Gianni Franchi

Jesús Angulo

COMPARATIVE STUDY ON MORPHOLOGICAL PRINCIPAL COMPONENT ANALYSIS OF HYPERSPECTRAL IMAGES

Keywords: Statistical Learning, reduction of dimension, Hyperspectral images, Morphology

This paper deals with a problem of reducing the dimension of hyperspectral images using the principal component analysis. Since hyperspectral images are always reduced before any process, we choose to do this reduction by adding spatial information that can be useful then for classification process; to do it we choose to project our data in new spaces thanks mathematical morphology.

INTRODUCTION

Conventionally, hyperspectral images which allow us to reconstruct the spectral profiles of objects imaged by the acquisition of several tens or several hundred of narrow spectral bands are often reduced in dimension before any treatment. Many hyperspectral reduction methods are linear and do not care of the multiple sources of nonlinearity presented in [START_REF] Guilfoyle | Further investigations into the use of linear and nonlinear mixing models for hyperspectral image analysis[END_REF]. However lately, non linear reduction techniques have been developed, and some of them have been used in hyperspectral images [START_REF] Bachmann | Exploiting manifold geometry in hyperspectral imagery[END_REF]. However, most of these techniques present disadvantages [START_REF] Van Der Maaten | Dimensionality reduction: A comparative review[END_REF] in comparison to the principal component analysis that is why we choose to work with the PCA and to add spatial information, which are nonlinear. Since mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures, we choose to explore this kind of processing like [START_REF] Fauvel | Spectral and spatial classification of hyperspectral data using svms and morphological profiles[END_REF][START_REF] Pesaresi | A new approach for the morphological segmentation of high-resolution satellite imagery[END_REF], however in our case we use mathematical morphology to improve the reduction of the dimension.

NOTATIONS AND NOTIONS OF MATHEMATICAL MORPHOLOGY

Morphological Decomposition

In this section we are going to introduce the notation that would be used on the rest of this paper. Let E be a subset of the discrete space Z 2 , which represents the support space of a 2D image and F ⊆ R D be a set of pixels values in dimension D. Hence, in our case the value of a pixel x∈ E is represented by a vector v ∈ F of dimension D. Additionally, we will write higher order tensors by a calligraphic uppercase letters (I, S, . . .). Moreover if I ∈ R n1×n2×n3 , for all i ∈ [1, n 3 ] I :,:,i represents a matrix of size n 1 × n 2 where the third component is equal to i. We can associate a tensor to the hyperspectral image, we called this tensor F ∈ R n1×n2×D .

Let f be a grey scale image which can be represented by a function. Area openings (resp. area closings) are morphological filters that remove from an image the bright (resp. dark) connected components having a surface area smaller than the

parameters l ∈ N [6] : γ a s l (f ) = i {γB i (f )|Bi is connected and card(Bi) = s l } and ϕ a s l (f ) = i {ϕB i (f )|Bi is connected and card(Bi) = s l }
, where γ B (f ) and ϕ B (f ) represent respectively the morphological flat opening and closing according to structuring element B .

Let us consider {γ a s l }, l = 1...S and {ϕ a s l }, l = 1...S, two families indexed one of openings and one of closing. Typically, the index l is associated to the size of the structuring element or in our case to the surface area. The notion of morphological decomposition is related to granulocytic axiomatic [START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF]. Namely, based on [START_REF] Velasco-Forero | Classification of hyperspectral images by tensor modeling and additive morphological decomposition[END_REF] we have :

f = 1 2   S l=1 (γ a s l-1 (f ) -γ a s l (f )) - S l=1 (ϕ a s l (f ) -ϕ a s l-1 (f )) + γ S (f ) + ϕ S (f )  
Therefore we have a decomposition of the initial image into S scales, together with the last opening and closing. We remark that residue (γ a s l-1 (f )-γ a s l (f )) represents bright details between levels s l and s l-1 . Identically (ϕ a s l (f )ϕ a s l-1 (f )) stands for dark details between levels s l and s l-1 . We can now calculate a decomposition of each band of the hyperspectrale cube. However there are some issues to be taken into account : by decomposing an image into scales we have now to deal with an object of bigger dimensionality, and also the decomposition may not be optimal: it depends on the discretization of the S scales, the size of the pixel scales, etc... Then in next section we are going to introduce the pattern spectrum and how it can be used to deal with the problem of discretization.

Pattern Spectrum (PS)

The pattern spectrum provides the probability density function (pdf) of the granulometry. The area normalized pattern spectrum of f is at size s l : P S a (f, l) =

Mes(γ a s l (f ))-Mes(γ a s l+1 (f )) Mes(f ) , P S a (f, -l) = Mes(ϕ a s l+1 (f ))-Mes(ϕ a s l (f )) Mes(f )
, where "Mes" represents the integral of the image. Based on the analogy between the pdf and the PS, we can calculate the cumulative distribution function of the spectrum for the opening part and also one for the closing part. Afterwards we sample these cumulative distribution functions where the number of sample is fixed and is equal to S, under the constrain that the sampled cumulative distribution function must be as much as possible similar to the original function. Since in probability, the cumulative distribution function is a way to characterised a distribution such as the pdf then thanks to this property, we can be sure that our discretization represents the original image.

Distance function

Let us consider a binary image b f , and X a close set of this image, the distance function corresponding to this close set X gives to each point x ∈ X a real number that depends on the position of x with respect to X such as : d(x, X) = min{ρ(x, y) : y ∈ X c }, where ρ(x, y) is the Euclidean distance between x and y, and where X c is the complemented of set X. Now let us consider a gray-scale image f ,and {X s (f )} s its upper level sets. Then, according to [START_REF] Ilya | Distance transforms for realvalued functions[END_REF], the gray-scale distance transform of f is :

d(x, f ) = 1 255 × b s=a d(x, X s (f ))
, where a = min{f (x), x ∈ E}, and b = max{f (x), x ∈ E}, where E is the index of the position of the pixel of f .

MORPHOLOGICAL PRINCIPAL COMPONENT ANALYSIS (MPCA)

3.1. Classical PCA Principal Component Analysis (PCA) starts with a set vector v i ∈ R D , 1 ≤ i ≤ n where n represents the number of vectors, in our case it corresponds to the number of image pixels, i.e., n = n 1 n 2 . The goal of the PCA is to reduce the dimension of this vector space, namely

F = {v i } n i=1 -→ F ′ = {v ′ i } n i=1 , with v ′ i ∈ R d , where d ≪ D. In our case, F ∈ M n,D (R) represents the hyperspectral image F , where each column F k ∈ R n , 1 ≤ k ≤ D corresponds
to a vectorized spectral band. PCA maximizes the objective function : L(w j , λ) = w T j V w jλ(w T j w j -1), where λ ∈ R and V = n -1 (F T F ), V ∈ M D,D (R), is the covariance of F . This reduction can be done by projecting the data on d eigenvectors of V corresponding to the d higher eigenvalues of V

MPCA and its variants

The fundamental idea of Morphological Principal Component Analysis (MPCA) consists in replacing the covariance matrix V of PCA, which represents the statistical interaction of spectral bands, by a covariance matrix V Morpho computed from a morphological representation of the bands. Therefore, mathematical morphology is fully integrated in the dimensionality reduction problem by standard SVD computation to solve V Morpho w j = λ j w j . The corresponding principal components w j provides the projection space for the hyperspectral image F .

Scale-space Decomposition MPCA. Using the surface areabased nonlinear scale-space discussed in previous section, the grey-scale image of each spectral band F :,:,k is decomposed into residues of area openings and area closings according to the discretization into S scales for each operator, i.e., r l (F :,:,k ) = γ a s l-1 (F :,:,k )γ a s l (F :,:,k ) and r -l (F :,:,k ) = ϕ a s l (F :,:,k )ϕ a s l-1 (F :,:,k ), 1 ≤ l ≤ S. Thus we have increased the dimensionality of the initial dataset from a tensor (n 1 , n 2 , D) to a tensor (n 1 , n 2 , D, 2S + 1). As discussed in [START_REF] Velasco-Forero | Classification of hyperspectral images by tensor modeling and additive morphological decomposition[END_REF], this tensor can be reduced using high order-SVD techniques. We propose here to simply compute a covariance matrix as the sum of the covariance matrices from the various scales. More precisely, we introduce

V Morpho-1 ∈ M D,D (R) with : V Morpho-1 = S l=1 (V (l)) + S l=1 (V (-l))
where the covariance matrices at each scale l is obtained as V (l) k,k ′ = Covar (r l (F :,:,k ), r l (F :,:,k ′ )), 1 ≤ k, k ′ ≤ D. We note that involves an assumption of independence of the various scales. We remark also that this technique is different of classical approaches of differential profiles as [10, ?] where all the images of the morphological decomposition are used as columns to compute a covariance matrix in M 2S+1,2S+1 (R).

Pattern Spectrum MPCA. In fact, we can consider a much compact representation of the morphological information associated to area-based nonlinear scale-space of each spectral band. It simple involves to consider the area-based pattern spectrum of spectral bands as the variable to be used to find statistical redundancy on the data. In other words, the corresponding covariance matrix V Morpho-2 ∈ M D,D (R) is defined as : V Morpho-2 k,k ′ = Covar (P S a (F :,:,k , l), P S a (F :,:,k ′ , l)) , with 1 ≤ k, k ′ ≤ D and where P S a (F :,:,k , l), -S ≤ l ≤ S, is the area-based pattern spectrum obtained by area-openings and area-closings. We note that the pattern spectrum can be seen a size a pdf of image structures and consequently the MPCA associated to it explores intrinsic dimensionality of sets of distributions instead of sets of vectors.

Distance Function MPCA. Classical PCA for hyperspectral images is based on exploring covariances between spectral intensities. The previous MPCA involves to change the covariance to a morphological scale-space representation of the images. An alternative is founded on transforming each spectral band from an intensity based map to a metric based map where at each pixel the value is associated to both the initial intensity and the spatial relationships between the image structures. This objective can be achieved using the Molchanov gray-scale distance function for each spectral band dist(F :,:,k ). The new covariance matrix V Morpho-3 ∈ M D,D (R) is now defined as:

V Morpho-3 k,k ′ = Covar (dist(F :,:,k ), dist(F :,:,k ′ )) , with 1 ≤ k, k ′ ≤ D.
Spatial/Spectral MPCA. As we have discussed, V Morpho-2 represents a compact morphological representation of the image, however the spectral intensity information is also important for dimensionality reduction. Let us write X and Y two random variables such as X represents the spectral information of the data, and Y the morphological/spatial information. To come with a new variant of MPCA we assume the independence of the spectral and spatial information so of X and Y . This imply that var ((1β) Pr(X) + β Pr(Y )) = (1β) 2 var Pr(X) + β 2 var Pr(Y ), with β ∈ [0, 1]. More concretely, that means that we can build another covariance matrix V Morpho-4 that would represent the spectral and spatial information without increasing the dimensionality by :

V Morpho-4 β = (1 -β) 2 V + β 2 V Morpho-2
, where obviously V k,k ′ = Covar (F :,:,k , F :,:,k ′ ) and β stands for a regularization term that balances the spatial over the spectral information.

MPCA APPLIED TO HYPERSPECTRAL IMAGES

4.1. Criteria to evaluate PCA vs. MPCA

We can now use PCA and the four variant of MPCA to dimensionality reduction of hyperspectral images. In order to evaluate the interest for such purpose, it is necessary to establish quantitative criteria that should be assessed. We want to show the improvement of classical PCA with respect to the following criteria. Criterion 1. (C1) The reconstructed hyperspectral image F using the first d principal components should be regularized in order to be more spatially/spectrally homogeneous; Criterion 2. (C2) Hyperspectral image F should preserve the edges of the main image structures; Criterion 3. (C3) Separability of spectral classes should be improved in the dimensionality reduced space. That involves in particular a better pixel classification.

In order to assess C2, we compute for initial image F the gradient of each band k, denoted ∇F k , and compare it to the gradient of the reconstructed image F , by measuring the Euclidean distance. In order to have an estimator of the error, we integrate for all the bands, i.e., Error Grad =

D k=1 n1,n2 i,j=1 | ∇F i,j,k -∇ F i,j,k | 2 .
To assess C1, which involves image homogeneity, we propose an approach based on a partition of the image into regions. First, working on the d eigenvectors, we compute the image partition associated to the α-flat zones, the partition is denoted π α . We remind that two neighboring pixels belong to the same α-flat zones if their distance is lower or equal to α [START_REF] Gueguen | Local mutual information for dissimilarity-based image segmentation[END_REF]. In our case, the pixel distance corresponds to the Euclidean distance of vector values in the eigenimages and the choice of α is done in order to have a number C of α-flat zones similar for all the approaches of PCA and MPCA to be compared. By fixing the number of zones in the partition, we guarantee that the difference between a partition and another one depends exclusively on the homogeneity of the image.

Then, using the partition π α , we compute the spectral mean value of pixels from original image F in each zone, in order to produce a simplified hyperspectral image denoted F πα . Finally, we assess how pixels of the original image from each α-flat zone are far from their mean by computing the following error Error Homg = D k=1 n1,n2 i,j=1 |F i,j,k -F πα i,j,k | 2 . Finally, C3 is related to supervised classification of hyperspectral image. We have considered SVM with a linear kernel as learning technique, where the classifier is validated using 5-fold cross validation. Sensitivity and specificity of classification are then computed.

Evaluation of Pavia hyperspectral image

The assessment of the performance of PC and MPCA was carried out using the well known University of Pavia hyperspectral image, which has dimensions n 1 = 1610 × n 2 = 340 pixels, D = 103 spectral bands and its geometrical resolution is of 1.3 m. We have applied classical PCA and the different variants of MPCA to Pavia image. Fig. 4.2 shows the first three eigenimages, visualized as a RGB false color. We note that the PS MPCA requires d = 5 to represent 90% of the variance whereas the other approaches only imposes projected. We have shown that the best results results are obtained when we combine spatial and spectral information (V Morpho-3 , V Morpho-4 β , β = 0.2).

Fig. 1 .

 1 Fig.1. On the left the Pattern Spectrum with opening of a grey scale image, on the right in blue its corresponding cumulative distribution function of the spectrum, and in red its approximation with S = 8.

Fig. 2 .

 2 Fig. 2. (a) band 1 of Pavia, (b) PS of band 1 of Pavia (c)distance function band 1 of Pavia, idem for (d), (e) and (f) but with band 100.

Fig. 3 .d = 3 .

 33 Fig. 3. RGB false color visualization of first three eigenimages from Pavia image: (a) spectral PCA, (b) scaledecomposition MPCA, (c) pattern spectrum MPCA, (d) distance function MPCA.

Table 2 .

 2 We have introduced in the paper the notion of MPCA which has been declined into four different approaches. MPCA allows to deal with a spatial/spectral representation of the image based on mathematical morphology tools for SVD-based dimensionality reduction. It is important to note that it involves only to change the covariance matrix used in the SVD to obtain the eigenvectors where the spectral bands are then Sensitivity Specificity ±σ(10 -5 ) ±σ(10 -2 ) V 0.99 ± 1.03 0.44 ± 3.44 V Morpho-1 0.99 ± 1.03 0.45 ± 3.39 V Morpho-2 0.99 ± 1.03 0.56 ± 3.38 V Morpho-3 0.99 ± 0.93 0.76 ± 3.35 V Morpho-4 β , β = 0.8 0.99 ± 0.93 0.39 ± 3.35 V Morpho-4 β , β = 0.2 0.99 ± 0.93 0.78 ± 3.35 V Morpho-4 β , β = 0.5 0.99 ± 0.93 0.47 ± 3.35 Comparison of hyperspectral supervised classification on principal component space from Pavia image, linear kernel SVM and 5-fold cross validation.

Table 1 .

 1 two eigenvectors is how PCA and the scale-space decomposition MPCA cluster the bands linearly, since bands close in the projection are also near in the spectral domain, whereas the patter spectrum MPCA and distance function MPCA tends to cluster spectral bands which are not necessary spectrally contiguous. Therefore the nonlinear embedding from V Morpho-2 and V Morpho-3 is clearly illustrated. Obviously, a similar behavior is observed for V Morpho-4 β . From a quantitative viewpoint, one can see in Table1that globally MPCA produces a more homogenous regularization of the image than classical PCA, especially the distance function MPCA and Spatial/Spectral MPCA with an appropriate β = 0.2, which give the lowest values of Error Homg . Finally, Table2summarizes the results of supervised classification of Pavia. We note the sensitivity is excellent for all the methods, however we can see how MPCA improves the results on the specificity. Once again V Morpho-3 and V Morpho-4 β=0.2 are significantly better than the others variants. Comparison of principal component analysis from Pavia image using results of criteria C1 and C2. The values have normalized to worst case, which gives 100.

		V	V Morpho-1	V Morpho-2	V Morpho-3
	ErrorHomg	100	100		95.9	79.3
	Error Grad	55.41	54.88		55.25	100
		V Morpho-4 β	V Morpho-4 β	V Morpho-4 β
		β = 0.8	β = 0.2	β = 0.5
	ErrorHomg	93.2		83.9		88.3
	Error Grad	38.9		98.5		78,5

Acknowledgement

The authors would like to thank Prof. P. Gamba, University of Pavia, for providing the ROSIS data set


Jeannot Latts

WHEN NON SOCIAL PUBLIC SERVICES TAKE CARE

Ecole nationale des ponts et chaussées

INTRODUCTION

A few years ago the company in charge of the Paris underground set-off a communication campaign with the slogan : "the metro, the second car" targeting the upper and middle classes inorder to convince them that one could own a car and at the same time use public transport. Today the same public company has put in place a project called the "coup de pouce" (with a little help) which aims at facilitating the reinsertion of the homeless who spend their day in the tube stations. Furthermore the company has organised socioeducational activities for the suburban youth inorder to avoid conflictual contacts with bus conductors. This change of tone can be also seen in most administrations and public services. The rise of poverty has put the administration and the public services in a paradoxal situation, the more society becomes twofold the less the internal division between social agencies and the others is pertinent.

The role of the post office is to transmit letters or to assume banking, a transport company to offer commutation, a hospital to take care of sick people and maintenance services to clean public areas. Given their defined tasks these agencies should be distinguished from services such as shelters for the homeless or educational agencies for young delinquants, which are specifically oriented towards social problems. Such an opposition is only relative (we could think of hospitals which were originally charity institutions for the poor) and the problem of public non-social services dealing with social problems is not new. The evolution of the economic situation however obliges a formalisation of the question which until now had not been treated directly. To put it differently these agencies have to learn how to produce social responsiveness of non social services.

The problem arose explicitly in two fields of action for the French administration. The first was linked to an experimentation in neighbourhood public services [START_REF] Picard | L'amélioration du service public dans les quartiers[END_REF]) and the second in an evaluation initiated by President of the French Republic on the theme "the reception of under-privileged persons by the public service" [START_REF] Jacques | Les services publics et les populations défavorisées, évaluation de la politique d'accueil[END_REF]). The first project was set-up after several agents from different public services (post offices, schools) were victims of aggressions in a suburban town outside Paris. The experimental step was to assemble agents which dealt directly with the public in different services of the neighbourhood inorder to ameliorate their functioning. The group started off with hot questions such as stress when facing aggression and dealing with a new re-organization of the services in general. The second project started in a global framework of modernisation of the administration called "the renewal of public services". A program of inquiries and hearings lead to an evaluation report which specifically brought into light the relatively recent caracter of this preoccupation and the absence of a general policy. The present article is based on elements gathered during the experimentation and the final evaluation report.

When public services engage in social affairs, management methods have to simultaneously integrate objectives of a different nature, this is in particular crucial in the established relationship between agents and clients. Moreover different economic logics are to co-exist. In the social domain, redistribution predominates whereas the question of balancing income and expenditure is essential for the public services even when subsidy mecanisms are in place. However before dealing with the above-mentioned problems even the foundation which justify public action, is in itself put under question as is the definition of responsiveness.

WHICH ADAPTATION?

In France, when we speak of social adaptation of non-social public services we are confronted with three distinct traditions defining public collectivities' intervention. First; the tradition of the "service public", second; social work and third; community action.

At the beginning of the century as the public sector took on more service rendering functions such as transport, hygiene etc.,the definition of the Administration as a service-giving body was put forward as a question. This was primarily a legal problem. French law has specific laws dealing with administrative action, and its annex activities, whether they were undertaken by public agencies or not, depended on either administrative or private law. Thus public agencies' treatment and its legal derogatory treatment had to be justified. That is why the doctrine of "service public" was elaborated to somehow define the proper tasks of such services. This doctrine covers three principles. "Equality of access"; including especially accessibility in rural areas; "mutability"; i.e. adaptation to changing needs, and "continuity" that is if we affirm that the service rendered is of public utility it has to be maintained in a constant manner in time (Chevallier (1987)). These elements which made up the doctrine at the beginning of the century are now in the process of evolving especially due to the confrontation with a European policy of regulating competition. In the chart of public services proposed by France to the European Commission, two supplementary principles appear; "universal service", in other words minimal service guaranteed for all the population, and "client participation" in defining assignments in general and more specifically organizational modalities of public services' assignments. We wonder if these principles are still respected in certain underprivileged neighbourhoods and if other models should not be used.

The principles of social work are not as clearly defined as those relating to the public service. In the first case, they lie in a framework of legal precedent; in the second one they are the unwritten principles of professional action shared by agents and organizations which practice them. Moreover these create strong tensions linked to the questioning of the origins of the function. In fact the activity of social workers which is at the heart of the plan of action, originates from the patronage activities led by women of the bourgeois milieu among working-class families but also superintendants who controlled workers in factories. The model of an educational function set in a moralistic global approach to a person in a confidential encounter has been revitalized since the 1950's when a psychological approach of "case work" was introduced [START_REF] Verdes-Leroux | Le travail social[END_REF]).

The community model (Dunham (1963)), is afterall more original in the French tradition. Nonetheless, it is the same type of model which predominated operations called "Social development in neighbourhood" for the renewal of life in suburban counsel housing projects. The model is to be placed in a more recent and less visible tradition which started in the 1950's. It privileges closeby communities and collective undertaking of services or their distribution in the neighbourhood. Jacques [START_REF] Ion | Le travail social à l'épreuve du territoire[END_REF] has shown that the professional model put in place in the "Social development of the neighbourhood" project in fact resulted in the exclusion of social workers who considered it as questioning their professional role. The collective treatment was a substitute for an individual person to person, private relationship between the social workers and their clients.

The term "responsiveness" has no direct equivalent in French. Even more in the models proposed by the OECD such as "compréhensibilité", "accessibilité", "adaptation" and "participation" we only partially find the same objectives as in the original terms. In each of these models certain aspects of these objectives are inherent in their definition while other elements could find their place through field adaptation. In return the question of "compréhensibilité" as well as user "participation' have only just recently found their place in the reference model of the public collectivity and not yet in the user's. The social work model gives an essential status to comprehensibility and accessibility, social workers even make their way into families in order to "create rights" by explaining to people their own rights, and adapt through the conforming of particular social categories. Individual reception of needs overpowers the question of individual user hearings. However contrary to the two preceding models, community action, at least in theory, leaves greater space for user participation while the others are entwined in prisms of proximity and inter-acquaintance of individuals in the same neighbourhood.

The amelioration of public services confronted with growing poverty tend to mobilise one or the other of the models which have a historical basis in the country. What is involved here is a range of solutions, rather than simple rhetoric, to allow resolving of the same problem. The analysis of innovating experiences carried out spontaneously by different services have shown the following : in most cases, the end solution consists of creating a space of action following the patterns of social work in its traditional or community form, however integration in everyday action, as an answer to the needs of pauperized populations, is still to be invented.

ADAPTING PUBLIC SERVICES

Although there is no organised policy as regards the reception of the poor by public services, there are nonetheless numerous experiences which could allow an evaluation of the situation. These experiences vary in scope and in most cases lack in coordination, however similar solution patterns can be observed. In terms of social work, we can first of all, try to adapt to the specific inquiries of the populations in difficulty by treating them separately.

Gate keeper

A distinction should be made between cases involving social treatment and those involving ordinary services. An agent in charge of client-orientation, evaluates the client's need(s). For example the presence of a social worker to deal with "social emergency" cases in hospital emergency units.

Interpreter

This decision is an answer to specific problems created by language barriers with foreign populations. The presence of an interpreter is very common in post offices situated in neighborhoods with a high percentage of a non-French speaking population.

Special counters per category of clients

The model can be generalized under the form of a special counter for a specific category of clients in difficulty (for example those earning the minimum salary : RMI). In this case the reception service not only takes care of communicating with different public and social services, but also coordinates the contacts between these services.

Follow up

In this model, the generalist public service no longer interferes with the treatment of the inquiry. An exterior agent helps the inquirers reach the public or administrative service corresponding to their needs. This function has always been undertaken by social workers. These, in particular, help the individuals file different administrative papers and documents. The novelty in this area is the increasing role assumed by charity associations. The follow up can go as far as upholding a claim for the right to reach a specific service.

These different experiences have contributed in bringing back the question to one of the classic categories of social work. We can find others that are closer to the community model.

The Intermediary

We should move from the idea that the difficulty in reaching public services is unequal for the persons in the same neighbourhood. For example, some parents never attend parent-teacher meetings to discuss their children's schooling. Other parents with whom contact is easier and more accesible assume the responsibility of a go-between and exchange information between both groups.

The patrolman

Policing along with the "patrol police" is a more developed approach in Anglo-Saxon countries. The model can be generalized, and we may re-consider the complex role that building porters for example, can play in guarding common spaces, or we can even give the postman the task of providing information on different elements about deterioration of the public spaces, while distributing the mail.

The citizens' house

Behind this term lies the project of installing a unique counter in suburban neighborhoods. This space can provide the possibility of bringing and making more accessible and visible the generalist services for the population and allowing better coordination. In practice these services have gained a growing social function in the above-mentionned areas.

Co-production

The active participation of the inhabitants along with the service activities is also presented as a solution to the problems encountered. In France the "régies de quartiers", ad-hoc groups of individuals in a neighbourhood, to contribute to the maintainance of housing and public spaces, have developed increasingly.

These initiatives are praiseworthy and are satisfactory for the clients. But it is yet to be proven if they can really solve the problem of social adaptation of non social public services.

The following example enables us to discover the limits of opening a specialized reception desk with a social vocation in a public service. A young woman of north African origins was recruited as an interpreter in a post office. Not only persons of north African descent where sent to her for language problems, but so were the Turkish and other diverse African nationals. Thus a de-facto creation of a sub-service dealing with all "problematic" inquiries. As a result, the creation of the above mentioned reception enabled other agents of the service to divert all the difficult cases, therefore avoiding global handling of the problems by the service. The most interesting aspect of this experience is that the young woman was able to assist the Turks and black Africans in resolving their problems. The language was not an unsurmountable barrier, and with some patience each agent would have been able to manage such difficulties himself. Behind the image of an interpreter lies the presupposition that the fact of being poor relates to a series of handicaps, and thus demanding a special treatment, such as not mastering the language of the country. A similar presupposition is made in the case of the "gate-keeper" and "follow up" models. Yet, we have discovered that it is difficult to define specific know-how for social work. While social work is trying to liberate itself from its original function of education and moralization, social workers can be defined as people capable of adapting general rules to particular cases. (Ion, Tricart (1992)). Thus, public service officials think they have resolved the problems by creating such exits toward social workers, while the latter's main preoccupation is to direct the persons they deal with back into the normal circuits.

The Community approach can be less criticized in this perspective since it does not assume an exclusive social "profession". But on the contrary we can seriously question the relevance of the application of the two basic principles of the Community model; proximity and the undertaking of non social public services by the members of the community. Reducing the question of accessibility to that of proximity does not respond to the expectations of part of the population of suburban neighborhoods. It has been established, for example, that the youth of these neighborhoods are more regular clients of the down town shopping areas than the inhabitants of less working-class areas of the city (Bavoux (1991)). In a more general survey on the expectations of the suburban population from public services, the question of spatial proximity occupies a rather limited place.

THE CONDITIONS OF AN INTEGRATED MODEL

What the individuals from the lowest layers of the working class claim is more service in general rather than a particular service. Even those claims which seem particularly "dephased" for the service performer, still show an expectation from the service. Persons with a very low income can in the morning draw 100 Francs from the post office (that assumes a banking service in the French system), and deposit the change in the evening, thus jamming the service's time by multiplying transactions. These demands are detached from the normal functioning of the services, but they still relate to the roots of the service's functions.

As for the waiting time, it has been observed that clients, very often unemployed, are much less picky about time spent on queueing at a counter than they are when dealing with financial transactions. For example the transfer of social security family benefits generally takes place on the fourth day of each month. For technical reasons such as the fact that the computers which send the transfer orders, do not function between Sunday and Monday evenings, this date can be delayed for one or two days. Thus tens of people can show up to receive their money on the official day, causing tension and friction with the post office agents who haven't yet received the money (Suzanne [START_REF] Rosenberg | Enquête action pour une mise en oeuvre des projets de services publics de quartier, préfecture de la région Ile de France[END_REF]). As a general rule, any delay in the contribution of money from the "assistance economy" is difficult to manage, and as a result more than half of the applications for exceptional benefits received by social workers correspond to delays in welfare benefit payments. On the other hand social housing authorities have to monitor and avoid the accumulation of debt contracted by individuals waiting for their monthly allowance, that could never be reimbursed.

Other expectations, such as information on the clients' personal files, coordination between the services, access and reception facilities and use of facilities, are more problematic for a category of the population who cannot afford solving certain problems anywhere outside the service's domaine.

Even the homeless, taking refuge in the French metropolitain stations for a day or two could be considered as clients of the transport system. One of the main reasons why the homeless prefer the metro to other public spaces is the opportunities related to commuting that privilege the possibilities of exchange and sociability among this specific population, set in the general framework of urban mobility.(Damon (1993)). A typical day for the metro homeless is spent "travelling", and his time is divided between moments of sleep, wandering around, social encounters, dicussions. The underground authorities have very often insisted that the function of the metro is not only limited to transport, and that services other than urban transportation were also made available. The homeless are one of the figures of this model. Adaptation, therefore, does not fundementally involve the development of another service, but it rather involves a multiplication and a variety of services rendered. In this perspective, the entity of public services in their regular and everyday functioning should be approached under the angle of confrontation with these populations. Our analysis privileges three subject orientations; the sociology of interaction, work sociology applied to street level agents and an economic approach.

Managing interactions

A series of studies carried out on service encounters have emphasized on the importance of "breakdowns" that appear in interaction between agents and clients. A technically simple operation where a service has been rendered can be considered as a bad experience for the client because the elements surrounding the relationship were not taken into account [START_REF] Joseph | La relation de service, les interactions entre les agents et les voyageurs[END_REF]).

Such attention granted to details of civility in a service relationship may seem somewhat of a luxury in a situation where even primary levels of technical performance are not always attained. This does not seem to be the case when we study surveys carried out on clients. The question of dignity is prefered to the question of "quality" or the "commercial" caracter of the relationship.

A survey in Strasbourg

Few surveys present client opinion in regards public services, and there are even less concerning the poorest categories of the population. A survey carried out in Strasbourg, amoung individuals in contact with charitable associations, enables us to propose a few hypotheses (Klinger (1992)). A series of questions and semi-directive interviews, attempted to determine the reasons that led the clients to keep a good or bad souvenir of their encounter with a public service.

The most visited services were: the town halls (both the administrative service of the "civil status" and the social service), hospitals (which demonstrates the population's fragile health; out of a sample of 169: 53 hospitalisations and 32 consultations over a six month period), social security, employment services, post offices and schools. The "best souvenirs" were related to the generalist services. "The 'all public' agencies of public services were not the ones causing problem for the surveyed population. It seems that the 'best souvenirs' are often related to services which are part of their everyday inquiries (post offices, hospitals, nurseries)". The surveyed population seemed to be able to meet everyday demands and seemed to value the egalitarian character of these services. Contrary to what the middle classes see as a disfunctioning, the surveyed appreciated the post office services, basically because it respects the principle of "first come, first served". Many complaints came from hospital emergency services where this principle is not respected, and a hierarchy is established in accordance with the degree of sickness or injury. Persons unaware of these principles, judged that they were discriminated against when priority was given to others. "The demand for a specialized service for penny-less populations, is never expressed in their speech. In fact our informers seem to consider a 'general reception' as an important element for their dignity. It is observed that nowhere is reference made to a collectif 'us', as a community sharing the same fate characterized by social precariousness." An attitude which is approved by the agents : "positive discrimination provokes a mixed feeling of justice and injustice for the agents, and is a source of feelings of disqualification".

The importance of the symbolic character of these trite contacts with generalist public services is particularly relevant in their attitude towards hospitals. Their speech is focalized, in this case, on the doctor's charismatic figure. Even though interaction with the "big boss" hardly exceeds a few minutes, direct access to what the society presents as its best, is of very great importance.

The questions of civility are therefore reinforced in encounters with these populations. It has been particularly observed that cases of performance refusal are perceived very violently by clients who have nowhere else to turn to. Even though these clients may not have the right to a specific service,it does not necessarily mean that they should be mistreated or refused an explanation. To conclude the survey underlines the fact that discretion also seems to be an important preoccupation for the clients. Although all common operations are carried out publicly in public services and administrations, poverty is rarely something people enjoy showing. Many request the installation of individual booths where they can explain their cases to the agent in charge.

Insécurity and vandalism

Interactionist analysis enlightens us also on such difficult questions as insecurity and vandalism. The primary problem advanced by agents of public transport; bus, underground and suburbun trains, is that of security. The personnel have regularly shown their great sensitivity: the most effective strikes have been called following physical agressions against agents. As a solution to this insecurity, armed squads of policemen now patrol trains. These squads are well perceived by the clients, but the fact that they cannot be permanently present shows the limits of this decision. How can a rail inspector, after having been accompanied by policemen, encounter the same commuters, alone and unarmed? Putting in place protection is also putting in place a situation of open conflict, and this inevitably tends to consolidate the public service's power while contributing to the weaking of other travellers' responsibilities. It has been observed, for example that public transport clients assist victims of aggression more readily when they have no responsible authority in view [START_REF] Py | Stratégies de diagnostic en situation d'urgence, Abstract of the "séminaire acessibilité et situations d'urgence[END_REF]). An inspector gives a vulnerable image of himself which in turn is echoed in the public service's image. To a certain extent comparable elements may be found in the development of the image of public services in relation with vandalism. There seems to be a certain challenge in damaging what is offered to the public. In relation with building porters the hypothesis of a transfer of dignity between the residents and the agent has been proposed. As if the fact of bringing the latter to cleaning tasks and maintenance would help the residents regain self-respect.

These examples portray the importance of exposure of the clients to agents and their presence.

Street level agents

An important part of the study on the modernization of the public services relates to the progressive suppression of the agents in direct contact with the clients. In a big public enterprise such as the Paris Metropolitain, ticket-punchers controling tickets at the entry of stations have been suppressed, also metro maintenance and cleaning are partially carried out by mechanized devices, and even train operators have been suppressed in more modern trains. For example metro tickets can now be purchased from automatic distributors. The Post authority is progressively equiping post offices with automatic devices that weigh parcels and letters and distribute stamps. Not to mention all the common banking operations that are now treated automatically, thanks to credit cards. These automatic devices are the most visible aspects of the mentioned transformation. But it should not be forgotten that a great effort has been made to facilitate subscription and payment of different services. For example electricity supplies; there has been a progressive effort towards establishing bills without checking the house meters and the possibility of a monthly deduction directly from the clients bank account. This has contributed to the fact that the client can have no direct contact with a given service for years. A certain amount of townships have also established a system enabling people to pay such different services as childrens's school canteens or all year tickets for public transport, using their spécial crédit card. This general trend is less true once we take into account socially underprivileged populations. These persons are obliged to take care of more complicated operations with much more limited means. Foreigners may have to send international money orders or frequently establish the compliance of their residence with the law. Poverty often practically prohibits the use of automatic deductions on bank accounts and even the fact of owning a bank account. Most operations are therefore carried out either in cash or by money order. In general the fact of entering the benefit system supposes penetrating a vicious circle where each file, necessitates a document that necessitates a file in another administration, obliging clients to move around and wait,sometimes with no possiblity to break out of the system. In the face of such complicated situations the persons mentioned above have less access instruments. There is the language barrier; directions for the use of the different automatic devices for example are already not very understandable for the native French, they are absolutely impossible for persons who do not master the language. There are also the problems related to the fact of being cut off from progressive initiation phenomena, such as schooling or even from the job market.

Thus, the generalization of automatic procedures has established a filter that preferentially sends socially disadvantaged individuals into direct contact with agents. This model of filter that rejects the well to do populations is the counterpoint of the model mentioned previously which excludes individuals that have the most difficulties. In most of the cases it is implicit but it is sometimes openly applied; in a suburban post office, the installation of automatic stamp distributors was justified when observed that it made it possible for middle class populations to avoid waiting in line before the others. By exaggerating the model we can therefore conclude that as a general tendancy the underprivileged client is the client that encounters agents. This emphasizes the importance of agents in the question we are facing. Lipsky's analysis, most of all, applies to public service agents that are confronted with social problems. They appear divided between their will of being the defenders of the clients and the obligation to put up with the limited means in the bureaucratic reference model that privileges the equal treatment of everyone (Lipsky (1980)). We will try to develop the specific aspects linked to the particular case of public services confronted with populations in difficulty.

In certain cases, and for a limited period, the limiting factor of revenue can be less present than in specifically social services. The agents, therefore dispose of a certain liberty to concentrate on their will of being the clients' defenders. Here the example of the services in charge of assisting people to purchase their own property, of the Ministry of housing, can be studied. The fact of becoming a proprietor is not usually a sign of poverty. Still a voluntarist policy of assistance to persons willing to become owners has enabled couples with a relatively low income to buy the small house they have always dreamt of. The position of these owners is nevertheless quite fragile and certain events such as a divorce can stop them from paying their loan. The economic recession has contributed to the multiplication of similar cases, and the administrative services in charge of the treatment of such cases are receiving an increasing amount of assistance files. It is observed that the agents of the lowest categories have shown a real desire to take care of these files. They would receive the persons in difficulty and would spend a long time listening to their problems which went far beyond the simple administrative function they assumed. The agents claimed that this new function gave a sense to a disincarnated administrative task, they could directly help certain individuals and judge the outcome [START_REF] Favrot | Les conditions actuelles de mise en oeuvre des politiques d'habitat social dans les directions départementales de l'Equipement[END_REF]).

The reaction of these agents can partially be explained by the degree of proximity existing between them and the clients, since they come from the same social categories. This backing is still very fragile, since close causes can produce very different effects. Another study in similar services showed a different attitude, agents used the small social difference between them and the clients to reinforce their own image by "dominating" the underprivileged clients.

Here we find the same classic analysis on the social workers' behaviour [START_REF] Spinousa | La cause de l'usager : la relation à l'accédant en difficulté[END_REF]).

The experiments triggered by the Piccard report are based on this same proximity between the agents and the clients [START_REF] Picard | L'amélioration du service public dans les quartiers[END_REF]; [START_REF] Rosenberg | Enquête action pour une mise en oeuvre des projets de services publics de quartier, préfecture de la région Ile de France[END_REF]). What is emphasized is not so much the symbolic aspect of "identification" that can produce very different effects, but the practical proximity. If in a purely social service, the worker may never be at the same position as the client, in services with a generalist mission the agents are sometimes clients. The most original part of the system consists in gathering the agents in direct contact with the clients of different public services, in order for them to express their opinions on other services they would visit as clients. The system can be developed and the agents can be asked to prepare a report after fictive visits to their colleagues as clients.

This system can be interpreted in two different ways. We can first relate it to the problem of "discretionarity". Following what Lipsky has established, the discretionary power of agents in contact with the public is very strong, and not only it is worthless to try to reduce it (each new rule enabling new byways, and therefore increasing the power), but also the quality of the service often depends on this discretion, which if used skillfully, can be the service's best adaptation factor. The discretionary power appears as the best or worst of things if not channelled. These type of operations actively participate in the creation of a professional code of ethics that corresponds to a certain definition of the public service based on the agents' understanding of it. This supposes that the agents are capable of defining the mentioned "qualité de service' for the clients, which leads us to a representation theory. As Suzanne Rosenberg,one of the principal promoters of these experiments, points out, this option is taken while it has been observed that all the attempts to permit the expression of residents' autonomous demands through associative forms have been a failure. If the forms of coproduction implicating the participation of the clients have led to the adoption of the agents' point of view by the clients, then in the present case the adoption of the clients' point of view by the agents is seeked. Such a procedure can only be developed if the agents have the possibility to influence the service's terms of organization well beyond what corresponds to their good will. One of the approaches adopted in the ground of the experiments, has been the attribution of a credit to the agents which contributes to a certain amount of localized improvement. But this should be pushed further and should integrate the recomposition elements of the organization, and therefore the elements of return to the economic mechanisms of regulation.

The services' economy

Public services are confronted with the question of the balance of costs: contrary to social services which only have to deal with the distribution of free benefits, public services have their own income and expenses. Although these organizations act in protected markets and sometimes even in monopolistic situations, they are basically confronted with growing competition. Confrontation with competition has surely been the factor that has triggered modernization. The efforts have been directed towards the rationalization of production as well as a quest for more efficiency. The wide use of accounting instruments is at the heart of this system. This accounting approach is the main source of the hardening of relations with disadvantaged populations. A series of problems have surfaced which can only be resolved by finding a way for a global treatment of the economy of these services.

A first question is that of the relevance of these accounting systems in relation with the internal economy of the mentioned organizations. These accounting systems do not correspond to a global accounting balance sheet, with income and expenditure, as it may be in the case of small companies. They correspond to sketchy aspects of the activity. These plans are based on limited indicators such as the number of operations carried out. Proceeding in such a way we are unable for example to estimate the overcharge of the mail services in rural areas.

A second question is that of the global economy of redistribution. In a period of relative wealth, the underprivileged could have benefited from a certain amount of flexibility. Today the reduction of costs at all levels prohibits adaptation processes and indirect redistribution. For example, the E.D.F.( French electricity authority), has installed electrical meters with tokens in the disindustrialized zones of northern France. The social workers criticize such measures which lead to depriving the poor from light and heating (which are amoung the most essential needs) at the end of the month.

This leads to what is considered as "positive discrimination" that permits the attribution of supplementary means to public services in suburban neighbourhoods, enabling them to reach the same results but in more difficult conditions. This is the case of the imposition of a budget line upon neighbourhood public services or the creation of a special bonus for teachers working in areas with schools with a high population of pupils having flunked and finding themselves in classes which don't correspond to their age. It is useless to evoke positive discrimination, as long as we do not have an accurate global figure of the financial flows coming from the administration. Indeed, how could we determine if the supplementary contribution linked to the "city" policy (politique de la ville) are not less than the different forms of subsidies related to other policies carried out in other sections of the territory.

The third question is that of the adherence of the mentioned services to a global economy and specially that of the economic phenomenon of deterioration. The case of the Mail authority is the most explicit. Post offices assume both mail and banking services. The attribution of services to an office open to the public depends on two factors. The first is the number of operations carried out on the basis of a coefficient representing the average time spent with a client for a specific service. The second is the volume of financial operations (the clients' investments) that are a source of income for the service. The income coming from banking service is at its lowest for post offices situated in working class neighbourhoods. Notwithstanding the fact that the operations carried out, as we previously observed, tend to be longer than average. As a result there is a chronic lack of agents, causing longer delays. When this becomes chronic the middle class clients that have access to another office, for mailing or banking purposes, tend to opt for other services. This increases the proportion of persons with economic and cultural difficulties and therefore reinforces the mentioned disfunctioning in a cycle of deterioration. Thus in order to guarantee what is refered to in the European system as the universal service (a minimum service should be available for each citizen), the cost can be minor in the beginning of the process (adding a few agents to maintain the quality of the standard service); it can become enormous once we get to a social public service globally financed by the community.

CONCLUSION: THE INTEGRATED MODEL: RESOURCES AND CONSTRAINTS

If the question implicates "more" service, then the question of "productivity" should be prefered to that of adaptation in our quest for an integrated model. That is how to offer more service to different categories of clients.

What is noticable in the different integrated model approaches is the fact that we are no longer in a game where the outcome is always zero and in which all that has to be defined is the portion that is going to be allocated to the disadvantaged. It is impossible to distinguish a specific social cost from the agents who have the mission to assist persons in difficulty or take care of security problems, without avoiding that this distinction change the facts of the problem. The feeling of security, that of being assimilated in the society, the efficiency of public servants at work, the vandalism exercised by some clients on public equipment, and even the value of public money according to the fact that it comes from the profits of other public service's sections or from the redistribution of tax, are not stable data. It is therefore essential to be in a position where the ratio of offered advantages and the consented investment can be derived when the data fluctuates according to different situations. The mentioned examples show that simultanious treatment of all clients can motivate the personnel. It can also permit the definition of new ways for a better coordination between the services, that a wise investment of funds can have a superior effect in comparison with a simple redistribution mecanism, and finally, that a symbolic image of accessability responds more directly to the strong claim of certain populations.

These "ressources" are not free of constraint, and the fact of approaching this question proves it. In a certain way the treatment of the poorest has taken place at the margin of the existing system. This manoeuver margin is still limited by a double constraint; an increase in claim (particularly linked to unemployment) and to rationalization policies of the services' production (automatization, the establishment of analytical accounting...). The integration efforts of a 'little more' of social services in non social services permit a temporary reinforcement of this margin, since the heart of the activity of social workers in this area consists in the facilitating the return toward the general service. We cannot indefinitively enlargen this treatment without risking the creation of an annex sub-service that would not respond to the claims.

Since we cannot live in the margins of this model, we should formalize the necessary evolution. This leads not so much to a new model but rather to the renewing of the existing model. The service has always had a redistribution function, but we have been more capable in treating the problems linked to an unequal distribution in the territory, than those linked to social inequalities. The letter with a unique stamp rate, no matter its destination or its origin is a typical example of the latter. The questions of organization and more specially the coordination between services, must be taken into account. These functions that have been unformally taken care of by social workers, can be integrated in the routine functioning of their services. The quest for 'more' service also leads to the question of the qualifications of the agents in contact with clients. Instead of developing vague functions of specific reception, we can develop qualifications directly linked to the offered service. Such an orientation can facilitate the mobilization of the staff. But the main reorientation that should be carried out concerns the symbolic aspect of things. Specialists of social action have often emphasized the passage from the question of inequality to that of exclusion, and the biggest risk may not be so much the fact of not having a public service for the poor rather than having a public service exclusively for the poor.

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