M.-O Berger

N Noury

Inverse-depth parameterization can successfully deal with the feature initialization problem in monocular simultaneous localization and mapping applications. However, it is redundant, and when multiple landmarks are initialized from the same image, it fails to enforce the "common origin" constraint. The authors propose two new variants that addresses both of these issues. The experimental results indicate that the proposed approach achieves a better performance at a lower computational cost.

I. INTRODUCTION

HE monocular simultaneous localization and mapping (SLAM) problem involves the estimation of the location of a set of 3D landmarks in an unknown environment (mapping), in order to compute the pose of a sensor platform within this environment (localization), via the photometric measurements of these landmarks acquired by a camera, i.e. the 2D images [START_REF] Davison | MonoSLAM: Real-Time Single Camera SLAM[END_REF]. The best-known solutions [START_REF] Davison | MonoSLAM: Real-Time Single Camera SLAM[END_REF]- [START_REF] Eade | Scalable Monocular SLAM[END_REF] utilize either an extended Kalman filter (EKF) [START_REF] Smith | On the Representation and Estimation of Spatial Uncertainty[END_REF], or a particle filter [START_REF] Montemerlo | FastSLAM: A Factored Solution to the Simultaneous Localization and Mapping[END_REF] (with the notable exception of [START_REF] Nistèr | Visual Odometry[END_REF]), and point landmarks or small planar patches [START_REF] Jin | A Semi-Direct Approach to Structure from Motion[END_REF] to describe the map. The estimation procedure aims to maximize the SLAM posterior, which is defined as [START_REF] Whyte | Simultaneous Localization and Mapping: Part I[END_REF], ( )

0 k : 0 k k x Z M x , | , p p SLAM = , (1)
over the pose and the landmarks. In (1), x k and M k denote the pose and the map estimates at time instant k, respectively. Z 0:k stands for all past and current measurements, and x 0 , the initial pose estimate. The maximization involves projecting M k to the measurement space, i.e. the image plane of a camera at the estimated pose (prediction), and backprojecting the difference between the predicted and the actual measurements to the state space, to update x k and M k (correction). The above scheme is common to all mainstream SLAM algorithms. What sets apart the monocular SLAM is the landmark initialization stage: Since a camera is a bearingonly sensor, a single measurement can constrain the position of the corresponding landmark only to a ray originating from the camera center (the projection ray). A straightforward solution to obtain the depth along this ray is performing the initialization from two consecutive measurements via triangulation. However, in low parallax case, which occurs when a distant landmark is observed, or the camera is moving slowly, triangulation is not reliable. Tracking the image feature between two frames with a sufficiently wide baseline may still render it a viable strategy, unless the camera has a narrow field-of-view. However, it is wasteful in terms of information, as the intervening measurements between the two frames are not incorporated into the state estimate.

One method to cope with this problem is employing an auxiliary process, as proposed in [START_REF] Davison | Real-Time Simultaneous Localization and Mapping with a Single Camera[END_REF]: A set of depth hypotheses is obtained by sampling along the projection ray. For each hypothesis, an associated measurement search region is computed from the uncertainty of the ray and the camera, and an individual matching is performed. Each hypothesis is scored via a monotonous function of the distance between the predicted and the actual measurement. When the match-score procedure is repeated for a number of frames, the cumulative score function collapses to a single peak, where it is safe to approximate the landmark position uncertainty with a Gaussian. This method is capable of handling any form of uncertainty. One limitation is that only a finite number of hypotheses can be evaluated, as the search space for the depth must be discrete and bounded, a shortcoming which is alleviated in [5], by adjusting the sampling density so that the potential modes of the cumulative score function are examined at a higher resolution. However, the measurements obtained during the initialization do not contribute to the main SLAM process; hence, the underutilization problem remains unaddressed.

Another alternative is retaining the Gaussian model, but changing the underlying parameterization. The inversedepth parameterization (IDP), proposed in [START_REF] Eade | Scalable Monocular SLAM[END_REF], is inspired by the observation that, the uncertainty of inverse of depth can be approximated very well by a Gaussian at low parallax, hence can be estimated by an EKF successfully.. Moreover, IDP landmarks can be used to update the pose estimates, both in particle filter [START_REF] Eade | Scalable Monocular SLAM[END_REF] and EKF-based systems [START_REF] Montiel | Unified Inverse Depth Parameterization for Monocular SLAM[END_REF]; therefore, the available information is fully utilized. This eliminates the need for a separate initialization process: The map is represented with a hybrid set of regular 3-parameter (Cartesian coordinates) and IDP landmarks, with each landmark type having its own measurement function, but still operating seamlessly within the same EKF. Since only a single hypothesis is evaluated, it is In this work, the authors study the generation of multiple IDP landmarks from a single frame. This is a case in which, in the original IDP, the constraint that all such landmarks share a common origin is not enforced. Its practical significance stems from the fact that, a SLAM algorithm gathers information by observing the landmarks, and the sooner it captures the salient features of the scene, the more information it can incorporate into the estimation process. Multiple landmark generation improves the responsiveness to new salient structures, hence, the quality of the results. The authors propose two variations of the IDP, and apply them in an EKF-SLAM system to demonstrate that it is possible to achieve gains in both computational cost, and accuracy by respecting the "common origin" constraint.

The paper is organized as follows: In the next section, an EKF-SLAM system that exclusively utilizes IDP landmarks is described. In Section 3, the shortcomings of the IDP in multiple-initialization case are discussed, and two alternatives to the original parameterization are proposed. An experimental comparison of the original and the proposed parameterizations are presented in Section 4. Finally, Section 5 concludes the paper.

II. EKF-SLAM WITH INVERSE-DEPTH PARAMETERIZATION

In the system implemented for this study, the state vector of the EKF is composed of two parts: x k , the camera parameters, and M k , the set of IDP landmarks that comprise the map. x k is defined as

[ ] T k k k k k w t q c x = , (2)
where c k and q k denote the position of the camera center in 3D world coordinates, and, its orientation in quaternions, respectively. t k and w k are the translational and rotational velocity, which describe the constant velocity model employed in the system. The definition of

M k is [ ] T Nk 1k k L L M L = , (3)
where L ik is the ith landmark, and N is the number of landmarks at the time instant k. Each IDP landmark is described by 6 parameters as [START_REF] Montiel | Unified Inverse Depth Parameterization for Monocular SLAM[END_REF] (

) ( ) [ ] T ik ik ik Φ Θ λ 0 ik 0 ik 0 ik 0 ik 0 ik ik q u q u c L , , = . (4)
In the above equation, c 0 ik is the coordinates of the camera where the landmark is first observed, Θ ik and Φ ik are the azimuth and the elevation of the projection ray in the world reference frame, and λ ik is the inverse of the distance (depth) of the landmark from c 0 ik , along the projection ray. Both Θ ik and Φ ik are functions of the first 2D image measurement pertaining to the landmark, and the orientation of the camera which made this measurement, namely, u 0 ik and q 0 ik . Their dependence on k signifies that, any update to the angles implicitly means an update to the first orientation and measurement.

The IDP is related to the minimal 3D point parameterization through the expression

[ ] T Θ Φ Φ Θ Φ cos cos sin sin cos 1 - + = λ 0 3D c L , (5)
and the measurement equation is simply the projection of L 3D ik to the image plane of the camera [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF] , i.e.

[ ] ( )[

]

T z ik y ik y y z ik x ik x x T z ik y ik x ik h h h h h h h       - - =       - - = α ν α ν p ik 3D ik k k u L c I q R 1 , (6)
where (ν x ; ν y ) denote the principal point of the camera and (α x ; α y ), the focal length-related scale factors. u p ik is the predicted image measurement for the landmark L ik . R(q) maps the quaternion q to the corresponding rotation matrix.

The EKF-SLAM used in this work is very similar to the one described in [START_REF] Montiel | Unified Inverse Depth Parameterization for Monocular SLAM[END_REF]. The inputs are the initial pose and a small number of initial landmarks, known with high accuracy, to set the correct scale for the map. For a short period, the algorithm operates in the initialization mode, i.e., only uses the initial landmark set for updating the state, to ensure that the velocities converge to the correct range. New landmarks are added using FAST [START_REF] Rosten | Fusing Points and Lines for High Performance Tracking[END_REF], when the number of observations in an image falls below a certain number (T min ), and in regions where the number of observations is less than the average. For matching, normalized cross correlation is utilized [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF]. A landmark is deleted when it is missed for a number of consecutive frames, or when the ratio of the number of observations to the number of attempts is below a certain threshold.

III. IMPROVED INVERSE DEPTH PARAMETERIZATION

A. Problem: IDP and Multiple Landmark Initialization Equation (4) implies that the IDP actually encodes the pose estimate of the camera that first observed the landmark (i.e. c 0 ik and q 0 ik ), the image coordinates of the first observation (u 0 ik ) and the inverse depth. A cluster is a set of landmarks initialized from the same image. All members of a cluster share the same c 0 and q 0 . The "common origin" constraint enforces that this commonality is preserved throughout the entire estimation process. However, the IDP encodes these parameters separately for each individual landmark, i.e., keeps multiple representations of the c 0 -q 0 pair of the cluster, with two important consequences:

• When the pose uncertainty (which is closely related to the initial covariance of c 0 , Θ and Φ) is much smaller than the measurement noise, the pose related parameters remain very close to their initial values, hence, each other, and the multiple copies become redundant. Such redundancy increases the size of the state vector and the computational cost. • When the pose uncertainty is sufficiently large to allow significant updates, the copies may diverge. Such violation of the common-origin constraint deteriorates the performance. The solution lies in factoring out the common pose parameters, and encoding the clusters, instead of the individual landmarks, as discussed next.

B. IDP1-"The Quick"

A straightforward application of the above idea is defining a super-landmark (IDP1), which is composed of a single c 0 , and the azimuth and elevation angles, and the inverse depth values of the member landmarks, i.e.,

[ ] T

M ik

1 ik 0 ik Q ik l l c L L = , ( 7
)
where M is the number of landmarks in the ith superlandmark at time instant k. l j ik contains the remaining parameters of the landmark it corresponds to, i.e. M decreases over time, as the members of a superlandmark are lost. When M=1, the super-landmark is identical to an IDP landmark, and when M=0, it is deleted.

A super-landmark encodes a cluster of size M with 3M+3 parameters, as opposed to the original IDP, which needs 6M parameters. Since the operations performed on a superlandmark is identical to those applied to an IDP landmark, a decrease in the computational cost is guaranteed when M>1. It also partially enforces the common-origin constraint, therefore is expected to be more accurate.

C. IDP2-"The Strict"

A logical extension of the IDP1 is the removal of the duplicate orientation components, i.e.

+ =         - - = = . ( 10
)
Equations ( 6) and ( 10) constitute the measurement equation. IDP2 achieves a complete separation of the pose and the first image measurement, and strictly enforces the commonorigin constraint. However, this comes at a cost of reduced computational efficiency, as a cluster of size M is represented with 3M+7 parameters, and after each state update, all quaternions must be normalized.

D. Related Work

Very recently, two more inverse depth parameterizations, which offer an accuracy vs. efficiency trade-off, were reported. In [START_REF] Marzorati | Monocular SLAM with Inverse Scaling Parameterization[END_REF], the trade-off involves, in effect, setting the uncertainty of c 0 to 0, to obtain a 4-component representation. On the other hand, [START_REF] Pietzsch | Efficient Feature Parameterization for Visual SLAM Using Inverse-Depth Bundles[END_REF] is a multi-landmark parameterization which can encode each member of a cluster by a single parameter, under the assumption that the initial measurement, u 0 , is not subject to any error.

IV. EXPERIMENTAL RESULTS

The performance of the proposed parameterizations is studied via a pose estimation task. For this purpose, a bed, which can translate and rotate a camera in two axes with a positional and angular precision of 0.48 mm and 0.001°, respectively, is used to acquire the images of an indoor scene, with the dimensions 5x2x3 meters. In the sequence S1, the camera moves on a horizontal trajectory of 50 cm, with constant translational and zero angular velocity. In S2, the movement is on a 65-cm oblique path, with rotation, and obeys the constant angular and translational velocity model. S1d and S2d are derived from S1 and S2, respectively, by discarding 2/3 of the images randomly to obtain a nonconstant-velocity motion. Figure 1 depicts the setup, and the initial and final images of the sequences.

The pose estimation task involves the computation of the position and the orientation of the camera from the sequences by using the EKF-SLAM scheme described in Section 2, with the map representation alternatives described in Sections 2 and 3. The maps utilize exclusively the original IDP, or one of the proposed variants. For all experiments, T min is set to 30. New landmarks are added in batches of 5. The recovered maps are similar, but not identical, as each parameterization leads to a different trajectory estimate, and the lifetime of landmarks are linked closely to the pose estimates.

The following criteria are utilized for the evaluation:

• Position error: The Euclidean distance between the estimated and the actual camera path, in millimeters. • Orientation error: The angle between the the estimated and the actual normals to the image plane (i.e., the principal axis vectors), in degrees. • Relative execution time: Execution time with respect to that of the IDP. The adoption of this criterion as a measure of the computational load is due to the fact that the alternative, the absolute execution time, also depends on the hardware, and the maturity and efficiency of the code, factors that are not within the scope of this paper. • # Measurements for convergence: Linearity index, proposed in [START_REF] Montiel | Unified Inverse Depth Parameterization for Monocular SLAM[END_REF], is a measure of the Gaussianity of the depth uncertainty of an IDP landmark.

Convergence occurs when the linearity index of a landmark falls below 0.1, an empirically determined threshold [START_REF] Civera | Inverse Depth to Depth Conversion for Monocular SLAM[END_REF], and at that point, it is safe to switch to the 3-parameter, minimal parameterization. The lower the number of measurements necessary for convergence, the better, as this implies a faster convergence rate. The results are presented in Table I and Figures 2345. The first row of Table I indicates that both IDP1 and IDP2 fulfill their promise of reduced computational cost. Especially, IDP1 achieves a 250-300% increase in processing speed. The gains provided by IDP2 are more modest in comparison, as discussed in Section III-C, but still significant. In [START_REF] Montiel | Unified Inverse Depth Parameterization for Monocular SLAM[END_REF], it is maintained that a hybrid map that uses both the IDP and minimally parameterized landmarks can achieve 30 frames per second (fps). Since a map represented only with IDP1 landmarks can already be processed at 15-25 fps when T min =30, it can reasonably be expected that in a hybrid map application, both IDP1 and IDP2 can go beyond 30 fps.

The the trajectory and the map estimates in Figure 2 and Figure 3 for S2d, the most challenging sequence, suggest that the gain in computational cost comes without a compromise in performance. On the contrary, in Figure 4, it is observed that, the IDP2 consistently outperforms the IDP and the IDP1, owing to employing a superior parameterization that enforces the common-origin constraint. However, Figure 4 also hosts some unexpected results: In S1 and S2, the performances of the IDP and IDP1 are almost identical. A closer study reveals the cause as the low pose uncertainty case, described in Section III-A: The initial pose and map estimates are known with very high accuracy, and the measurement covariance is much lower than the initial uncertainty of the velocity parameters. Therefore, the angular and translational velocities are very responsive to the updates, and given that the actual motion perfectly satisfies the constant-velocity model, their covariances are reduced rapidly. Since the state vector contains the same information, the predicted measurements, the measurement errors, and the state updates, hence the next estimate of the state vector, remain the same. S1d and S2d further support this explanation. The less predictable camera motion leads to a higher pose uncertainty, and in this case, the IDP1 performs better. Such a phenomenon is not observed in the IDP2, as it has a considerably different state vector, i.e. a landmark is described by 10 parameters, instead of 6, hence, traces a different path through the solution space.

As for the orientation estimation, Figure 5 indicates that the error is already small, especially in S1 and S1d, so any performance comparison is not meaningful. The increasing error observed in S2 and S2d in all parameterizations is a byproduct of the accumulation of the linearization errors, and is expected in the absence of a loop closure. The convergence rate for various sequences and parameterizations are presented in Table I. In all cases, the median rate is an indicator of convergence for the landmarks on the table, as they vastly outnumber the landmarks on the wall. On the other hand, the maximum rate always belongs to a wall landmark, as it takes longer for farther landmarks to achieve the necessary parallax.

The only cases where there is a difference between the parameterizations are the wall landmarks in S1d and S2d. In such landmarks, the utilization of the common-origin constraint is important, as unlike the closer landmarks, the constraints provided by parallax are weak. This statement also holds for S1 and S2, but both are 3 times longer than S1d and S2d, hence, the weakness of the individual parallax constraints are offset by their sheer numbers.

V. CONCLUSION

The IDP is introduced in [START_REF] Eade | Scalable Monocular SLAM[END_REF] to the landmark initialization problem in monocular SLAM as an effective tradeoff between computational efficiency and information utilization efficiency. However, when multiple landmarks are initialized, a case with practical importance, the IDP fails to enforce the common-origin constraint. The authors propose two alternatives in order to alleviate the efficiency and performance hazard this condition causes, and experimentally demonstrate that, the IDP2 is superior to the IDP both in computational cost and in performance, whereas the IDP1 delivers a similar performance to the IDP at a much lower computational burden.

  variant, dubbed IDP2, is linked to the minimal 3D point parameterization as

Fig. 1 .

 1 Fig. 1. Top left: The bed used in the experiment to produce the ground truth trajectory. Top right: The initial image for S1 and S2. Bottom row: The final images of S1 and S2, respectively.

Fig. 3 .

 3 Fig. 3. Top view of the trajectory and structure estimate for S2d.in IDP2 case. Blue circles indicate the estimated landmarks. Those closer to the camera belong to the table, whereas the farther ones are located on the wall. The figure is representative of the IDP and IDP1 cases.

Fig. 2 :

 2 Fig. 2: Trajectory and orientation estimates for S2d. Left: Trajectory. Right: Orientation, i.e, principal axes. In order to prevent cluttering, only the IDP2 case is plotted, and the trajectory is downsampled by 4.

Fig. 4 .

 4 Fig. 4. Euclidean distance between the estimated and the actual trajectory. Top-left: S1. Top-right: S2. Bottom-left: S1d. Bottom-right: S2d.

Improved Inverse-Depth Parameterization for Monocular Simultaneous Localization and Mapping

	computationally more efficient than the hypothesis testing
	method described above. Besides, it does not suffer from
	any resolution or search range problems: The IDP can
	express every point from infinity up to the camera center.
	The only downside is that an IDP landmark is represented E. Imre, M.-O. Berger, N. Noury by 6 parameters, whereas the minimal representation of a
	landmark in 3D space requires only 3 parameters. Hence,
	the IDP is employed as an intermediate stage, to be
	upgraded to the minimal parameterization, as soon as the
	uncertainty of the latter becomes approximately Gaussian.
	T

TABLE I RELATIVE

 I EXECUTION TIME AND LANDMARK CONVERGENCE

			D1			D2			D1r			D2r
	Parameter	IDP	IDP T1	IDP T2	IDP	IDP T1	IDP T2	IDP	IDP T1	IDP T2	IDP	IDP T1	IDP T2
	Relative Execution Time (IDP)	1	0.36 0.71	1	0.27 0.43	1	0.39 0.71	1	0.37 0.62
	Median # Measurements for Convergence	27	27	28	27	27	29	14	14	15	15	16	16
	Maximum # Measurements for Convergence	55	58	58	75	75	75	119	74	44	78	87	43


Marie-Odile Berger

Jonathan Ponroy

Brigitte Wrobel
email: brigitte.wrobel@loria.fr

Realistic face animation for audiovisual speech applications: a densification approach driven by sparse stereo meshes

Keywords: Face animation, densification, PCA with missing data

Being able to produce realistic facial animation is crucial for many speech applications in language learning technologies. Reaching realism needs to acquire and to animate dense 3D models of the face which are often acquired with 3D scanners. However, acquiring the dynamics of the speech from 3D scans is difficult as the acquisition time generally allows only sustained sounds to be recorded. On the contrary, acquiring the speech dynamics on a sparse set of points is easy using a stereovision recording a talker with markers painted on his/her face. In this paper, we propose an approach to animate a very realistic dense talking head which makes use of a reduced set of 3D dense meshes acquired for sustained sounds as well as the speech dynamics learned on a talker painted with white markers. The contributions of the paper are twofold: We first propose an appropriate principal component analysis (PCA) with missing data techniques in order to compute the basic modes of the speech dynamics despite possible unobservable points in the sparse meshes obtained by the stereovision system. We then propose a method for densifying the modes, that is a method for computing the dense modes for spatial animation from the sparse modes learned by the stereovision system. Examples prove the effectiveness of the approach and the high realism obtained with our method.

Introduction

There is a strong evidence that the view of speaker's face visual information noticeably improves the speech intelligibility. Hence, having a realistic talking head could help language learning technology in giving the student a feedback on how to change articulation in order to achieve a correct pronunciation. In [START_REF] Munhall | The moving face during speech communication[END_REF], Munhall and Vatikiotis provide evidence that lip and jaw motions affect the entire facial structure below the eyes. High levels of details are thus required to obtain highly realistic and perceptibly correct facial animation of the complete face.

Though the utility of visual information to speech perception has been known for a long time, progresses to develop talking faces which both look real and convey linguistic relevant information are more slower. What causes the intelligibility enhancement afforded by the visible component of speech is difficult to determine. For these reasons, many works argued the necessity for animating face directly from visible articulatory data either in 2D [START_REF] Ezzat | Trainable videorealistic speech animation[END_REF] or in 3D [START_REF] Blanz | A morphable model for the synthesis of 3d faces[END_REF][START_REF] Kalberer | Face animation based on observed 3d speech dynamics[END_REF][START_REF] Kuratate | Talking Head Animation System Driven by Facial Motion Mapping and a 3D face Database[END_REF][START_REF] Muller | Realistic speech animation based on observed 3d face dynamics[END_REF]. Most of these data are 3D meshes of the face which can be sparse -when they are acquired using markers or sensors glued on the face-or dense using laser scanner acquisition. It must be noted that do not operate with a sufficient speed for speech acquisition (an acquisition rate of 120 Hz is required to acquire fast articulatory gestures of consonants). As a result, high resolution scanners can be used for sustained sounds as vowels but it is not obvious that they can be used to acquire all the dynamics of speech production.

Most methods for animating face are based on the extraction of the basic modes of spatial deformations during speech using principal component analysis (PCA). They span a space which describes at best all the plausible face deformations corresponding to speech production. Constructing such a space requires to physically match the points of the meshes at each time instant. This task is easy when sparse meshes are considered but it becomes complex for dense meshes. In this latter case, a generic head template is generally used [START_REF] Kuratate | Talking Head Animation System Driven by Facial Motion Mapping and a 3D face Database[END_REF][START_REF] Muller | Realistic speech animation based on observed 3d face dynamics[END_REF] to align all the scans using prominent features such eyes, nose. Obtaining rough alignment is largely automatic but accurate alignment requires a manual adaptation of the model to the speaker specificities. In this paper, we favor a fully automatic method and propose an automatic matching process guided by the sparse stereo meshes.

Though PCA can be used both on sparse or dense meshes, it is difficult to obtain the speech dynamics from dense meshes since the set of visemes that can be acquired is limited to sustained sounds due to technical limitations in scanner acquisition. It is thus not obvious to recover the complete speech dynamics from a reduced set of 3D scans. For these reasons, we propose in this paper an approach that makes use both of a small set of 3D scans acquired for sustained sounds and of the speech dynamics learned from a stereovision sequence of the face painted with markers. The main idea is to transfer the dynamics learned on the sparse meshes onto the 3D dense meshes in order to generate realistic dense animations of the face. This paper is an extension of our previous work [START_REF] Berger | Realistic face animation from sparse stereo meshes[END_REF]. In this past work, only one dense mesh was used which turned out to be not accurate enough for generating sounds which are too far from the reference dense mesh. We thus propose in this paper significant extensions of the work in order to transfer the dynamics learned from the sparse meshes onto the dense face.

Computing PCA modes for face animation from sparse meshes acquired by stereovision is difficult because all the markers may not be observable at every time instant. When the mouth is closed, points may become invisible, or at least not sufficiently visible, to be correctly detected and reconstructed. Though this difficulty is often ignored in the literature, this make the PCA more complex and needs to resort to PCA with missing data techniques [START_REF] Roweis | Em algorithms for pca and spca[END_REF]. A novel way of computing the face modes taking into account possible unobservable points is thus presented in section 3.

Our approach for computing the dense modes is presented in section 4. It borrows concepts from transfer techniques [START_REF] Summer | Deformable transfer for triangle meshes[END_REF] used in computer graphics to map an object onto another. We specifically used this technique in section to physically and automatically match the dense meshes using the underlying sparse mesh to guide the transfer. This avoids doing manual adaptation of a generic mesh to our talker. Finally, we propose a densification method which allows the basic modes of the dense head to be computed from the sparse modes computed from the learning sequence. As a result, this allows us to animate a dense head using only a reduced set of 3D scans.

We demonstrate experimentally in section 5 that the proposed method is efficient and allows us to obtain very realistic dense faces.

System overview

Our method requires the acquisition of a set of 3D dense meshes of the talker. In our study, these dense meshes were acquired with the Inspeck mega capturor (www.inspeck.com) for 15 sustained sounds (vowels, fricatives and lip closure). These dense meshes are also called visemes in the following.

In order to learn the face kinematics, a classical stereovision system with two cameras was used to record a corpus. The acquisition rate of the cameras is 120 images/frames which is sufficient to capture fast movements of the articulators (further details on this system can be found in [START_REF] Wrobel-Dautcourt | A low-cost stereovision based system for acquisition of visible articulatory data[END_REF]). Markers were painted on the talker's face in order to make the matching and the reconstruction stage automatic. With 45 points on the lips and a total of 209 points on the part of the face that is influenced by speech, the recovery of face kinematics is quite detailed. Our experiments proves that between 5 to 7 PCA modes are sufficient to describe the face kinematics.

The experimental set-up and the input data are shown in Fig. 1. The first raw exhibits a stereo image pair of the talker. Note that the points located on the top of the head are used to compensate for head motions. Fig. 1.c is an example of a sparse mesh obtained with the stereo system. Finally, Fig. 1.d is the dense mesh acquired for the /a/ sound.

PCA with missing data for computing the sparse modes

The 3D coordinates of each marker can theoretically be computed at each time instant of the learning sequence using the stereovision system. In the following, the 3D sparse mesh of the face computed at time instant

t (t ∈ [1..T ]) are denoted X t = [X 1,t , ..., X N,t ],
where N is the number of markers and X i,t are the 3D coordinates of the marker i at time instant t. Here, N=209 markers were painted on the face. The duration of the corpus recorded for learning kinematics was 6 minutes, giving rise to T=39000 stereo pairs. However, some markers may become unobservable during uttering when the lips are very close. Practically, these markers may not be reliably detected in the images by low level algorithms. It is especially the case for sounds like /u/, /o/, /i/. Markers may also become unobservable in one of the image pair due to slight head motions which make some points disappear from the field of view. Stereo reconstruction is thus not possible for these points. Practically speaking, 77% of the markers are always observable and thus reconstructed. 17% of the markers have a reconstruction rate in the range [70%, 95%] and 6% of the markers have a reconstruction rate less than 50% and are mainly located on lips (Fig . 2). As a result, some data are may be missing in the X t data. Most of the algorithms for building principal subspaces are based on the decomposition of the covariance matrix of the input data and cannot be used when some data are missing, as in the present case. However, there exist probabilistic approaches where PCA is considered as a limiting case of a linear Gaussian model. Principal axis can then be computed using Expectation-Maximisation (EM) algorithms [START_REF] Roweis | Em algorithms for pca and spca[END_REF]. Such algorithms can be extended to handle the problem of missing data [START_REF] Skocaj | A robust pca algorithm for building representations from panoramic images[END_REF][START_REF] Roweis | Em algorithms for pca and spca[END_REF].

In this paper, we adapt these ideas to our particular problem in order to compute the sparse modes. These ideas are also used in section 4 to compute the dense modes. We first compute the principal components for the markers R which are always reconstructed over the sequence. The components can be easily computed with classical methods since all the data are available for these markers. We then complete the entries of the principal components by introducing the markers which are not observable at every time instant using EM techniques.

Let {u r k } k≤q ∈ R r , be the q principal components computed from the set of markers which are always observable and let Xr be the mean of these meshes. Let u ∈ R N be the extended basis we are looking for. Given a mesh X t acquired at time instant t, let X r t be the reduced mesh, where only the markers always reconstructed are considered. X r t can be approximated on the q principal components as:

X r t ≈ Xr + q k=1 α k,t u r k t = 1..T (1)
The goal of the complete components is to approximate any mesh as a linear combination:

X t ≈ X + q k=1 β k,t u k t = 1..T (2)
As X r t is a sub-vector of X t -77% of entries of X t are the entries of X r t in our set-up-, it is likely that β k = α k is very close to the mean square solution of (2). In the same way, we can consider that the entries of X which correspond to always reconstructed markers are identical to the entries of Xr .

We then build a linear system which incorporates all the observations on the non always observable markers. For each observation of a marker i at time instant t, equation (2) gives rise to the following linear equation : Stacking all the equations for each visible marker at each time instant t leads to a linear system where the unknowns are the missing u k,i (i / ∈ R) and the missing components of the mean X. The α k,t are computed by projecting the reduced meshes onto the reduced components {u r k } . Considering all the markers which can be reconstructed at some instant of the sequence, we obtained a set of linear equations which can be solved in the least square sense, giving rise to the missing entries of the principal components and of the mean.

X i,t = Xi + q k=1 α k,t u k,i
The principal components are then refined using the classical EM algorithm:

-Given the components u k and X, compute the coefficients α t,i for all the meshes available in the sequence. -given the α t,i , refine the u k,i and X by solving for each i the system of linear equations:

X i,t = Xi + q k=1 α k,t u k,i , t = 1..T
in the least square sense.

Generating dense modes from sparse modes

Dynamic realism is needed for linguistic expressions. Achieving realism needs to have a high resolution 3D model as well as knowledge about the facial kinematics.

In our case, high resolution scanners of the face can only be obtained for sustained sounds as vowels. We thus propose in this paper to transfer the change in shape exhibited on the sparse meshes onto the dense mesh and to infer dense animation modes from the sparse ones.

Here gain, as in the computation of the sparse mode, we use a densification process to compute the dense modes from the sparse ones.

Overview

Let X dense 1 , .., X dense d be the set of d dense visemes which were scanned. This set contains 15 visemes of the french vowels as well as a neutral expression and a face with closed mouth.

We first suppose that these meshes physically matched, which means that the vertex i in every mesh fits the same physical point in all the dense meshes. Additionally, we also suppose that the dense and the sparse meshes are registered. How to obtain such data will be considered in the next section.

The aim of PCA is to express each viseme as a linear combination of the dense modes:

X dense i ≈ Xdense + k=1..q β i k u dense k , i = 1..d (3)
The space spanned by the sparse modes is built so as to describe the plausible appearances of a face. There thus exists a sparse mesh X i which best fits each dense mesh X dense i . Hence, we can compute coefficient α k,i such that:

X i ≈ X + q k=1 α k,i u k (4)
where u k is the set of sparse modes computed in section 3. Unlike the preceding case, X is not dense in X dense : the number of vertices of the sparse mesh is 209 whereas the dense mesh contains around 13000 vertices. However the vertices of the sparse mesh are distributed on the whole face and vertices are more present in mobile areas of the face during articulation. For these reasons, we also consider that β k = α k can be considered as a fair least square solution of equation [START_REF] Ezzat | Trainable videorealistic speech animation[END_REF].

These first estimates of β are then use to solve (3) in the least mean sense in the unknown modes u dense k and the mean Xdense . Note that we estimate less than 7 modes. As we have 15 dense visemes, the system always has a solution.

Obtaining physically matched dense visemes

Dense visemes are recorded with a laser scanner and the recovered meshes do not physically match. Remeshing of the visemes must thus be performed.

However, physically matching points between deformable surfaces is known as a very difficult problem. We thus take advantage of the underlying sparse model to obtain a physically coherent parametrization.

The first step is to identify the sparse mesh which best fits each dense viseme. As the sparse shapes are described using a reduced number of sparse modes, this can be done by computing the rigid displacement which minimizes the distance between the dense mesh and the sparse mesh thank to an iterative closest point algorithm. We are thus looking for the displacement T and the coefficient α which minimize:

M in T ,α1,..,αq distance(T -1 ( X + α k u k ), Dense M esh)
Doing this, we both identify the sparse mesh which best fits the dense viseme as well as the displacement between the two surfaces. For sake of simplicity, the registered dense visemes T (V dense ) are still denoted V dense in the following.

It is important to note that the registered visemes contains all the vertices of the sparse model. This property is used to physically match the dense visemes under the control of the sparse meshes. We here consider the /a/ viseme as the reference mesh. Remeshing is achieved with respect to this reference viseme and is performed on the basis of an extended affine matching between each pair of corresponding facets for the sparse visemes.

Given a facet ABC of the sparse reference viseme and its 3D position A ′ B ′ C ′ in the viseme to be matched (see figure 5), let M be a point of the reference dense visem. Each point of the dense mesh is associated to a sparse facet using the algorithm we described in [START_REF] Berger | Realistic face animation from sparse stereo meshes[END_REF]. The main idea is to define M as a function of the vertices of the facet and of the normals. The line HM , with H belonging to the facet, is affinely defined with respect to the facet: H is defined as the point with affine coordinates (α, β, 1 -α -β) such that HM and αN a + βN b + (1 -α -β)N c are collinear. We then define H ′ M ′ as the line with the same affine coordinates with respect to the facet A ′ B ′ C ′ and its normals. M ′ is finally obtained as the intersection of this line with the dense mesh.

Results

Figure 4 shows the first dense mode computed from the sparse mode. Figure 5 shows examples of dense faces computed from the corresponding sparse meshes. Given faces randomly taken within the sparse meshes in the database, the coefficients of the sparse mesh onto the sparse mode were computed. The dense face was then reconstructed from these coefficients using the 000000000000000 000000000000000 000000000000000 000000000000000 000000000000000 000000000000000 000000000000000 000000000000000 computed dense modes. The first row 5 shows the sparse mesh and the corresponding dense face. Other reconstructed dense faces are shown in the second and third row. These examples prove the high realism of the obtained face with a global motion of the face under the eyes coherent with the speech gesture. A full dense sequence is available on the webpage http://www.loria.fr/˜berger/teteParlante. Given a speech sequence of our corpus, the PCA coefficients were computed using the sparse modes and the dense head was generated for each image. The visual impression of the resulting sequence is very good and proved that our method is able to produce realistic facial animation.

It must be noted that the reconstruction is somehow incomplete in the inner region of the lips. This is due to the fact that the transfer procedure only allows the dense face in the neighborhood of the sparse mesh to be computed. We plan to investigate in future works methods to complete the lips from the acquired dense meshes. Lip modeling as realized in [START_REF] Kuratate | Talking Head Animation System Driven by Facial Motion Mapping and a 3D face Database[END_REF] is a possible research direction.

Conclusion

We have proposed an approach that produces automatically highly realistic face animation. This method does not require expensive materials: two cameras are required for the stereovision system and only a reduced set of 3D scans of the talker are needed. The main strength of the approach is to transfer the speech dynamics which can be easily learned on sparse data onto the dense face. To this aim, we have proposed an original densification approach which allows to compute the dense modes from the sparse modes. This method produces highly realistic dense postures. In the near future, we plan to conduct perceptive evaluation of the head with the aim to prove that this very realistic face improves speech intelligibility.

Fig. 1 .

 1 Fig. 1. Input data of the system: (a and b) a couple of stereovision images. White points/markers were painted on the face ; (c): reconstruction of the sparse mesh; (d): the 3D dense map obtained for the /a/ sound.

Fig. 2 .

 2 Fig. 2. The markers in black are the ones which are reconstructed in every frame and are taken into account in the reduced PCA.The markers in red are not always reconstructed in the sequence and are considered in the computation of the principal components using an iterative EM algorithm.

  Figure 4 shows the first dense mode computed from the sparse mode. Fig 4.a shows the mean shape of the sparse meshes and Fig. 4.b the computed dense mean shape. The second row exhibits the sparse first modes as well as the computed corresponding dense modes.Figure5shows examples of dense faces computed from the corresponding sparse meshes. Given faces randomly taken within the sparse meshes in the database, the coefficients of the sparse mesh onto the sparse mode were computed. The dense face was then reconstructed from these coefficients using the

Fig. 3 .

 3 Fig.3. How a physically registered dense mesh is obtained using the underlying sparse meshes.

Fig. 4 .

 4 Fig. 4. First row: the mean shape of the sparse meshes and the computed dense mean mode. Second row: mean -3 × u1 and mean + 3 × u1 are exhibited for the sparse modes and the computed dense modes.

Fig. 5 .

 5 Fig. 5. Examples of dense faces generated using 7 dense modes.First row: a sparse mesh and the corresponding dense mesh. Second and third row: examples of dense faces computed from various sparse meshes.


Vincent Poireau

Charmonium Spectroscopy at BaBar

Introduction

We discuss the study of charmonium resonances performed at the BaBar experiment. The BaBar experiment [1], which ran between October 1999 and September 2007, is located on the PEP-II asymmetric ring, at the SLAC National Accelerator Laboratory. It recorded 531 fb -1 of data with e + e -collisions, including 433 fb -1 at the Υ(4S) energy. This corresponds to a total amount of 475 × 10 6 BB pairs produced, and 633 × 10 6 cc pairs.

A charmonium resonance is a bound state of a charm and an anti-charm quark (cc). Figure 1 shows the actual state of knowledge on the charmonium spectrum. Basically all states below the open-charm threshold are observed and explained. However, as it can be seen from the figure, many new states have been discovered since 2003. These new states do not seem to correspond to the expected charmonium masses, and could be well the first indication of exotic states, i.e. states that are not made of the aggregation of two quarks. These exotic states are predicted by theory, but none have been definitively confirmed. Several models have been discussed. These exotic states could be hybrid states: these consist of ccg states with excited gluonic degrees of freedom. The lowest-mass hybrid is predicted at a mass of about 4.2 GeV/c 2 . They are expected to decay predominantly in DD * final states. Another possibility for exotics would be tetraquark states which are bound states of four quarks: they are predicted to have a small width above the open-charm threshold. A large number of such states is predicted. Exotic states could also be constituted of loosely bound states of a pair of mesons (molecular states). They are also predicted to have a small width above the threshold, while only a small number of states is expected.

A clear exotic signature will be non-charmonium J P C , unnaturally small width or non-null charge. In the following, we will investigate a few of these new states with the X(3872), the Y (4260), Y (4350), and the Z(4430).

X(3872)

The X(3872) meson was discovered by Belle [3] in B ± → X(3872)K ± with X(3872) → J/ψπ + π -in 2003, and quickly confirmed by the BaBar, CDF and D0 experiments [3]. Its mass is known very precisely, 3871.4 ± 0.6 MeV/c 2 , and its width is less than 2.3 MeV at 90% confidence level. This state is very close to the D * 0 D 0 threshold which is at (3871.8 ± 0.4) MeV/c 2 . This resonance was also observed in the final state J/ψγ [4], which implies that its C quantum number is equal to +1. The study of the π + π -invariant mass distribution by Belle and an angular analysis by CDF shows that J P C = 1 ++ is favored (although 2 ++ is still possible) [4]. It has also to be noted that a search for a charged partner was performed by BaBar, but no signal was found [4].

The BaBar experiment has recently performed an update of the study of the decays of B + → X(3872)K + and B 0 → X(3872)K 0 with X(3872) → J/ψπ + π - [5], using 413 fb -1 of data. The invariant masses of the J/ψπ + π -combination are shown in Fig. 2 for the two channels. A clear signal is observed in the charged channel, with a significance of 8.6σ. The neutral channel indicates the presence of the signal with a significance of 2.3σ. From these fits, they obtain the branching fractions B(B + → X(3872)K + ) × B(X(3872) → J/ψπ + π -) = (8.4 ± 1.5 ± 0.7) × 10 -6 and B(B 0 → X(3872)K 0 )×B(X(3872) → J/ψπ + π -) = (3.5±1.9±0.4)×10 -6 , where the first error is statistical and the second error is systematic. The ratio of the neutral over charged channel is measured to be 0.41 ± 0.24 ± 0.05. The natural width of the X(3872) is constrained to be below 3.3 MeV at the 90% confidence level. The BaBar Collaboration also studied the final states X(3872) → J/ψγ and X(3872) → ψ(2S)γ in the decays B + → X(3872)K ( * )+ and B 0 → X(3872)K ( * )0 [6]. Using 424 fb -1 , they obtain the invariant mass distributions shown in Fig. 3 in the B + → X(3872)K + final states. They find a 3.6σ evidence for the X(3872) → J/ψγ final states and find the first evidence of the decay mode X(3872) → ψ(2S)γ with a 3.5σ significance. No signal is found in the final states with a neutral or excited K meson. These observations imply a C-parity quantum number equal to +1. They measure the products of the branching fractions B(B + → X(3872

)K + ) × B(X(3872) → ψ(2S)γ) = (9.5±2.7±0.6)×10 -6 and B(B + → X(3872)K + )×B(X(3872) → J/ψγ) = (2.8 ± 0.8 ± 0.1) × 10 -6 .
The ratio of these two branching fractions is found to be 3.4 ± 1.4.

In 2006, the Belle experiment did a study of the channel B → D 0 D 0 π 0 K and observed a clear excess in the D 0 D 0 π 0 invariant mass [7]. The singularity of this result comes from the measurement of the mass: 3875.4 ± 0.7 +1.2 -2.0 MeV/c 2 , which is in disagreement with the mass measured in the X(3872) → J/ψπ + π -channel. This discrepancy was confirmed by the BaBar experiment [7], looking at the B → D 0 D * 0 K channels (where both decays of D * 0 , D 0 π 0 and D 0 γ, are taken into account, and where the B and K mesons are either charged or neutral). Figure 4 shows the D 0 D * 0 invariant mass using 347 fb -1 of data. An excess with a 4.9σ significance is observed in the D 0 D * 0 invariant mass, with a mass of 3875.1 +0.7 -0.5 ± 0.5 MeV/c 2 . This mass measurement is 4.5σ away from the X(3872) mass in the J/ψπ + π -channel. A measurement of the width of this state was also performed and the value found is Γ = 3.0 +1.9 -1.4 ± 0.9 MeV. The angular study was inconclusive. Recently, the Belle experiment presented an update [7] of this analysis in this channel with 605 fb -1 and they find a mass of 3872.6 +0. 5 -0.4 ± 0.4 MeV/c 2 , which is in better agreement with the measurement performed for the J/ψπ + π -final states. This result is however in disagreement with the BaBar result in D 0 D * 0 . Several authors have proposed an explanation for this discrepancy between the J/ψπ + π -and D 0 D * 0 final states. For example, in Ref. [START_REF] Braaten | [END_REF], they argue that there is no proximity of a threshold in X(3872) → J/ψπ + π -, and in consequence the mass and width measurement correspond to the real particle. On the contrary, for the X(3782) → D 0 D * 0 , the threshold D 0 D * 0 is very close to the resonance. In particular, if the X(3872) is just below the threshold, the lineshape could create an artificial peak above the threshold, which is the one measured experimentally, and which parameters would not correspond to the real particle properties. Another possible explanation for this mass shift is given in Ref. [START_REF] Dunwoodie | [END_REF]: if the X(3872) width is of the order of 2-3 MeV, then the peak position is sensitive to the angular momentum due to the proximity of the threshold. A mass shift of about 3 MeV/c 2 is expected if the X(3872) has quantum numbers J P = 2 -. The interpretation of the X(3872) state is rather difficult [10] since there is no Points are data events, the solid line represents the fit to the data, the dashed line shows the contribution of the X(3872) signal, and the dotted line shows the background contribution.

satisfactory cc assignment for this resonance. The coincidence between this resonance mass and the D 0 D * 0 mass led some authors to propose that the X( 3872) is a bound state of the D 0 and D * 0 mesons with small binding energy (molecular state). One of the predictions of this model is that B 0 → X(3872)K 0 is suppressed by approximately a factor 10 compared to B + → X(3872)K + . Experimentally, this ratio is measured by BaBar to 0.41 ± 0.24 ± 0.05 in the X(3872) → J/ψπ + π -channel. This model favors D 0 D * 0 decays over J/ψπ + π -, itself favored over J/ψγ, consistent with the observations. However, the model predicts X(3872) → ψ(2S)γ to be suppressed, which is in contradiction with the observation. It has also been proposed that the X(3872) resonance is a tetraquark state. In this case, the model predicts two neutral states and two charged states, with a difference of mass between the two neutral states (produced respectively in B 0 and B + decays) of (7 ± 2) MeV/c 2 . The experimental results in BaBar show a mass difference of (2.7 ± 1.6 ± 0.4) MeV/c 2 in the X(3872) → J/ψπ + π -channel. Furthermore, no evidence for charged partners have been found so far. Another explanation for this state is that the X(3872) could be a mixing of a D 0 D * 0 state and a cc state. Further experimental results should help to better understand this resonance.

Y (4260) and Y (4350)

The Y (4260) state constitutes also quite a mystery. This state, with J P C = 1 --, was discovered by BaBar in 2005 in e + e -→ γ ISR (J/ψπ + π -), with a photon radiated in the initial state [11] (ISR). BaBar recently updated [11] this measurement with an integrated luminosity of 454 fb -1 . The invariant mass of the J/ψπ + π -combination can be seen in Fig. 5. From the fit to the invariant mass distribution, a mass of M = (4252 ± 6 +2 -3 ) MeV/c 2 and a width of Γ = (105 ± 18 +4 -6 ) MeV are obtained. This state was also seen by the Belle experiment with M = (4247 ± 12 +17

-32 ) MeV/c 2 and Γ = (108 ± 19 ± 10) MeV while CLEO measures M = (4284 +17 -16 ± 4) MeV/c 2 [11]. Belle also reported an enhancement at a mass of about 4050 MeV/c 2 in this channel, which is not confirmed by the BaBar study.

BaBar performed recently a study [12] of the exclusive production of DD, D * D, D * D * in initial-state-radiation events with an integrated luminosity of 384 fb -1 . Effectively, the Y (4260) is expected to decay dominantly in these final states if it is a charmonium resonance. A plot combining the three decay modes is shown in Fig. 5. We observe from this plot that no Y (4260) is seen in these channels. A 3σ enhancement was also reported by BaBar in B → Y (4260)K -, followed by Y (4260) → J/ψπ + π - [11], although this result needs confirmation by other experiments. Searches for this resonance were performed in other channels (e + e -→ γ ISR (Φπ + π -), e + e -→ γ ISR (pp), e + e -→ γ ISR (J/ψγγ)), but no positive results were reported [11].

It was natural to search for the decay of Y (4260) going to ψ(2S)π + π -in ISR production [13]. A clear signal is observed in this channel (see Fig. 6) with 298 fb -1 , however with a mass measurement incompatible with the previous BaBar result. The mass found in this channel is (4234 ± 24) MeV/c 2 with a width of (172 ± 33) MeV. This result was later confirmed by Belle with a mass of (4361 ± 9 ± 9) MeV/c 2 and a width of (74 ± 15 ± 10) MeV [13]. The interpretation of these two new states is far from obvious [14]. There is no cc assignment for 1 --states of these masses.

) 2 ) (GeV/c ψ )J/ - π + π m(2(

Z(4430)

Belle has reported [15] in 2008 a new charged charmonium-like state in the decay B → Z -K followed by Z -→ ψ(2S)π -, with a significance of 6.5σ. This result is intriguing since this is the first report of a charged resonance carrying hidden charm, and its minimal quark content should be (ccud). The reported mass and width are respectively (4433 ± 4 ± 2) MeV/c 2 and (45 +18 -13 +30

-13 ) MeV. Using the same data sample (605 fb -1 ), Belle has confirmed this result using a Dalitz plot analysis [15]. They updated the value of the mass and the width to (4443 +15 -12 +17

-13 ) MeV/c 2 and (109 +86 -43 +57

-52 ) MeV. BaBar performed a search [16] for the Z(4430) resonance (using 413 fb -1 ) in the channels B → ψπ -K where the ψ stands either for J/ψ or ψ(2S) and where B and K are either charged or neutral. In this analysis, the Kπ -system is carefully treated to take into account the structures in mass and angular distributions (by means of Legendre polynomials). The reflections of the Kπ -structure are then projected in the ψπ -mass distribution, and used to determine if additional contributions are needed above this Kπ -projection. It is shown that a good description is obtained with such a method and that no additional structure is needed to describe the data. Figure 7 shows the ψπ -invariant masses for the different channels after efficiency correction. A S-wave Breit-Wigner is used to describe the Z(4430) signal. Figures 7 (a) and(d) are for the entire data samples, Fig. 7 (b) and (e) are for the K * regions, and Fig. 7 (c) and (f) are for the K * (892) and K * (1430) veto region combined (corresponding to the Belle selection). No enhancement is seen in the J/ψπ -channel. In the ψ(2S)π - channels (d) and (e), enhancements are present with a significance lower than 3σ and masses different from the one from Belle. Using the same selection as Belle (f), BaBar find a compatible mass, but with a significance of only 1.9σ. We can conclude that no Z(4430) signal is observed in the current BaBar data sample.

Conclusions

Although no new resonances were discovered in many years, BaBar has given an impressive list of new results since 1999. Many of these new resonances could not be explained by usual quark content. The nature of the X(3872), the Y (4260), the Y (4350), and the Z(4430) is still unclear. These states are not charmonium states, and are probably the first occurrences of non-standard quark content. Theoretically, these states are still actively in debate, and new ideas will probably emerge in the near future.

Analyzes are still in progress with the current data set in BaBar: more decay modes for the resonances presented here are being investigated. We also expect contributions from LHCb and Super-B/Belle II experiments which will collect data at high luminosity.

Figure 1 :

 1 Figure 1: Spectrum of the known charmonium states. Blue squares represent the charmonium states that are established and well measured, red squares show charmonium(-like) states which were discovered recently at the B-factories. The empty rectangles indicate the prediction by the potential models [2]. The horizontal line shows the open-charm threshold.

Figure 2 :

 2 Figure2: Invariant mass distributions for the J/ψπ + π -final state for B + → X(3872)K + (left) and B 0 → X(3872)K 0 (right). The dots are the data, the dashed line represents the combinatorial background fit and the solid line the total fit.

Figure 3 :

 3 Figure3: Number of extracted signal events versus the invariant mass for B + → X(3872)K + followed by X(3872) → J/ψγ (left) and by X(3872) → ψ(2S)γ (right). The dots are the data, the solid line represents the fit to the data.

Figure 4 :

 4 Figure 4: Invariant mass distribution of D 0 D * 0 in the decay channel B → D 0 D * 0 K.

Figure 5 :

 5 Figure 5: Left plot: J/ψπ + π -invariant mass spectrum. Points with error bars represent the data, the solid curve shows the result of the fit, while the dashed curve represents the background component. Left plot: sum of the e + e -→ DD, e + e -→ D * D, and e + e -→ D * D * cross-sections. The arrow indicates the position of the Y (4260).

Figure 6 :

 6 Figure 6: ψ(2S)π + π -invariant mass spectrum.

  Possibilities that have been mentioned are tetraquark state [cs][cs], hybrid meson (where we expect a suppression of D ( * ) D ( * ) final states) or ωχ c1 molecule.

Figure 7 :

 7 Figure 7: Results of the fits to the corrected mass distributions. The solid line is the total fit while the dashed line is the background contribution. The vertical lines indicate the position of the hypothetical Z(4430).


Serge Abiteboul

Luc Segoufin

Victor Vianu

Modeling and Verifying Active XML Artifacts *

Introduction

Shared evolving data is central to an increasing range of human activities. In response to the need for computerized support of such activities, the notion of business artifact has been proposed at IBM as a model of such evolving data [START_REF] Nigam | Business artifacts: An approach to operational specification[END_REF]. The model captures both the flow of control (workflow) of the application and the evolution of the relevant data (data cycle); see [START_REF] Hull | Artifact-centric business process models: Brief survey of research results and challenges[END_REF] for a brief survey. In the same spirit, we propose a new artifact model building upon Active XML (AXML for short), an extension of XML with embedded service calls [START_REF] Abiteboul | The Active XML project: an overview[END_REF]. The services are hosted by autonomous peers that evolve and interact by exchanging XML data. We claim that this can provide the foundation for an appealing artifact model, combining the advantages of semistructured data and of the Web service paradigm. With the model in place, we consider the verification of data-intensive applications, which is particularly critical for such systems due to their vulnerability to costly bugs. Despite the expressiveness of the model, we show that verification remains possible under reasonable restrictions.

Workflow and database systems are two essential software components that often have difficulties interoperating. Data-centric workflow systems are meant to integrate the control aspect of workflows with the underlying data. They allow managing data evolution by tasks with complex sequencing constraints as encountered for instance in scientific workflow systems, information manufacturing systems, e-government, e-business or healthcare systems. One can distinguish two main approaches for combining the database and workflow components. One consists in starting from a workflow approach, enriching it with data, e.g., by explicitly introducing state variables and specifying how they may evolve. The second emphasizes data placed at the center of the specification, but enriches it with means of controlling how it evolves. There is no fundamental separation between these two kinds of approaches but more a bias coming from where the emphasis is placed. However, when an emphasis is placed on the data (as we do here), one tends to prefer declarative specifications based on constraints on the evolution rather than control-based specifications.

We follow here a data-centric workflow approach where both data and tasks, but also the "actors" (humans, processes, systems) are captured by AXML artifacts [START_REF] Abiteboul | The axml artifact model[END_REF]. The basis of this work is thus the Active XML model. AXML documents [START_REF] Abiteboul | The Active XML project: an overview[END_REF][START_REF]Active XML[END_REF] are XML documents with embedded function calls realized as Web service calls. Observe that the central notion is a document, so data, but that the model also involves computation, i.e., Web services. A main issue in the AXML technology is "when is a Web service call" evaluated. In query processing, a call may be activated because its result may impact the result of a query; this is in the spirit of recursive query processing. A call may also be activated bacause some event occurred, as in active databases. In the present work, we want activation to be guided by the logic of the application, e.g. by some workflow constraints. In particular, we want to be able to specify some particular sequencings of the Web service calls inside a document.

An example of AXML documents is shown in Figure 3. Function warehouseOrder is used to obtain the parts from a warehouse. Function deliveryOrder is used to start the delivery process. It is likely that the system will delay the activation of this second function until after the computer has been built. On the other hand, the parts should be obtained from the warehouse before the construction starts.

The calls in an AXML document may be activated from inside (the artifact as client) and then receive answers in push or pull mode. Calls may also be activated from outside (the artifact as server). Rules are used to specify the logic of functions declaratively [START_REF] Abiteboul | Static analysis of Active XML systems[END_REF]. We use such documents to represent artifacts. In the spirit of [START_REF] Khalaf | Business processes for web services: Principles and applications[END_REF][START_REF] Nigam | Business artifacts: An approach to operational specification[END_REF], an AXML document represents a process that evolves in time. A function call may be seen as a request to carry out a subtask whose result may lead to a change of state in the document.

An Active XML system specifies a set of interacting AXML documents. In such a system, there is an important distinction between internal and external services. An internal service is a service that is completely specified within the system whereas an external one captures interactions with other services or with users. One important goal is to statically analyze the behavior of such systems, which is especially challenging because the presence of data induces infinitely many states. We illustrate this aspect by mentioning some work on the verification of restricted centralized AXML systems [START_REF] Abiteboul | Static analysis of Active XML systems[END_REF]. These results can be easily transferred to distributed systems of AXML artifacts.

In this paper, we briefly present the AXML artifact model [START_REF] Abiteboul | The axml artifact model[END_REF] (Section 2). We also mention some work on data-centric verification from [START_REF] Abiteboul | Static analysis of Active XML systems[END_REF] (Section 3). The last section provides brief conclusions.

The AXML Artifact model

Artifacts present several facets that, in our opinion, should be captured by an artifact model. An artifact is an object with a universal identity (e.g., URI). Its state is self-describing (e.g., XML data) so that it may be easily transmitted or archived. An artifact may host other artifacts as components, yielding a hierarchy of artifacts. At the physical level, each artifact at the root of the hierarchy is hosted by a peer. During its life cycle, an artifact is created, evolves in time, migrates among hosts, may hibernate and be reactivated, or dies according to a logic that is specified declaratively. Its evolution may be constrained to obey some laws, e.g. a workflow. An artifact interacts with the rest of the world via function calls (e.g., Web services) both as a server and a client. An artifact provides for communications, storage and processing for the artifacts it hosts. As in scientific workflows, an artifact has a history including time and provenance information that may be recorded and queried. These requirements have been in part motivated by [START_REF] Bhattacharya | A data-centric design methodology for business processes[END_REF].

To illustrate, consider a simplified view of the Dell manufacturing system [START_REF] Kapuscinski | Inventory decisions in Dell's supply chain[END_REF] (Figure 1). When a new Web order arrives (1), a new webOrder artifact is created and creates a subartifact that is sent to a credit service (2). Once credit has been approved, the subartifact returns to the webOrder but now its state contains all the credit data. A plant is then selected and the artifact moves to that plant (3). It initiates a new subartifact for gathering parts, that is sent to a warehouse and another local artifact for communications with the customer (4). Once the product has been built, the artifact is sent to a delivery service [START_REF]Active XML[END_REF]. Finally, once the Web order has been completed, the artifact moves to an archive where it is stored as a text-based XML serialization that includes all the information it has gathered during its life cycle [START_REF] Abiteboul | Static analysis of Active XML systems[END_REF]. (Subartifacts may also be archived separately.) The Dell example can be naturally modeled in AXML. See Figure 3 where the tree is represented using an XML syntax (a text-based serialization of the tree). The figure shows part of a webOrder artifact immediately after it enters the plant. The creditApproval element denotes a subartifact (the one that has been processed by the bank). The functions ?warehouseOrder and ?comm will be activated next in order to create the warehouseOrder and communication subartifacts that will then work concurrently (and somewhat autonomously).

More broadly, the use of AXML as a basis for an artifact model is motivated by the fact that it can be easily adapted to support all the requirements identified above. In particular, AXML naturally captures the distribution and autonomy of artifacts and provides reliable synchronous or asynchronous communication, allowing an artifact to send a message to another artifact just by knowing its ID. Also, because of its nested structure, AXML naturally supports hierarchies of artifacts. Two functionalities have to be added to AXML in order to fully support the above requirements. First, since we want artifacts to move from place to place in the system, we need an identification mechanism serving as a URI for artifacts. We also augment the rule-based workflow specification provided by AXML with workflows specified in a transition-based BPEL style that is more familiar to application designers. The core of an application is a schema specifying a set of of peers and a set of classes (e.g., webOrder, financialService). The definition of a class provides typing of the data (document types), dynamic constraints on artifacts evolution (their workflows) and the interface of functions that the artifacts in this class export. From an implementation viewpoint, a peer provides storage, communications and computing resources for the artifacts it hosts. Artifacts are allowed to exchange data with other peers or to move to other peers. AXML data (e.g., in function arguments and results) is sent as strings and reconstructed at the receiving peers.

The semantics of functions is specified by rules. The declarative semantics facilitates reasoning about the runs of such systems and performing optimization. Function call activation is controlled by call guards that are specified by Boolean combinations of tree-patterns over the documents. Observe that the guards impose constraints on the evolution of documents in the style of condition-action rules. This may be seen as specifying workflow constraints on the runs of the system. Alternatively, one might prefer a more standard workflow approach in the style BPEL. The workflow is then specified by defining stages in the evolution of the artifact and admissible transitions between them. We are currently working on a comparison of the two styles of workflow specifications.

The notions of task, service, state, stage, and activity, that are essential in the artifact context, can all be formally captured in the AXML artifact model. The notion of activity, often arising in functional decompositions of business processes, may be seen as a view over a system of artifacts. The notions of time and provenance that are central to scientific workflows can be captured as well, because this information can be recorded and maintained in XML documents.

Related work

Although the notion of artifact has been recently articulated by [START_REF] Nigam | Business artifacts: An approach to operational specification[END_REF], similar ideas of data centric workflows have been around, e.g., in AXML [START_REF] Abiteboul | The Active XML project: an overview[END_REF], in the Vortex system [START_REF] Dong | A framework for optimizing distributed workflow executions[END_REF] or scientific workflows [START_REF] Davidson | Provenance and scientific workflows: Challenges and opportunities[END_REF]. The models that are considered are often restricted, e.g., [START_REF] Bhattacharya | Towards formal analysis of artifactcentric business process models[END_REF][START_REF] Bhattacharya | A data-centric design methodology for business processes[END_REF]. For instance, a single artifact is usually considered, vs. a system of artifacts in the present paper. Also, these models are often based on the relational model so have difficulties with collections of artifacts or nested tasks/artifacts. Formal models for data-centric workflows have been considered in [START_REF] Deutsch | Automatic verification of data-centric business processes[END_REF] (that focuses on verification) and [START_REF] Fritz | Automatic construction of simple artifact-based business processes[END_REF] (that discusses the synthesis of artifacts).

Verification

The need for reasoning about artifact systems arises in many contexts and is particularly challenging because of the presence of data. We briefly summarize results obtained in [START_REF] Abiteboul | Static analysis of Active XML systems[END_REF] on static analysis of AXML systems, in particular on automatic verification of temporal properties of their runs.

Classical automatic verification techniques operate on finite-state abstractions that ignore the critical semantics associated with data in such applications. The need to take into account data semantics has spurred interest in studying static analysis tasks in which data is explicitly present. We have started an investigation of the automatic verification of Active XML systems. We consider properties expressed in Tree-LTL, an extension of LTL where propositions are interpreted as tree patterns. For instance, one may want to verify whether some static property (e.g., all ordered products are available) and some dynamic property (e.g. an order is never delivered before payment is received) always hold. Tree-LTL allows to express a rich class of such properties. An example of Tree-LTL formula can be found in Figure 4.

We have identified a significant fragment of Active XML, called non-recursive Guarded AXML for which the verification of Tree-LTL properties is decidable. This fragment is expressive enough to describe meaningful applications. We use also it as a convenient formal vehicle for studying decidability and complexity boundaries for verification in AXML in general. We briefly describe next AXML (GAXML for short) and its non-recursive fragment.

Every product for which a correct amount has been paid is eventually delivered (note that the variable Z is implicitly existentially quantified in the left pattern): In GAXML, document trees are unordered. With ordered trees, verification quickly becomes undecidable. Finally, the most novel feature of the model in the AXML context is a guard mechanism for controlling the initiation and completion of subtasks (formally function calls). Guards are Boolean combinations of tree patterns. They facilitate specifying applications driven by complex workflows and, more generally, they provide a very useful programming paradigm for active documents.

∀X∀Y [G(
We obtain decidability by disallowing recursion in GAXML systems, which leads to a static bound on the total number of function calls in runs. We prove that for such non-recursive GAXML, satisfaction of Tree-LTL formulas is CO-2NEXPTIME-complete. We also consider various relaxations of the non-recursiveness restriction and show that they each lead to undecidability. This establishes a fairly tight boundary of decidability of satisfaction of Tree-LTL properties by GAXML systems.

Related work

Most of the previous work on static analysis on XML (with data values) deals with documents that do not evolve in time (static constraints). This motivated studies of automata and logics on strings and trees over infinite alphabets, see [START_REF] Segoufin | Static analysis of xml processing with data values[END_REF] for a survey. Previous work on AXML also considered the evolution of documents. For instance, this is considered in [START_REF] Abiteboul | Positive Active XML[END_REF] for a monotone AXML language, positive AXML. The setting is very different from ours, as their systems are monotone but possible recursive. In contrast, we consider verification for nonmonotone systems. Static analysis is also studied in [START_REF] Genest | Tree pattern rewriting systems[END_REF] using a model based on tree rewriting. Verification of temporal properties of Web services has mostly been considered using models abstracting away data values (see [START_REF] Hull | E-services: a look behind the curtain[END_REF] for a survey). Verification of data-aware Web services was studied in [START_REF] Deutsch | Specification and verification of data-driven web applications[END_REF][START_REF] Deutsch | Verification of communicating data-driven web services[END_REF], and a verifier implemented [START_REF]A Verifier for Interactive, "A. deutsch and m. marcus and l. sui and v. vianu and d. zhou[END_REF]. While this is related in spirit to the present work, the technical differences stemming from the AXML setting render the two investigations incomparable.

Conclusion

We briefly mention some remaining issues related to the work presented here. A most interesting direction of research is to enrich beyond non-recursive GAXML the class of AXML artifact systems that can be verified. For example, one would also like to be able to reason about time (this is complicated for several reasons, including the absence of a global clock). When full verification cannot be performed, abstraction may be useful. Recent work considers a related approach based on interfaces in the context of AXML [START_REF] Benveniste | Interface for Active XML[END_REF]. Besides verification, a main issue for such systems is monitoring. A P2P monitoring system for AXML is studied in [START_REF] Abiteboul | Distributed Monitoring of Peer to Peer Systems[END_REF][START_REF] Abiteboul | Satisfiability and Relevance for Queries over Active Documents[END_REF]. Finally, largely unexplored in this context are access control mechanisms, allowing different actors to keep control over their own data without imposing unacceptable constraints on the system.

Figure 1 :

 1 Figure 1: Artifacts in the Dell application

Figure 2 :

 2 Figure 2: A GAXML query Figure 3: An AXML artifact

Figure 4 :

 4 Figure 4: A Tree-LTL formula

* Work supported by the Webdam Grant of the European Research Councild (FP7); n. 226513. The work of the first two authors is also supported in part by the EC FoX Grant. The work of the last is supported in part by the National Science Foundation under grant number IIS-0916515.