R Fablet
email: rfablet@irisa.fr

P Bouthemy
email: bouthemy@irisa.fr

STATISTICAL MODELING FOR MOTION-BASED VIDEO CLASSIFICATION AND RETRIEVAL

We have developed an original approach for content-based video indexing and retrieval. By introducing a causal Gibbsian modeling of the spatio-temporal distribution of appropriate local motion-related measurements, we have designed a general and efficient statistical framework for non parametric motion modeling, motion recognition and classification, and motion segmentation. It is exploited for motionbased video indexing and video retrieval for both global and partial queries by example.

INTRODUCTION AND RELATED WORK

Video archives are at the core of various application fields. The efficient use of these databases requires to offer reliable and relevant access to visual information. In particular, it implies to index and retrieve visual documents by their content. A great deal of research amount is currently devoted to image and video database management, [START_REF] Aigrain | Content-based representation and retrieval of visual media : A state-of-the-art review[END_REF][START_REF] Gelgon | Determining a structured spatio-temporal representation of video content for efficient visualization and indexing[END_REF][START_REF] Irani | Video indexing based on mosaic representation[END_REF][START_REF] Zhang | An integrated system for content-based video retrieval and browsing[END_REF]. Nevertheless, it remains hard to easily identify the relevant information for a given query, due to the complexity of image and sequence interpretation.

Content-based video editing, indexing, browsing, and retrieval primarily require to recover the elementary shots of the video and to recognize typical forms of video shooting such as static shot, traveling, zooming and panning [START_REF] Aigrain | Content-based representation and retrieval of visual media : A state-of-the-art review[END_REF][START_REF] Zhang | An integrated system for content-based video retrieval and browsing[END_REF] 1 . At a second stage, it appears necessary to provide an interpretation and a representation of the shot content. Dynamic content analysis is of particular interest and its combination with static content descriptions should offer new functionalities for video navigation, browsing or retrieval. A first class of approaches, which rely on parametric or dense motion field estimation, includes image mosaicing [START_REF] Irani | Video indexing based on mosaic representation[END_REF], segmentation, tracking and characterization of moving elements in order to determine a spatio-temporal representation of the video shot [START_REF] Muffit Ferman | Effective content representation for video[END_REF][START_REF] Gelgon | Determining a structured spatio-temporal representation of video content for efficient visualization and indexing[END_REF]. However, these techniques turn out to be unadapted to certain classes of sequences with complex dynamic contents such as motion of rivers, flames, foliages in the wind, or crowds, etc. Therefore, in the context of video indexing, it seems also relevant to adopt a global point of view that avoids any explicit motion segmentation step.

We have developed an original approach for motionbased video indexing and retrieval. It aims at interpreting dynamic contents without any prior motion segmentation and without any complete motion estimation in terms of parametric models or optical flow fields. Preliminary researches in that direction have defined extraction techniques of "temporal texture" features, [START_REF] Nelson | Qualitative recognition of motion using temporal texture[END_REF][START_REF] Szummer | Temporal texture modeling[END_REF]. Motions of rivers, foliages, flames, or crowds, for instance, can indeed be regarded as temporal textures. In [START_REF] Nelson | Qualitative recognition of motion using temporal texture[END_REF], features issued from spatial cooccurrences of normal flows are exploited to classify sequences either as simple motions (rotation, translation, divergence) or as temporal textures. In previous work, we have found global features extracted from temporal cooccurrence distributions of local motion-related measurements more appropriate than the use of normal velocity fields [START_REF] Bouthemy | Motion characterization from temporal cooccurrences of local motion-based measures for video indexing[END_REF].

This paper is organized as follows. Section 2 outlines the general ideas underlying our work. Section 3 describes the local non-parametric motion-related information that we consider. In Section 4, we introduce the statistical modeling of the temporal distribution of motion-related quantities computed from a video sequence and the associated estimation scheme. Section 6 presents several applications of our statistical non-parametric motion modeling framework to motion-based video indexing and recognition.

PROBLEM STATEMENT

To cope with video databases involving various dynamic contents, it is necessary to determine an optimal set of features and the associated similarity measure [START_REF] Santini | Similarity measures[END_REF]. These issues can be tackled using Principal Component Analysis [START_REF] Milanese | Correspondence analysis and hierarchical indexing for content-based image retrieval[END_REF] or some feature selection techniques [START_REF] Jain | Feature selection: evaluation, application and small sample performance[END_REF]. Nevertheless, feature space is usually of high dimension, and the considered distance is likely not to capture properly uncertainty attached to feature measurements. Therefore, statistical methods appear more appropriate in that context than numerical feature values. Our aim is to supply within the same framework a global description of the dynamic content as well as efficient probabilistic tools for video database classification and retrieval with query by example.

To this end, we adopt a motion-classification approach for video indexing which relies on a statistical analysis of the spatio-temporal distribution of local non-parametric motionrelated measurements. We aim at identifying probabilistic models corresponding to different dynamic content types to be discriminated. In [START_REF] Elfadel | Gibbs random fields, cooccurrences and texture modeling[END_REF][START_REF] Gimel'farb | Texture modeling by multiple pairwise pixel interactions[END_REF], a correspondence between cooccurrence distributions and Markov Random Field (MRF) models are established in the context of spatial texture analysis. We propose an extension to temporal textures. We have introduced causal models allowing us to compute the exact expression of the corresponding likelihood functions. We have thus developed a general statistical framework exploitable for video indexing and retrieval.

LOCAL MOTION-RELATED MEASUREMENTS

The first step is to define relevant local motion-related measurements whose spatio-temporal distributions will be modeled within a causal Gibbsian framework described in Section 4. Since our goal is to characterize the actual dynamic content of the scene, we first cancel camera motion. As a consequence, we estimate the dominant image motion between two successive images, which is assumed to be due to camera motion. Then, to cancel it, we wrap the successive images to the first image of the shot by combining the elementary dominant motions successively estimated over the consecutive image pairs.

Dominant motion estimation

To model the transformation between two successive images, we consider a 2D affine motion model. The estimation of the six affine motion parameters is achieved with the robust gradient-based incremental estimation method described in [START_REF] Odobez | Robust multiresolution estimation of parametric motion models[END_REF]. The use of a robust estimator allows the motion estimation not to be sensitive to secondary motions due to mobile objects in the scene. The minimization is performed by means of an iterative reweighted least-square technique embedded in a multiresolution framework.

Local motion-related quantity

In order to characterize the residual motion information in the motion-compensated image sequence, we consider the following local motion-related quantity :

¡¢£ ¤¥¦ § £© ¤¦ ! ¤¦ "#$ %&' ( ) £© ¤¦ '0 (1)
where ¤¥¦ is the intensity function at point ¥ in the wrapped image, 1 ¤¥¦ is a small window centered on ¥ , &' a predetermined constant related to the noise level in uniform areas, and ! is the temporal derivative of the intensity function . ! ¤¥¦ is approximated by a simple finite difference. Whereas the normal flow measure 23 4 56 23 5 turns out to be very sensitive to noise attached to the computation of spatio-temporal derivatives of the intensity function, the considered motion-related measurement forms a more reliable quantity, yet simply computed from the intensity function and its derivatives. Obviously, the information relative to motion direction has been lost, which prevents from discriminating for instance two opposed translations with the same magnitude. However, this is not a real shortcoming, since we are interested in interpreting the type of dynamic situations observed in the considered video shot and not in identifying a specific motion value.

STATISTICAL NON-PARAMETRIC MODELING OF MOTION CONTENT

Temporal Gibbsian modeling

In order to characterize the motion activity, we exploit the probabilistic framework presented in [START_REF] Fablet | Statistical motionbased video indexing and retrieval[END_REF] which relies on non-parametric motion models. We briefly outline it hereafter. Let 7 § 8 79 ( @@@( 7A B be a sequence of C D E maps of quantized motion-related quantities and F the spatial support of these maps. F can be the entire image, a given region, or a block, depending on the global or local nature of the targeted characterization. We first evaluate the associated distribution of temporal cooccurrences G ¤ 7 ¦ defined by: H

¤I( IP¦ Q R' G ¤I( IP 7 ¦ § A STU V© W X ¤I Y 7 S ¤`¦¦ X ¤IP Y 7 SaU ¤`¦¦ (2)
where R is the set of possible discrete values of the quantized motion-related measurements. We assume that sequence 7 is the realization of a random process b such that the conditional likelihood cd ¤ 7 ¦ of sequence 7 w.r.t. to a model e is expressed as:

cd ¤ 7 ¦ § E f g $h i p d q G ¤ 7 ¦ r ( 3
)
where f is a known normalization constant independent of e and 7. p d is the set of potentials 8 p d ¤I( IP¦ B stsu ©vw which explicitly specifies model e. p d q G ¤ 7 ¦ denotes the dot product between model potentials p d and cooccurrence distribution G ¤ 7 ¦ given by:

p d q G ¤ 7 ¦ § stsu ©vw p d ¤I( IP¦ G ¤I( IP 7 ¦ (4)
The availability of such an exponential formulation presents several interests. First, it makes the computation of the conditional likelihood cd ¤ 7 ¦ for any sequence 7 and model e feasible and simple. Then, the use of these probabilistic models for recognition or classification issues based on ML or MAP criteria is straightforward. Second, all motion information exploited by these models is contained in the cooccurrence distributions. In particular, in order to evaluate the conditional likelihoods 8 cd ¤ 7 ¦ B w.r.t. models 8 e¡B for a given sequence 7, it is not necessary to store the entire sequence 7. We only need to compute and store the related temporal cooccurrence distribution G ¤ 7 ¦ . The evaluation of the conditional likelihoods 8 cd ¤ 7 ¦ B is then simply achieved from the products 8 p d q G ¤ 7 ¦ B using expression (3).

This modeling approach is non-parametric in two ways. First, it does not correspond to 2D parametric (affine or quadratic) motion models [START_REF] Odobez | Robust multiresolution estimation of parametric motion models[END_REF]. Second, from a statistical point of view, it does not involve parametric distributions (i.e., Gaussian) to model the law cd ¤I IP¦ . In some way, it is learnt from data.

Besides, the ML (Maximum Likelihood) estimation of model e best fitting the motion distribution attached to a given sequence 7 reveals straightforward. The potentials of the model ¢ e, which verifies ¢ e § #£¤ "#$ d cd ¤ 7 ¦ , are readily given by [START_REF] Fablet | Statistical motionbased video indexing and retrieval[END_REF]:

p ¥ d ¤I( IP¦ § ¦ § G ¤I( IP 7 ¦© ©v G ¤ ( IP 7 ¦ (5)

Spatio-temporal Gibbsian modeling

The statistical modeling of motion information described above does not explicitly characterize spatial aspects (spatial patterns) of motion information, since it only relies on the evaluation of temporal cooccurrences of motion-related measurements. In order to combine within a single statistical framework the characterization of both spatial and temporal aspects of motion information, we have investigated three different alternatives:

q First, we have used causal spatio-temporal neighborhood instead of the use of a single temporal neighborhood [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]. The main drawback of this approach is that the computation of the likelihood function cd and ML model estimation becomes more complicate;

q Second, we have exploited spatio-temporal random walks through the sequence of maps of motion-related measurements [START_REF] Fablet | Motion recognition using spatiotemporal random walks in sequence of 2D motion-related measurements[END_REF]. Similarly to temporal Gibbs model, the likelihood function cd has an exponential form involving the dot product between model potentials and spatio-temporal cooccurrence measurements. Furthermore, ML model estimation is also readily determined from cooccurrence distributions;

q Third, we have investigated the characterization of spatial aspects of motion distribution through a multiscale strategy [START_REF] Fablet | Non parametric motion recognition using temporal multiscale Gibbs models[END_REF]. In fact, instead of using a single motion-related measurement at each location in the sequence, we consider a vector of motion-related quantities computed at different scales. The statistical modeling of motion information is then based on the computation of temporal and scale cooccurrences, while sharing characteristics similar to temporal Gibbs models, both in terms of computation of the likelihood function cd(x) and in terms of ML model estimation.

SIMILARITY MEASURE OF MOTION CONTENT

Designing a similarity measure between dynamic contents is of key interest for motion-based video indexing and retrieval. We can exploit the statistical motion modeling introduced in the previous section to define such a similarity measure.

Given two video shots U and ', the associated sequences of maps of motion-related measurements, 7 and 7 w , and statistical motion models, e U and e ' , the motionbased similarity measure A ¤ U ( ' ¦ is defined as:

A ¤ U ( ' ¦ § E i C ¤ e ' e U ¦ D C ¤ e U e ' ¦ r (6)
where C ¤ e ' e U ¦ is the Kullback-Leibler divergence.

When using temporal Gibbs model, C ¤ e ' e U ¦ can be approximated by [START_REF] Fablet | Statistical motionbased video indexing and retrieval[END_REF]:

C ¤ e ' e U ¦ § i p d Y p d w r q G ¤ 7 ¦ (7)

APPLICATION TO MOTION-BASED VIDEO INDEXING AND RETRIEVAL

We have exploited these statistical motion models for various applications related to motion recognition and classification.

In [START_REF] Fablet | Motion recognition using spatiotemporal random walks in sequence of 2D motion-related measurements[END_REF][START_REF] Fablet | Non parametric motion recognition using temporal multiscale Gibbs models[END_REF], we have tackled the motion recognition issue for a video base containing different classes of motion content: temporal texture (rivers, grass motion, trees in the wind,. . . ), sequences of pedestrians, traffic video shots. Based on the computation of the motion similarity measure given by relation [START_REF] Fablet | Non parametric motion recognition using temporal multiscale Gibbs models[END_REF], we have obtained promising results with a mean recognition rate higher than ¡¢.

We have addressed the classification of video databases in [START_REF] Fablet | Statistical motionbased video indexing and retrieval[END_REF]. Still using relation [START_REF] Fablet | Non parametric motion recognition using temporal multiscale Gibbs models[END_REF], we can build a binary tree which expresses in a hierarchical way video similarities in terms of motion content. This kind of hierarchical structure can be useful for retrieval or browsing in video databases.

We have also dealt with the extraction of entities of interest in images w.r.t. motion information in [START_REF] Fablet | Non-parametric motion activity analysis for statistical retrieval with partial query[END_REF]. Based on the general characterization of motion information in terms of motion activity, statistical motion models are used to merge blocks of an initial partition of the image w.r.t. motion content similarity. Our approach enables to handle a wide range of dynamic entities of interest: single moving entity or group of entities in sport video shots, entities formed by a moving texture,... In addition, simultaneously to the extraction, we can provide a characterization of the movement of the entity of interest by means of the estimated statistical motion model.

Finally, the designed statistical motion models can also be used for motion-based retrieval with query by example. The retrieval process is in fact viewed as a Bayesian inference issue based on the MAP criterion. It first comes to build a database of statistical motion models. Then, the reply to a given query is determined by finding in the database the model best fitting the query. It involves the use of relation (3). We can handle both global query involving a whole video sequence [START_REF] Fablet | Modélisation statistique non paramétrique et reconnaissance du mouvement dans des séquences d'images ; application à l'indexation vidéo[END_REF][START_REF] Fablet | Statistical motionbased video indexing and retrieval[END_REF] as well as partial query (the query is concerned by a given area in the image) [START_REF] Fablet | Modélisation statistique non paramétrique et reconnaissance du mouvement dans des séquences d'images ; application à l'indexation vidéo[END_REF][START_REF] Fablet | Non-parametric motion activity analysis for statistical retrieval with partial query[END_REF]. In the later case, from a given database of video shots, we first build the database of statistical motion models attached to entities of interest extracted from the keyframe of each video shot.

In the sequel we will also use the term of sequence to designate an elementary shot.


Ronan Fablet
email: rfablet@cs.brown.edu

Patrick Bouthemy
email: bouthemy@irisa.fr

Extraction of regions of interest based on motion activity for video retrieval with partial query

Keywords: entities of interest, motion activity, probabilistic models, Markovian segmentation.. 9th Int. Conf. on Information

This paper presents an original approach to extract regions of interest in image sequences according to motion information. It relies on motion activity analysis from non-parametric probabilistic models of local motion information. It can handle a wide range of dynamic scenes from rigid motion situations to non-rigid motion types such as articulated motions or temporal deformable entities.

Introduction and related work

The extraction of entities of interest within images w.r.t. motion information is of key interest in applications such as video surveillance [START_REF] Haritaoglu | W ) : Real-time surveillance of people and their activities[END_REF], obstacle detection for vehicle navigation, or contentbased video indexing and retrieval [START_REF] Brunelli | A survey on the automatic indexing of video data[END_REF]. Proposed approaches can be roughly classified into motion detection schemes [START_REF] Irani | Detecting and tracking multiple moving objects using temporal integration[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF][START_REF] Paragios | Geodesic active contours and level sets for the detection and tracking of moving objects[END_REF] and motionbased segmentation algorithms [START_REF] Altunbasak | Region-based parametric motion segmentation using color information[END_REF][START_REF] Ayer | Layered representation of motion video using robust maximum-likelihood estimation of mixture models and MDL encoding[END_REF][START_REF] Odobez | Direct incremental model-based image motion segmentation for video analysis[END_REF]. The first ones only determine a binary partition into regions conforming or not to the dominant image motion supposed to be due to the camera motion. The latter ones aim at defining a complete motionbased partition into homogeneous regions usually in terms of 2D parametric motion models.

Motion segmentation methods are known to be computationally expensive. Furthermore, they are likely to divide articulated or deformable objects, or group of objects, into several subregions, since they rely on motion-based homogeneity criteria w.r.t. 2D parametric motion models. Yet, in the context of dynamic scene analysis, the key issue is to extract semantically meaningful entities. Motion detection schemes are usually far less CPU time consuming. However, they cannot hold one group of objects as a whole. In many situations such as ones involving "fluid" or "temporal texture" configurations (e.g., fluttering leaves, sea waves, torrents,...), or comprising groups of motion entities (e.g., players in sport videos) (see Figure 1), regions of interest do not consist of one single object. To handle these kinds of dynamic contents, it is not relevant to exploit 3D models or 2D parametric motion models. Furthermore, using an intensity-based or contourbased approach is also questionable, since explicitly defining boundaries for such entities is not easy. In this paper, we are addressing the extraction of meaningful moving regions within image sequences without any a priori information, on motion types nor on object appearance (texture, shape). We also aim at handling a wide variety of situations from rigid motion to non-rigid motion and temporal texture examples. To this end, we investigate the use of more general characterization of dynamic contents in terms of motion activity [START_REF] Bouthemy | Motion characterization from temporal cooccurrences of local motion-based measures for video indexing[END_REF][START_REF] Fablet | Non parametric motion recognition using temporal multiscale gibbs models[END_REF]. We propose a general statistical framework able to extract entities of interest based on non-parametric motion activity characterization. This simultaneously provides us with self-learned motion models for further analysis in terms of motion recognition or classification. The remainder of this paper is organized as follows.

Section 2 presents the local motion-related measurements considered for non-parametric motion activity modeling. In Section 3, the statistical modeling of motion information and the estimation of these models are addressed.

Local motion-related measurements

Dominant motion estimation

Since our goal is to characterize the actual dynamic content of the scene, we have first to cancel camera motion. To this end, we estimate the dominant image motion between successive images, and we assume that it is due to camera motion. We then warp the images of the processed sequence to a reference frame.

To model the global transformation between two successive images, we consider a 2D affine motion model (a 2D quadratic model could also be considered). The velocity ¢¡ ¤£ ¥ §¦ , at pixel ¥ , re- lated to the affine motion model parameterized by ¨is given by:

©¡ ¤£ ¥ §¦ "! $# % "& (' 0) 1 "2 $# % "3 (' 54 (1)
with ¥ 6 7£ # 98 @' ¦ and ¨ 7A B 9 "! "& C 0) C "2 "3 (D . The six affine motion parameters are computed with the robust gradient-based incremental estimation method described in [START_REF] Odobez | Robust multiresolution estimation of parametric motion models[END_REF]. An important feature of this robust approach is to supply a map of weights

Local motion-related measurements

We compute the local motion-related measurements in the image sequence Q SR generated by compensating for the estimated dominant image motion. More precisely, we consider a weighted local average of normal flows given by [START_REF] Bouthemy | Motion characterization from temporal cooccurrences of local motion-based measures for video indexing[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF]:

T VU XW `Y a£ ¥ §¦ b Y @c ad 1e F af hg (i Q R £ qp r¦ g 1s "t Q R u £ qp r¦ t v xw y S ! 8 b Y @c ad 1e F af g (i Q R £ qp r¦ g ! $ (2)
where £ ¥ §¦ is a % window centered on ¥ , ! a predetermined constant related to the noise level (typically, 7 ). i Q hR £ ¥ §¦ and Q "R u £ ¥ §¦ are respec- tively the spatial gradient and the temporal derivative of the intensity function Q SR . The considered motion-related measurement T "U XW `Y a£ ¥ §¦ forms a more reliable quantity than normal flow, while still simply computed from intensity derivatives. It has already been successively used for motion detection [START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF], and for motion-based video indexing and retrieval [START_REF] Fablet | Non-parametric motion activity analysis for statistical retrieval with partial query[END_REF][START_REF] Fablet | Statistical motion-based video indexing and retrieval[END_REF].

Statistical motion activity modeling

Temporal Gibbs models of motion activity

To model and characterize motion activity, we exploit the probabilistic framework we previously presented in [START_REF] Fablet | Non parametric motion recognition using temporal multiscale gibbs models[END_REF][START_REF] Fablet | Statistical motion-based video indexing and retrieval[END_REF]. We briefly outline it hereafter. It can be viewed as an extension of texture modeling for grey level images with local motion quantities playing a role similar to grey levels for texture analysis. Since we exploit cooccurrence statistics, we have to deal with motionrelated quantities defined over a finite set. Hence, we have to perform a quantization of the continuous motion measurements within a predefined bounded interval. It will also allow us to compare motion activity models associated to different entities for recognition issues. Another motivation to fix an upper bound is to reject spurious motion measurements.

Let be the discretized range of values for

T VU XW `Y a£ ¥ §¦ , ¡ the time instant of the current image to be processed and ¢ # ¤£ ¦¥ § ¦© the pair of maps of quantized motion-related quantities for the processed video sequence computer over successive images at time instants £ ¡ I r8 ¡ ¦ , and £ ¡ 8 ¡ I ¦ .

Let denote the spatial region of interest in the image ¡ and ¢ # £ 8 @# £ "! the restriction of the pair ¢ # £ "! 8 @# £ # over region $ . We assume that the pair # ¢ # £ 8 @# £ "! is the realization of a first- order Markov chain:

% '& £ # ¦ C % '& £ # £ ¦ )( F c % '& £ # £ "! £ ¥ §¦ t # £ £ ¥ §¦ @¦ (3)
where 0 refers to the motion activity model.

% '& £ # £ ¦ designates the a priori distribution of # £ . We will consider in practice a uniform law for

% '& £ # £ ¦ .
In this causal modeling framework, we evaluate only temporal interactions, i.e., cooccurrence of two given motion quantities at the same grid point for two successive instants. First, it means that we focus on the temporal evolution of motion content and we can handle certain kinds of temporal non-stationarity. Second, it makes feasible an exact computation of the conditional likelihood % '& £ # ¦ . This is crucial since it will enable to achieve model estimation in an easy way and to define an appropriate similarity measure between motion activity models based on the Kullback-Leibler divergence [START_REF] Basseville | Distance measures for signal processing and pattern recognition[END_REF].

In addition, we consider an equivalent Gibbsian formulation of

% 1& £ # £ "! £ ¥ §¦ t # £ £ ¥ §¦ @¦ .
It implies the introduction of potentials 2 3& 54 # £ "! £ ¥ §¦ 8 @# £ £ ¥ §¦ 76 specifying the motion activity model 0 as follows:

% '& 54 # £ "! £ ¥ §¦ t # £ £ ¥ §¦ 76 8 y 9 A@ 2 3& 54 # £ "! £ ¥ §¦ 8 @# £ £ ¥ §¦ 76 CB (4)
As in [START_REF] Gimel'farb | Texture modeling by multiple pairwise pixel interactions[END_REF][START_REF] Zhu | Filters, random fields and maximum entropy (FRAME) : towards a unified theory for texture modeling[END_REF], a relation can be established between this Gibbsian setting and cooccurrence distributions. The conditional likelihood % '& £ # ¦ can be expressed according to an ex- ponential formulation involving 2 D& FE HG , the dot product between the cooccurrence distribution

G , £ G £ PI 8 I Q ¦ @¦ e SR ¥ R UT f c WV YX , and the potentials ¢ 2 3& £ PI 8 I Q ¦ e SR ¥ R UT f c WV YX , defined by: à a b a a c G £ PI 8 I Q ¦ b F c d £ PI # £ "! £ ¥ §¦ @¦ d £ PI Q # £ £ ¥ §¦ @¦ 2 3& eE fG b e SR ¥ R UT f c WV YX 2 3& £ PI 8 I Q ¦ s G £ PI 8 I Q ¦ (5)
where

d
is the Kronecker symbol. We finally get:

% '& £ # ¦ % '& £ # £ ¦ s 8 y 9 3@ 2 3& eE fG B (6)
This modeling scheme can be stated as nonparametric in two ways. On one hand, the statistical model 0 does not refer to a 2D parametric motion model, but expresses in a broad sense the notion of motion activity. On the other hand, ¢ 8 y 9 2 3& £ PI 8 I Q ¦ e SR ¥ R UT f c WV YX is not assumed to fol- low a known parametric law (Gaussian,. . . ).

The availability of the exponential formulation ( 6) presents several interests. First, it makes the computation of the conditional likelihood % g& £ # ¦ , for any sequence # and region , feasible and simple. Second, for classification or recognition issues, the storage of the motion-related quantities # is not required. In fact, all the motion information exploited in our approach is captured by the cooccurrence distribution G .

Maximum likelihood estimation

Given a set of motion-related quantities # h within a region , we have to identify the model i0 specified by its potentials ¢ 2 i & qp £ PI 8 I Q ¦ e SR ¥ R UT f c WV YX which best fits # . We adopt the Maximum Like- lihood (ML) criterion:

i0 w sr ut v xw y & wv xv & £ # ¦ with v xv & £ # ¦ C y % '& £ # ¦ (7)
The considered temporal Gibbsian model reduces to a product of t t independent condi- tional transitions from instant ¡ to instant ¡ I , and is specified by the transition matrix

¢ % i & qp £ PI t I Q ¦ e SR ¥ R UT f c WV YX .
Therefore, the ML model estimate i0 is readily determined from the em- pirical estimation of the transition probability

% i & p £ # £ "! £ 0¦ t # £ £ 0¦ @¦ as follows: 2 i & p £ PI 8 I Q ¦ C y G £ PI 8 I Q ¦ b c WV G £ 8 I Q ¦ (8)
We now describe how we exploit the nonparametric statistical motion modeling described above to extract meaningful entities, comprising pertinent motion activity, in frame ¡ of the processed image sequences. Motion activity properties are learned in an unsupervised way at the level of a group of pixels (elementary blocks or subset of blocks). We initially consider a blockbased partition of the image (typically, ¡ ¡ blocks).

We believe that the loss of accuracy induced by considering small blocks is not a real shortcoming here. First, for cases involving few mobile objects, the interest is mainly to identify pertinent entities and not necessarily to accurately determine their boundaries. Second, this formulation allows us to handle a wider range of motion types compared to other techniques. Besides, this approach will prove far less time consuming than motion-based region segmentation or level-set algorithms.

Let us consider a partition of the image defined by the set of ¢ W ¤£ blocks ¢ ¦¥ ¨ § § c © ¥ ¥ . We further assume that motion activity within each block ¥ ! § is characterized by means of the associated statistical model 0 #" %$ derived from the cooccurrence distribution G " %$ as explained in Section 3.

Statistical similarity measure related to motion activity

Considering two regions and Q (regions and Q can be elementary blocks among .

¢ ¦¥ & § § c © ¥ ¥
We have designed a similarity measure relying on the Kullback-Leibler (KL) divergence [START_REF] Basseville | Distance measures for signal processing and pattern recognition[END_REF]The KL divergence evaluates the distance between two probability distributions as the expectation of their log-ratio. The motion activity similarity measure ' £ 0 8 0 T ¦ is a symmetrical version of the KL divergence:

' £ 0 8 0 T ¦ C @ )( v £ 0 g 0 T ¦ ( v £ 0 T g 0 ¦ B (9)
where ( v £ 0 g 0 T ¦ denotes the KL diver- gence. It is approximated as [START_REF] Fablet | Statistical motion-based video indexing and retrieval[END_REF]: (10) Since 0 is the ML model estimate asso- ciated with the cooccurrence distribution G , ( v £ 0 g 0 T ¦ is positive and equals 0 if the two statistical distributions are identical. In fact, this ratio quantifies the loss of information occurring when substituting 0 T for 0 to account for motion activity within area .

( v £ 0 g 0 T ¦ 10 I t t y % & qp £ # ¦ % & qp T (£ # ¦ 4

Region-level graph labeling

We now present the labeling stage of the blockbased partition of the image, ¢ ¦¥ 1 § § c © ¥ ¥ .

It will be exploited to extract regions of interest comprising significant motion activity as described in the next section. It relies on a Markovian region-level labeling framework applied to the adjacency graph 2 £ 43 8 65 ¦ where 3 is the set of nodes of graph 2 and 5 the set of its arcs. Each node 7 8 § @9 3 holds for block ¥ & § with A B9 ¢ H 8 DC DC DC 8 ¢ W ¤£ , and 5 represents the set of arcs between graph nodes corresponding to connected blocks (in practice, we consider a four-connectivity block neighborhood). Over this graph structure 2 , we define a region-level Markov random field model the sites of which are the nodes of graph 2 . In addition, two-site clique neighborhood system is deduced from the set of arcs 5 .

Let us assume that a set of labels E relative to different motion activity models has been specified. We further consider that to each label F G9 HE is attached the cooccurrence distribution G £ and the associated motion activity model 0 £ . We will more precisely explain in the next subsection how these motion activity models are defined and estimated.

Let us note I ¢ PI RQ $ § c © ¥ ¥ the label field with I RQ $ taking value in E , and S ¢ ¦S PQ $ § c © ¥ ¥ the observation field. In our case, at each node 7 8 § , S PQ $ refers to the motion activity characterization attached to block ¥ ! § , i.e. both cooccurrence distribution G " %$ and motion activity model 0 #" %$ . Adopting the Maximum A Posteriori (MAP) criterion, the Markovian labeling scheme comes to solve for:

I w sr ut v ¡ ¢ c ¤£ ¦¥ § £ I 8 S ¦ (11)
where § £ I 8 S ¦ § ©¨£ I 8 S ¦ § W £ I ¦ , with § ©¨t he data-driven energy term, and § W the regularization term. Both are split in the sum of local potentials and they are defined by: (12) with a parameter tuning the relative importance of the regularization term and 9), and is given by: ¨£ I DQ $ 8 S PQ $ ¦ C 8 y 9 A@ ' 4 0 ¢ $ 8 0 " %$ 6 CB (13) We introduce an exponential form to get values of potential ¨w ithin the range A H 8 PI (D , which en- ables to more easily set the regularization parameter . The minimization issue ( 11) is tackled using the HCF (Highest Confidence First) algorithm [START_REF] Chou | The theory and practice of Bayesian image modeling[END_REF], since the number of nodes of the considered graph is relatively small.

à a b a a c § ¨£ I 8 S ¦ 1 b Q $ c ¨£ I DQ $ 8 S PQ $ ¦ § W £ I ¦ C b e Q $ ¥ Q f c s d £ I DQ $ I DQ ¦

Separation of entities of interest from static background

We want to separate regions of interest from background. Since we consider image sequences compensated for the estimated dominant image motion assumed to be due to the camera motion, this issue reduces to extract regions which do not conform to the dominant image motion.

In a first step, we determine a binary labeling of the initial block partition of the image in terms of blocks conforming or not to the dominant image motion. As the image segmentation proceeds from motion activity characterization, we have to establish a model corresponding to the static background. Even if we could merely infer an activity model corresponding to zero-value motion measurements, we prefer to explicitly estimate the background model from actual motion-related quantities at points attached to the extracted background, since camera motion cannot be perfectly cancelled. To achieve this, we exploit the map of weights E issued from the robust multiresolution estimation of the affine motion model accounting for the dominant image motion (see Section

2). By thresholding map E , we can roughly de- termine the support associated to the estimated dominant image motion. It is formed by points

¥ satisfying E §F "! $# . Using our statistical motion activity modeling framework, we can estimate the model 0 &% ' attached to the background ( 0) . If

( 1) designates the complementary set of ( 2) (corresponding to the outlier map), we can evaluate in the same way the associated motion activity model 0 % 3' .

At this stage, we achieve afirst Markovian blockbased labeling, as described in subsection 4.2, considering only two labels referring to statistical models attached to regions ( 0) and ( 1) (i.e. label set E contains only two labels in that case). The obtained binary segmentation allows us to update the support of regions ( 0) and ( 1) , and consequently their associated models 0 4% ' and 0 % ' can be updated too. Since ( 0) includes the regions of interest we are seeking, we determine its connected components. Let us denote ¢ § § c © ¥ ¥ 65 87 @9 the ¢ BA ¢ DC resulting regions.

For each region G § , we estimate its motion activity model 0 $ . We then perform a second region-level labeling stage applied to the original block-based partition as explained in subsection 4.2, with now t E t ¢ A ¢ DC I . We consider ¢ BA ¢ DC I different labels ¢ ¦F 8 DC )C 8 F 65 87 @9 correspond- ing to the updated model 0 E% ' (label F ) and to models ¢ ¦0 $ § c © ¥ ¥ 65 87 @9 . Once convergence is reached, regions F § formed by blocks with labels F § HG F are regarded as the entities of interest for the processed image sequence. Moreover, the dynamic content within each extracted entity F § is characterized by its motion activity model 0 PI $ , which is updated at the final step of our scheme.

Results

Illustration of the successive method stages

We first illustrate the different stages of our method in Fig. 2. The parameters involved are set as follows: the motion-related measurements have been quantized within A H 8 ¡ rD As illustration, we have considered a wide-angle shot of a basketball game with one of the processed images displayed in Fig. 2.a. This sequence involves a slight panning and zooming of the camera. Fig. 2.b contains the support of the dominant image motion estimated between the considered frame and the preceding one in the sequence. Extracted regions of interest are shown in Fig. 2.c. These two entities indeed comprise the interesting parts of the scene content. It should be pointed out that one player does not appear in any of these two areas since he is static. Our method also appears efficient in terms of computational complexity. It requires about H C second of CPU time to process images of size I H I ¢ H compris- ing 20 blocks of size ¡ ¢ ¡ on a Sun Creator workstation 360MHZ.

Experimental evaluation of the extraction of regions of interest

We report in Fig. 3 five examples of extraction of regions of interest in image sequences. We have considered four kinds of dynamic scenes: sequences involving a single or only a few moving elements, rigid motion situations, wide-angle sport shots where regions of interest are formed by several players, and sequences involving temporal texture samples. For all situations, we have succeeded in identifying meaningful entities. As far as sport sequences are concerned, it should be pointed out that superimposed logos or score captions are also extracted as illustrated in Fig. 3. This is due to the fact they are associated to important residual motion displacements in case of a moving camera, since we perform motion activity analysis in images compensated for the estimated dominant image motion.

The last two examples shown in Fig. 3 are particularly interesting. The first one is a wide-angle shot of a rugby match with the camera tracking the action. We successfully recover an area comprising all players except one. The last example appears to be a particularly difficult situation. It involves a camera tracking a windsurfer with the background formed by a static area (sky) and wavy sea. Furthermore, the boundary of the windsurf board is not well-defined due to the presence of waves with foam. In spite of these difficulties, we identify a relevant area comprising almost all the windsurfer and his board.

As shown in Figure 4, our approach for scene activity segmentation could also be exploited for tracking entities of interest within image sequences. For "Stefan" sequence, we succeed in extracting from image to image the region of interest in the scene, i.e., the tennis player.

Conclusion

We have presented an original approach for the extraction of regions of interest in an image sequence upon a broad notion of pertinent dynamic content. Motion information is expressed as non- parametric statistical motion models. These models are directly estimated from the data (image sequences). They supply a characterization in terms of motion activity and are far more flexible compared to 2D parametric motion models or 3D motion models. In particular, it allows us to cope with a wide variety of dynamic content such as rigid motion, articulated motion, deformable and fluid motion (temporal texture), and group of moving entities. The extraction of regions of interest according to motion activity is formulated as a block-based labeling issue embedded in a properly formalized statistical framework. Moreover, our method directly discriminates regions comprising relevant motion activity from the non-pertinent background. We have provided a convincing validation of our method on real image sequences representative of various dynamic scenes (car sequences, sports videos, temporal textures). We have in particular demonstrated its capability to extract meaningful regions of interest comprising several moving objects, as in wide-angle shots of sport sequences, or to handle temporal textures such as wind blown trees ow wavy sea..

Another important feature of our segmentation method is that it simultaneously delivers motion activity characterization within extracted entities of interest, which could be straightforwardly exploited for motion classification or recognition purpose, or for video retrieval with partial query by example. In particular, in [START_REF] Fablet | Non-parametric motion activity analysis for statistical retrieval with partial query[END_REF], we have shown the effectiveness of our approach to tackle motion-based video retrieval with partial query by example. To this end, we first build a database of entities of interest extracted from video shot keyframe and characterized by a statistical motion activity model 0 ¡

. Then, given an area in the image proposed as partial query £¢ , we compute the associated set of motion-related measurements # ¥¤ and temporal cooccurrence distribu- tion G ¥¤ . The retrieval operation is then stated as a Bayesian inference issue w.r.t. the MAP criterion and relies on the ranking of the conditional likelihood

% & §¦ £ # ¥¤ ¦ for all the elements of the database of entities of interest.

Figure 1 :

 1 Figure 1: Examples of dynamic scenes to be dealt with: (a) tracking of a given hockey player; (b) focus on a group of players on a rugby playing field; (c) wind blown trees.

  or groups of blocks), we have to evaluate the degree of similarity between their respective motion activity contents. Let us note 0 and 0 T the statistical models of motion activity attached to regions and Q resp. cor- responding to the pair of motion-related measurements. # ¢ # £ 8 @# £ "! and #

7 §

 7 how relevant the description of observation S PQ $ by label I RQ $ is. It involves the similarity measure ' , defined in relation (

Figure 2 :

 2 Figure 2: Illustration of the successive stages of our method to motion activity segmentation: (a) one image of the processed sequence; (b) support (in white) of the dominant image motion estimated between the considered image (a) and the preceding frame in the sequence; (c) result of the motion activity segmentation (parameter setting is given in text in subsection 5.1). The black area holds for the region regarded as the static background and the two extracted regions of interest are displayed and delimited by a white border.

Figure 3 :Figure 4 :

 34 Figure 3: Extraction of regions of interest according to motion activity in image sequences. The extracted areas are delimited in white or in black depending on the examples.

  E . At each point ¥ in the image, the weight value E GF , comprised in A H 8 PI (D indicates whether the point

	is likely or not to belong to the part of the im-
	age undergoing the dominant image motion. The closer E §F to 1, the more the point ¥ conforms to
	the dominant image motion.

Work done while the first author was at IRISA, Campus universitaire de Beaulieu 35042 Rennes Cedex, France.

Acknowledgments

The authors wish to acknowledge the support of INA, Département Innovation, Direction de la Recherche, for providing the MPEG-1 car sequences, which are excerpts of the INA/GDR-ISIS video corpus, and to National University of Singapore for supplying the sequences of temporal textures.


Antoine Groué

Jean-Philippe Tranchier

Marie-Noelle Rager

Geoffrey Gontard

Marion Jean

Nicolas Vanthuyne

Harrison R Pearce

Andrew L Cooksy

Hani Amouri

Unique Class of Enantiopure N-Heterocyclic Carbene Half-Sandwich Iridium(III) Complexes with Stable Configurations: Probing Five-Membered versus Six-Membered Iridacycles

published or not. The documents may come

Supporting Information Placeholder

ABSTRACT: A unique class of enantiopure Nheterocylic carbene half-sandwich iridium complexes is reported. These compounds display stable configurations at the metal center as demonstrated by their chiroptical properties. Remarkably, due to the nature of the naphthalimide molecule, two isomers containing fivemembered (R)-2a, (S)-2a and six-membered (R)-2b, (S)-2b iridacycles were obtained. DFT-calculations are advanced to rationalize their relative stability.

Half-sandwich compounds with three-legged piano stool geometry with different substituents are archetypal examples of optically active chirality-at-metal center. and [CpRe(L)(NO)(PPh3)][BF4] (L = CH2Cl2, C6H5Cl) complexes gave an impetus to the development of modern chiral organometallic chemistry. [START_REF] Brunner | Optical Activity at an Asymmetrical Manganese Atom[END_REF][START_REF] Merrifield | Optical Resolution, and Absolute-Configuration of Pseudotetrahedral Organorhenium Complexes (η-C5H5)Re(NO)(PPh3)(X)[END_REF] Depending on the metal and the nature of ligands as well, such compounds tend to exhibit labile or stable configuration in solution. For instance, the related chiral Cp*Ir complexes were found to exhibit labile configuration in solution. [START_REF] Brunner | Stability of the metal configuration in chiral-at-metal half-sandwich compounds[END_REF][START_REF] Mimassi | Chiral recognition and resolution of the enantiomers of supramolecular triangular hosts: Synthesis, circular dichroism, NMR, and X-ray molecular structure of [Li ⊂(R,R,R)-{Cp*Rh(5-chloro-2,3-dioxopyridine)}3][Δ-TRISPHAT[END_REF][START_REF] Mimassi | Chiral supramolecular triangular hosts: Anion metathesis, solution behavior, and high stability of the metal configuration[END_REF] More recently, however, the use of strongly coordinating Nheterocyclic carbene (NHC) ligands brought some stability to the metal center but only a few examples of enantiopure half-sandwich Cp*Ir complexes were reported by Crassous and Peris. [START_REF] Hellou | Electronic and chiroptical properties of chiral cycloiridiated complexes bearing helicenic NHC ligands[END_REF][START_REF] Corberan | Highly stable Cp*-Ir(III) complexes with N-heterocyclic carbene ligands as C-H activation catalysts for the deuteration of organic molecules[END_REF] On the other hand half-sandwich metal complexes have received considerable attention due to their importance in medicinal chemistry [START_REF] Liu | Organoiridium Complexes: Anticancer Agents and Catalysts[END_REF][START_REF] Liu | Organometallic halfsandwich iridium anticancer complexes[END_REF] , materials science [START_REF] Grotjahn | Evolution of Iridium-Based Molecular Catalysts during Water Oxidation with Ceric Ammonium Nitrate[END_REF][START_REF] Schulze | Near-IR Phosphorescent Ruthenium(II) and Iridium(III) Perylene Bisimide Metal Complexes[END_REF] and catalysis. [START_REF] Specht | Enabling Bifunctionality and Hemilability of N-Heteroaryl NHC Complexes[END_REF][START_REF] Gomez-Lopez | Synthesis and reactivity of bis(protic N-heterocyclic carbene)iridium(III) complexes[END_REF][START_REF] Peris | Smart N-Heterocyclic Carbene Ligands in Catalysis[END_REF] Thus we sought to design a novel class of stable half-sandwich Cp*Ir complexes in which the NHC unit is directly attached to a naphthalimide molecule (NI). The latter adopts a planar structure and contains three fused arenes, which should bring strong configurational rigidity around the metal center. Moreover it might also provide an entry to a novel class of luminescent compounds. To demonstrate the viability of our strategy, we first prepared the naphthalimideimidazolium salt (1) according to our described synthetic procedure. [START_REF] Lanoe | Deep-Red Phosphorescent Iridium(III) Complexes with Chromophoric N-Heterocyclic Carbene Ligands: Design, Photophysical Properties, and DFT Calculations[END_REF][START_REF] Lanoe | N-Heterocyclic Carbene Coinage Metal Complexes Containing Naphthalimide Chromophore: Design, Structure, and Photophysical Properties[END_REF][START_REF] Lanoe | Cyclometalated N-heterocyclic carbene iridium(III) complexes with naphthalimide chromophores: a novel class of phosphorescent heteroleptic compounds[END_REF] Significantly, treatment of two equivalents of 1 with [Cp*Ir(µ-Cl)Cl]2 in the presence of Ag2O and NBu4I in CH3CN for overnight reflux afforded in onepot reaction the iridium carbene complexes [Cp*Ir(NI-NHC)I] (2a and 2b) in 1:1 ratio. The regioisomers 2a and 2b were separated by column chromatography and fully characterized. They differ only by the size of the iridacycle, whether five-membered or six-membered, constructed by the carbene and the naphthalimide units (Figure 1). Indeed due to the structure of the naphthalimide molecule, which contains two fused arenes available for metal coordination, the iridacyclization process occurs in two different ways. This phenomenon has not been observed before in the literature for this class of half-sandwich metal carbene complexes.

The 1 H-NMR of 2a recorded in CDCl3 presented six multiplets in the range of δ 7.1 ppm and δ 9.2 ppm corresponding to the aromatic protons of the naphthalimide unit and to the diene protons of the NHC moiety. The n-Bu group of the naphthalimide unit displayed four multiplets in the range δ 0.9 ppm to δ 4.3 ppm while the methyl group of the carbene unit appeared as a singlet at δ 3.98 ppm. The Cp*Ir moiety gave a singlet at δ 1.96 ppm. The 1 H-NMR of isomer 2b in CDCl3 displayed a marked difference with respect to 2a where the Cp*Ir protons appeared downfield at δ 1.54 ppm and the aromatic protons of the naphthalimide and NHC moiety appeared in the range of δ 7.1 to δ 8.6 ppm and displayed a different pattern. Moreover 2D COSY, ROESY, HSQC and HMBC experiments allowed us to fully characterize both isomers (See supporting information Figures S1-S7). In addition, the molecular structures of isomers rac-2a and rac-2b were also ascertained by X-ray crystallography.

Crystals of cyclometalated carbene complex 2a were obtained from a mixture CH2Cl2/Et2O by slow diffusion. A view of the molecule is given in Figure 2. The structure of 2a is in accord with the spectroscopic data and confirms the formation of a five-membered iridacycle. As expected, the metal adopts a distorted tetrahedral geometry. The structure packing in the crystal shows the formation of a dimer assembly between two adjacent molecules, which are arranged in a head-to-tail fashion where each complex adopts an opposite configuration at the metal center (SIr, RIr). The dimer assembly arises from weak non-covalent C-H---π interactions (CH---C = 3.60(3) Å) between the n-Bu group and the naphthalimide moiety (Figure S8). [START_REF] Mccrea-Hendrick | Counterintuitive Interligand Angles in the Diaryls E{C6H3-2,6-(C6H2-2,4,6-iPr3)2}2 (E = Ge, Sn, or Pb) and Related Species: The Role of London Dispersion Forces[END_REF] To examine their configurational stability we decided to resolve these compounds into their single enantiomers and to investigative their chiroptical properties in solution (vide infra).

Enantiopure [Cp*Ir(NI-NHC)I] complexes (S)-2a, (R)-2a, and (S)-2b, (R)-2b

The optically active compounds (S)-2a, (R)-2a, and (S)-2b, (R)-2b were obtained by resolving the racemic samples using chiral column chromatography techniques. Full experimental details are given in the supporting information. Gratifyingly all of our enantiopure compounds were found to display stable configuration in strongly coordinated CH3CN solution and did not epimerize upon standing for several days in solution as demonstrated by their CD curves (vide infra). The same behavior is observed in CH2Cl2 (Figures S15-S16). The CD traces recorded in CH3CN show an excellent mirror-image relationship for the two enantiomers of 2a (Figure 4). In both cases, several peaks (with opposite signs for the two enantiomers) are visible at 240, 260, 290 and 320 nm, associated with the polarized π-π* transition of the naphthalimide unit. Moreover, bands of weak intensity attributed principally to MLCT electronic transitions are also visible at 350, 390 and 480 nm. We then investigated the chiroptical properties of the other isomer 2b to see whether the presence of a six membered cycle might affect the Cotton transitions (Figure 5). Again the CD curves recorded in CH3CN show an excellent mirror-image relationship for the two enantiomers of 2b. We also notice that several peaks (with opposite signs for the two enantiomers) are visible at 240, 260, 290 and 320 nm, associated with the polarized π-π* transition of the naphthalimide unit. Moreover, bands of more pronounced intensity relative to 2a attributed to MLCT electronic transitions are also visible at 370, 420 and 520 nm. These bands extend more into the visible red region compared to the five membered isomer 2a. We then attempted to obtain crystals of the enantiopure compounds in order to compare it to the racemic analogues. After many attempts, gratifyingly we were able to obtain convenient crystals of isomer (R)-2b for an X-ray determination (vide infra). Complex (R)-2b crystallizes in the Sohncke space group P21. A view of the complex is shown in Figure 6. The absolute structure was determined by refinement of the Flack x parameter equal to 0.033 (10). [START_REF] Flack | Reporting and evaluating absolute-structure and absolute-configuration determinations[END_REF][START_REF] Flack | Chiral and achiral crystal structures[END_REF][START_REF] Flack | The use of X-ray crystallography to determine absolute configuration[END_REF] The structure confirmed the formation of the sixmembered cycloiridated carbene isomer with (R)configuration. The iridium center adopts a pseudotetrahedral geometry and is bound symmetrically to : η-Cp*, the NI carbon centers, NHC unit and to the iodide halogen. The Ir---carbene bond distance is 2.03(2) Å similar to 1.97(1) Å reported for the analogous racemic compound. The solid-state packing, on the other hand, shows a completely different arrangement from that observed for the racemic complex 2b. Indeed in the enantiopure complex (R)-2b the individual molecules adopt the same configuration and form 1D supramolecular assemblies though non-covalent C-H---π interactions (C17---C22) = 3.42(5) Å) between the NI unit and the Cp*Ir moiety (Figure S10). [START_REF] Mccrea-Hendrick | Counterintuitive Interligand Angles in the Diaryls E{C6H3-2,6-(C6H2-2,4,6-iPr3)2}2 (E = Ge, Sn, or Pb) and Related Species: The Role of London Dispersion Forces[END_REF] We then investigated the solution behavior of both regioisomers in order to see whether a conversion of one regioisomer to the other might occur. Thus, refluxing isomer 2a in CD3CN for 24h resulted in no alteration and the starting material remained unchanged. Moreover when isomer 2b was heated under similar conditions no formation of 2a was observed. These results suggest that both compounds are stable in solution even at high temperature. This stability arises from the nature of the NIcarbene ligand that acts as a clamp and strongly chelates the metal center.

To shed light on their relative stability and mechanism of their formation, relative energies and other properties both complexes were calculated by density functional theory (DFT). The free energies of 2a and 2b were found to be remarkably similar, differing by less than 2.2 kcal/mol in all our calculations, employing different combinations of DFT method, basis set, and solvation model. Indeed, at the highest quality calculations employed Truhlar's M06 [START_REF] Zhao | The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals[END_REF] DFT method and a mixed pc-2/cc-pVDZ-pp basis [START_REF] Jensen | Polarization consistent basis sets: Principles[END_REF][START_REF] Peterson | Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd[END_REF] ", the two compounds were found to have equal free energies within 0.1 kcal/mol. These differences are well within the expected error of these calculations, a result that is consistent with the observation of both species in solution. There appears to be a balance of destabilizing ring strains in the two isomers, with the 2a iradacycle suffering from small bond angles (C-Ir-C=76 o , compared to 86 o in 2b; sp 2 bond angles = 111.5 o and 114.5 o ) whereas the conjugation of the arene system in 2b is disrupted by a 25 o twist of the imidazole unit relative to the neighboring naphthyl ring (compared to an 8 o twist in 2a). Surprisingly, alt-hough 2a has the more constrained ring system, frequency corrections consistently improve the relative stability of 2a by about 0.5 kcal/mol. This primarily results from small shifts to higher arene stretching frequencies in 2b, because the partial loss of naphthyl-imidazolyl conjugation strengthens the force constants within each ring. The calculations have been carried out only on the monomers, so we are not able to directly compare lattice energies. However, we note that the same 1-D chain assembly observed for 2b is not available to 2a, because the n-Bu axis is perpendicular to the Ir-Cp axis in 2a. Computed CD and UV/vis spectra are also found to be consistent with experiment (ESI Figures S17-S18). The supporting information includes details of the computational methods, including predicted UV spectra and a brief MO analysis of the principal electronic transitions.

CONCLUSION

In this paper we reported a unique class of enantiopure N-heterocylic carbene complexes displaying five-and sixmembered iridacycles not reported before. Remarkably these regioisomeric compounds display stable configuration in solution thanks to the naphthalimide-C-NHCchelate as demonstrated by their chiroptical properties. The use and future applications of these compounds are currently under investigation.

ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website. The synthesis and separation of complexes S-2a, R-2a and S-2b, R-2b. 1 H, [START_REF] Grotjahn | Evolution of Iridium-Based Molecular Catalysts during Water Oxidation with Ceric Ammonium Nitrate[END_REF] C and 2D ROESY Spectra of complexes 2a and 2b (Figures S1-S7). X-ray molecular structures (Figures S8-S10) UV and ECD spectra are given (Figures S11-S16). DFT calculations (Figures S17-S18). CCDC reference numbers 1880113-1880115 contain crystallographic data for complexes rac-2a, rac-2b and R-2b presented in this paper. These data can be obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

Unique

  Class of Enantiopure N-Heterocyclic Carbene Half-Sandwich Ir(III) Complexes With Stable Configurations: Probing Five-membered Versus Six-membered Iridacycles. Antoine Groué, a Jean-Philippe Tranchier, a Marie-Noelle Rager, b Geoffrey Gontard, a Marion Jean, c Nicolas Vanthuyne, c Harrison R. Pearce, d Andrew L. Cooksy, d and Hani Amouri,* a a Sorbonne Université-Campus Pierre et Marie Curie, Institut Parisien de Chimie Moléculaire (IPCM) UMR CNRS 8232, 4 place Jussieu, 75252 Paris cedex 05, France. b Chimie ParisTech, PSL University, NMR Facility, F-75005 Paris, France. c Aix Marseille Univ, CNRS, Centrale Marseille, iSm2, Marseille, France. d Department of Chemistry and Biochemistry, 5500 Campanile Drive, San Diego State University, San Diego, California 92182-1030. USA

Figure 1 .

 1 Figure 1. Schematic drawings of enantiopure carbene regioisomeric complexes (S)-2a, (R)-2a, and (S)-2b, (R)-2b described in this work. Priority sequence of ligands: I > η 5 -C5 > C-carbene > C-arene.22,[START_REF] Merrifield | Cleavage of the Rhenium Methyl Bond of (η-C5H5)Re(NO)(PPh3)(CH3) by Protic and Halogen Electrophiles -Stereochemistry at Rhenium[END_REF]

Figure 2 .

 2 Figure 2. Molecular structure of complex rac-2a. In a similar fashion, crystals of [Cp*Ir(NI-NHC)I] (2b) were obtained by slow diffusion of diethylether into a saturated CH2Cl2 solution of the complex. Details regarding crystal structure determination are given in the ESI. A view of 2b is shown in Figure3. The structure of complex 2b confirms the formation of the target molecule and shows that the iridacycle is composed of a six membered ring. The configuration around the iridium center is a distorted tetrahedral geometry. The crystal structure adheres to a similar head-to-tail dimer assembly as rac-2a, but with C-H---π interaction (C28A---C17 = 3.41(3) Å) between the n-Bu group and the Cp*Ir moiety (FigureS9).[START_REF] Mccrea-Hendrick | Counterintuitive Interligand Angles in the Diaryls E{C6H3-2,6-(C6H2-2,4,6-iPr3)2}2 (E = Ge, Sn, or Pb) and Related Species: The Role of London Dispersion Forces[END_REF]

Figure 3 .

 3 Figure 3.Molecular structure of complex rac-2b.

Figure 4 .

 4 Figure 4. CD traces of S-2a and R-2a showing perfect mirror image. Recorded in CH3CN at C = 0.24mM

Figure 5 .

 5 Figure 5. CD traces of S-2b and R-2b showing perfect mirror image. Recorded in CH3CN at C = 0.24mM.

Figure 6 .

 6 Figure 6. Molecular structure of complex (R)-2b.

ACKNOWLEDGMENT

Sorbonne Université-Campus Pierre et Marie Curie, CNRS are gratefully acknowledged, and Ile de France Region for financial support of 500 MHz NMR spectrometer of Chimie-Paristech in the framework of the SESAME equipment project.

AUTHOR INFORMATION

Corresponding Author *E-mail: hani.amouri@sorbonne-universite.fr. Phone: +33-1-44273083.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


Rousseau Franc

Ronan Fablet
email: rfablet@ifremer.fr

Christian Barillot
email: cbarillot@irisa.fr

ROBUST STATISTICAL REGISTRATION OF 3D ULTRASOUND IMAGES USING TEXTURE INFORMATION

We investigate a new registration method for ultrasound volumes relying on on a statistical texture-based similarity measure. Texture information is given by spatial Gabor filters and represented by statistical kernel-based distributions. The registration similarity measure is then defined as a probabilistic distance, derived from Bhattacharyya coefficient, between two statistical distributions. Given this similarity measure, parametric ultrasound image registration is stated as a robust minimization issue. We also exploit frequency properties of spatial Gabor filters to propose a multiresolution approach to perform this minimization. We provide a preliminary evaluation of the new registration technique on clinical data.

INTRODUCTION

3D Registration of monomodality medical images is of key interest to visualize and quantify temporal changes in anatomy and physiology. Image registration has more particularly considered for brain imaging issues. However, whereas ultrasound imagery is well adapted for other body parts (throat, abdomen, heart,...), only few studies dealt with ultrasound image registration, since this type of image is of weak interest for brain imaging. Besides, the extension of registration techniques developed in the latter context is not straightforward due to low-quality ultrasound images for nonrigid organs. In addition, ultrasound is intrinsically a 2D measure. These different factors undoubtedly explain the lack of investigation concerning ultrasound image registration.

As it is mostly non-invasive and has a real time capability and a relatively low cost nature, 2D ultrasound is popular. Its major drawback is its weak capability of issuing quantitative accurate morphometric information [START_REF] Fenster | Threedimensional ultrasound imaging[END_REF]. In fact, conventional ultrasound exams are limited by 2D viewing, and follow-up studies are then not easily reproducible. 3D ultrasound imaging overcomes these limitations. In addition, it facilitates extensive investigation and allows accurate measurements of organ volumes.

The registration issue is to find the best alignment between two volumes. One of the volumes is chosen as the reference volume, and the other is transformed iteratively until the optimal alignment between the two data sets is found. Registration is required by ultrasound examinations for two main reasons. First, the combination of several volumes, called spatial compounding, can significantly improve the contrast-to-speckle noise ratio. Second, the registration of different ultrasound data set permits the comparison of serial examinations performed on the same patient.

Medical imaging techniques for image-based registration mainly rely on internal anatomic point, contour and surface landmarks, or voxel similarity. Internal landmark based registration techniques are limited since they require a specific segmentation. Contour and surface based registration methods also rely on accurate segmentation of anatomical structures. However, due to poor quality of ultrasound images, segmentation of ultrasound volumes is a very difficult task. Hence, voxel similarity-based methods seem to be more suited to ultrasound volume registration. As they require no segmentation, they are expected to be fully automatic.

A few voxel similarity-based methods have been proposed for ultrasound registration. Three main similarity measures were used: mutual information measure ( [START_REF] Shekhar | Mutual imformationbased rigid and nonrigid registration of ultrasound volumes[END_REF]), correlation coefficient on intensity values [START_REF] Xiao | Nonrigid registration of 3-d free-hand ultrasound images of the breast[END_REF] or on gradient images [START_REF] Rohling | Automatic registration of 3d ultrasound images[END_REF], and intensity values using optical flow hypothesis [START_REF] Pratikakis | Robust multiscale non-rigid registration of 3d ultrasound images[END_REF]. While ultrasound images are of relatively poor quality, they are highly textured. Besides, texture information has been proven to characterize ultrasound images, as highlighted for ultrasound image segmentation [START_REF] Boukerroui | Segmentation of echocardiographic data. multiresolution 2d and 3d algorithm based on gray level statistics[END_REF][START_REF] Chen | A textural approach based on gabor functions for texture edge detection in ultrasound images[END_REF].

As a consequence, it is highly attractive to consider on texture information for ultrasound image registration. In this paper, we investigate such an approach. Texture information is handled by means of spatial Gabor filters, which were shown to provide an accurate texture-characterization for texture classification and segmentation [START_REF] Dunn | Texture segmentation using 2-d gabor elementary functions[END_REF][START_REF] Jain | Unsupervised texture segmentation using gabor filters[END_REF]. Texture information is rather a region feature than a pixel one. Thus, texture characteristics supplied by Gabor filters will be analyzed using local kernel-based density estimation [START_REF] Comaniciu | Mean shift : a robust approach toward feature space analysis[END_REF]. Rigid ultrasound image registration is then stated as a robust multiresolultion minimization issue relying on a statistical similarity measure defined between the considered texture-based probabilistic distributions.

The paper is organized as follows. Section 2 presents texture features extracted by spatial Gabor filters. Section 3 introduces the statistical similarity measure exploiting nonparametric kernel density estimation. The registration algorithm is described in Section 4. Experiments are given in Section 5, and concluding remarks in Section 6 .

TEXTURE FEATURE EXTRACTION

In order to extract texture features from ultrasound volumes, we use a dyadic Gabor filter bank ( [START_REF] Jain | Unsupervised texture segmentation using gabor filters[END_REF][START_REF] Dunn | Texture segmentation using 2-d gabor elementary functions[END_REF]). Such texture features were successfully used for ultrasound image segmentation with success in [START_REF] Chen | A textural approach based on gabor functions for texture edge detection in ultrasound images[END_REF]. The impulse response of an even-symmetric Gabor filter is given by:

¢¡ ¤£ ¢¥ §¦ ¨¥ © ! #" %$ ! & ! $ (' 0) ! & ! ) ' 0) ! & ! ) 1 2 43 65 7 ¡ 98 A@ ¡ 9B DC FE G£ IH PB DQ RE G¦ SH PB DT §E 6© § (1)
where

¡ UB C E D¥ RB Q E V¥ B T E % is the

SIMILARITY MEASURE

We present in this section the statistical texture-based similarity measure exploited to formulate the registration issue between the two ultrasound volumes. We will in particular rely on kernel-based density estimator and on the Battacharrya as investigated by [START_REF] Comaniciu | Mean shift : a robust approach toward feature space analysis[END_REF] for color image segmentation and filtering.

Multivariate Kernel Density Estimate

Let h be a set of points in 0 , a -dimensional space. We denote by B ¡ ¤ ¢ the multivariate density kernel estimate computed at point as follows:

B u¡ ¤ ¢ ¢ d e f (2)
where ¡ ¤ ¢ is the kernel and the window radius. The optimal kernel yielding minimal mean integrated square error is the multivariate Epanechnikov kernel. Its expression is given by:

hg ¡ i ¢ kj b l ¡ H P8 # %¡ xm R nm b po qB rm R nm ts q u Vv w x Fy Fz to |{ F (3)
where l is the volume of the unit -dimensional sphere.

Texture Representation

As stated previously, texture is rather a region information. Thus, we exploit kernel density estimation to represent at a given point texture information provided by spatial Gabor filters. Let y h } u R |~ be the voxel locations centered at in a ultrasound volume. Given a texture value , the associate probability in voxel is given by:

¨ ¡ n u D f 4 ¡ p ¡ w (4)
where is the normalization constant, is the Kronecker delta function. Texture value is in fact a vector of tex- ture feature values, h¡ is the texture feature vector for the voxel . The resulting density is the discrete esti- mated density using an histogram formulation. The further the voxels from the considered voxel , the lower weights they are assigned by kernel . This property increases the robustness of the estimation.

Bhattacharrya Coefficient

Given the evaluation of statistical texture-based distributions, we define a probabilistic similarity measure between registered voxels using the the Bhattacharyya coefficient. This quantity is widely used, in particular for computer vision applications [START_REF] Comaniciu | Mean shift : a robust approach toward feature space analysis[END_REF], to evaluate distance between probabilistic distributions. Given such two distributions and , for the voxels and D respectively, the Bhattacharyya coefficient ¡ ¡ G¥ ¡ D w is defined as:

¡ ¡ G¥ ¡ w y r ¡ ¡ (5)
where is the feature representing here texture information.

The larger the coefficient, the more similar the two distributions. Spatial Gabor filters provide at each voxel a texture feature vector of high dimension (typically, more than q

). Since kernel-based estimator are known to fail for high-dimensional space, we assume texture features at different scales and orientations are statistically independent. This assumption is also widely used when Gabor features are exploited for segmentation or classification purposes. Given this assumption, the global texture-based density is written as:

r ¡ ¡ ¢ u T ¤£ ¡ (6)
where ¦¥ is the size of a texture feature vector, © D

is the o ¨ § © § response given by the Gabor filter bank. Thus, each Gabor texture feature is analyzed separately, and associated to one-dimensional probabilistic density. The Bhattacharyya coefficient is now given by:

¡ ¡ G¥ ¡ w ¡ ¢ ¡ T £ ¡ 6¥ T ¤£ ¡ w (7)
From the Bhattacharyya coefficient, the similarity measure between two voxels the voxels and # is finally de- fined as:

¡ ¥ ¡ ¡ G¥ ¡ w (8)
This similarity measure depicts a rich texture information in a well-formalized probabilistic framework, and will be straightforwardly exploited for rigid ultrasound registration as explained in the following Section.

ROBUST RIGID REGISTRATION

In this section, we present our robust multiresolution framework for rigid ultrasound registration. We first introduce the parametric deformation model to be estimated. We will then state the registration issue as a robust minimization based on the statistical texture-based similarity measure. We will finally discuss its implementation within an incremental framework.

Parametric Deformation Model

We consider a generalized affine transformation involving the combination of four different transformations: scaling, shearing, rotation and translation. We use an affine parametric model with 12 parameters:

¡ ¡ ¡ i (9)
where ¡ ¡ is the displacement vector for the voxel

¡ i£ #¥ §¦ ¡ D¥ §© % : ¡ ! " # %$ H # v £ nH # t ¦ ¡ H # '& © # H # )( £ nH # '0 ¦ ¡ H # '1 © # b H # '2 £ 3 nH # $ ¦ ¡ H # G© 4 5
and i ¡ # '$ ¥ 76 86 86 ¢¥ # § % ¨9 , a vector of 12 parameters which have to be estimated.

Robust formulation

Solving for the optimal alignment between two 3D ultrasound volumes is stated as the recovery of the model parameters i which minimizes a distance computed over the whole set of voxels of the transformed volume. The considered global distance is simply taken as the sum of the local probabilistic texture-based similarity measure introduce previously. In addition, M-estimators are considered to handle outliers during the minimization scheme ( [START_REF] Pratikakis | Robust multiscale non-rigid registration of 3d ultrasound images[END_REF]). More precisely, the registration issue comes to solve for:

@ i BA DC FE HG PI RQ 'S UT ¡ ¡ ¡ G¥ ¡ H ¡ ¡ § w ( 10
)
where T is the M-estimator. Robust M-estimation is equivalently formulated as an alternate weighted least-square minimization:

@ i A DC FE HG PI RQ S z m ¡ ¡ G¥ ¡ H ¡ ¡ w Fm b (11)
z is an auxiliary variable acting as "weight", computed from the influence function V ¡ i£ T ¡ i£ ¤W D£ associated to considered M-estimator T ( [START_REF] Pratikakis | Robust multiscale non-rigid registration of 3d ultrasound images[END_REF]). The M-estimation involves two steps. First, the computation of the robust weights for given residual errors, and, secondly, the weighted least-square minimization for given weights. In our experiments, we exploit the Cauchy estimator as M-estimator.

Incremental Estimation

We adopt an incremental strategy to solve for each weighted least-square minimization. Given a current estimate i DX , it comes to estimate a small increment such that: i i DX H Y i X . This incremental strategy then involves a linearization of the quadratic criterion around the current solution in order to derive a close-form solution of the increment estimate.

More precisely, The linearization of the Bhattacharrya coefficient is given by:

¡ ¡ G¥ ¡ H ¡ ' ¦` ¡ w ¡ ¡ G¥ ¡ H ¡ ¡ w uH ba 9 dc Y i (12)
where a fe " hg V"

Y i xw S z S a ya 9 ¦ S z S ¡ ¡ ¡ G¥ ¡ H ¡ ¡ w § w ¨a (13) with a b S £ ¡ H ¡ ¡ b f 9 c ¡ (14) w¡ ¤y A u " ¢ X ¢¡ £ u ¤ ¦¥ § ¡ ¦¥ § ¡ H ¡ ' ` ¡ § 4 5 2 # £ u ©¨ ¥ ¡ ¥ ¡ H ¡ ' ¦` ¡ w c ¡ £ p £ ¡ w (15)
This incremental minimization is stopped when the increment estimate is beyond a given threshold.

In addition, we exploit the characteristics of Gabor features to conduct this robust registration within a multiresolution framework. In fact, the minimization is initiated with low resolution Gabor features, while higher resolution Gabor features are incrementally introduced during the minimization.

EXPERIMENTS

Registration was applied to clinical ultrasound volumes of carotid. Affine transformations have been applied on these volumes. We have created an artificially deformed volume by using a Thin Plate Spline deformation. This produces a global smooth deformation which simulate non-rigid motion in tissues. Thus, the proposed method can be evaluated qualitatively and quantitatively.

1) 2)

3) 4)

Fig. 1. Carotid Ultrasound Volumes. 1) original volume, 2) deformed volume, 3) difference between original and deformed volume, 4) difference original and registered volume.

To evaluate the preliminary results, we compute the mean error . Moreover, as a qualitative measure, the difference image between the original volume and the registered one has been chosen (Figure 1). More experiments have to be done to validate the proposed method.

CONCLUSION

We have presented a new registration algorithm for ultrasound volumes that includes texture information using a sta-tistical similarity measure. Texture feature vectors obtained with a Gabor filter bank, have been represented by kernelbased distributions. A robust parametric registration algorithm have been proposed, using also the multiresolution properties of Gabor filters. Preliminary promising results have been presented. Further investigations are needed, more experiments will be done to validate the proposed registration method.

  center frequency of the filter, W C, . Other orientations can be obtained by rotating the reference coordinate system.As[START_REF] Jain | Unsupervised texture segmentation using gabor filters[END_REF] suggested, five radial frequencies and four orientations have to be used in 2D with . In 3D, we use thirteen orientations : i X pFq r¥ s t u¥ s b ¥ v §s b h and w xX yVq (¥ s t ¥ s b ¥ v s b h , i and w are the rotation angles around the © and ¦ axes respectively.

  manipulations, the incremental solution of (11) is:

¡ 9 A

 9 V¥ b concerning the translation vector and the matrix including rotation, shearing and scaling transformations using the Frobenius norm: ¡ ¤ ¥ b 0 ¡ 9q c ¥ q c 8