Mercedes Volait, InVisu (CNRS/INHA)

Egypt : Global architecture before globalization 1914 did not represent a major disruption in the development of Egyptian architecture; that is, architecture on Egyptian soil. Forces that had shaped its norms and forms during the previous half century continued to be at play throughout the subsequent decades. The relentless quest for modernity pursued by Egypt's rulers and its ever growing state apparatus in the wake of the Ottoman reforms of the 1830s represents one such enduring factor. The strategy had meant to emulate Europe in order to resist its expansion. Although architectural modernity in the non-Western world is commonly attributed primarily to colonial agency, its development and domestication in the Egyptian context occurred within a top-driven endogenous process, embedded in Ottoman cosmopolitanism, and prone to all sorts of hybridizations. 1 The British occupation of Egypt from 1882 to 1922 (with Protectorate status from 1914 to 1922) did not alter much this general pattern. 2 In other words, an established tradition of borrowing and naturalizing European techniques and aesthetics characterized Egyptian architecture as it entered into the 20 th century. Major civil engineering undertakings such as hydraulic infrastructure (from the 1830s), the railway network (starting in 1854), or the digging of the Suez Canal (1859-69), had led many European firms to establish local branches. By 1893, metallic structures were locally produced (by the Belgian Baume & Marpent); reinforced-concrete construction, along the system patented in 1892 by the French François Hennebique, had started the following year. 3 A time of thriving expansion in the building sector, the turn of the century had seen the launching of large scale real estate developments: the 1 Khaled Asfour, "The domestication of knowledge: Cairo at the turn of the century," Muqarnas, X, 1993, 125-137.

2 Mercedes Volait, "Making Cairo modern : (1870-1950) : Multiple Models for a "European-style" Urbanism », in Joe Nasr and Mercedes Volait, eds, Urbanism -Imported or Exported? Native Aspirations and Foreign Plans, Chichester : Wiley-academy, 2003, p. 17-50. 3 Claudine Piaton, Ezio Godoli, David Peyceré, eds. Building beyond the Mediterranean. Studying the Archives of European Businesses (1860Businesses ( -1970)), Arles : Honoré Clair, 2012; virtual exhibition on http://www.archmuseum.org/Gallery/building- beyond-the-mediterranean_41.html.

garden suburbs of Garden-City, Giza, Maadi and Heliopolis, to name only Cairene schemes, all starting in 1903-06. The flows of European capital and migration attracted by Egypt's westernization, again a long-time phenomenon, had their share in the building boom. The peak of foreign residents was reached in 1927 with 225 000 people out of a population of 14 million. Professionally wise, Italians and Eastern Europeans outnumbered any other national in the building industry, from architects and contractors to ceramists and cabinet makers. The foreign presence decreased sharply after 1937, and became insignificant after the Suez Canal War of 1956, but it had contributed in the meantime, along with local elites, to the internationalization of Egyptian architecture.

Finally, the pace of westernization was sustained by substantial public commissions. The international competition organized in 1894 for the Museum of Antiquities, the first held in the Middle East, was followed by many others: for the Alexandria railway station in 1912, for a hospital

Subsidized housing

There is one sector where the interwar years made a difference: low-cost and subsidized housing.

Most of postwar schemes, and indeed Nasserite projects, are rooted in initiatives developed during Egypt's so-called "Liberal Experiment period". As elsewhere, WW1 had caused construction work to stop. The supply of coal and of building materials had ceased during wartime, and no alternate power had been devised to continue manufacturing bricks, lime or cement locally. The acute housing shortage that ensued, coupled with dramatic inflation, affected not only the lower income groups, but indeed the middle class. Governmental intervention was envisioned in the immediate aftermath of the war in order to stimulate the construction of affordable dwellings. Land development companies and major employers were encouraged to lead the effort. The Suez Canal Company and the Heliopolis Oasis Company implemented significant subsidized housing schemes in 1920-23; in the process, new typologies, such as the 4-appartment house with individual gardens in the Heliopolis Housing scheme or attached dwellings in the new garden suburb of Port-Fuad, were introduced. The Misr textile group, a holding created in 1927 to encourage Egyptian industry, started building large company towns during WW2, at Mahalla al-Kubra (in 2 phases, 1941-47, and1946-51, the latter on designs by Aly Labib Gabr) and Kafr al-Dawwar (near Alexandria, 1943-44, Mahmud Ryad, arch.).

Considered as "outstanding examples of housing for industrial workers" and the "last word of modernity", these self-contained schemes included all modern amenities: central restaurants and hospitals, markets and coffee shops, an open-air cinema, welfare centers, sporting fields, bathhouses and automated laundry facilities. (It is no accident if unionism grew stronger in such communities, ultimately contributing leading forces to the 2011 uprisings). By 1950, 22 other enterprises had erected dwellings for their employees. 7 As social reformers raised their voices louder in the 1930s, slum clearance and the provision of healthy dwellings in urban and rural areas came to the forefront. The largest share of the population (75% in 1927) lived in the countryside in appalling conditions. A number of initiatives were developed to sanitize the Egyptian village. Regulations were passed in 1933; model villages were built by progressive landowners and model designs were disseminated through publications and industrial 7 Ministry of Social Affairs, Social Welfare in Egypt, Cairo, 1950, p. 66;further details in M. Volait, (1995)." Réforme sociale et habitat populaire : acteurs et formes ". In Entre réforme sociale et mouvement national : identité et modernisation en Egypte (1882Egypte ( -1952)). A. Roussillon (ed.). Le Caire: Cedej, p. 379-410 (Arabic version in Misr wa al-'alâm al-'arabî, n° 4, 1995, p. 9-54).

fairs. A ministry of Social Affairs was established in 1939, with a department devoted to the Peasant (fellah); it embarked itself upon model village construction. It was in this context that Hassan Fathy started experimenting what will make him internationally acclaimed: mud brick architecture, for a model village at Bahtim (1940) (fig. 8), following the idea that adobe was commonly used for construction in Arizona and California, two regions with climates resembling that of Egypt. 8 After trial and error, essays in mud for roofing, using Nubian techniques, proved successful, and Fathy started building New Gourna, a self-sufficient pilot community in Upper Egypt, his most iconic achievement (fig. 9). 9 In 1949, reformer Ahmed Husayn and architect Mahmud Ryad were entrusted with the task of designing a scheme to provide housing for groups with limited income (Machru'a litawfir al-sakin lil-tabaqat al-mahduda al-dakhl fi misr). A number of measures followed, including the creation in 1950 of a department of "Popular Housing" at the Ministry of Social Affairs that Ryad headed. In 1951 the Parliament passed a law on subsidized housing, drafted after consulting German and American experts, and adopted an ambitious Social Housing scheme that started to be implemented in 1953 with the building of 4000 units in suburban Cairo. Experiment with new materials and techniques, both resulting from wartime research in Europe, was conducted in parallel: foam concrete construction was carried out in 1951 using "Betocel", a porous cement-type material invented in 1944 by French engineer René Fays; pilot projects in standardized housing were conducted by a German specialist, architect Hans Spiegel, in 1951-53. 10 These early attempts at coping with poverty and housing shortage show that many projects commonly associated with the new regime of the Free Officers that came to power in 1952including the monumental Mugamma' on Midan al-Tahrir (fig. 10) -had in fact started much earlier on, and were deeply rooted in the progressive and reforming ethos of Egypt's early steps to independence.

8 Mercedes Volait, "Réforme sociale et habitat populaire: acteurs et formes )", Entre réforme sociale et mouvement national: identité et modernisation en Egypte (1882-1952), A. Roussillon (ed.). Cairo, Cedej, p. 379-410. 9 Leila El-Wakil and Nadia Radwan (eds.), Hassan Fathy dans son temps, Gollion: InFolio, 2013. 10 Hans Spiegel, « Arbeit für den sozialen Wohnungsbau in Agypten », Bauwelt, vol. 44, 2 november 1953, p. 866-870.

  and medical school at Manial al-Roda in 1921-22, for the premises of the Cairo's Mixed Court in 1923-24, for the reconstruction of the historic mosque of Amr in 1927, for the creation of a Fine arts Campus in 1930, to mention but a few. In parallel, a number of imposing educational facilities, including Cairo University campus and al-Azhar University campus(1932)(1933)(1934)(1935)(1936), together with hospitals, museums and administrations, were erected by the State buildings department, the specialized body within the ministry of Public Works in charge of most public buildings.4 Religious structures were the prerogative of the ministry of Endowments (Awqaf), itself a major builder, and indeed promoter of innovation. The mosque of Abou Abbas al-Morsi built in 1929-39 in Alexandria, on designs by Eugenio Valzania and Mario Rossi, featured the first octagonal plan ever considered in Egyptian mosque architecture.5 The state engagement in construction represents again a characteristic of Egyptian architecture that cuts across temporalities and regimes: equipping the 4 Mercedes Volait, Architectes et architectures de l'Egypte moderne, Genèse et essor d'une expertise locale. Paris: Maisonneuve et Larose, 2005. 5 Mariangela Turchiarulo, Building "in a style": Italian architecture in Alexandria, Egypt ; the work of Mario Rossi, Roma : Gangemi, 2012.nation with modern facilities, from culture to transportation, from education to healthcare, has been a concern for almost every ruler, from Khedive Ismail (r. 1863-79) to President Nasser (in office 1956-70), and beyond. The architectural outcome of these globalizing forces was of marked heterogeneity. Structures of every possible origin and essence coexisted almost side by side. European-style historicism, as illustrated by the neo-Renaissance design proposed at a 1914 competition for the newly founded Egyptian University (Ernesto Verrucci, arch.) (fig.1) remained fashionable well into the 1930s for official and domestic architecture alike. Local expressions of historicism, such as Mamluk revivalism (villa Harari, 1921) (fig. 2) and Pharaonicism (Saad Zaghlul mausoleum, 1927-31, Mustafa Fahmy, arch.), flourished. While the latter cultural movement was short-lived (nonetheless, for the paganism associated with Ancient Egyptian civilization), the former had been a recurrent theme in Egyptian architecture since the 1870s and persisted as such in the 20 th century, when the struggle for independence led to search for a national idiom in architecture based on Egypt's Islamic heritage. French architecture was represented by over ornate Art déco and all possible variations of modern classicism. A good example is the Cairo Mixed Court (1924-34), featuring French Renaissance details and elaborate Art déco ironwork and flooring, on plans by the French firm Azéma, Edrei and Hardy. Exceptions to the mainstream of neo-styles and mild modernism include the avant-garde residences designed by Auguste Perret for two eager local modernists, banker Gustave Aghion in Alexandria (1926-30, demolished in 2014) (fig. 3) and lawyer Elias Awad bey in Cairo (1930-37, demolished in 1970) (fig. 4). The Italian community developed its own architectural language, along the functionalist "Mediterranean spirit" advocated by MIAR (Movimento Italiano per l'Architettura Razionale) within the expanding Fascist ideology. Its early icons were the schools built in Alexandria in 1929 (fig. 5) and in Cairo in 1933 on designs by Clemente Busiri-Vici; strongly promoted by the local Italian press, their style had a decisive impact on Italian building in Egypt. 6 The affluent Greek community sponsored in Alexandria in 1937 an early application of the compact hospital, a new 6 Ezio Godoli, Milva Giacomelli, eds. Italian architects and engineers in Egypt from the nineteenth to the twenty-first century, Florence : Machietto, 2008.concept developed by French architect Jean Walter following a mission to the US and tested in France in 1935. In contrast and paradoxically, the British left few architectural traces of their presence while in power, besides the winning design for the Qasr al-Aini hospital and medical school(1923-33, Charles Nicholas & John Edward Dixon-Spain, arch.) and the Cairo's University campus(1925-1935, Eric Newnum, arch.) designed in a grand imperial manner reminiscent of Luytens' Delhi, although devoid of any reference to its local setting. As the 1930s came to a close, functionalism and International style penetrated more strongly in Egypt, under the lead of Syro-Lebanese architects (such as Raymond Antonious, Charles Ayrout, Antoine Selim Nahas, Albert Khoury, Albert Zananiri, Jean Kfoury, etc.) and clients. The journal al-'Imara, the first architectural magazine in Arabic language edited by Egyptian architect Sayyid Korayem was created in 1939 to promote International style in the country, and in the region at large. Increased travel to Europe, and later to the US, of Egyptian elites was also instrumental in channeling Modern movement architecture to Egypt. Post-war politics reinforced the process, with American, and later Russian, aid entering the game. Education abroad was another vector. Whether Egyptian or non-Egyptian, what architects brought to their early or even mature works, had much to do with what they were exposed to during their formative years. The series of apartment and administrative buildings designed by Liverpool-trained architect Mahmud Ryad, who also interned on the site of the Empire State building in New York, are good examples of British and American Beauxarts style (Misr Insurance buildings, 1948, fig. 6; The Arab League headquarters, 1955 and Cairo municipality ̶ later Socialist Union ̶ building, 1959). The villas designed by Salah Zeitoun in the late 1950s do reflect the time he spent as a Taliesin fellow in 1947 in contact with Frank Lloyd Wright (Richter house, 1958-61 No. 20 Road 20, fig 7).


Jose Luis

Patino Vilchis

Hamid Benhadda

Francois Bremond

Francois Bremond Data

Luis Patino

Data Mining in a Video Data Base

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The term "data mining" denotes both a process and a set of techniques used to automatically discover the knowledge contained in very large databases. Its main goal is to extract non-trivial information that may be hidden among the mass of data. Data mining techniques have been used in various domains such as marketing, medicine and finance. These techniques can be divided into two main methods: "supervised" methods, which are based on existing models to recognize new objects or events, and "unsupervised" methods, which discover hidden and useful models in the data. Regarding the application of data mining in the domain of video, we can cite the classification of videos into "categories" for quick searching (video on demand), detection of unusual or suspect activities in prerecorded video-surveillance sequences and selection of traffic models to optimize and best manage traffic. This chapter deals with the issue of unsupervised extraction of activities observed in a video scene recorded by a video-surveillance camera. To do so, we use clustering techniques, which facilitate automatic discovery of typical behaviors and trajectories observed in the scenes. The aim is to automatically learn the zones of activity and use these zones to generate information about the behaviors and events of the trajectories being analyzed. By analyzing both trajectories and events, we can discover significant models of activity which are difficult to apprehend from the raw data.

To obtain semantically interpretable results, we find that the activities we wish to discover are characterized on the basis of contextual elements of the scene under observation. These contextual elements may be zones of activity such as building entrances, areas where people come together, road areas, etc.

The global process of analysis presented here is divided into three main stages. In the first stage, the trajectories of the mobile objects evolving in the recorded video scenes are extracted and analyzed to identify the points at which those mobile objects enter and exit the scene and, with them, deduce the various activity zones. In the second stage, the moving objects are characterized in relation to learned zones of activity. Three types of behaviors are considered:

-the moving object stays in a given activity zone; -the moving object passes from one activity zone to another; -a combination of the above two behaviors (the moving object stays for a certain amount of time in a given zone and then goes into another).

In the third stage, a high-level "clustering" algorithm, based on relational analysis [BEN 07], is used to classify the moving objects identified in the scenes and group them together in clusters, based on the similarity of their behaviors. This enables us to reveal both frequent (habitual) behaviors and unusual (uncommon) behaviors.

These three stages are detailed in sections 14.3-14.5 of this chapter. "Soft computing" techniques are used in the first two stages to deal with the uncertainty inherent in low-level trajectory data. This family, for which a more formal definition was given by L.A. Zadeh [ZAD 94], encompasses techniques imitating human reasoning and based on fuzzy logic, neural networks, genetic algorithms and probabilistic techniques.

State-of-the-art

Although the general issue of unsupervised learning has been widely studied over the course of the past two decades [MAS 08, PON 08], the use of data mining tools to extract activities from videos is a relatively new discipline, and its application in the field of video behavioral analysis is as yet rather limited. At present, only a few systems use soft computing techniques to determine the characteristic traits of the activities observed in video scenes [

Pre-processing of the data

To discover significant activities, it is of crucial importance that we have detailed information that can be used to detect the different possible interactions between the objects. Given that the approach presented here is based on trajectory analysis, the first stage in preparing the data that will be used as input for the method of activity clustering is to break down each trajectory into subtrajectories with near-constant velocity, called "tracklets", which characterize the state of an object. This preprocessing stage is illustrated in Figure 14.1.

Object detection and tracking

Segmentation of the trajectories

Video

Tracklets tkj,i

j = 1…N i = 1…nj

Trajectories trj j = 1…N The description of object detection and tracking algorithms is beyond the scope of the work presented in this chapter. We can refer to Chapters 7 and 8 of this book, or to [CHA 11].

NOTATION. -The data set is made up of N objects O j (j = 1, …, N), each object being characterized by its trajectory tr j , which is, itself, defined as a series of positions [x j (t), y j (t)], taken at regular intervals over the course of the observation. In addition, a velocity measurement is defined at each moment by: 22 () ( ' () ' () )

jj j vt x t y t =+ [14.1]
where x j '(t) and y j '(t) denote the (approximate) time derivatives of the functions x j (t) and y j (t), respectively.

The aim is to detect the points at which the velocity changes, in order to segment the trajectory into tracklets of near-constant velocity, so that the trajectory is summarized as a series of stationary states or movements at constant velocity. The velocity of the moving objects is studied as part of a multiresolution analysis for a series of discrete temporal data v(k) with a Haar wavelet smoothing function, ρ s (k) = ρ(2 s .k), dilated to different scales s. In this context, the approximation A of v(k) by ρ is such that A s-1 v is an approximation whose lowest resolution is A s v:

ρ s (k) = ρ(2 s .k), A 0 v = v, A s v = ρ s *v = ρ*A s-1 v [14.2]
where * denotes the convolution operator.

By analyzing the temporal series v at coarse resolutions, it is possible to take out the insignificant details and choose points associated with significant changes; the location in time of these points is then refined by using finer scales. The points at which the velocity changes are then used to segment the original trajectory tr j into a series of n j tracklets tk j,i , i = 1, …, n j , each tracklet being defined by its start and end positions: [x j,i (1), y j,i (1)] and [x j,i (end), y j,i (end)]

[14.3]

The number M of tracklets extracted from the set of trajectories detected in a scene is equal to the sum of the numbers of tracklets for all the trajectories:

1 N j j M n = = ∑
By globally re-indexing all the tracklets (let m represent the subscript that denotes the m th tracklet tk m in any trajectory tr j from those detected in the scene and m = 1, …, M), we can get the following tracklet feature vector tk m :

tk m = [x m (1), y m (1), x m (end), y m (end)] [14.4]

Activity analysis and automatic classification

The general approach is illustrated in Figure 14.2. We define an activity as being the set of interactions that occur between the moving objects themselves and between those objects and the environment. We use an analysis based on the trajectory of the moving objects in the video to discover the points at which they enter and exit the scene and, finally, deduce the different zones of activity from these observations. In the second stage, the moving objects are characterized in relation to the learned zones of activity. In the third stage, a clustering algorithm is applied to the moving objects, grouping them together based on their behaviors and thereby revealing frequent/normal and inhabitual/abnormal behaviors and events. The high-level clustering algorithm used to do this is based on the theory of relational analysis.

Extraction of the zones of activity

Characterization of the objects

Clustering based on behavior Tracklets

Figure 14.2. Stages of processing for activity analysis and automatic classification

Unsupervised learning of zones of activity

Modeling the spatial context of a given scene is essential for the recognition and interpretation of the activities observed in that scene. Because it is difficult to manually define all the contextual zones of a given scene, it is not possible to describe all the situations or actions evolving in the scene under observation; hence, it is necessary to learn additional zones for an exhaustive description of that scene.

The feature vector defined in equation [14.4] constitutes a set of descriptors that we can use to describe the activities in a great variety of domains (e.g. traffic surveillance, subway monitoring, surveillance of smart environments), because they primarily define the origin and destination of an object.

In our system, the moving objects that begin (or end) their displacement at positions near one another are considered to share a common zone of activity. Thus, the task of finding the zones of activity in the scene may be considered tantamount to clustering the entry/exit points of the tracklets. Therefore, a number of classification algorithms -e.g. k-means clustering or self-organizing maps (SOMs)can be used, but these algorithms present two drawbacks: on the one hand, we have to fix the number of clusters that must be known in advance and, on the other hand, the morphology of the zones resulting from these techniques is always circular in form (the result of the very definition of the cluster obtained: a center of the cluster and a radius of influence), which cannot correspond exactly to the actual topology of the scene. In our approach, we attempt to find zones of activity with high spatial resolution (small surface), which are then clustered to obtain larger zones of activity, using a hierarchical agglomerative clustering algorithm.

Clustering of the start/end points of the tracklets

Clustering of the start/end points of the tracklets is performed by a well-known clustering algorithm called "Leader" [HAR 75], which offers the advantage of being able to be executed without having to specify the number of clusters in advance. In this method, it is supposed that a distance threshold T from the center of each cluster is given. The algorithm constructs a partition of the entry space (defining a set of clusters) and a representative or "leader" for each cluster, so that each object in a cluster is at a distance less than T from the leader. The threshold T is thus a measure of the diameter of each cluster. The algorithm processes the entire data set, assigning each object to the cluster whose leader is closest, and constructs a new cluster and a new leader for objects whose distance from all the existing leaders is greater than the threshold. The value of T depends on the application. To set T, we have used the configuration suggested by [PAT 11].

Consider the location of an object to be L; its zone of influence Zn is defined by a radial basis function (RBF) centered on the location L; whether or not a new point p belongs to that zone is measured by equation [14.5]:

Zn(L, p) = φ(L, p) = exp(-||p -L|| 2 . T 2 ) [14.5]
The RBF has a maximum value of 1 when its input is p = L, and therefore acts as a similarity detector; its values decrease as p gets further away from L. An object will be included in a cluster Zn if Zn(L, p) ≥ 0.5. The receptive surface (hypersphere) of the cluster is controlled by the learned parameter T.

Merging of the tracklets' entry/exit zones

We find the definitive zones of activity by merging similar entry/exit zones of the tracklets. The new zones are obtained by satisfying two relations:

-R1: the zone Zn i must overlap zone Zn j ; -R2: the zone Zn i must not overlap a contextual zone Zctx q , defined beforehand by the user.

The process is illustrated in Figure 14.3. R2 is transformed into a new relation (R3) of similarity between zones Zn i , obtained by transitivity in relation to the overlap of the zones Zn i with the contextual zones Zctx q . Then, by merging relations R1 and R3 into a final relation R, we can establish the similarity/overlap between zones Zn that do not overlap the zones Zctx q defined by the user. Definitive zones of activity are obtained by thresholding this relation matrix R. In other words, the summation is performed for a set of points belonging to three concentric circles centered around L i (thus inside Zn i ). These points are evaluated in order to verify whether they also belong to Zn j to calculate the overlap/similarity between Zn i and Zn j . This helps avoid problems of homogeneity with the clusters defined on scattered regions (certain clusters can be defined with a larger number of points than others); -R2 iq : Zn i overlaps Zctx q :

( )

( ) ( ) 3 1, , 2c t x ( , ) ik ik iq q kp x y X Y R Zp x y =∈ ⎡⎤ ⎢⎥ = ⎢⎥ ⎣⎦ ∑∑ [14.7]
-R3 ij : Zn i and Zn j are linked to the same contextual zone:

( ) 3m a x m i n 2 , 2 ij iq qj q RR R = [14.8]
-R ij : Zn i overlaps Zn j and the two zones are not linked to the same contextual zone.

Note that 3 R , the counterpart of R3 given by 3 R = -R3, represents the relation between Zn i and Zn j if neither cluster is linked to a contextual zone. R1 and 3 R can be aggregated by using a soft computing aggregation operator such that:

( )

1 3 1 , 0 max 3 1 - + = ∩ = R R R R R [14.9]
Next, R is rendered transitive with:

{ } max min ( , ), ( , )

ik k j k R R R Zn Zn R Zn Zn ⎡⎤ = ⎣⎦ [14.10]
R is now a transitive relation matrix. R ij gives the extent of similarity between zones Zn i and Zn j . If we define a level of discrimination α in the closed interval [0,1], the value of the α-cut can be defined such that:

R α (Zn i , Zn j ) =1 ⇔ R(Zn i , Zn j ) ≥ α [14.11] Thus, implicitly, 1 1 2 1 α α α α R R ⊂ ⇔ >
. Thus, R α induces a grouping of zones

{ } i Zn α π = such that 2 1 α α > implies that 1 α π is a refined version of 2 α π .
At this point, the difficulty lies in selecting an appropriate α-cut value such that α π of R α represents the best distribution of the data. This is always a difficult and open-ended question that we have chosen to deal with by selecting the value of the α-cut, which causes a significant change from k α π to 1 + k α π . To automatically detect significant changes, we have chosen to examine the surface of the cluster and the number of clusters caused at each partition α π . We achieve this objective as part of a multiresolution analysis. By analyzing the partitions caused at coarse resolutions, it is possible to take out the small details and select the α-cut values associated with significant changes.

Definition of behaviors

Our aim is to create a system to recognize and interpret human activity and behavior, and to extract new information that could be beneficial to end users. The low-level information should thus be transformed into useful descriptions of a high semantic level. In our application, we establish semantic meaning based on the model of the scene constructed as described in section 14.4.1. The behavior can thus be expressed with semantic concepts, instead of using quantitative data, with the learned zones (contextual zones). Suppose we have K contextual zones Zctx k in the scene in total, defined a priori or after the zone-learning procedure. Two types of behaviors can then be identified:

-objects moving from zone Zctx k1 to Zctx k2 ; -objects inside zone Zctx k .

Relational analysis

To carry out an in-depth, high-level analysis of activities that are not easy to highlight using raw video data, we use an automated classification technique, "relational analysis", which will enable us to extract complex and hidden correlations between the moving objects in the scenes of the video, on the one hand, and between the moving objects and the contextual objects, on the other hand.

General principles of relational analysis

The foundation of relational analysis goes back to the work of the Marquis de Condorcet on the voting system [CON 85] in 1785. This work was based on the principle of "consensus" or "majority rule", which stipulates that when a number of judges give their respective opinions about the "validity" or "non-validity" of a decision, the final result must be in line with the majority of opinions given by these judges. In other words, the final decision will be that in favor of which the suffrage represents at least 50% of the judges.

Relational analysis is a clustering technique that lends itself very well to the processing of categorial (or qualitative) data. For this type of data, each of the variables measured on the objects to be clustered may be considered to be a judge, which decides, for each pair of objects, whether or not those two objects belong to the same category. The mathematical formulation in the form of a linear programming problem was first given in [MAR 78]. This formulation was defined as follows: if X is a square matrix, representing the final distribution to be found, in which each term x i,j is equal to 1 if i and j are of the same category in the final distribution and equal to 0 if not, and if ' ii c represents the number of variables (or voters) in favor of the decision that the objects i and i' belong to the same category and ' ii c is the number of variables (or voters) supporting the opposite decision (that the two objects are not in the same category), then the Condorcet criterion C(X) is defined by:

( ) ∑∑ == - = n i n i ii ii ii x c c X C 11 ' ' ' ' ) ( [14.12]
The mathematical formulation in the form of a linear programming problem, which we can use to find the "consensus" distribution, depending on the different variables measured on the objects, is given by equation:

( ) {} () ( ) ( ) ( ) ( ) ( ) ( ) 2 ' 2 '' 3 '' " " Max ( ) 0,1 , ' binarity
( ) 1 reflexivity 0, ' s y m m e t r y 1 , ', " transitivity

X ii ii ii i i ii i i ii CX xi i xi xx i i xx x i i i Ω Π Ω Ω Ω ⎧ ⎪ ⎪ ∈∀ ∈ ⎪ ⎪ =∀ ∈ ⎨ ⎪ -= ∀ ∈ ⎪ ⎪ +-≤ ∀ ∈ ⎪ ⎩ [14.13]
The classes (or clusters) obtained are described by the modalities that have played the greatest part in their formation. Two indicators are used to this effect: the "characteristic ratio" (CR) and the "discriminating ratio" (DR). For a given class C with cardinal |C| and a modality j, if C j n is the number of objects in the class exhibiting the modality j and n j is the total number of objects in Ω with that modality, the two indicators are defined by:

j C j C j n n j DR C n j CR = = ) ( ) ( [14.14] 14.4.3.2

. Application of relational analysis to video data

The main two types of concepts on which we perform high-level clustering are the moving objects (or "mobiles") observed and the events that have occurred in a video scene. To analyze these concepts, and with the aim of putting the data into a format appropriate for data mining, we have extracted the following specific characteristics from the raw data:

-Mobile ID: the label identifying the object; -Start: the instant when the object is seen for the first time in the scene; -End: the instant when the object is seen for the last time in the scene; -Duration: the total duration of the period when the object is observed in the scene (expressed in seconds); -Dist_org_dest: the total distance covered between the origin and the destination of a trajectory (expressed in meters); -Average_velocity: the average of the instantaneous velocities calculated at all the points on the trajectory of the mobile object; -Significant_event: the main event deduced for the object, with the learned zones taken into consideration.

Results and evaluations

The algorithm for unsupervised learning of zones of activity (described in section 14.4.1) was applied to an hour-long video scene, recorded in one of the entrance halls of the metro station in Turin. The final relation R given in equation [14.10], which verifies transitive closure, is thresholded for different α-cut values ranging from 0 to 0.9 and with a "step" value of 0.05. The algorithm automatically selects the best α-cut value, attributing a precise composition of activity sectors in the scene, as mentioned in section 14.4.1. Figure 14.4 presents the learned zones corresponding to the video scene being analyzed. As mentioned in section 14.4.2, we characterize the behaviors by matching the low-level detections with the learned zones. The collection of activities observed in the scene can then be spoken of as a set of behaviors referring to the learned zones. For instance, for the ticket machine area (zone Zn1), the activity report obtained is given in Table 14.1. Zone Zn1 is in fact the second busiest of all the zones, just after Zn2, which corresponds to the main concourse (39.85% occupancy; not shown in Table 14.2). Most people who go toward the vending machines come from the main concourse (Zn2), and all who move away from the machines go toward the main concourse. Those people who go directly to the automatic ticket machines from one of the entrances to the station do so from the entrance zones, Zn5 or Zn7. In the first stage of discovery of new information, we apply the process of relational analysis (see section 14.4.3). The input variables are those corresponding to the table of moving objects described above and in section 14.4.3.2, which, in the case of the particular video being analyzed, contains 409 detected objects in total. The variables are weighted so as to favor the formation of as many clusters as there are significant events in the table. The advantage of such a procedure is to use other variables to explain what characterizes each of the significant events. After the application of relational analysis, 23 clusters of activity are obtained; Table 14.2 shows some examples of the clusters obtained. In this table, for instance, Cluster 2 corresponds to the activity of people in zone Zn1, which is the ticket machine area. We can observe that people move little (less than 4 m) and slowly (velocity less than 1.5 m/s) for a short period of time (0-4 s): characteristic behaviors of people buying their tickets. This activity is the second most common activity in the station, just after "inside zone Zn2", corresponding to people remaining in the main concourse (Cluster 1; not shown). Cluster 4 corresponds to people moving away from the ticket machines into the main concourse ("zone 1 to zone 2"); as we can see in the table, these people move a greater distance (between 3.84 and 7.68 m), walking faster (2.88 to 4.32 m/s). The last cluster, Cluster 19, represents a rare activity (only two elements are contained in this activity): the people go from "zone 7 to zone 1". These people are characterized, in particular, by the time at which they are seen (no mobiles detected around the same time). Thus, relational analysis can help us cluster people exhibit similar behavior. This is of particular interest for the users, because the activities in the metro station can be better quantified. We also apply the proposed method to another domain: the monitoring of traffic control and specific detection of abnormal events in a dedicated bus lane. The advantage of working on this data set is that the ground truth events are available for 45 min of video. We apply the processing chain explained above to this data set; to begin with, our system learns, in an unsupervised manner, the zones of activity in the scene; then we extract the behaviors of the detected mobile objects, associating them with the learned zones. Finally, we apply relational analysis to extract highlevel information. Figure 14.5 shows the zones of activity learned from the scene. Zn6, Zn7 and Zn9 correspond to people's zones of activity, whereas the other zones of activity are vehicular zones (see the overlap with the bus lane). The behaviors are then characterized either as remaining in a given zone or moving from one zone to another. We mark south-to-north movement between zones as abnormal activity. Table 14.3 shows the abnormal behaviors established from the learned zones. By applying high-level relational analysis, all the abnormal events -as expected -are gathered together in a single cluster. To test the correctness of the proposed processing chain, we compare the abnormal events detected by our approach against those indicated by the available ground truth. The results of this comparison can be seen in Table 14.4. The measure of recall is fairly high, and the precision is acceptable. This is mainly because our system produces a relatively high number of false detections, which can occur because of detections on the boundary of the bus lane, which are not included in the ground truths. This is a general problem of human perception, where mobiles only partially observed by the camera are not considered by the expert annotating the video, but those objects are still detected by the system.

Conclusion

In this chapter, we have presented a system for unsupervised extraction of the main activities observed in a video scene. We have proposed a general processing chain comprising three main stages, beginning with unsupervised learning of the main zones of activity in the scene. The moving objects are then characterized by employing the learned zones of activity, such as "staying in a given zone of activity", "moving from one zone of activity to another" or a combination of the two activities if the monitoring of the moving objects in the scene takes place over a long enough period of time. Finally, an automatic classification algorithm based on the theory of relational analysis is used to cluster the objects observed based on the similarity of their behavior and to discover correlations that are not at first evident simply from the raw data.

We apply the process to two scenarios. The first scenario relates to the monitoring of the activities in the entrance concourse of a metro station. The results obtained show which zones have the most intense activity in the scene under observation, and rare/uncommon behaviors such as "entering a zone with low occupancy activity" or frequent behaviors such as "buying tickets".

The second scenario relates to the surveillance of a road lane reserved for buses. Again, we are able -on the one hand -to learn the topology of the scene and -on the other hand -to reveal the normal activities (the passage of a bus into the zone) and abnormal activities (the passage of other vehicles into the reserved lane). By comparing the results obtained with the ground truth, a high level of recall and an acceptable degree of precision are obtained. We will attempt to improve these results in our future work by enriching the data and adding new informative variables to the process.

  DOU 00, LEE 02]. In view of the complexity of configuring the parameters or acquisition of knowledge, most systems are limited to object recognition [DAL 06]. Three main categories of learning techniques have been studied for behavior recognition. The first category deals with the parameters of a video interpretation program. The techniques under this category have been widely used in the case of event-recognition methods based on neural networks [FOR 04] or Bayesian classifiers [LV 06, WIL 01]. The second category consists of using unsupervised learning techniques for the detection of abnormal events on the basis of observed events [XIA 05]. The third category is centered on deducing the behavior of objects from their trajectories. This category is the most popular because of its efficiency in detecting normal/abnormal behaviors, e.g. for detecting abnormal trajectories on the roads [PIC 05, STA 05], categorizing pedestrians' trajectories [ANJ 07] or characterizing daily domestic activities [PUS 12, ZUN 12]. Hidden Markov models have also been used to detect different predefined states of normal behaviors [BAS 07, POR 04]. The approach presented below belongs to the third category.

Figure 14 . 1 .

 141 Figure 14.1. Stages in pre-processing of the data

Figure 14 . 4 .

 144 Figure 14.4. (a) Original scene observed by the camera. A1 to A5 are the zones defined by the user delimiting the scene; (b) the learned zones. Zn1 to Zn8 correspond to the zones of activity discovered by our algorithm

Figure 14 . 5 .

 145 Figure 14.5. (a) Bird's-eye view of the bus lane with the zones learned by our system. The arrow indicates the direction of the flow of buses; (b) and (c) two examples of activities with objects moving against the normal flow of traffic. The ellipses indicate the departure point of these moving objects

  )

	R	ij	=	ik ik kp x y X Y =∈ ⎡⎤ j j Zn L p x y ⎢⎥ ⎢⎥ ⎣⎦ ∑∑	[14.6]
	where
	(	, ik ik XY	)	() 38 1 cos , 0,..., ,...2 i T L π θ θπ + ⎧⎫ k =⋅ += ⎨⎬ ⎩⎭

Table 14 .2. Example

 14 of clusters of activity obtained following the application of the procedure of relational analysis

	Cluster 2 (106 elements)		Cluster 4 (16 elements)
	Modality	C ratio D ratio	Modality	C ratio D ratio
	Event in Zone 1	100	100	Event Zone 1 to Zone 2	100	100
	Dist_org_dest 0-3.84	89	92	Dist_org_dest 3.84-7.68	43	12
	Duration0-4.2	75	26	Duration 0-4.2	37	2
	Velocity 0-1.44	57	44	Velocity 2.88-4.32	37	20
	Cluster 19 (2 elements)
	Modality	C	D ratio
		ratio
	Event Zone 7 to Zone 1	100	100
	Start 22:16:20	50	100
	End 22:16:24.4	50	100

Comment [sk3]: AQ : Please provide full reference detail for references [DAL 06 ; [FOR 04; POR 04].

Comment [sk4]: AQ : Please check if the sentence [This ... activities] edited retains the intended sense.

Comment [sk5]: AQ: Perhaps you mean [take out], so we have replaced [iron out] with [take out].

Comment [sk6]: AQ: Perhaps you mean [take out], so we have replaced [iron out] with [take out].

Perhaps it should be replaced with [events]. Please check and confirm. We have replaced the word [detection] with [selection]. Please check and confirm.


F Placais

A Ducastelle

Loiseau

J Loayza

J Barjon

A Pierret

A Betz

B Plaçais

F Ducastelle

A Loiseau
email: annick.loiseau@onera.fr

Near-band edge optical properties of exfoliated h-BN layers

Figure 1 :

 1 Figure 1: Left: AFM image of an exfoliated h-BN flake. Thickness measurement by AFM along the cross section indicated by the dashed green line, indicates that the flake is composed up to 9 atomic sheets. Right: CL spectrum recorded at 4K on the area of the flake indicated by the red square. The near band edge emission is composed of S and D lines.

Abstract

Hexagonal boron nitride is a wide band gap semiconductor (~ 6.5 eV), which meets a growing interest for graphene engineering [1]. In particular electron mobility of graphene is shown to be preserved when it is supported by a h-BN film, in particular when mechanically exfoliated from h-BN crystallites. Nevertheless the use of BN sheets grown by CVD techniques remains an open issue as this material might present structural defects degrading graphene properties. It is therefore highly desirable to better know optical and electronic properties of thin BN layers, in correlation with their structural properties and the impact of the underlying BN layer on electronic properties of graphene. Until recently, these properties were poorly known due to both the scarcity of crystals and suitable investigation tools. This situation has changed thanks, first, to the development of dedicated photoluminescence (PL) and cathodoluminescence (CL) experiments running at 4K and adapted to the detection in the far UV range [2,3,4], and second to the availability of high quality single crystals [5]. H-BN has been shown to display original optical properties, governed by strong Frenkel-type excitonic effects, in the 5.5 -6 eV energy range [2,3,6]. The existence of these high energy excitons has been confirmed by reliable theoretical calculations [7,8]. Furthermore, since excitons are highly sensitive to their environment, they are easily trapped on defects such as dislocations, as revealed by combined cathodoluminescence measurements and transmission electron microscopy (TEM) observations [4]. In this work, we examine how these properties can be further exploited for the characterization of BN layers to be used as support for graphene. We carry out optical and structural characterizations of this material by combining CL at 4K in the UV range (up to 6eV) and electron microscopy. Thin layers have been obtained by mechanically exfoliating small crystallites. Exfoliated flakes were reported on SiO 2 substrates for AFM thickness measurements, as described in [9]. Results are illustrated in Figure 1 and detailed in [10]. As for the bulk, excitonic emission consists of two series of lines called S and D. In the bulk, S excitons have been found to be self-trapped, due to a Jahn-Teller effect [3]. Emission r e l a t e d t o D l i n e s i s f o u n d t o b e l o c a l i z e d o n d e f e c t s s u c h a s g r a i n boundaries, whereas in defect free areas, D lines completely vanish and only S lines are observed. D/S ratio can therefore be used as a qualification parameter of the defect densities present in the layers. Furthermore, when film thickness stands below 5-6 atomic layers, energies of S and D lines are shifted towards higher energies. This shift can be due to a perturbation in the strain environment of the exciton induced by the reduction in thickness or by the exciton confinement. Ongoing investigation of single and double atomic layers will permit to further investigate this effect and understand its exact origin. This shift in energy could be used for the determination of the number of layers, complementary to AFM measurements.


Pr Philippe Robert
email: probert@unice.fr

E Castelli

Pau-Choo Chung

T Chiroux

C F Crispim-Junior

P Mallea

F Bremond

SWEET HOME ICT technologies for the assessment of elderly subjects

Keywords: Alzheimer disease, functional impairment, Information and communication technologies, Video sensors, audio sensors

Functional assessments are designed to ascertain a person's ability to perform activities of daily living (ADL) and provide valuable diagnostic as well as care-planning information. Currently, the gold-standard for the assessment of functional ability involves clinical rating scales however scales are often limited in their ability to provide objective and sensitive information. In contrast, information and communication technologies (ICT) may overcome these limitations by capturing more fully the functional, well as behavioural and cognitive disturbances associated with Alzheimer disease (AD).

In this context, the ANR Tec San 2009 SWEET-HOME project aims at building an innovative framework for modelling ADL.

The first result of the SWEET-HOME project has been the installation in a classical consultation setting of a specific room equipped with audio and video sensors. This leads to the following results:

-physical activity recognition done by patients, (e.g., balance test, repeated transfers between sitting and standing): the monitoring system is able to detected the full set of activities with a detection rate varying from 96.9% to 100% (true positive rate).

-Activity of Daily Living: the monitoring system had an average sensitivity of 90 % and an average precision of 83.51%. Using a functional score it is possible to differentiate AD patients from healthy controls.

-Acceptability of the system: results of the survey (all the 64 participants who accepted to be assessed using the system) indicated that the assessment has been perceived as pleasant (83%)

The elderly population is expected to grow dramatically over the next 20 years. The number of people requiring care will grow accordingly while the number of people able to provide care will decrease. Without receiving sufficient care, elderly are at risk of loosing their independence. This is particularly important for persons suffering from neuropsychiatric diseases.

Alzheimer disease (AD) and related disorders represent a major challenge for health care systems with aging populations. In AD, "dementia" is diagnosed when the disease has reached the stage that the cognitive or behavioral (neuropsychiatric) symptoms interfere with social functioning or instrumental activities of daily living [START_REF] Dubois | Revising the definition of Alzheimer's disease: a new lexicon[END_REF]. The National Institute on Aging and Alzheimer's Association workgroup [START_REF] Mckhann | The diagnosis of dementia due to Alzheimer's disease: recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF] recommended that core clinical criteria, based on "functional impairment", be used to diagnose all causes of dementia, including AD, in all clinical settings. In order to determine whether functional impairment is present, the standard clinical assessment relies on questions posed to caregivers using retrospective recall of events at home, some standardized rating scales and/or the observations by a trained occupational therapist of a patient's performance during daily leisure and living activities. However, all these techniques are limited in that they cannot provide an accurate, objective and continuous measure of functional ability and no single assessment captures all areas of interest.

Finding an acceptable method of assessing functional impairment is vital since disease domains other than cognition are increasingly recognized as important outcome measures for treatment trials well as in clinical trials of anti-dementia drugs. The choice of outcome measures in these trials is often constrained by tradition and availability, and cognition-based psychometric measures are usually the preferred option. The Alzheimer's Disease Assessment Scale Cognitive subscale (ADAS-Cog), is the primary neuropsychological outcome measure for most trials in AD [START_REF] Burns | Meaningful treatment outcomes in Alzheimer's disease[END_REF]. However, the clinical relevance and « meaningfulness » of such measures has been questioned as they may not adequately identify responders to therapy or address important aspects of outcome [START_REF] Sampaio | Clinical relevance on Alzheimer's disease endpoints[END_REF], [START_REF] Olin | Clinical evaluation of global change in Alzheimer's disease : identifying consensus[END_REF]. Functional ability, on the other hand, may impact on significantly on all aspects of the disease manifestation as well as on several caregiver aspects, and may be a more sensitive marker of disease progression or treatment response.

For this reason, information and communication technology (ICT), in particular, techniques involving imaging and video processing are of interest. Such techniques enable the patients' performances and actions in real time and real life situations to be captured and accurately evaluated. ICT methods, if used to focus on caregiver-clinician-patient desired functional outcomes, may provide more clinically relevant information to identify a meaningfull response to treatment as well as to enable an accurate diagnosis of dementia. Furthermore, unanticipated changes that conventional psychometric measures may fail to capture, can be identified by such methods [START_REF] Marshall | Instrumental activities of daily living impairment is associated with increased amyloid burden[END_REF].

In this context, the ANR Tec San 2009 SWEET-HOME project aims at building an innovative framework for modelling activities of daily living (ADLs). This will be illustrated in this article with some results coming from the clinical assessment done with elderly subjects in the observation room designed for the SWEET-HOME project.

Methods

Ecological assessment of autonomy based on a Video monitoring system and multi-sensors

The aim of the ecological assessment of autonomy was to determine the extent to which the participant could undertake a list of daily activities with the respect of constraint after having been given a set of instructions. The clinical scenario was divided in several parts covering basic to more complex goal directed activities; 1/ directed activities in order to identify characteristics of gait and walk parameters, 2/ semi directed activities in order to determine the extent to which the participant could undertake a list of daily activities (for more information see Romdhane & al [START_REF] Romdhane | Automatic Video Monitoring system for assessment of Alzheimer's Disease symptoms[END_REF]).

The SWEET-HOME project was carried out in French and Taiwanese experimental sites. The ecological assessment of IADL was conducted in a specific observation room. The first one was developed at the Nice Research Memory Center. This room was equipped with everyday objects for use in ADLs and IADLs, e.g. an armchair, a table, a tea corner, a TV, a PC, and a library. The room was equipped with household appliances. Experimental data was recorded using a 2D video camera (AXIS®, Model P1346, 8 fps -frames per second), and an ambient audio microphone (Tonsion, Model TM6, Software Audacity, WAV file format, 16bit PCM/16kHz). A motion sensor (e.g., MotionPod®) was fixed on the chest of the participant to quantify their movements. MotionPod® sensor provides an index of activity and estimation about the patient posture (standing, sit-ting, lying, walking), both of them with a resolution of 1 data per second.

The Taiwanese experiments took place in indoor and outdoor environments. For the indoor experiments a room equipped with household appliances was used and experimental data was recorded using eight ambient 2D video cameras (AXIS, Model 215PTZ, 30 fps). For outdoor experiments a tri-axial accelerometer mounted on the shoes of the participants was used to analyze their gait parameters (for more information see the Crispim article [START_REF] Crispim-Junior | Alzheimer's patient activity assessment using different sensors[END_REF]).

Study participants and clinical assessment

The study was promoted by the Nice University Hospital and funded by the National Research Agency in France (ANR -ANR-09-TECS-016-01). Ethical approval was received from the Protection of Person Committee "Sud méditerrannée V" (CPP N°11029 from 2011/05/24) and the "Agence Française de Sécurité Sanitaire des Aliments et des Produits de Santé" (AFSSAPS n°B110465-30 from 2011/04/14). The informed consent was retrieved before the first assessment. Subjects were recruited at the Nice Research Memory Center including subjects with Alzheimer's Disease, Mild Cognitive impairment and normal healthy controls (for more information see Sacco& al [START_REF] Sacco | Detection of activities of daily living impairment in Alzheimer's disease and mild cognitive impairment using information and communication technology[END_REF]). In addition to the demographic and clinical assessments French participants also had to fulfill a survey in order to rate the acceptability of the experiment and use of the sensors.

The indoor directed activity step of the scenario includes repeated transfer and walking test. In Taiwan the directed activities were done in an outdoor environment aiming at analyzing During this walking period he/she performs a simple walking test of 40 m on a straight line; and a dual task test where he/she needs to walk the same distance while counting down from 100 to 1. For the semi directed activities part of the scenario the participant have to undertake a list of daily activities in a given order, after having been given a set of instructions (see Table 1).

Results

Indoor and outdoor directed activities

The proposed system uses a constraint-based ontology to model and detect events based on different sensors readings (e.g., 2D video stream data is converted to 3D geometric information that is combined with a priori semantic information, like defined spatial zones or posture estimations given by accelerometer). The ontology language is declarative and intuitive (as it uses natural terminology), allowing medical experts to define and modify the IADL models. The proposed system was tested with 44 participants (healthy=21, AD=23). A stride detection algorithm was developed by the Taiwanese team for the automatic acquisition of patients gait parameters (e.g., stride length, stride frequency) using a tri-axial accelerometer embedded in a wearable device. It was tested with 33 participants (healthy=17, Alzheimer = 16) during a 40 meters walking test. The proposed system detected the full set of directed activities of the first part of our clinical protocol (e.g., repeated transfer test, walking test) with a true positive rate of 96.9 % to 100%.

Semi directed activities

Sixteen participants with mild-to-moderate AD and 10 age-and gender-matched Healthy Control (HC) participants from the Nice Memory Center were evaluated clinically, cognitively, and functionally (Using the Instrumental Activity of Daily Living Evaluation: IADL-E). During the semi directed activity part of the scenario a measurement instrument of functional impairment was computed from quantitative and qualitative parameters collected from video recordings manually annotated by two independent clinicians (blind to the participants' clinical state).

Using data from the video monitoring system (VMS), A VMS-functional index (derived from a ratio of efficacy in ADLs [= k * time spent to correctly do the list of activities/total time in the observation room]) was validated and found to correlate strongly with cognitive (MMSE, Rho=0.81) and IADL-E scores (Rho=-.65), thus accurately differentiating AD (age=76.7 ± 4.0, MMSE=20,7± 2.0) from HC participants (age=73.9 ± 4.5, MMSE= 28.1 ± 1.3). Figure 1 shows the different functional impairment scores according to the number of qualitative parameters used to adjust the weighted ratio of efficacy RE ff (Index 0 ). The differentiation between the AD and the healthy control groups increased progressively when the cumulative impact of weights k 1 (weight related to the omission, Index 1 ), k 2 (weight related to the repetition, Index 2 ), k 3 (weight related to the realization in the correct order, Index 3 ) and k 4 (weight related to the number of attempts before completing one activity, S (ĸ 1 , ĸ 2 , ĸ 3 , ĸ 4 )) were taken into account. Each of the functional impairment scores differed significantly between the two groups (p<.05).

Feasibility survey

All the 64 French participants (22 Healthy controls, 30 MCI, 12 AD) who accepted to be tested using the system indicated that the assessment has been perceived as pleasant (83%).

The duration and level of difficulty of the assessment has been perceived as adapted respectively by 98% and 96 % of the participants. Finally 67% of the participants were ready to accept such assessment using multiple sensors in a room of their own home but only for a limited time during the day.

Conclusion

The first result of the SWEET HOME project has been the installation in France and in Taiwan of specific rooms equipped with audio and video sensors. This leads to the following results: 1/ it is possible to recognize physical activitiesperformedby patients.

The monitoring system is able to detect the full set of activities with a detection rate varying from 96.9% to 100%. 2/ using a VMS functional score it is possible to differentiate AD patients from healthy controls. This VMS score has the potential to automatically provide a pragmatic, objective and continuous measure of cognitive and functional ability which may be useful in clinical assessments of AD patients [START_REF] Mulin | Functional dementia assessment using a video monitoring system: Proof of concept[END_REF](Mullin & al) as well as for MCI patients as well as having a role as an outcome measure in clinical trials. 3/ results of the survey indicate that the assessment has been perceived as pleasant (83%).

Table 1 -List of the activities proposed to the patient during the semi directed clinical scenario •1.Walk to the reading table and read something for 2 mn •2.Walk to the coffee corner where the kettle is and boyle some water.

•3.Walk to the phone and compose this number: xxxxxx.

•4.Take the watering can and water the plant.

•5. Walk to the television and turn it on with the remote control.

•6. Walk to the reading table, take the playing cards and classify them by color (reds with reds, blacks with blacks).

•7. Take the green "ABCD" folder on the desk with the A, B, C, D sheets in it.

•8. Match the A, B, C, D sheets from the folder to one's dispersed all over the room; A with A, etc… •9. Put the "ABCD" folder back on the desk.

•10. Get out of the room.

  using the tri-axial accelerometers and the stride algorithm developed in the project. The participant is asked to walk around the ring region in the NCKU campus.

Acknowledgments

This study was supported by a grant from the ANR-09-TECS-016-01 -TecSan -SWEET HOME, by the Innovation Alzheimer and ARMEP associations and by the platform patients of the Nice CHU member of the CIU-S.


Kazuhisa Matsuzono
email: matsuzono@nict.go.jp

Vincent Roca
email: vincent.roca@inria.fr

Hitoshi Asaeda
email: asaeda@nict.go.jp

Structured Random Linear Codes (SRLC): Bridging the Gap between Block and Convolutional Codes

Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a simple yet efficient coding technique, for instance massively used for Network Coding applications. However the price to pay is a high encoding and decoding complexity, especially when working on GF (2 8 ), which seriously limits the number of packets in the encoding window. On the opposite, structured block codes have been designed for situations where the set of source packets is known in advance, for instance with file transfer applications.

Here the encoding and decoding complexity is controlled, even for huge block sizes, thanks to the sparse nature of the code and advanced decoding techniques that exploit this sparseness (e.g., Structured Gaussian Elimination). But their design also prevents their use in convolutional use-cases featuring an encoding window that slides over a continuous set of incoming packets.

In this work we try to bridge the gap between these two code classes, bringing some structure to RLC codes in order to enlarge the use-cases where they can be efficiently used: in convolutional mode (as any RLC code), but also in block mode with either tiny, medium or large block sizes. We also demonstrate how to design compact signaling for these codes (for encoder/decoder synchronization), which is an essential practical aspect.

R0-7 R3

I. INTRODUCTION

Application-Level Forward Erasure Correction (AL-FEC) codes have become a key component of many content delivery systems. They are widely used as an efficient technique to recover packet losses in Internet (usually caused by congested routers) or wireless communications (often caused by a short term fading problem). Such a network can be regarded as a packet erasure channel (or equivalently a Bit Erasure Channel, BEC), characterized by the property that the transmitted data packets are either received without error or erased (lost). Packet loss resilience may also be achieved with Automatic Repeat reQuest (ARQ) techniques (e.g., with TCP), but: a Round Trip Time (RTT) is needed to recover from a loss, which can be a issue for delay-sensitive applications (e.g., video-conferencing), the return channel may not exist (e.g., in case of a unidirectional broadcast network), and it does not This work was supported in part by the ANR-09-VERS-019-02 grant (ARSSO project). This work has been carried out in part while K. Matsuzono was visiting Inria (France) as a Post-Doctoral fellow.

scale well with the number of receivers in case of multicast or broadcast transmissions.

AL-FEC codes are a key building block of content broadcast technologies such as the FLUTE/ALC [START_REF] Paila | FLUTE -File Delivery over Unidirectional Transport[END_REF] protocol stack for the reliable and scalable transmission of files to a potentially huge number of receivers, and the FECFRAME framework [START_REF] Watson | Forward Error Correction (FEC) Framework[END_REF] when dealing with real-time delivery services as in streaming applications. AL-FEC is now deployed in all systems relying on FLUTE/ALC (e.g., 3GPP MBMS service [START_REF]Multimedia Broadcast/Multicast Service (MBMS); Protocol and codecs (Release 6)[END_REF] or ISDB-Tmm [START_REF] Yamada | Overview of ISDB-Tmm services and technologies[END_REF]) and sometimes at the link layer as well (e.g., the MPE-FEC layer of DVB-H systems [START_REF]Digital Video Broadcast (DVB); IP datacast: Content delivery protocols (cdp) implementation guidelines part 1: IP datacast over DVB[END_REF]).

In all of the previous use-cases (real-time delivery included), only block codes are considered, and the set of source packets is first grouped into blocks where AL-FEC encoding/decoding is performed. In the present work we introduce an alternative and practical AL-FEC solution that aims at encompassing both block oriented and sliding window oriented use-cases.

Random Linear Codes (RLC) are another class of AL-FEC codes. They are increasingly popular due to their simple yet powerful encoding techniques, in particular in the context of Random Linear Network Coding (RLNC) where encoding/decoding can be performed at the various network nodes, namely either at intermediate nodes (e.g., WiFi Access point or routers) or end nodes [START_REF] Ho | The Benefits of Coding over Routing in a Randomized Setting[END_REF]. At a source (sender) node or intermediate node, RLC generates encoded packets (also called encoded symbols in this paper) just by linearly combining the available symbols using encoding vectors (also called coefficients) randomly selected from a given finite field (e.g., GF (2 8 )). In general, the set of available symbols evolves over the time, i.e., RLC are used as convolutional codes. In [START_REF] Tournoux | On the fly erasure coding for time-constrained applications[END_REF], RLC is also utilized in a convolutional manner, but end-toend (i.e., there is no re-encoding within the core network), with feedback information from the receiver, which enables to achieve a full reliability when desired. The authors show that the recovery delay for lost packets is in that case independent of the RTT. However the main issue to be considered with RLC is the high decoding complexity, typically a Gaussian Elimination (GE) over a dense linear system. This problem becomes even more pronounced when the number of source symbols involved is large, and/or when the finite field is GF (2 8 ) (or higher) so as to improve the erasure recovery capabilities [START_REF] Nazir | Peformance evaluation of Raptor and Random Linear Codes for H.264/AVC video transmission over DVB-H networks[END_REF].

Since we believe that RLC can play a key role in network coding systems for the erasure channel [23], we have focused on the design of new improved RLC techniques. Our goal is to design RLC codes that:

• can be used either as block or convolutional codes;

• can be used with encoding window sizes in 2-10,000s symbols range, as very large sizes are beneficial to bulk file transfers while small values are useful for real-time contents;

• have excellent erasure recovery performance, and at the same time enable fast encoding/decoding which is essential for devices with limited computational and memory capabilities;

• enable compact signaling (e.g., transmitting the full encoding vector does not scale); In other words, we try to bridge the gap between block and convolutional AL-FEC codes. With these goals in mind, we have designed the so-called Structured Random Linear Codes (SRLC) [START_REF] Matsuzono | Not so random RLC AL-FEC codes[END_REF].In the present work, as a first step to a complete evaluation, we only focus on use-cases that require only endto-end encoding (i.e., there is a single end point for AL-FEC encoding/decoding, no matter whether this end is a "host" or a "middlebox") and we evaluate the SRLC effectiveness in terms of erasure recovery performance only.

The remainder of this paper is organized as follows: Section II introduces related work. Section III describes the proposed Structured Random Linear Codes (SRLC) in detail. Section IV evaluates the recovery performances of SRLC, and we conclude in Section V.

II. RELATED WORK

In [START_REF] Yang | Coding for a network coded fountain[END_REF], [START_REF] Ng | Finite-length analysis of BATS codes[END_REF] BATched Sparse (BATS) codes are proposed for file distribution through a communication network where intermediate nodes have coding capabilities [START_REF] Li | Linear Network Coding[END_REF]. These codes are designed so as to control the computational and storage requirements at the source, intermediate nodes, and destination, as well as the transmission overhead when transmitting the coding vector. This is made possible by the use of both an outer code (sender), that forms "batches" of coded packets, using a specific distribution for defining the number of input packets considered to create each batch, and inner codes (intermediate nodes) that perform random linear codings of packets of a given batch. The authors show the good performance of these BATCH codes, when associated to "inactivation decoding" as in [START_REF] Roca | RS+LDPC-Staircase codes for the erasure channel: Standards, Usage and Performance[END_REF], [START_REF] Shokrollahi | Raptor codes[END_REF].

In [START_REF] Mahdaviani | Gamma codes: a low-overhead linear-complexity network coding solution[END_REF], [START_REF] Mahdaviani | Overhead-optimized gamma network codes[END_REF], Gamma Codes are proposed as a family of sparse random linear network codes with outer code like BATS codes. The codes also manage "chunked" encoded packets. The key idea is to enable the outer code to play as soon as the first chunked packets are recovered, which realizes a joint decoder scheme that coordinates a proper combination of an outer coding and a basic sparse random linear network coding. It was presented that Gamma codes can achieve better reception overhead while keeping lower encoding/decoding complexity in fixed block length configuration.

These works differ from ours. We designed RLC in order to be flexibly used as either block or convolutional codes, over wide ranges of block/encoding-window sizes. Additionally, we do not distinguish outer/inner codes per se, but add a structure to the RLC approach in order to find an appropriate balance between computational complexity and erasure recovery performance.

III. STRUCTURED RANDOM LINEAR CODES (SRLC)

Let us now describe the SRLC codes, characterized by: 1) a mostly sparse binary structure, which reduces the number of symbol XOR operations and improves ITerative (IT)/Structured Gaussian Elimination (SGE) decodings [START_REF] Zyablov | Decoding complexity of low-density codes for transmission in a channel with erasures[END_REF][15] [START_REF] Pomerance | Reduction of huge, sparse matrices over finite fields via created catastrophes[END_REF]. It is a key feature to favor high speed encoding and decoding; 2) a limited use of non-binary (over GF (2 8 )) coefficients in encoding vectors. It is a key feature to favor a good erasure recovery performance; 3) the addition of a dedicated repeat-and-accumulate structure (as in Irregular Repeat-Accumulate (IRA) [START_REF] Jin | Irregular repeat-accumulate codes[END_REF] and LDPC-Staircase codes). It is a second key feature to favor a good erasure recovery performance. In the following, we first explain the SRLC approach when used in block mode, and later we extend it to the case of convolutional coding.

A. First Idea: Mixing Binary and Non-Binary Coefficients

The first idea consists in using both binary and non-binary coefficients. All the examples of this section are for the block mode case, when considering a fixed set of k source symbols. Fig. 1 shows an example parity check matrix, H, when the number of source symbols is fixed (here k = 40 source symbols) and both binary and non-binary coefficients are used. The H matrix is composed of two parts, the left side H lef t and the right side H right . The columns of H lef t correspond to the source symbols from S 0 to S 39 (A.K.A. source packets), while those of H right correspond to the repair symbols to be generated (A.K.A. repair packets). Each row of H lef t represents a constraint (or equation) used for instance to generate the repair symbol of the same row. For example, the R 0 repair symbol in the first row is generated by 1 :

R 0 = S 0 + • • • S 18 + 29 * S 19 + • • • S 38 + 77 * S 39 1 NB: "1" coefficients are omitted.
Three key parameters exist:

• k: the source block length (or encoding window size); • D bin : the density of each "sparse binary sub-matrix", given as the ratio of the number of non-zero coefficients to the total number of coefficients in a sub-matrix:

D bin = nb 1

coeffs total nb coeffs in binary submatrix

• D nonbin : the ratio of the number of non-binary columns to k (i.e., the total number of columns) in H lef t :

D nonbin = nb nonbinary columns k H lef t should be largely composed of sparse binary parts so that most equations are sparse with binary coefficients, because this is a key for high encoding/decoding speeds. However, a trade-off between speed and erasure recovery performance must be considered since being too sparse and binary negatively impacts the erasure recovery performance. Fig. 2 shows the average erasure recovery performance of a fully binary RLC with various D bin values as a function of k. The performance metric is the "average decoding inefficiency ratio", defined as the ratio of the average number of symbols needed for decoding to complete successfully to k:

inefficiency ratio = (nb symbols needed )/k = 1 + ǫ
where ǫ is called "decoding overhead", and also often expressed as a percentage. The closer to 1 (achieved with ideal codes) the ratio, the better. Assuming that our target average decoding overhead is set (arbitrarily) to 0.1%, we can see in Fig. 2 that none of the codes achieves the goal, even with binary RLC (where D bin = 1/2) which performs the best.

On the opposite, we see in Fig. 3 that adding a few dense non-binary columns (we used D nonbin = 1/40 and the same values for D bin ), the target average decoding overhead is easily achieved with k > 200. And adding more non-binary columns easily enables to further improve the decoding performance with smaller k values. We will address the question of what are the appropriate {D nonbin , D bin } tuples as a function of k in section III-C.

In the SRLC design, dense non-binary coefficients are always gathered in columns (i.e., assigned to certain symbols). The motivation is to enable the use of the high speed Structured Gaussian Elimination optimization [START_REF] Lamacchia | Solving large sparse linear systems over finite fields[END_REF], [START_REF] Pomerance | Reduction of huge, sparse matrices over finite fields via created catastrophes[END_REF], [START_REF] Roca | RS+LDPC-Staircase codes for the erasure channel: Standards, Usage and Performance[END_REF]. In this approach, when a stopping set is encountered during IT decoding, certain well chosen symbols of the system (i.e., corresponding to unknown/non-recovered source symbols) are logically removed from the linear system. This process enables IT decoding to pursue. Finally, decoding finishes with a classic Gaussian Elimination over the removed symbols, and their values are finally re-injected into equations where they were involved. Because non-binary coefficients are affected to well identified source symbols, these symbols are immediately logically removed from the linear system. The linear system therefore remains a sparse binary system, not "polluted" by non binary coefficients, and most operations consist of fast XOR operations over symbols, a key for high speed decoding.

B. Second Idea: Adding a Structure

Adding a structure to codes can be highly beneficial. For instance, the repeat-and-accumulate structure of IRA and LDPC-staircase codes significantly improves their performance: because the number of source symbols a repair symbol actually depends on increases with its index, the erasure recovery performance is improved while keeping a sparse system. However, adding this particular structure would make signaling prohibitively complex when the codes are used in convolutional mode 2 .

In order to solve this problem, we propose to add a single accumulative row to create R 0 , defined as the "heavy repair symbol", and to make all repair symbols depend upon R 0 . Fig. 4 shows an example of the proposed SRLC in block mode. In this example, R 1 is generated by:

R 1 = R 0 + S 0 + ... + 77 * S k-3 + S k-1
This simple structure enables a compact signaling to enable a receiver to determine the relationships between source and repair symbols. This is accomplished, in block mode, by the knowledge of the matrix generation algorithms (specified in a non ambiguous way in the specifications), plus the {k, D nonbin , D bin } tuple that is sent once at encoder/decoder synchronization time 3 . Because the full encoding vector is not sent along with repair packets (it is useless if H is known), the approach can scale with very large k values. We will see in section III-D how to perform signaling when SRLC are used in a sliding window mode.

C. Parameter Settings for D nonbin and D bin

Let us now determine the most appropriate values for the {D nonbin , D bin } tuple for a given k and target average performance. Of course:

• D nonbin should be as small as possible to reduce computation complexity, and

• D bin should be as small as possible so that IT decoding performs well. To find appropriate values, we did as described in Algorithm 1. We set the target average overhead to 0.1% (same value as in Fig. 3) plus a security margin (set to 0.5) so as to accommodate some fluctuations during the optimization process. As a result, we obtain a table of {D nonbin , D bin } tuples, with an entry for each k value. Note that this table (not reproduced here) does not need to be sent to the receiver(s) as the {k, D nonbin , D bin } tuple is communicated at synchronization time to the receiver(s). This provides additional flexibility since the the target code performance may be changed dynamically for the following transfers, at the discretion of the sender.

D. Application to Convolutional Coding

Convolutional coding is appropriate to situations where a fully or partially reliable delivery of continuous data flows is needed, especially when these data flows feature realtime constraints, as in [START_REF] Tournoux | On the fly erasure coding for time-constrained applications[END_REF]. SRLC can then be used as a convolutional code, in a systematic way (i.e., source symbols are sent on the network), as described in Algorithm 2. The way the encoding window is managed (i.e., how to set the encoding window start and the number k of source symbols in the window) is a key aspect that depends on the protocol in use. Set D nonbin (nb nonbinary columns); store results(k, D nonbin , D bin ); 26: end for symbol is sent after two source symbols. The only exception is at session start: the encoder waits for k = 4 source symbols to be available, and then generates two repair symbols, including a heavy repair one, R 0-3 (i.e., the XOR sum from S 0 to S 3 ). Then, after sending two more source symbols, S 4 and S 5 , the SRLC encoder considers the union of the encoding windows since the previous repair computation (i.e., from S 1 to S 5 ) and generates a new repair symbol, R 2 . R 2 accumulates the current heavy repair symbol, R 0-5 (i.e., the XOR sum from S 0 to S 5 ) to the encoding vector:

R 2 = S 1 + S 4 + 29 * S 5 + R 0-5
Here also, the encoding vector is set according to the {k, D nonbin , D bin } tuple, using pre-calculated tables as described in Section III-C, and a Pseudo-Random Number Generator (PRNG) that can be seeded by a specific value communicated to the receiver. Note that the repair symbol identifier may be used as a seed.

From a signaling point of view, we can assume that the {k, D nonbin , D bin } tuple and all the algorithms are known by both ends. In that case, it is sufficient for the sender to let the receiver know the union of the encoding windows considered (e.g., from S 1 to S 5 in the case of R 2 ), the repair symbol identifier, along with the PRNG seed (if different from the repair symbol identifier). This is all the SRLC decoder needs W ait new src symbols();

5:

Send new src symbols(); for all (new source symbol s) do

7:

h ← h ∧ s; in all tests. However SRLC is by nature rateless and the actual code rate is of little importance (i.e., the decoding overhead does not depend on the code rate). Because we do not want to define any specific channel model (e.g., the two transition probabilities of a Gilbert model), in all tests we assume the source and repair symbols are transmitted in a fully random order, which means that only the packet loss rate is of importance. Finally we assume that Gaussian Elimination decoding is used for maximum performance, rather than IT decoding (we do not consider decoding speeds in this work).

B. Recovery Capabilities in Block Mode

Let us focus on the SRLC in block mode. We measure both the average inefficiency ratio as a function of k and the decoding failure probability as a function of the number of received symbols in addition to k (in both cases decoding is said to fail as soon as at least one erased source symbol can not be recovered). The first goal of tests is to demonstrate the efficiency of the use of a heavy repair symbol. The second goal is to assess the performance of SRLC codes. However, due to the space limitations, we only show the results when k is small, from 50 to 500 symbols. Fig. 6 compares the two options for {D nonbin , D bin } = {1/50, 1/10} or {1/100, 1/20}. We see the benefits of using the heavy repair symbol, especially when k is small, on average. Let us look at Fig. 7, when k = 200 and {D nonbin , D bin } = {1/50, 1/10}. In both cases, the decoding failure probability curves are similar when the number of received symbols is only slightly higher than k (i.e., for low overheads). However we clearly see a difference when the overhead is higher, meaning that there is a significant number of tests where decoding fails without any heavy repair symbol: 245 extra symbols need to be received (22.5% overhead) for the decoding failure probability to go below 10 -5 . On the opposite, the full featured SRLC solution reaches a decoding failure probability lower than 10 -5 with 209 symbols only (a 4.5% overhead). Fig. 7-(b) also confirms the excellent recovery performance of SRLC codes, not only on average, but also when looking precisely at the decoding failure probability.

C. Recovery Capabilities in Convolutional Mode

Let us now consider SRLC in convolutional mode. Since we are focusing on real-time flows, like video/audio realtime streaming systems, a full reliability is not necessarily required (this is different from typical use in block mode, for file transfer applications). Therefore we measure the SRLC average source packet loss ratio (once decoding is finished) as a function of packet loss probability, and compare it with those of binary RLC (i.e., {D nonbin , D bin } = {0, 1/2}) and of RLC over GF (2 8 ) (all coefficients are randomly chosen in GF (2 8 )). Additionally, to make the comparison more visible, we measure the decoding failure probability of the three codes.

The performance results for the transmission of 500 source symbols in total and a window of size k = 20 symbols, are shown in Fig. 8. We see that SRLC performs the best, even when compared to RLC over GF (2 8 ), which is exceptional.

The performance results for a larger encoding window, of size k = 100 symbols, are shown in Fig. 9(a). We see that all the average loss ratios improve when compared to the k = 20 case, because a larger encoding window size offers better protection. Therefore there is no significant differences among the three codes especially on average. However, when looking at the decoding failure probability in Fig. 9(b), the SRLC performance pronouncedly becomes worse than that of RLC codes over GF (2 8 ). One reason is that SRLC uses the {D nonbin , D bin } table optimized for the block mode case. A new table should be calculated for the convolutional case.

V. CONCLUSIONS AND FUTURE WORK

This work introduces the SRLC codes, an end-to-end AL-FEC solution that is sufficiently flexible to be applied in block mode and convolutional mode. In order to enable excellent erasure recovery performance as well as fast encoding and decoding speeds, these codes have been designed in a manner that favors a mostly sparse and binary structure, with some well chosen non binary coefficients, plus a heavy binary row. Additionally, the design is such that it facilitates an efficient signaling, the parameters exchanged to synchronize encoder and decoders being kept to a minimum. These considerations make SRLC codes a very practical solution, no matter the block or encoding window size: small, medium or large. Our evaluation of their erasure recovery performance confirms the benefits

In future works we will analyze the encoding and decoding complexity (similarly the associated speeds) of SRLC codes. We will also further optimize the value of the code internal parameters when used in convolutional mode, both in a fixedsize configuration and in elastic window configuration (e.g., as in [START_REF] Tournoux | On the fly erasure coding for time-constrained applications[END_REF]).

Fig. 1 .

 1 Fig. 1. Example when used as a block code, considering only binary and non-binary coefficients.

Fig. 2 .

 2 Fig. 2. Average inefficiency ratio of binary RLC, for various binary densities (1/2, 1/5, 1/10, 1/20), as a function of k.

Fig. 3 .

 3 Fig. 3. Average inefficiency ratio of RLC with non-binary column (1/40) with the same binary densities, as a function of k.

Fig. 4 .

 4 Fig. 4. SRLC example as a block code.

Fig. 5 6 : 7 : 8 :

 5678 illustrates the use of SRLC in the simple sliding window mode. Here the encoding window has a fixed size, k = 4, and slides in a regular way over the source symbol flow. The target code rate (CR = 2/3 is such that one repair Algorithm 1 Finding the right {D nonbin , D bin } values. 1: target overhead ← 0.001; /* for instance */ 2: security margin ← 0.5; /* for instance */ 3: for k = 2 to 10000 do 4: /* First of all, find D nonbin if D bin is set to 0.5 */ 5: D bin ← 0.5; Get nb 1 coeffs(D bin ); for nb nonbinary columns = 0 to k do Get average overhead(k, 9: nb nonbin column, nb 1 coeffs); 10: if (average overhead < target overhead * security margin) then 11:

Algorithm 2 1 :

 21 Building repair symbols in convolutional mode. Alloc repair symbol buffer(r); /* reset to zero as well */ 2: Alloc heavy repair symbol buffer(h); /* reset to zero */ 3: while (true) do 4:

Fig. 5 .Fig. 6 .

 56 Fig. 5. SRLC example as a convolutional code, with fixed k = 4 CR = 2/3

Fig. 7 .

 7 Fig. 7. Decoding failure probability when k = 200 and (D nonbin , D bin ) = (1/50, 1/10)

Fig. 8 .

 8 Fig. 8. Performances of SRLC, Binary RLC and RLC over GF (2 8 ) in a sliding window (convolutional) mode when the total number of source symbols tot src = 500, encoding window size k = 20, CR = 2/3.

Fig. 9 .

 9 Fig. 9. Performances of SRLC, Binary RLC and RLC over GF (2 8 ) in a sliding window (convolutional) mode when the total number of source symbols tot src = 2500, encoding window size k = 100, CR = 2/3.

  Then find smallest D bin for the selected D nonbin */

	12:	break;
	13:	end if
	14:	end for
	15: /* 16: while (true) do
	17:	nb 1 coeffs --;
	18:	Get average overhead(k,
	19:	nb nonbin column, nb 1 coeffs);
	20:	if (average overhead > target overhead) then
	21:	Set D bin (nb 1 coeffs + 1);
	22:	break;
	23:	end if
	24:	end while
	25:

This is because the encoding window may move in a non predictable way, and in presence of erasures, identifying the exact way all the previously erased symbols have been encoded is not easy.

This can take several forms, usually in the "file" description part of a File Delivery Table (FDT) with FLUTE[START_REF] Paila | FLUTE -File Delivery over Unidirectional Transport[END_REF].

Set nb repair to send(total new src symbols, if (Decide to send heavy repair()) then 13:

Send repair symbol(h); Reset repair symbol memory(r);

16:

Set new union of encoding windows(k); for all (src symbol s in encoding window) do nb repair to send --;

34:

end while 35: end while to know to generate the constraint equation associated to this repair symbol, even for large encoding window sizes.

In practice, the heavy repair symbols are transmitted periodically in order to remove the long term dependencies they create. This is useful if past source symbols remain impossible to recover by a given receiver (who for instance joined the session late).

IV. PERFORMANCE EVALUATION RESULTS

In this section we evaluate the SRLC erasure recovery performance both in block and convolutional modes.

A. Experimental Setup

All the tests are carried out with the performance evaluation tools provided by our OpenFEC.org project [START_REF]OpenFEC.org: because open, free AL-FEC codes and codecs matter[END_REF] and a modified version of the Kodo library [START_REF]Kodo network coding library[END_REF] for the codec implementation. We use the pre-calculated values for {D nonbin , D bin } (see Algorithm 1) and we choose CR = 2/3 S0 S1S2S3S4 S6S7 S8 S9S10 S12 . . . . . S5 S11