great autonomy, between the Administrative Publicly-owned establishments (example: Center National of Cinematography) and the Industrial and Commercial Publicly-owned establishments (examples: National Theatres). This part of the ministerial financing globally represents 280 million euros.

The third mode of intervention relates to the subisidies the State brings to local authorities or structures. Here, the cultural policy of the Ministry meets the objectives, references and means of territorialized partners. The ministerial action rests on the labels which it defined (dramatic National Center ; National Choreographic center, National Scene, Scenes of Contemporary Music,… etc) to express its own requirements and orientations. It passed by an important volume of conventions of cultural development, since the Eighties. Those are the subject of open negotiations with the local authorities and the managers of a cultural or artistic project. The intervention of the State is thus much more indirect than in the preceding cases, even if its capacity of negotiation remains important, and that it is, directly, the government officials which take part in these negotiations and contracts.

The fourth mode of intervention relates to the subsidies the Ministry brings directly to the artists (individual or collective) on the base of an artistic project. Such a part concerns:

-public commands in visual arts, literature, music, dance, theatre, etc… ; -support to the theatre and choreographic companies, or to the musical sets for the production of works; -requests for protection of sites or patrimonial objects; -acquisitions of works for the public libraries… These choices are generally very sensitive, insofar as enter of the questions preferably aesthetic, of taste, even of artistic clientelism. In all these fields, the State aid passes systematically through committees of experts or commissions which are made up of personalities who don't generally belong to the Ministry: artists, persons in charge for cultural equipements, university scholars, art critics. It is thus where the intervention of the State is (virtually) closer to the private patronage, by the direct support to people, that it is surrounded by external councils. Admittedly, such a model cannot be compared with the Anglo-Saxon model of the deputy decision (At Arms' lenght) or of Councils of Arts system. In fact, these committees do not have, in theory, an advisory capacity. The formal decision remains in public administration's hands. But it would be sociologically wrong to consider that the government officials have an arbitrary capacity on the subsidies to artists and individual projects.

In the context of these two last functions (subsidies to public structures and assistances with the artistic teams), the State is minority in the public financing, at the sides of the local authorities.

To these financial supports, directly managed by the Ministry of Culture, it is necessary to add the indirect impact of the specific statute for the workers in the performing arts field (the "intermittents of spectacle" statute). This one is financed within the framework of the Social Security, as a mechanism of inter-professional solidarity [START_REF] Menger | Les intermittents du spectacle. Sociologie d'une exception[END_REF]. It is thus theoretically balanced by the receipts provided by the contributions of the employers and paid. But this sector is in a chronic situation of deficit. One can thus estimate that the assumption of responsibility of this deficit corresponds to an indirect source of public financing of the performing arts in France. The deficit, in 2005, reached 979 million euros, for the unemployment insurance of 100000 people (and thus much more than the single budget of the ministry for the culture for the performing arts).

The local authorities are traditional actors of the support for the performing arts, but their weight has been increasingly important in this field. At the beginning of the 20th century, the municipalities took part in the construction of spectacle places, primarily for the theatre and the opera. After the second world war, the movement of decentralization of theatre caused the implication of the cities in the assistance with the artistic teams. After a period marked by the determining influence of the State in the local choices, the political and administrative devolution (1983) diversified and amplified their role. Diversification is related to the emergence of other levels of intervention: the general councils (equivalent of the provincial level in the Latin countries) and the regional councils entered the system. They took part in the financing of the places of spectacle, the artistic teams and the cultural events (festivals). They are predominant today in these financings. For example, here the distribution of the financings of the festivals of music and dance, on the basis of our investigation in 2006 (79 festivals scrutinized): As table n°2 shows, the local authorities are from now largely dominant, compared to the State (nearly 2 billion euros against 1,6 billion, including the social deficit related to the statute of "intermittent of spectacle"). The distribution in a specific area (2,5 million inhabitants) shows in more details this public expenditure. The ministry for the Culture is the level which concerns more the professional actors. It however supports the structures of sensitizing and the practices amateurs with height of 1,6 million euros (11% of its budget for the performing arts), thus a little less than the 5 General Councils together (2,1 million). The financing of the festivals is the smallest expenditure (6%). The direct subsidies to the professional teams account for 17% of the total budget. The greatest part goes to the financing of the places of spectacle (equipements). In a context of increase in the cultural expenditure, the Regional Council has priorities that are distinct from those of the State. Its financing of the festivals (24%) is twice more important than that of the State. In the same way, the structures of sensitizing are helped in proportion: 18,6% against 11% for the State. Reciprocally, the regional Council is less present on the artistic teams (12,4% of her budget against 17%), and on the places or equipments (44% of its budget against 66% of that of the ministry). These differences are less contradictions than complementarities.

The Department Councils privilege the financing of the places and the festivals (with 32% for each one). The financing of the structures of sensitizing (such as the ADDM departmental associations for the development of music) and of the amateurs' practices comes second-rate (with 22%). In third rank, we find the financing of the professional or semi-professional artistic teams (14%). But the departmental authorities have different strategies, according to their urban or rural identity, and of their perception, more or less dynamic, of the stakes of the performing arts. The cities have a more convergent behavior than that of the General Councils. It must take account of the rise of the intercommunalities, which we will comment on further, and who distorts a little the analysis isolated from their strategies as regards performing arts. The weight of the structures of sensitizing and practical amateurs is relatively weak. It is the support to the places which concentrates the greatest part, and by far, of the expenditure of the cities (73% on average). For the Co-operation Districts, one sees that the greatest part is also the support to places of spectacle. It is logical, since one of the objectives of these Districts is to manage, instead of the cities, part of these equipments. On the other hand, these new authorities do not intervene in the financing of the practices amateurs.

This multilevel distribution of the support to the performing arts, within a single region, is representative of French reality, except for one aspect : the role that the great Parisian institutions play, strongly financed by the ministry for the Culture at the central level. The diversity of financing testifies to the existence of different strategies. But it develops within a framework of very usual partnerships. The support of the State for the teams and the places of spectacle is very often managed through labels (national Centers dramatic and choreographic, national scenes, officially agreed teams artistic) which pass by the support of the local authorities. The cross financings are thus almost systematic when a certain level of artistic excellence is reached. On the other hand, the support for the amateurs' practices and the festivals remains more fragmented, and the partnership between the three levels of local authority is less frequent. Lastly, the distribution of the financings, in space terms, remains a major stake: certain cities occupy a considerable place, by their cultural dynamism, in the distribution of performing arts financings. For example, Montpellier (230 000 inhabitants -10% of the population of the Languedoc-Roussillon region) represents nearly 50% of the total of the performing arts public funds.

Promising perspectives

We wish to stress two dimensions. The first relates to the rescalings of certain urban policies as regards performing arts. The second relates to the new role of the festivals in the support for them.

Stake of territorial rescaling

The emergence of the Co-operation Districts is recent. It is related to the 1999 reform, which reinforced the incentives of the State for the creation of institutions of co-operation between municipalities (Négrier 2005). The cultural field was considered, at the beginning, as less strategic than the sectors of the economic action, housing, the social or transport policies. The implementation of this law was a success. It led to the creation of 186 Urban Cooperation Districts (and 2500 Rural Co-operation Districts). Especially, the culture has been unexpectedly considered as a strategic sector by much of these new institutions and their local actors. 80% of them state to want to intervene in the cultural field. 60% intervene already in this sector. The performing arts are the third field of intervention of these districts in the cultural domain. That results in the transfer of management, from the municipal level toward the intercommunal level [START_REF] Faure | La politique culturelle des agglomérations[END_REF]. The interest of this new phenomenon lies in the three following aspects:

-the competence of the Co-operation Districts makes it possible to improve the financing of the equipment of spectacle, because the transfers of management are accompanied by added tax supports on behalf of the State. For example, in Amiens, these transfers had as a consequence, in two years, an increase of 20% of the cultural financings on the territory of co-operation. Generally, the Co-operation Districts which are very dynamic in the cultural field enriched the cultural offer on their territory.

-the transfer of responsibility also allows to develop the presence of the performing arts on a territory vaster than that, traditional, of the central cities. In the map of the equipment of spectacle, one sees that the majority of them are located today in the old centers of the towns. However the demographic development occurs today in a massive way in the periphery of the cities. The transfer of management makes it possible to put in coherence the structure of the cultural financing and the dynamic demographic ones. For that purpose, certain institutions of co-operation develop strategic plans, which aim to improve the geographical presence of the places of spectacles.

-lastly, these co-operative policies aim to reinforce cultural democratization, by improving the access to the spectacle by the population. That passes through the creation of new spectacle equipements, in urban sectors where they missed. That also passes through the access improvement of the populations to the existing places. Certain Co-operation Districts thus modified the obligations of their professionals, so that they decentralize, on the peripheral territories, part of their spectacles. Other institutions are implementing initiatives of free transport to reach the spectacles. In any case, a co-operative policy has a direct effect on the social access: it prohibits the discrimination of the tariffs according to the places of leaving. This is very important for the access to the spectacles. But it is even more important for the structures of artistic teaching (academies of theatre, dance and music). This movement of transfer of responsibility is, still today, rather fragmented. Fourteen cooperation districts spend more than 10 million euros for the culture, while thirteen spend less than 1 million euros. There are resistances to these transfers, on behalf of the local councillors, cultural actors and certain managers of artistic places. It is a traditional resistance against change, but also the fear of a concentration of the capacities to the profit of one single institution or politician. However, one can consider that these transfers will make it possible to concretize new objectives of democratization of the access to the culture, and with the performing arts in particular.

Festivals and the support for the Performing Arts

France is a particular case in the debate on festivals. Its tradition is less old than that of England, but the State, as from the Eighties, encouraged their creation. The local authorities, as seen below, strongly took part in this rise. Today, the tendency is to a certain criticism against the "festival multiplication". The ministry for the Culture would wish that the local authorities take part rather in the creation of permanent places, and consider that the festivals are only transitory events, which divert the public money from more legitimate targets (in terms of public, of support for employment, of permanent programming). A recent study, on the festivals of music and dance, made it possible to show that these criticisms are not valid for all the festivals, and clarifies on the contrary the interest of the festivals in various dimensions. First of all, the festivals make it possible to attract, more than the other actors of the spectacle, the private financing. The patronage and sponsorship account for on average 15% of the resources of the festivals of music. Then, the level of subsidy (approximately 50%) corresponds to that of the artistic expenditure. This means that the public money is a direct support for artistic and cultural employment. Thirdly, these festivals play an important part in the support to contemporary creation, through public commands of new masterpieces, the programming of music or contemporary dance, or the coproduction between festivals. Fourthly, the studied festivals play, more and more, a complementarity role between the moment of the specific event and the annual season of the artistic places. The partnership between places and festivals develops and the teaching actions make it possible to associate the local public (and specifically young people) to these demonstrations. The festivals are a crucial element for cultural and artistic employment: 234 artistic employments and 62 cultural employments per festival on average. Lastly, the festivals have an impact on their territory. One estimates at 122.000 euros on average the direct repercussions of a festival (that is to say 23% of their expenditure) upon its territory. These reports makes it possible to relativize frontal criticisms with regard to the festivals in general, by revealing "good practices" as regards innovation, employment, economic valorization and territorial attractivity. They allow today the development of new institutional practices, such as conventions between public partners to support the festivals whose strategies are in coherence with these objectives. The stakes are of three types: the stabilization of the resources; improvement of the social and space access; the territorial attractivity.

Table 1 .

 1 Financial partnership of French Festivals (2005)

Music Festivals (69) Danse Festivals (10)

	Total partnership	26 111 969 €	9 071 772 €
	Average	378 434 €	907 177 €
	Municipalities	14%	27%
	Cooperation districts	7%	20%
	Departments	26%	14%
	Regions	21%	9%
	Ministry Culture	6%	12%
	Sponsorship	15%	10%
	Others	11%	8%
	Total	100%	100%
	Source : E.Négrier, M.T.Jourda (2007)

Table 2 .

 2 Performing arts and sub-national authorities (in millions €)

	Level	Ministry of	Financial impact of	Municipalities	Department	Regions	Total
		Culture	the worker's special		s
			status
	Total	601	979	1378	498	115	3571
	*including cultural subsidies to amateurs

Table 3 .

 3 Volumes and Types of Public Support to Performing Arts inLanguedoc-Roussillon (2004)

	Public Authority	Total amount	Sensitization	Professional and	Festivals	Performing
			and amateur's	semi-		arts buildings
			practices	professional
				groups
	Ministry of	14,2	1,6	2,4	0,8	9,4
	Culture
	Regional Council	6,5	1,2	0,8	1,6	2 ,9
	Department	10,4	2,5	1,3	3,1	3,5
	Councils
	6 main	9,0	0,5	0,6	1,3	6,6
	Municipalities
	4 Cooperation	34,2	0	5,8	3,2	25,2
	Districts
	Total panel	74,3	5,8	10,9	10,0	47,6
	Source : Négrier dir. 2007