Stefan Duffner

Christophe Garcia

Visual Focus of Attention estimation with unsupervised incremental learning

Keywords: Unsupervised learning, pattern clustering, image sequence analysis

In this paper, we propose a new method for estimating the Visual Focus Of Attention (VFOA) in a video stream captured by a single distant camera and showing several persons sitting around table, like in formal meeting or videoconferencing settings. The visual targets for a given person are automatically extracted on-line using an unsupervised algorithm that incrementally learns the different appearance clusters from low-level visual features computed from face patches provided by a face tracker without the need of an intermediate errorprone step of head-pose estimation as in classical approaches. The clusters learnt in that way can then be used to classify the different visual attention targets of the person during a tracking run, without any prior knowledge on the environment and the configuration of the room or the visible persons. Experiments on public datasets containing almost two hours of annotated videos from meetings and video-conferencing show that the proposed algorithm produces state-of-the-art results and even outperforms a traditional supervised method that is based on head orientation estimation and that classifies visual focus of attention using Gaussian Mixture Models.

I. INTRODUCTION

G ENERALLY, the Visual Focus of Attention (VFOA) of a person denotes the target -an object or another person -the person is looking at, at a given point in time (see Fig. 1). The automatic estimation of the VFOA of a person from video is of great importance in many applications, such as human-computer interaction, video-conferencing, smart meeting rooms, or human behaviour analysis in general, and much research has been conducted in this area in the past years.

A. Related Work

Principally, the VFOA of a person is defined by the person's eye gaze direction. Many studies about automatic gaze estimation from video exist [START_REF] Wang | Study on eye gaze estimation[END_REF], [START_REF] Wang | Eye gaze estimation from a single image of one eye[END_REF], [START_REF] Morimoto | Eye gaze tracking techniques for interactive applications[END_REF], [START_REF] Weidenbacher | Detection of head pose and gaze direction for human-computer interaction[END_REF], [START_REF] Magee | A human-computer interface using symmetry between eyes to detect gaze direction[END_REF], [START_REF] Funes Mora | Gaze estimation from multimodal kinect data[END_REF], but their use is mostly limited to close-up and near-frontal views of a person's face, for example in Human-Computer Interaction applications. Other works [START_REF] Voit | Tracking head pose and focus of attention with multiple far-field cameras[END_REF], [START_REF]Deducing the visual focus of attention from head pose estimation in dynamic multi-view meeting scenarios[END_REF], [START_REF] Dong | Visual focus of attention recognition in the ambient kitchen[END_REF] rely on the fusion of information from several cameras. But often the spatial camera configuration is very constrained or a preceding calibration step is required, which can be difficult or even impossible depending on the application and environment. Also depth sensors, like Kinect, have been used for head pose and eye gaze estimation [START_REF] Funes Mora | Gaze estimation from multimodal kinect data[END_REF]. Although, their precision depends highly on the distance of the person from the sensor, this is an S. Duffner and C. Garcia are with the Université de Lyon, CNRS, INSA-Lyon, LIRIS, UMR5205, F-69621, France interesting direction for future research beyond the scope of this work. In this paper, we will focus on (non-intrusive) scenarios where a single camera is fixed at a few meters from the filmed persons and where the persons stay roughly at the same places, like in formal meetings or video-conferencing applications (as illustrated in Fig. 1).

Previous work on VFOA analysis in such open spaces has mostly been based on the estimation of head pose as a surrogate for gaze [START_REF] Stiefelhagen | Modeling focus of attention for meeting indexing[END_REF], [START_REF] Langton | Do the eyes have it? cues to the direction of social attention[END_REF], [START_REF] Stiefelhagen | Tracking focus of attention for human-robot communication[END_REF], [START_REF] Stiefelhagen | Head orientation and gaze direction in meetings[END_REF], [START_REF] Siracusa | A multi-modal approach for determining speaker location and focus[END_REF], [START_REF] Ba | A Rao-Blackwellized mixed state particle filter for head pose tracking[END_REF], [START_REF] Otsuka | Conversation scene analysis with dynamic bayesian network based on visual head tracking[END_REF], [START_REF]Deducing the visual focus of attention from head pose estimation in dynamic multi-view meeting scenarios[END_REF], [START_REF] Zhang | Monitoring visual focus of attention via local discriminant projection[END_REF], [START_REF] Ba | Recognizing visual focus of attention from head pose in natural meetings[END_REF], [START_REF] Peters | Investigating shared attention with a virtual agent using a gaze-based interface[END_REF], [START_REF] Benfold | Unsupervised learning of a scene-specific coarse gaze estimator[END_REF], [START_REF] Chen | We are not contortionists: Coupled adaptive learning for head and body orientation estimation in surveillance video[END_REF], [START_REF] Asteriadis | Visual focus of attention in non-calibrated environments using gaze estimation[END_REF], [START_REF] Bazzani | Social interactions by visual focus of attention in a three-dimensional environment[END_REF]. This is done either globally, e.g. by learning to classify image patches of the head at different angles based on low-level visual features or locally, i.e. by localising certain facial features [START_REF] Xiong | Supervised descent method and its applications to face alignment[END_REF], [START_REF] Ren | Face alignment at 3000 fps via regressing local binary features[END_REF] and by geometrically and statistically inferring the global orientation, or a combination of the two [START_REF] Asteriadis | Visual focus of attention in non-calibrated environments using gaze estimation[END_REF] (see [START_REF] Murphy-Chutorian | Head pose estimation in computer vision: a survey[END_REF] for a literature survey). However, these algorithms mostly require the person(s) to face the camera more or less and be rather close to it in order to have a relatively high image resolution of the face. Using video, head pose estimation can be included in a joint head and pose tracking algorithm [START_REF] Lu | Model and exemplarbased robust head pose tracking under occlusion and varying expression[END_REF], [START_REF] Ba | A Rao-Blackwellized mixed state particle filter for head pose tracking[END_REF], [START_REF] Lanz | Joint bayesian tracking of head location and pose from low-resolution video[END_REF], [START_REF] Ricci | Learning large margin likelihoods for realtime head pose tracking[END_REF]. Early works of Stiefelhagen and Zhu [START_REF] Stiefelhagen | Modeling focus of attention for meeting indexing based on multiple cues[END_REF], for example, used a Gaussian Mixture Model (GMM) on head pose angles to estimate VFOA. The model is initialised with k-means and further updated with an Expectation-Maximisation algorithm. They also showed that using the other participant's speaking status increases the VFOA performance. Note that, in this paper, we will concentrate on methods that are relying on visual information, although there are previous works that use audio, actions or or types of cues to infer the VFOA [START_REF] Stiefelhagen | Modeling focus of attention for meeting indexing based on multiple cues[END_REF], [START_REF] Siracusa | A multi-modal approach for determining speaker location and focus[END_REF], [START_REF] Ou | Predicting visual focus of attention from intention in remote collaborative tasks[END_REF], [START_REF] Ba | Visual activity context for focus of attention estimation in dynamic meetings[END_REF]. Otsuka and Yamato [START_REF] Otsuka | Conversation scene analysis with dynamic bayesian network based on visual head tracking[END_REF] proposed a method based on a Dynamic Bayesian Network that also analyses the group behaviour and detects certain conversational patterns. A GMM and Hidden Markov Model (HMM) approach for modelling and recognising VFOA was proposed by Smith et al. [START_REF] Smith | Tracking the visual focus of attention for a varying number of wandering people[END_REF] for people walking by an outdoor advertisement and by Ba and Odobez [START_REF] Ba | Recognizing visual focus of attention from head pose in natural meetings[END_REF] for analysing meeting videos. In the latter work, the authors also presented a MAP adaptation method to automatically adapt the VFOA model to the individual persons as well as a geometrical model (based on findings from [START_REF] Freedman | Eye-head coordination during headunrestrained gaze shifts in rhesus monkeys[END_REF], [START_REF] Hayhoe | Eye movements in natural behavior[END_REF]) combining head orientation and eye gaze direction. Voit and Stiefelhagen [START_REF]Deducing the visual focus of attention from head pose estimation in dynamic multi-view meeting scenarios[END_REF], [START_REF] Voit | 3D user-perspective, voxel-based estimation of visual focus of attention in dynamic meeting scenarios[END_REF] built on this geometrical model and presented VFOA recognition results on a dynamic dataset with multiple cameras. Recently, Ba and Odobez [START_REF] Ba | Multiperson visual focus of attention from head pose and meeting contextual cues[END_REF] extended their approach on VFOA estimation for meetings with a Dynamic Bayesian Network (DBN) that incorporates contextual information, like speaking status, slide change, and modelling conversation behaviour. Dong et al. [START_REF] Dong | Visual focus of attention recognition in the ambient kitchen[END_REF] proposed an approach also based on a DBN which is similar to ours in the fact that they recognise VFOA by comparing tracked face image patches with a set of clusters modelling the face appearance for each attention target. However, the difference to our approach is that the clusters in their algorithm are trained before the tracking and in a supervised way. Thus, the number of targets and the targets itself are known in advance.

The recent work of Benfold et al. [START_REF] Benfold | Unsupervised learning of a scene-specific coarse gaze estimator[END_REF] is similar to ours in that they also perform unsupervised training on head images in order to determine where people look at in a given video. However, their approach is not incremental (although they claim that it could be extended) and needs an initial training of prior models using hand-labelled ground plane velocities and gaze directions of persons in a given video. They do not extract VFOA but head orientation (using a given number of classes), and they apply their approach to video surveillance data where they take advantage of people moving, which is different from our indoor scenario. On the one hand, the advantage of their probabilistic model -a conditional random field (CRF) -is that a more powerful discriminative head pose classifier can be learnt taking into account several hidden variables (walking speed, angle velocities etc). On the other hand, the complexity of learning and inference is increased, and the model is also independent from the head tracking as opposed to our approach that allows for a purely sequential and joint inference.

B. Motivation

As experimental results of these previous works show, head pose can be used effectively to estimate the VFOA of a group of people, e.g. in a meeting room, to a certain extend. However, there are certain drawbacks of this approach: for example, in uncontrolled environments it is difficult to estimate head pose reliably because it often requires a large amount of annotated training data of head appearances or shapes beforehand in order to model all the possible variations of a head and face among different people as well as for a given individual. These data are often not available, or too time-consuming to produce. Further, for accurate head pose estimation results, a relatively precise localisation of the head, the face, or facial featurescommonly called face alignment -is crucial but challenging in unconstrained application scenarios.

Another difficulty in automatic VFOA estimation is to determine the number of semantic visual targets for a given person in a video and to map them to given head pose or eye gaze angles. A preceding supervised training step is commonly performed on separate video data, and in some approaches the model (e.g. a GMM) is adapted on-line to a given video. However, it is desirable to avoid this scenedependant training step or in some applications it might even be impossible. Further, the subsequent model adaptation can in many cases not cope with a different number of focusing targets or when the persons' locations differ too much from those in the training data.

In this paper, we propose a novel approach that alleviates these problems. Our algorithm, given a video stream from a single camera and the rough 2D position estimation of a person's head, incrementally learns to automatically extract the VFOA of the person without explicitly estimating head pose or gaze and without any prior model of the head, face, the room configuration, or other external conditions. The proposed method learns on-the-fly the different classes of targets in an unsupervised way directly from the low-level visual features. This means also that, as opposed to supervised algorithms, it will not assign labels to the different targets (e.g.'table', 'screen', 'person 1'). However, we will experimentally show that the proposed unsupervised approach is able to identify and estimate the (unlabelled) targets with higher accuracy than a classical supervised approach. The fact that no pre-trained model is needed makes this approach especially interesting for applications where the specific environment, as well as the configuration of the room and the filmed persons is not known a priori, and where an explicit training phase is not possible.

C. Contribution

In [START_REF] Duffner | Unsupervised online learning of visual focus of attention[END_REF], we introduced a basic algorithm for unsupervised incremental learning of VFOA clusters from low-level features. We have improved this work in the following way:

• The VFOA recognition has been changed from a simple frame-by-frame classification into a Hidden Markov Model (HMM) with full Bayesian inference on an automatically learnt observation model and state transition distribution.

• The VFOA estimation process has been integrated in the Particle Filter framework that now performs a combined face and VFOA tracking. • The cluster management of the incremental learning algorithm has been extended, notably to allow also for merging two clusters into one during the training. • Finally, more extensive experiments have been performed varying different parameters of our approach, showing an improved classification accuracy compared to [START_REF] Duffner | Unsupervised online learning of visual focus of attention[END_REF] as well as a classical supervised VFOA recognition approach. The outline of the paper is as follows. Section II briefly describes the overall VFOA estimation procedure. In section III, the overall face and VFOA tracking algorithm is explained. Section IV describes the unsupervised incremental learning algorithm. Finally, experimental results are presented in section V, and in section VI we draw our conclusions.

II. OVERALL PROCEDURE

The principal procedure of our approach is illustrated in figure 2. First, a basic tracking algorithm is initialised and tracks a rectangular face region throughout the video stream. The image patch inside the tracked face region is extracted and visual features are computed to initialise the VFOA model at the first video frame and to update it at each subsequent frame during the training phase (see section IV). An incremental clustering algorithm on these low-level features is used to learn face appearances corresponding to attention targets of the person. At the same time a matrix modelling the transition probabilities between the different targets is learnt, and together with the clusters forms a continuous HMM. Note that this incremental learning is done on-the-fly and does not require any prior knowledge on head pose or room configuration.

After a given number of iterations (a couple of minutes from the beginning of a video) the training phase stops and the Particle Filter continues to jointly track face position and VFOA of a person using the learnt HMM model, i.e. the transition probabilities and the face clusters. (see section III).

Note also that we assume that the VFOA targets are not moving, and our incremental algorithm learns the underlying "static" distributions in a sequential manner as opposed to on-line learning algorithms which are also sequential but can further adapt to non-stationary distributions.

In order to facilitate understanding, before describing the main contribution of the paper, i.e. the unsupervised VFOA learning, we will first explain the underlying tracking framework in the following section.

III. FACE AND VFOA TRACKING

For tracking the face position and VFOA of a person, we used the Sequential Monte Carlo algorithm, commonly known as Particle Filter (c.f . [START_REF] Pérez | Color-based probabilistic tracking[END_REF], [START_REF] Ricci | Learning large margin likelihoods for realtime head pose tracking[END_REF], [START_REF] Duffner | A track creation and deletion framework for long-term online multiface tracking[END_REF]). It provides a solution for the classical recursive Bayesian model, where, assuming we have the observations Y 1:t from time 1 to t, we estimate the posterior probability distribution over the state X t at time t:

p(X t |Y 1:t ) = 1 C p(Y t |X t ) × Xt-1 p(X t |X t-1 )p(X t-1 |Y 1:t-1 ) dX t-1 , (1)
where C is a normalisation constant. In our experiments, the state X t = ( Xt , v) is composed of the state of the face Xt = (x, y, s) with x, y being its position and s being its bounding box scale factor, as well as the current VFOA target index v ∈ 1..V . The dynamics of the face state p( Xt | Xt-1 ) are defined by a first-order auto-regressive model with Gaussian noise:

p( Xt | Xt-1 ) = N ( Xt-1 ; 0, Σ p ) . (2)
The dynamics of the discrete VFOA target index v are defined by transition probability matrix

A := [a ij ], i, j = 1..V with a ij := p(v t = j|v t = i) (3)
being the transition probability from VFOA target i to j.

The co-variance matrix Σ p = diag(σ px , σ py , σ ps ) of the autoregressive model is fixed, whereas the matrix A is learnt online during the tracking of a person in a given video stream. Details on how A is learnt are presented in section IV-B.

The observations likelihood is defined as the product of a colour likelihood and texture likelihood::

p(Y t |X t ) = p(Y C t |X t )p(Y T t |X t ) , (4)
where the colour likelihood is used to track the position and size (x, y, s) of the face bounding box, and the texture likelihood is mainly used to track the VFOA target v. We define:

p(Y C t |X t ) ∝ exp -λ 1 9 r=1 D 2 C [h * r , h r (X t )] , (5)
where λ 1 is a constant, h r (X t ) are HSV colour histograms extracted from a grid of r = 9 cells centred at X t , h * r is the reference histogram initialised from the face region in the first frame, and D C is the Bhattacharyya distance. As in [START_REF] Pérez | Color-based probabilistic tracking[END_REF], the histogram bins for the H and S channels are decoupled from the V channel. Also the quantisation is applied at two different levels, i.e. 4 bins and 8 bins, to improve the robustness under difficult lighting conditions. This leads to an overall colour observation vector size of 9 • (8

• 8 + 8 + 4 • 4 + 4) = 828.
The texture likelihood is defined similarly:

p(Y T t |X t ) ∝ exp -λ 2 16 r=1 D T [µ r,v , t r (X t )] , (6)
where λ 2 is a constant, t r (X t ) are Histograms of Oriented Gradients (HOG) (see description below) extracted (similarly to h r ) from a grid of 16 cells (indexed by r) centred at X t , and µ r,v are the reference histograms corresponding to the VFOA target index v in X t . The overall texture model is composed of a set of N -dimensional clusters with means µ r,i where each cluster i ∈ 1..V corresponds to a VFOA target. D T is the normalised Euclidean distance:

D T (µ r,i , t r (X t )) = N j=1 (t r,j (X t ) -µ r,i,j ) 2 σ 2 j + ǫ , (7)
with ǫ being a small constant avoiding division by zero. The feature vectors t r (X t ) constitute the visual observations used for recognising the VFOA targets of a person in a video by means of p(Y T |X t ). They are computed on a 4 by 4 grid of non-overlapping cells on a face image patch as illustrated in Fig. 3(a). For each cell, two normalised twodimensional histograms of unsigned oriented gradients and magnitudes are computed using a specific quantisation scheme illustrated in Fig. 3(b). The gradient orientation is quantised in 4 bins and the magnitude in 2 bins. An additional bin (with no orientation) is used for very weak gradients (in the centre of the half circle in the diagram). Also, to improve the overall robustness and discriminative power, we compute two histograms at different quantisation levels for orientation: 4 and 8, and normalise each of them separately. Thus, the dimension N of the feature vector is: 16

• (4 • 2 + 1 + 8 • 2 + 1) = 416.
One advantage of these histogram features is that they are relatively robust to small spatial shifts of the overall bounding box, which frequently occur with common face tracking methods.

IV. LEARNING VFOA

The VFOA model can be regarded as a dynamic HMM estimating the hidden variable v, the VFOA target index, from the observed features t r (X t ), illustrated in Fig. 4. It consists of two main parts. First, the data model that is used for the likelihood computation in Eq. 6 and that contains the k cluster means µ i and a global co-variance matrix Σ, and second, the matrix A (Eq. 3) defining the transition probabilities from one cluster to another. All, these parameters are learnt online during the training phase, and used subsequently in the tracking (c.f . section III). After training, the learnt parameters µ i , Σ, and A of the HMM are used in the Particle Filter framework explained in the previous section to jointly estimate the posterior probability of the state X t at each time step. In the following, the training procedures are described in more detail.

A. VFOA clustering

The visual feature vectors t r ( Xt ) computed on the image region corresponding to the mean state of the current distribution at time t are used to incrementally learn the VFOA classes. To this end, we propose a specific sequential k-means clustering algorithm with an adaptive number of clusters. The algorithm constructs a model of k clusters corresponding to the VFOA classes and described by their mean feature vectors µ r,i (i = 1..k) and a global diagonal co-variance matrix Σ = diag(σ 1 , . . . , σ N ). For better readability, in the following notation, we drop the indexes for the cell r and the time step t, denoting the current cluster means as µ i and the current feature vector as t. Algorithm 1 summarises the main learning procedure. At each time step the observed feature vector t Algorithm 1 Incremental VFOA cluster learning algorithm

k = k ini µ i = t 0 i = 1..k n i = 0 i = 1..k Σ = Σ ini for t = 1 to T do c = argmin i (D T (t, µ i )) ⊲ get closest cluster DT = 2 N (N +1) k i=1 k j=i+1 (D T (µ i , µ j )) if D T (t, µ c ) > θ c DT then ⊲ add new cluster k ← k + 1 n k = 1 µ k = t else n c ← n c + 1 ⊲ update closest cluster µ c ← µ c + 1 nc (t -µ c ) end if incrementally update Σ for each cluster pair (i,j) do ⊲ merge clusters if D T (µ ci , µ cj ) < θ d DT then µ i = (n i µ i + n j µ j )/(n i + n j ) n i = n i + n j remove cluster j k ← k -1 end if
end for end for is computed, and the closest cluster c is determined using the normalised Euclidean distance (Eq. 7). Also, the mean distance DT between each of the k clusters is calculated, and a new cluster is created if the distance of the current feature vector to the closest cluster is greater than θ c DT , where θ c is a parameter of our algorithm (set to 2 in our experiments). Then, the mean vector µ c of the closest cluster as well as the global covariance matrix Σ are incrementally updated using the current feature vector t. In the previous version [START_REF] Duffner | Unsupervised online learning of visual focus of attention[END_REF] of the algorithm, the closest cluster means of the previous time steps and neighbouring clusters were also updated. However, with the integration of the model into the Particle Filter framework, this did not improve the overall performance significantly. Thus, we removed this step. Finally, pairs of clusters are merged together if the distance of their means are below the threshold θ d DT (with θ d = 0.01 in our experiments). At each time step, the algorithm classifies the observed features t from the mean state of a face into one of the k clusters: c, and, as we will show in the following experimental results, the learnt classes correspond to a large degree to specific targets of VFOA.

B. VFOA Transition Model

The transition probability matrix A of equation 3 is learnt on-line during the training phase at the same time as the cluster centres. The main procedure is the following. The visual feature vectors t of the image patch corresponding to the current mean state are extracted, and the closest cluster c t according to the normalised Euclidean distance (Eq. 7) is computed. Then, the transition probabilities a ct-1,j := p(v = j|v = c t-1 ) are linearly updated, using the following equation:

a ct-1,j = γ½ j=ct + (1 -γ)a ct-1,j ∀j ∈ 1..k, (8)
where ½ x denotes the indicator function, and the constant γ = 0.001. Thus, the transition probability from c t-1 to c t is increased, and from c t-1 to any other cluster j is decreased. Also, a new row and column is added if a new cluster is created and inversely if a cluster is removed. At the end of each iteration, the row c t-1 that has been updated is normalised to sum up to 1.0. Algorithm 2 summarises the overall procedure. In many cases, the learnt transition matrix will have high Algorithm 2 Incremental learning of the transition matrix initialise A to uniform distribution:

a ij = 1 k i, j ∈ 1..k for t = 1 to T do adapt the size of A to k × k c t = argmin i D(t, µ i ) a ct-1,j = γ½ j=ct + (1 -γ)a ct-1,ct
normalise row c t-1 to sum up to 1.0 end for values on the diagonal (staying in the same state most of the time) and low values elsewhere. Of course, this depends on the dynamics of the scene. In our formal meeting setting, people are interacting frequently and changing their attention targets quite often. Thus, this seems not to be a limitation. But even in more static settings (e.g. a person giving a talk), this model is still appropriate. And we can observe this with less active persons in some videos in our experiments. Clearly, transitions with very low probabilities can still be "triggered" if the observation likelihood of the target state is high enough. Nevertheless, to prevent extreme cases where a transition probability becomes zero and thus a state inaccessible, in our experiments, we set a very small lower boundary (10 -3 ) for the transition probabilities.

V. EVALUATION

A. Data

We evaluated the proposed approach on three public datasets from different scenarios, each containing a certain number of persons sitting around a table and filmed roughly from the front (see Fig. 5). Note that we do not evaluate the accuracy of face or head pose tracking, as this is not the main contribution of the paper. Our main goal is to correctly estimate the VFOA of a person, which requires a robust face tracking system. The VFOA targets are different for each datasets, due to the scenario and the layout of the room. The three datasets are:

TA2 1 [41]: in this set there are two videos from two different rooms where people communicated over a video-conferencing system and performed a shared task on a laptop in front of them. In the first video, there are four persons and in the second there are two. The defined VFOA targets are the table, the camera, and the other persons, i.e. 5 targets for the first video and 3 for the second. For each person, 7 500 frames (5 minutes 30 minutes in total, have been annotated.

IHPD 2 [42] PETS 2003 3 : this dataset contains two videos from a formal meeting of six participants (scenario D), where each video shows 3 of the persons roughly from the front (similar to IHPD). Here, the VFOA targets that have been annotated for each participant are the other five participants. The provided VFOA annotation for the 6 persons and 47 000 frames (∼30 minutes) in total has been used.

Table I summarises the properties of these datasets. Annotation has been done manually and frame-by-frame, where frames with ambiguous visual focus and transition phases have not been annotated.

B. Qualitative evaluation

First, we will show some qualitative results on the clustering that is obtained on some of the videos. Fig. 6 illustrates the result of the proposed on-line clustering algorithm (Alg. 1) for six different persons and videos. Each point represents a 2D projection of the 416-dimensional gradient feature vectors t r ( Xt ) extracted from the mean state at time t (after the training phase). The linear embedding has been performed by applying multi-dimensional scaling with Euclidean distance measure on the whole data. Different colours (and point shapes) correspond to different labels produced by a k-Nearest Neighbour classifier using the normalised Euclidean distance, Eq. 7, and the learnt cluster means µ i as references. Note that the clusters means have been trained during the training phase, i.e. the first few minutes of a video. There are two difficulties that we want to emphasise here: first, the test data might be distributed slightly differently (e.g. the person's main focus changes), and second, the training data arrives sequentially and in a non-random order, i.e. a person's focus changes slowly and might be static for long periods. Note also, that the 2D projection of all points suggests that clustering is difficult in many cases, like in the top middle, bottom left, and bottom right example where cluster centres and frontiers are not so clear. Nevertheless, the output of the algorithm looks reasonable, apart from the bottom right example.

In order to experimentally verify if the learnt clusters correspond to different VFOA targets, we saved for each tracking run the face image regions corresponding to the feature vectors t r ( Xt ) that were closest to the cluster centres µ i . Fig. 7 shows some examples. We can see that the images come from different head poses mostly corresponding to real VFOA targets. Clearly, some targets might not be captured by the model, as in the top right example of Fig. 7 (corresponding to the leftmost person in the top-left image of Fig. 5) because the three other persons are almost seated in the same gaze direction. In the bottom right example, two clusters (corresponding to the second and fourth image) have been created for the same VFOA target: the table. Apart from these errors, the results mostly make sense. Finally, Fig. 8 visualises the VFOA tracking over time for two example videos. At each time step t, the red circles show the ground truth targets, and the blue crosses the output of the tracking algorithm, i.e. the v component of the mean state Xt . Some targets have not been learnt by the initial clustering and thus are not recognised. This is because these targets are less frequent (apart from target 4 in the bottom example), and thus, potential clusters would be sparsely represented and difficult to estimate. In the bottom example, from the IHPD dataset, targets 2 and 4 corresponds to persons that are sitting very close to each other. Here, the person's VFOA is mostly controlled by his eye gaze, and the head pose is almost the same. Thus, only target number 2 is recognised. Note that, as our algorithm is unsupervised, we do not have the actual estimated VFOA targets (i.e. meaningful labels) that we can directly compare to the ground truth. For evaluation purposes, after running our method on a whole video, we therefore assign to each cluster the target that maximises VFOA accuracy, i.e. we assume that we know which target label each cluster corresponds to. We believe that this is not a very restrictive assumption, as the labels could be assigned in a separate processing step, for example by incorporating a more general discriminative classifier trained beforehand.

C. Quantitative evaluation

Additionally, we quantitatively evaluated the complete VFOA tracking algorithm on the three datasets described above by initialising it manually with a bounding box around the face and measuring the VFOA recognition accuracy by assigning a label to each cluster as described above, and counting the Frame-based Recognition Rate (FRR) of the VFOA for all the videos and averaging it over each dataset and over several runs. The FRR is simply the proportion of frames with correctly recognised VFOA:

F RR = N c N t , (9)
where N c is the number of correct classifications, and N t is the total number of annotated video frames. As our algorithm is learning the VFOA model incrementally, we need to account for a certain training phase, which we do not include in the evaluation. We used 8 000 (∼ 5 min.) training frames in the beginning of the videos (not annotated), and evaluated the FRR on the following sequence with annotation. This length has been chosen in order to have enough training data for all the VFOA targets of a person, as sometimes a target is focused for the first time only after several minutes. A more detailed analysis on this parameters is given below (Fig. 9). In our first experiment, we studied the influence of using a variable number of clusters k, i.e. dynamic cluster creation and merging in Alg. 1, compared to using a fixed k. Table II shows the results for the three datasets. It can be seen that the k with the highest average FRR depends on the dataset. However, on average, a variable cluster number gives the best average FRR over all datasets. Therefore, we used a variable k for the following experiments (as presented in Alg. 1).

Further, we replaced the normalised Euclidean distance D T of Eq. 7 with the simple Euclidean distance:

D ′ T (µ r,i , t r (X t )) = N j=1 (t r,j (X t ) -µ r,i,j ) 2 , (10)
as well as the Bhattacharyya distance:

D ′′ T (µ r,i , t r (X t )) = 1 - N j=1 t r,j (X t )µ r,i,j . (11)
The results summarised in table III show that the normalised Euclidean distance D T (Eq. 7) largely outperforms the other distances in terms of the FRR on all the dataset. In another set of experiments, we varied the number of iterations for our incremental training algorithm in order to understand the impact of this parameter on the overall VFOA recognition rate. Figure 9 shows the results. As for the other experiments, the VFOA recognition rates are averaged over several runs and always computed on the same number of frames (irrespective of the number of training iterations). It can be seen that using very few training iterations, i.e. below 1000-2000, deteriorates the performance for all datasets. And beyond around 4000 iterations, the performance stays relatively stable.

Finally, we compared the proposed approach with three other approaches:

• supervised: a state-of-the-art supervised approach, that uses a specific face detection and tracking algorithm, a head pose estimator as in [START_REF] Ricci | Learning large margin likelihoods for realtime head pose tracking[END_REF], and Gaussian Mixtures Models (GMM) to model different VFOA targets in terms of head pose pan and tilt angles as in [START_REF] Stiefelhagen | Modeling focus of attention for meeting indexing based on multiple cues[END_REF], [START_REF] Ba | Recognizing visual focus of attention from head pose in natural meetings[END_REF]. In this approach, the head pose model is trained beforehand in a supervised way, and the GMM parameters have been partly trained and partly defined manually. • no PF: a variant of the proposed approach that does not integrate the VFOA estimation into the Particle Filter tracking, i.e. v is not included in the state vector and is estimated frame-by-frame by a k-NN classifier using the feature vectors t( Xt ) of the mean state and the cluster means µ i , as in our previous work [START_REF] Duffner | Unsupervised online learning of visual focus of attention[END_REF]. • PF, fixed TM: a variant of the our approach with Particle Filter VFOA tracking and a fixed, uniform transition probability matrix A. • PF, learnt TM: the proposed approach as presented in this paper, i.e. with Particle Filter VFOA tracking and learnt transition matrix A Table IV shows the average FRR for these different approaches. One can see that the proposed approach outperforms the supervised method with an average FRR of ∼60% compared to ∼45%. Tracking the VFOA with a Particle Filter, as opposed to a frame-by-frame estimation, and learning the transition probability matrix on-line also improves the recognition performance on the three tested datasets. These results are comparable or superior to those published in the literature, although the evaluation protocols are not exactly the same due to the unsupervised and incremental nature of our method. Note that we do not include any contextual information like speaking status or other external events in the VFOA estimation process as in other existing work. This may additionally improve the overall performance.

The overall tracking algorithm, implemented in C++, runs at ∼ 80 -90fps on a 3.6GHz processor for a 720 × 576 video, where around ∼ 11% of CPU time is spent on feature extraction for VFOA (gradient computation on the whole image), and less than 1% on the VFOA learning and classification.

VI. CONCLUSION

We presented a VFOA tracking algorithm that incrementally, and in an unsupervised way, directly learns a VFOA model from low-level features extracted from a stream of face images coming from a tracking algorithm. The VFOA estimation is based on an HMM whose parameters are learnt incrementally and which is tightly integrated into a global Particle Filter framework that is used for face tracking. In a meeting room or video-conferencing setting, the proposed method is able to automatically learn the different VFOA targets of a person without any prior knowledge about the number of persons or the room configuration. By assigning a VFOA label to each cluster a posteriori, we evaluated the VFOA recognition rate for three different datasets and almost two hours of annotated data. The obtained results are very promising and show that this type of unsupervised learning can outperform traditional supervised approaches.

Future work will investigate different types of visual features, more dynamic scenarios with moving persons and the possibility of automatically assigning meaningful labels to the clusters. Also, it would be interesting to study the generalisation capability of the algorithm to unseen videos (same room with different persons) as this might enable a broader range of practical applications. Finally, a combination of supervised and unsupervised learning might be beneficial and improve the overall performance of VFOA recognition. Especially when there are attention targets that are focused on only rarely and thus might not be captured by the proposed clustering algorithm.

Fig. 1 .

 1 Fig. 1. Graphical illustration of VFOA estimation and the type of setting that is used. Targets 1 to 4 are persons, 5 corresponds to the table.

Fig. 2 .

 2 Fig. 2. Principal procedure of the VFOA learning and tracking approach.

Fig. 3 .

 3 Fig. 3. Visual feature extraction for the VFOA model. a) HOG features are computed on a grid of 4 × 4 cells placed on the tracked face. b) To compute the histograms, gradient orientation is quantised into 4 bins (respectively 8 bins) and magnitude into 2 bins.

Fig. 4 .

 4 Fig.4. The Hidden Markov Model used to estimate the hidden discrete variable v (the VFOA target) from the observations tt (feature vectors) using the learnt transition probability matrix A.

Fig. 5 .

 5 Fig. 5. Example frames from the three datasets that have been used for evaluation. Top TA2 dataset, middle: PETS 2003 dataset, and bottom IHPD dataset. (Faces have been blurred artificially in this figure).

Fig. 6 .

 6 Fig. 6. Visualisation of the clustering of low level features produced by the proposed incremental learning algorithm (Alg. 1) for some examples. (Best viewed in colour.) From left to right, top to bottom: TA2 room 1, TA2 room 2, 2 x IHPD, PETS, and the last example shows a poor clustering result for one TA2 example.

Fig. 7 .

 7 Fig. 7. Four examples of face images that are closest to the corresponding learnt cluster centres. Upper-left and lower-left: from IHPD dataset. Upperright and lower right: from TA2 (first video).

Fig. 8 .

 8 Fig. 8. Visualisation of VFOA classification over time for two example videos from TA2 and IHPD (best viewed in colour.) Red circles show the ground truth VFOA targets and blue crosses the output of a k-Nearest Neighbour classifier with the proposed clustering algorithm. Clusters 1, 2, 3 from the top example and 4 and 5 from the bottom have not been found by the initial on-line learning algorithm, and thus are not recognised.

  : this dataset consists of the "meeting" part of the Idiap Head Pose Database. It contains 8 meeting recordings with four persons, where each video shows two participants behind a table. The annotated targets are the table, the slide screen, and the other persons (the whiteboard target has not been used here). 110 040 frames (∼ 1 hour 13 minutes) with VFOA annotation have been used in total for the evaluation.

	dataset	number of videos	number of persons	VFOA targets	annotated frames
	TA2	2	6	5 / 3	7500
	IHPD	8	16	5	110040
	PETS 2003	2	6	5	47000
	total	12	28	5/3	164540 (110 min.)
			TABLE I
	THE THREE DATASETS AND ANNOTATION USED FOR EVALUATION.

TABLE IV VFOA

 IV RECOGNITION RATE OF THE PROPOSED ALGORITHM WITH AND WITHOUT PARTICLE FILTER INTEGRATION, AND WITH FIXED OR LEARNT TRANSITION PROBABILITY MATRIX A COMPARED TO A CLASSICAL SUPERVISED APPROACH.

https://www.idiap.ch/dataset/ta2

https://www.idiap.ch/dataset/headpose


Frédéric Landragin

Coreference in the light of pronouns with indefinite reference

Introduction

When studying references to human beings in narrative texts, we observe examples with exact and unambiguous referring expressions, like (some) proper nouns and definite descriptions, i.e., expressions that refer to a specific and precise referent. When personal pronouns are immediately interpreted as anaphora, it is then easy to identify coreferring relations. By taking into account transitivity, it is then possible to build on coreference chains. Because of its links with theme, topic continuity and referents' salience, a coreference chain is a kind of discourse structure that is taken into account by an increasing number of linguistic studies and Natural Language Processing (NLP) applications.

But coreferring relations are often considered as strict: each referring expression of a text fully belongs to one coreference chain, i.e., following an all-or-nothing relationship.

Some other referring expressions, for instance those that refer to groups of persons, organizations, or generic referents, raise some problems when attributing the expression to a coreference chain. In NLP applications, those fuzzy cases are often ignored or simplified. In order to go deeper into the modelling and formalization of reference and coreference, we propose in this talk a model that implies three degrees instead of all-or-nothing coreferring relations. We show how pronouns with indefinite reference, and in particular the French Rimpersonal pronoun on, put a spotlight on such a model and allow reconsidering the semantic properties of such a complex marker.

Three degrees for coreferring relations and links with on

First degree: "strict coreference". In this case referents are identical, whether they are individual, groups or generic. Examples of such a coreferring 1 relation are the following, i.e., when on refers strictly to a precise referent, for instance the speaker (1), when the reference of on is explicitly and unambiguously mentioned (2), and when several occurrences of on are clearly coreferring, for instance because a referent change would break up the narration (3).

(1) On se dit ça, on se prépare (Jean-Luc Lagarce, Juste la fin du monde, page 21).

(2) On dormait un peu, leur père et moi, sur la couverture (J.-L. Lagarce, page 28).

(3) On gratte, on gratte et puis très vite on respire mal, on sue, il se met à faire terriblement chaud (Jean Echenoz, L'occupation des sols).

Second degree: "inclusive coreference". In this case one of the referents is a group, more precisely a fuzzy group, that is, a group for which we cannot say how many individuals are included -as opposed to a strict group, for instance the one with the mother and the father in (2). Together with the fuzzy group, the coreference chain includes another referent(s), which can be an individual like in (4) where on in on klaxonnait refers to the father who is driving, and the other occurrences of on refer to the whole family. This example emphasizes how the reference of on can be vague in context, as does example (5), where the three referring expressions are linked to different referents -the mother, the father, and both of them -but where all of them can be grouped into one coreferring 2 relation, which reflects the discursive intention (and which is a practical alternative to a model including three coreference chains).

(4) On disait qu'on « partait en vacances », on klaxonnait, et le soir, en rentrant, on disait que tout compte fait, on était mieux à la maison (J.-L. Lagarce, page 28). ( 5) On travaillait, leur père travaillait, je travaillais (J.-L. Lagarce, page 25).

Third degree: "fuzzy coreference". In this case both referents are fuzzy groups. The intersection itself between these groups can be fuzzy, as in ( 6), where a lot of interpretations of on can be proposed (group of characters, generic character, witness-narrator), and in ( 7) where the reader is unable to list the referents of on and ils.

(6) Ah ! nom de Dieu ! oui, on s'en flanqua une bosse ! Quand on y est, on y est, n'estce pas, et si l'on ne se paie qu'un gueuleton par-ci par-là, on serait joliment godiche de ne pas s'en fourrer jusqu'aux oreilles. Vrai, on voyait les bedons se gonfler à mesure […] (Emile Zola, L'assommoir, cf. [START_REF] Maingueneau | Instances frontières et angélisme narratif[END_REF]. ( 7) Et on renonce à moi, ils renoncèrent à moi (J.-L. Lagarce, page 30).

Back to the values of on

To us, on is the referring form that fits at best the notion of fuzzy group, and therefore the three degrees of coreferring relations we propose. With this study, we want to put forward a way to consider on in narrative texts. Instead of searching for several potential referents and for complex links between them -complex person, nondescript member of a group, witnessnarrator, partial schizophrenia, a-definites, selfhood, person enallage, etc. -we prefer consider on as an intrinsic fuzzy marker. Of course, there are a lot of cases where strict reference can be identified, but there is the need for fuzzy aspects in order to model these simple cases and complex examples together. Talking about fuzzy reference is a way to take into account the multiple values of on in a unified framework, and to allow NLP exploitations.

It is also a way to emphasize the fact that identifying the exact referent of on is not mandatory. Sometimes, the reader is not able to identify the referent of a referring expression, and can nevertheless go on reading and understanding the text. The resolution of the reference can be left unfinished, and "good-enough" approaches to language processing as well as the third degree of coreference is a way to model that phenomenon. Doing that, the importance of the referring act is diminished compared to the importance of the predicative act. Examples (1), ( 3), ( 4), ( 6) and ( 7) illustrate well this hypothesis. Events are essential, not referents. Discursive aspects are therefore more salient than the characters.


Ghislaine Gueudet
email: ghislaine.gueudet@espe-bretagne.fr

Birgit Pepin
email: birgit.pepin@hist.no

Hussein Sabra
email: hussein.sabra@univ-reims.fr

Luc Trouche
email: luc.trouche@ens-lyon.fr

THE DESIGN OF AND INTERACTION WITH E-TEXTBOOKS: A COLLECTIVE TEACHER ENGAGEMENT

Keywords: E-textbook/s, mathematics teacher resources, textbook design, activity system, collaborative work

This article reports on an investigation of the design/re-design processes of a French grade 10 e-textbook (including its associated resources), which has been designed by the French Sésamath teacher association. These processes have been fostered by new 'digital' possibilities: platforms; discussion lists, etc. The object of the study has been the French Sésamath association, which mainly involved secondary school mathematics teachers designing various kinds of online teaching resources. The focus has been on their design of a Grade 10 e-textbook, more precisely the chapter on 'functions'. This design has been considered as a documentation work, and the analysis conducted with the theoretical perspective provided by Cultural-Historical Activity Theory. The authors studied the activity system of the e-textbook designer community, with particular focus on the resources, the rules and the division of labour in this system, their evolutions, and the factors of evolution. Three moments were identified, corresponding to three successive objects of the activity: a full-web e-textbook; interactive exercises; and finally a digital textbook. For lack of space, only one of these moments is presented, as an example. There is evidence that there were particular resources crucial for this collaborative work.

INTRODUCTION

The traditional textbook has been recognized to play an important, perhaps crucial, role in teaching and learning (e.g. [START_REF] Pepin | Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning cultures[END_REF]. However, the e-textbook, as an emerging form of teaching material (including online materials and interactive functionalities), has been relatively sparsely investigated. One of the main issues is to determine, which specific features, different from the paper textbook, has an e-textbook. Gueudet, Pepin, Sabra & Trouche ICMT-2014 In terms of teacher learning, textbooks are said to have a vital role to play. It has been found that textbook presentations are likely to influence teachers' beliefs and instructional practice (e.g. [START_REF] Nathan | The symbol precedence view of mathematical development: A corpus analysis of the rhetorical structure of algebra textbooks[END_REF], and that they contributed to teachers' knowledge growth [START_REF] Ma | Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States[END_REF]. [START_REF] Ball | Reform by the book: what isor might bethe role of curriculum materials in teacher learning and instructional reform[END_REF] emphasize the textbook's role in supporting teacher learning and professional development, yet studies exploring the role of e-textbooks in supportive teacher learning environments have been scarce.

In this paper we report on an investigation of the design/re-design processes of a grade 10 e-textbook, which has been designed by the French teacher association Sésamath. It is hypothesized that the digital means challenge in particular the usual divide between experts as designers of resources and teachers as users: design and implementation/use are now intertwined, with teachers intervening in both [START_REF] Gueudet | Towards new documentation systems for mathematics teachers?[END_REF].

The research question studied here is: what are the design processes attached to the Sésamath e-textbook, and in which ways do the roles of group members evolve over the development of the textbook?

ANALYTICAL FRAMEWORK AND METHODOLOGY

In terms of context, our aim was to analyse the emergence of e-textbooks as new types of teaching resource systems, designed by a different kind of "authors" (i.e. mathematics teachers, whereas traditionally textbooks are designed by teacher educators, or inspectors), and to investigate the development of new kinds of interactions between authors and users. We chose the Sésamath association, whose members were developing such new types of resources. Sésamath is a French association of in-service mathematics teachers (mainly from middle schools, around hundred teachers, with a board of nine members) created in 2001, whose main goal is to "freely distribute resources for mathematics teaching": online exercises (Mathenpoche -standing for "mathematics in the pocket", MeP in the following); textbooks; and various software. These are designed by groups of teachers collaboratively working to develop/produce a given set of resources. Each project involves about fifty teachers, and the different project groups gather several thousand teachers sharing the same collaborative platform, who are not formally members of Sésamath, but interested in developing shared resources through the engagement with Sésamath.

We will focus in this paper on the design of a Sésamath e-textbook, choosing a moment of change between two edition models: the first one was a single static book, available both online (under a pdf, but also an odt format, allowing teachers to make modifications) and in hard copy, accompanied by separated animations online (in particular MeP exercises); the second one was a flexible and dynamic digital textbook, i.e. an e-textbook, which a teacher could organize according to his/her needs, with animations and extra exercises integrated in each chapter. After having successively published 'static' textbooks for grade 7 (2006), grade 8 (2007), grade 9 (2008) and finally grade 6 (2009),, Sésamath decided to design an e-textbook for grade 10 (first grade of high/upper secondary school in France), according to the second model, and gathered a group, named here e-textcom, for this purpose. We decided to follow, from June 2009 to December 2013, the design of a particular chapter, dedicated to functions, because this theme assembled diverse representations (graphs, tables of values, algebraic formulas) and offered possible links with the real world (in term of modelling), offering many opportunities for exchanging resources between e-textcom members.

Our investigations are anchored in the following data and their analyses: (1) for tracing the e-textcom activity, we have used its mailing list and the resources platform; (2) for tracing the interactions between the community and the members resources, we collected the designed resources shared by the members, during the realisation of the object; (3) for studying the interrelation between e-textcom and Sésamath board activity systems,, we used what we named a Small Agenda for Follow-up (SAF), filled in by two e-textcom members, chosen according their role in the community (Benoît, Sésamath Board; Alexis, debates coordinator). Analysing these data, we identified different moments of the activity system transformation.

In terms of theoretical frameworks, we refer to Gueudet, Pepin, Sabra & Trouche (submitted) combining two frames: the documentational approach of didactics [START_REF] Gueudet | Towards new documentation systems for mathematics teachers?[END_REF], in particular its meaning of resources, and the Cultural-Historical Activity Theory (CHAT) as defined by [START_REF] Engeström | Expansive learning at work: Toward an activity theoretical reconceptualization[END_REF].. Drawing on these we have analysed the evolution of the e-textcom activity system, focusing in particular on changes of the object of the activity (see Figure 1): we identified three successive objects of activity, each of them being associated to a particular moment. We show in the next section the activity system/s and its/their evolution during the first of these moments, and subsequently discuss the whole process.

THE FINDINGS: PRESENTATION OF ONEMOMENT IN THE EVOLUTION OF THE OBJECT

In June 2009, an initial group of 14 teachers, e-textcom, engaged in a Sésamath project, aiming to design a textbook "full Web" (flexible dynamic digital textbook) for grade 10. This project was the first Sésamath project for upper secondary school. During our observations from June 2009 to December 2013, we identified three moments. We present here in details the first moment, which took place between July 2009 and March 2010 corresponding to the object "designing a full web textbook for grade 10" (see figure 1).

Figure 1. The "e-textcom" activity system at the first moment.

E-textcom gathered only high school mathematics teachers; some of them were also members of the Sésamath board. The project started with various kinds of resources: resources brought by members (in particular their own resources); resources provided by the association, in particular the collaborative platform, previous textbooks, MeP, a mailing list; and institutional resources, like in particular the grade 10 official curriculum. We observe that traditional (paper) textbooks do not seem to intervene as resources. The grade 10 official curriculum formed a central resource: it provided mediation between members at this early stage of the project. One important rule, 'inherited' from the middle school Sésamath projects, was to start with a list of elementary "tasks" identified from the official curriculum. This list played an essential role: each member chose to design exercises corresponding to a given task. A coordinator (see the roles below) checked if all the tasks were tackled by the e-textcom members.

For this textbook, a new vocabulary was introduced. A member of the Sésamath board proposed the term "atom", to describe the elementary units that would constitute the book. This term "atom" was then kept by e-textbook members; but they used it in fact as synonymous of "task". Thus, the first resource designed by the e-textcom members (drawing on the official curriculum, and on their own courses ) was the list of "atoms".

The e-textcom members designed a new resource containing a list of 38 "atoms" for the chapter dedicated to functions in the grade 10 e-textbook Then e-textcom designed a "progression", i.e. a trajectory/order for the "atoms" to be taught/learnt. A "progression" is a very usual resource for teachers in France; each teacher, for a given class, has her/his "annual progression", the agenda of the contents to be taught during the year, sometimes designed with colleagues at the beginning of the school year. A "progression" can also be designed for a given theme; in the Sésamath middle school projects, for each theme the tasks were arranged according to a "progression". The multi-representational nature of functions (graphic, algebraic, table of values) offered several possible entries and orders, and made the choice of a progression especially difficult. This progression was developed by members through discussions mediated by the resource "list of atoms", the curriculum and suggested progressions of some members, shared with the community. This structure could also be viewed as providing rules for the community, and these rules reflected the ways functions should be introduced to students. In particular one rule was explicitly discussed on the mailing list: the functions theme should start with general statements, i.e. definition and properties, before developing more specific notions, i.e. "reference functions" (well-known examples) and applications.

The division of labour firstly drew on the division or labour retained in the middle school textbook project. Several roles were chosen, from the beginning; we identified them via the discussion on the mailing list and the associated resources: resource designers (each designer having to take into account the reviewers' propositions for resources which s/he designed); resource reviewers; a debate coordinator; a Sésamath 'torchbearer' aiming to keep the evolution of the project in the "orbit" of Sésamath projects.

The application of this division of labour followed a process organised in successive steps explicitly proposed by the coordinator:

1) design of a resource (exercise, or course) by a subject/member;

2) review of the resource by other subjects/members;

3) modification of the resource by the designer and proposal of a new version.

At each step, the coordinator had a crucial role. He managed the discrepancies coming from the reviewers, organizing the discussion between members (reviewers and designers).

During the nine months of this first moment, many exercises for the different atoms (exercises corresponding to the same "type of task") were written; and also a course corresponding to a part of the first chapter. Nevertheless, we observed structural tensions appearing in the activity system (tensions subjectsresourcesobject). E-textcom members were all teachers, and none were IT developers/specialists. But the design of a fully web-based textbook required technical skills, and the missing competence of an IT developer was an important obstacle.

In order to overcome these tensions, the e-textcom members contacted the Sésamath board: we observed here interactions between two activity systems, the Sésamath board and e-textcom activity systems. The contacts between the two systems led to the 'arrival' of IT developers as new members. They also led to change the object itself: since the present technical means and skills within e-textcom did not permit to reach the initial objective, the new object of the activity was the design of interactive resources for grade 10: this marked the beginning of the second moment

DISCUSSION AND CONCLUSIONS: COLLECTIVE DESIGN OF DIGITAL TEACHING RESOURCES-EVOLUTIONS IN A DYNAMIC ACTIVITY SYSTEM

In our analyses we identified three moments (exemplified by one in this paper) in the e-textbook activity system, corresponding to different objects of the activity. These evolutions, the changes in the object, were directly linked to the digital nature of the textbook to be designed: in line with the innovative nature of the resource, the members of the Sésamath board tried to develop new and more flexible learning paths, and new tasks that took advantage of the digital and flexible nature of the book, permitted by recent technological evolutions. Nevertheless, the initial project encountered technical obstacles, leading to a first change in the object, which evolved from a full-web textbook to interactive exercises. Conversely, unplanned technical means also brought evolutions.

From the evidence we present in this article (and other works on e-textbooks), it is clear that the collective design of an e-textbook is a complex matter. Our analysis proposes taking into account an evolving activity system (that of e-textcom), and its interactions with other activity systems (at least those of the Sésamath board, and of the middle school textbook developers), leading to the emergence of new roles and new rules. Specific roles were indeed required, not only authors and reviewers of resources (which exist for all textbooks) but also:

-a coordinator was crucial (also for an ordinary paper textbook) as soon as several authors intervened. S/he was especially needed in the case of e-textcom, because of:

 the large number of non-expert authors involved in the design of the textbook;  the length of the design process (several years);  the change of the actors involved all along the duration of the project.

a 'torchbearer' was important, since the Sésamath association provided the frame for the e-textbook project. The 'torchbearer' had to take charge of the coordination between the Sésamath board and e-textcom.

The rules appeared to evolve in line with the processes: the initial design was followed by a review step, then by a new design. However, this cycle could take several forms; it changed along the different moments. More generally, it seemed that e-textbooks, as shared resources designed by communities of teachers, evolving through interactions between individual and collective resource systems, constitute a promising field for new developments.