Matthieu Tourbier
email: matthieu.tourbier@ec-nantes.fr

Bundy Donguy

Bernard Peseux
email: bernard.peseux@ec-nantes.fr

Laurent Gornet
email: laurent.gornet@ec-nantes.fr

Bundi Donguy
email: bundi.donguy@ec-nantes.fr

Numerical modelling of the three-dimensional slamming problem

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

INTRODUCTION

Impact between water and a ship, i.e. slamming, that happen in severe sea conditions, entails high pressure loads on the ship hull which can be important enough to create plastic deformations to the hull external structure. Slamming loads may be responsible for the loss of ships.

To study such problems, there are two approaches. On the one hand, the Navier-Stokes equation have to be solved in velocity and pressure formulation, on the other hand, a velocity potential can be introduced under particular assumptions. Such an approach is used to model slamming problem.

Von [START_REF] Von Karman | The impact on a sea plane floats during landing[END_REF] and [START_REF] Wagner | Über Stoss und Gleitvorgänge an der Oberfläche von Flüssigkeiten[END_REF] were the pioneering workers to grapple with slamming problems through intuitive analysis. Their method has been extended by using matched asymptotic expansions for impacting bodies with small deadrise angles by [START_REF] Armand | Hydrodynamic impact analysis of a cylinder[END_REF] and Howinson (1991).

Drop tests of different shape models [START_REF] Cointe | Hydrodynamic impact analysis of a cylinder[END_REF][START_REF] Fontaine | Asymtotic theory of water entry[END_REF][START_REF] Zhao | Water entry of arbitrary two-dimensional sections with and without flow separation[END_REF][START_REF] Magee | A coupled approach for the evaluation of slamming loads on ships[END_REF]) validate the two-dimensional asymptotic solutions. For three-dimensional case, analytical solutions of the asymptotic problem are only known for particular geometry [START_REF] Faltinsen | The effects of hydroelasticity on ship slamming[END_REF][START_REF] Scolan | Three-dimensional theory of water impact. Part 1. Inverse Wagner problem[END_REF]). The asymptotic approach has been well compared for rigid cones [START_REF] Faltinsen | The effects of hydroelasticity on ship slamming[END_REF]. But extension of the previous approach for arbitrary 3-D geometry is far from being possible to find analytical solution. In all this studies, the body is assumed to be rigid. [START_REF] Korobkin | Wave impact on the bow end of a catamaran wetdeck[END_REF] and more recently, [START_REF] Donguy | On the ship structural response due to slamming loads[END_REF] have shown that the structural deformations present a strongly three-dimensional character and that the deformation velocity should be taken into account for the pressure distribution evaluation.

In this paper, in a first part, the three-dimensional governing equations for the fluid and the structure are presented, based on the asymptotic theory and the assumption of small perturbations for the structure. Numerical solution is performed with the Finite Element Method. In a second part, we present experimental investigation. Then numerical results are compared to experimental ones.

THREE-DIMENSIONAL PROBLEM 2.1 Potential formulation

Figure 1. Geometrical definitions

We consider the problem of the impact of a threedimensional body on a free surface (Fig. 1). The water entry problem is expressed within the framework of potential flow theory. Indeed, the fluid is assumed to be perfect and incompressible and the flow is irrotational. The velocity field can therefore be evaluated according to

φ grad = v , where ) t , z , y , x ( φ = φ
is the velocity potential. Under these assumptions, the velocity potential must satisfy an elliptic problem with a body boundary condition that expresses the continuity of the normal velocity component on the fluidstructure interface. The kinematic and dynamic free surface conditions, respectively, state that the free surface is a material surface along which the pressure is constant. Moreover, the fluid is assumed to be initially at rest. Finally, the problem to be solved in velocity potential formulation is

0 = φ ∆ in Ω f (1) n . u n s r & r = ∂ φ ∂ on the body (2) 0 gz p ) grad ( 2 1 t 2 = + ρ + φ + ∂ φ ∂ on the free surface (3) 0 z h grad . grad t h = ∂ φ ∂ - φ + ∂ ∂ on the free surface (4)
where (x,y,t) u s r is displacement of the body and h is the free surface elevation. The structural equations will be presented after.

Such a problem remains difficult to solve directly because of the unsteady non-linear boundary values and the free surface presents violent motions that are expressed experimentally by a jets developing along the body (see [START_REF] Greenhow | Wedge entry into initially calm water[END_REF].

According to Wagner, the problem is classically written on the plan z=0 on which the boundary conditions are projected. Γ B and Γ L are respectively the projection of the wetted body surface and the free surface. The contact line Γ(t), defined as the intersection between Γ B and Γ L is unknown a priori.

The problem requires the gravity effect and quadratic terms to remain small compared to the linear terms. Physically, the acceleration of the fluid has been assumed to be larger compared to gravity which can be neglected for the impact problem. The displacements of the body and the free surface must also remain small to justify the geometrical linearization of the boundary conditions. [START_REF] Cointe | Two dimensional water solid impact[END_REF] and [START_REF] Wilson | The mathematics of ship slamming[END_REF] have justified the linearization through an asymptotic analysis of the impact problem for a blunt and rigid body by introducing a small parameter. This one represents the ratio between the immersion and characteristic length scale of the wetted body area.

Using matched asymptotic expansions method entails to define two zones in which two asymptotic expansions are performed and matched successively:

! The far field domain, where the flow is similar to the one around a flat plate of unknown width in an unbounded fluid, ! The spray root domain near the contact line, were the flow over turns to create a jet.

It is worth noting that a third asymptotic expansion can be performed in the jet domain, along the body, but the contribution of this solution can be neglected in the leading order.

The perturbation procedure relies strongly on the blunt body assumption. In the far field, the body boundary condition can be written on the undisturbed position without introducing significant error. The exact dynamic condition is replaced on neglecting the quadratic terms for the leading order by a Dirichlet condition for the free surface. These quadratic terms have to be retained for the second asymptotic expansion to describe the flow within the jet.

The simplified kinematic free surface condition states that the vertical displacement of the free surface is equal to the fluid vertical motion, evaluated on the linearised position of the free surface.

Finally, the hydrodynamic problem, linearised with an asymptotic approach is written as

0 = φ ∆ in Ω f , (5) n . u n s r & r = ∂ φ ∂ on Γ B , (6) 0 = φ on Γ L , (7) z t h ∂ φ ∂ = ∂ ∂ on Γ L . ( 8
)
The pressure is given by the Lagrange linearized equation,

t p ∂ φ ∂ ρ - = (9) Γ B Γ ∞ Γ L Ω f s u & r
In order to describe the structure, the usual small perturbations assumption is made, and the equilibrium equation reads

f v i d u d s r r & & r + Σ = ρ in Ω s , ( 10
)
where Σ denotes the stress tensor, s u r corresponds to the structural displacement, and f corresponds to volume force associated for example with the gravity field. If gravity effects do not contribute to the local deformations here, they nevertheless influence the global motion of the body before impact. The boundary condition on the structure is (11) where the subscripts f and s respectively refer to the fluid and the structure.

n . n . s f r r Σ = Σ on Γ B ,
The structural modeling is performed within the framework of linear elasticity. Hooke's law is used to express the relation between the stresses and the strains which are given by the linearized Green-Lagrange tensor ε ,

( ) i , j j , i ij u u 2 1 + = ε (12)

Determination of the wetted surface

As mentioned previously, the wetted portion of the body is unknown. The contact line is determined by the volume of fluid conservation [START_REF] Wilson | The mathematics of ship slamming[END_REF][START_REF] Fontaine | A second-order solution for the wedge entry with small deadrise angle[END_REF] which is satisfied by the Laplace's equation. In order to find this line, it is easier to introduce a displacement potential, as suggested by [START_REF] Korobkin | Formulation of penetration problem as a variational inequality[END_REF], given by

∫ φ = ψ t 0 ds ) s ; z , y , x ( ) t ; z , y , x ( (13)
The problem to solve in the displacement potential is the same Neumann-Dirichlet boundary conditions problem as for the velocity potential. The wetted surface is determined through an iterative procedure. Starting from an initial surface guess for (Γ B ) 0 , the problem for displacement potential problem is solved until that the free surface elevation is equal to the position of the body at the boundary Γ(t)

z . u t) y, h(x, s r r = . ( 14
)
Once convergence has been reached, the position of the contact line is known. The linear system for the velocity potential is then solved.

Numerical resolution

The problem is solved using the Finite Element Method, for the fluid as well as the structure, based on a variational formulation. We have considered the weighting function ϕ for the fluid, which verifies the boundary condition ϕ = 0 on Γ L and U* for the structure kinematically acceptable to 0.

Galerkin's method is used to approximate the different functions φ, ϕ, U and U*,

{ } e f N ϕ > =< ϕ , ( 15
) { } e f N φ > =< φ , ( 16
) [ ]{ } e s s U N u = , ( 17
) [ ]{ } e s s * U N * u = , ( 18
)
where the shape functions N … depend on the types of elements, and the vector {…} e denotes the nodal unknown vector of the finite element (e). The problem after discretization, takes the following form, given by the equation ( 9). So the pressure imposed by the fluid drives the structural deformations and the structural deformations influence the pressure field through the body boundary condition In order to obtain a robust method to solve the coupled fluid -structure interaction problem, all the evolution equations are integrated simultaneously. The structural deformations are included in the fluid flow discrete formulation, while the pressure is expressed as the time derivative of the velocity potential in the discrete structural analysis.

[ ]{ } [ ]{ } U FS H & = φ , (19)
[ ]{ } [ ]{ } [ ] { } φ - = + & & & T f s FS ρ U K U M , ( 20
) { } [ ] ∫ = e B Γ s T f e dS N n } {N [FS] , (21)
This model is not sufficient to describe the fluid because of the pressure distribution, which is singular close to the boundary wetted surface. This singularity is due to the linearization. It is necessary to correct this pressure with the solution obtained in the spray root domaine.

The numerical resolution of the problem is performed using the commercial Finite Element Method code Castem. An external procedure is implemented for the evaluation of the coupling matrix [FS]. The correct implementation of the approach has been checked for the test case problem of sloshing in a rectangular tank including an elastic beam in its center for two-dimensional case [START_REF] Tourbier | Modelization and simulation of the three-dimensional hydrodynamic impact problem[END_REF]. This problem has been studied experimentally by Chaï (Chaï, 1996). For the three-dimensional case, it has been checked for a plate surrounded by water.

The fluid-structure interaction problem is then integrated starting from the initial conditions in a numerical temporal explicit or implicit scheme with a time step dt.

VALIDATION OF THE NUMERICAL PROCEDURE

Comparisons for a paraboloid elliptic shaped hull are presented in Figure 3. Hexahedron types of elements were used in the numerical simulation. Good agreement has been noted between numerical simulations and analytical results of the wetted surface for a rigid body. The free surface is well described by the displacement potential. Next, we present results for rigid wedge penetrating with a constant velocity V a free surface initially at rest. The numerical method previously described has been applied to this case. Comparisons between numerical and analytical pressure results are presented in figure 4. Triangular and quadrilateral elements were used for the numerical computation. Figure 5 illustrates the importance of including the inner solution which describes the formation of a jet. The analytical pressure distribution is matched to the numerical solution.

Figure 4. Pressure distribution for the impact of a wedge

To conclude this section, analytical and numerical results are very close to each others for both 2D and 3D cases, which validate the numerical approach. The evaluation of the free surface elevation remains nevertheless sensitive to the boundary between the structure and the fluid. To represent the ∆t

t n+1 p {u} ] FS [ } [H]{ = ψ t n p } u { ] FS [ } [H]{ & = φ 2δt {u} p = {u} n+1 {u} p = {u} n+1
Calculation of the pressure force

Structure resolution (implicit)

Fluid resolution

1 n 1 n } F { {u} ] K [ + + = t 2 } { } { ] FS [ } {F t 1 n t 1 n T f 1 n δ φ - φ ρ - = δ - + δ + + +

Numerical solution Asymptotical solution

singular behavior of the solution in the vicinity of this boundary, the finite elements mesh has to be refined in this zone. The regularity of the mesh is also an important parameter, which controls the accuracy of the numerical resolution.

Figure 5. Force evolution versus deadrise angle of wedge.

Comparison between outer solution (Wagner), corrected numerical solution (MEF) and non-linear solution

EXPERIMENTS

In this part, we present investigation tests the objective of which are to provide some experimental results to validate the previous numerical approach. We first describe the experimental test carried out at the Mechanical and Material Laboratory [START_REF] Donguy | Etude de l'intéraction fluide-structure lors de l'impact hydrodynamique[END_REF]. Then experimental results on rigid and deformable structures are presented and finally comparisons with the numerical results are carried out.

Experimental set-up

The investigation tests consist of free fall drop test of cone shaped model. Drop test with impact velocities varying from 2m/s to 8 m/s are realized from free falling rig system (see Figure 6) of 3.5 m height. The cone fell in a water tank of 1 m deep and 1.20 m diameter. A foam is on the bottom to progressively stop the cone.

Cones shaped models were rigidly attached to a cylindrical support of 322 mm diameter (see Figure 7). Three different cone shaped models with deadrise angles of 6, 10, and 14 degrees have been successively tested. To study the deformation influence, rigid body and elastic structure are tested. The effective thickness of the steel models were sufficiently important, reaching from 25 to 50 mm, so that the rigid body assumption is verified during impact. For elastic structure three thickness have been chosen equal to 0.5 mm -1 mm -1.5 mm. The use of a relatively large experimental facility allows for a typical size of 0.32 m for the tested models, therefore reducing the possible influence of surface tension effects. The impact velocity was chosen to increase by realistic values from approximately 2 to 6 m/s. (Zhao et al,92) Drop velocity and pressure measurements were performed during impact. Two quartz ICP compensated pressures sensors were set at 40 mm and 90 mm from the cone symmetry axis (fig. 8). These sensors are well suited for impact measurements. Their sampling frequency is up to 400 kHz, and the measurement range is 0 to 69 bar. They also allow for the use of relatively long wires (20 m) without altering the electric signal so that the data processing system does not need to be too close to the water.

The drop velocity was measured by mean of a cable sensor connected to the cylindrical support. Finally, pressure and velocity signals were plotted and recorded by a numerical memory oscilloscope. The cones were dropped against calm water. At least three drops were performed in each test condition to make sure of the repeatability of the measurements. Results presented below are representative of these drop test series. Figure 8 represents historical evolutions of the pressure on the two sensors p 1 , p 2 and the velocity during the impact for 10° deadrise angle cone and for an impact velocity of 2.5 m/s. For other velocities and cone characteristics, the evolutions are equivalent. Firstly, we controlled that the global velocity impact is constant during the water entry. The small perturbation on the signal is due to the mean of velocity measuring by cable sensor. We noticed a similar evolution of the measured pressure on both sensors. First, we observed a slight depression which comes before the pressure peak. The explanation of this depression is due to the separation of the jet and then to the creation of in-draught. Then, the pressure peaks are reached when the sensors are in the jet formation and more precisely at the stagnation point. The rise velocity of the pressure depends of the velocity impact and the conicity. It is 10 µs for the fastest and 200 µs for the slowest. After the peak pressure, we noted a slow decrease of the pressure in the meantime that the cone is progressing in the water. This is in accordance with the fact that the sensor goes away the free surface. Finally, a sudden decrease of the pressure happens simultaneously on the two sensors. At this instant, the jet zone is on the cylindrical support and the cone is then wholly in the water. There is separation of the jet in the air so that the pressure decreases suddenly on the cone. A blowup of a segment of figure 10 schemes this situation.

Signal on the rigid body

Signal on the elastic structure

For the test realized on the rigid body, the measured signal Figure 8 is representative of the whole measurement made for all the cone-shaped models. The test performed on the elastic structure presents more disparity. In particular, some phenomena not very perceptible in the case of rigid body become more important and new phenomena appear and bring to the fore the influence of structural deformation First, the phenomenom of depression becomes widely more important. And, as we can notice from Figure 11 this phenomenon can become enough important to influence the intensity of the value of the second pressure peak. New phenomena occur on all shaped models: this is an apparition of a second pressure peak. This peak of pressure is due to the geometrical configuration of the cylindrical support which presents a flat circumference. Due to the fact that the maximum value of the pressure varies versus the slope of the structure surface and more precisely is higher for small deadrise angle, it seems that when the jet formation is on the flat part of the cylindrical support, the pressure rises suddenly on the entire cone surface and creates the second peak pressure. Then this is the geometry configuration body which generates the second peak.

Comparisons between theory and experiments

Table 1 reports the two maximum values of the pressure on sensors p 1 , p 2 measured and calculated, for the three deadrise angles (β). Numerical and experimental results for the pressure levels are found to be in reasonable agreement although the pressure is always slightly over predicted, indicating that the numerical model is therefore conservative. On the first sensor the experimental value is by far over predicted for all deadrise angles but less for the 14° cone than the 6°. Difference is less pronounced for experimental values on the second sensor. Decay of the pressure can be explained physically by air entrapment. This phenomenon has also been observed by [START_REF] Chuang | Drops test of cones to investigate the three-dimensional effects of slamming[END_REF] on cones with deadrise angles smaller than 1°, and by [START_REF] Hagiwara | Fundamental study of wave impact loads on ship bow[END_REF] for wedges with deadrise angles lower than 3 degrees.

Examples of temporal evolution of the pressure on the two probes are presented in Figure 12 (a) (b) (c) corresponding to the different deadrise angles and impact for rigid body. The experimental distribution is globally well represented by the numerical simulation. Both signals show a pressure peak travelling along the body, followed by a plateau.

The location of the peak is clearly well described by the simplified theory. The wetted length seems therefore to be correctly estimated. This local quantity results nevertheless from global volume conservation property as mentioned previously. It is therefore not surprising that the modeling is able to give a good estimate of this quantity. The pressure rise immediately after impact is also well reproduced. The simplified model is indeed asymptotically valid for small times. The level of the peak, i.e., the maximum pressure, is reasonably estimated for the biggest deadrise angle, but the error increases with a decrease of the deadrise angle. According to the asymptotic solution, the level of the pressure peak should not vary along the body. The experiments clearly indicate that the peak intensity increases between the two probes. This discrepancy can be partially explained by air entrapment phenomenon. This phenomenon is not reproduced in the numerical simulation where the impact velocity remains constant.

As well as for the description of the pressure distribution on elastic structure, comparisons between numerical and experimental results are more difficult. On one hand, the depression zone can't be reproduced numerically because the air entrapment phenomenon hasn't been taken into account.

Cône 10° -e = 1,0mm

On the other hand due to the fact that the second peak zone comes from the geometrical configuration of the cone and occurs after the period of time we interested in, we haven't reproduced it. So, the major difference between numerical results and an experimental test comes from the velocity of the peak progression. Indeed we noticed the instant at which the peak pressure occured is different from experimental to numerical case. In spite of this dissimilitude, the global numerical pressure distribution fits well. We remarked moreover the comparison is better for the bigger conicity than the smaller for which the water perturbation are more significatve.

CONCLUSION

In the present paper, the three-dimensional slamming problem has been studied. After having presented the governing equation for the coupled problem, relying on asymptotic theory in velocity potential and small perturbations. Experimental investigations have been studied. It consisted in free fall drop-tests of deformable cone shaped models. Each cone presented different deadrise angles and thickness. The numerical results have been well confirmed by experimental ones.

All this study takes place within the asymptotic theory, entailing the boundary conditions projection. In order to avoid this assumption, we can used the ALE (Arbitrary Lagrangian Eulerian) or X-FEM (extended Finite Element Method) that are a priori able to follow the evolution of a free surface.

  where the mass and stiffness matrix, respectively [M s ] and [K], and the matrix [H], are obtained by assembly of the elementary terms calculated on each finite element (e). The terms [ ]{ } U FS & represent the continuity of the normal velocity on the wetted surface of the body and [ pressure on the same surface Γ B , pressure

Figure 2 .

 2 Figure 2. Resolution schema applied to solve the coupled problem

Figure 3 .

 3 Figure 3. Free surface elevation during impact of paraboloïd elliptic

Figure 6 .Figure

 6 Figure 6. Impact tower: experimental set-up

Figure 8 .Figure 9 .

 89 Figure 8. Pressure and velocity evolution during impact of the 10° rigid cone -V impact = 2.5 m/s

Figure

  Figure 10. Correspondence between the sudden pressure decrease and the cone position in the water

Figure 11 .

 11 Figure 11. Pressure and velocity evolution during impact of the 10° deformable cone (e=1 mm) V impact = 2.5 m/s

eFigure 12 .

 12 Figure 12. Pressure histories -Comparison between numerical (straight line) and experimental (dot line) results for rigid cone (at left) and for deformable structure (at right)

Table 1 . Comparison between predicted and experimental peak pressure value for different impact velocity of the rigid cone

 1

	V impact = 2.5 m/s	Exp.		Num.
	Cone 6°	2.8	2.7	4.6
	Cone 10°	1	1.4	1.6
	Cone 14°	0.7	0.7	0.8
	V impact = 5.2 m/s	Exp.		Num.
	Cone 6°	10.3	10.7	19.8
	Cone 10°	3.9	5.5	7
	Cone 14°	2.6	2.7	3.5


Jalila Filali
email: jalila.filali@ensi-uma.tn

Hajer Baazaoui Zghal
email: hajerbz@yahoo.fr

Jean Martinet
email: jean.martinet@univ-lille1.fr

Visually Supporting Image Annotation based on Visual Features and Ontologies

Keywords: Visualisation, image annotation, visual features, ontologies

Automatic Image Annotation (AIA) is a challenging problem in the field of image retrieval, and several methods have been proposed. However, visually supporting this important tasks and reducing the semantic gap between low-level image features and high-level semantic concepts still remains a key issue. In this paper, we propose a visually supporting image annotation framework based on visual features and ontologies. Our framework relies on three main components: (i) extraction and classification of features component, (ii) ontology's building component and (iii) image annotation component. Our goal consists on improving the visual image annotation by:(1) extracting invariant and complex visual features; (2) integrating feature classification results and semantic concepts to build ontology and (3) combining both visual and semantic similarities during the image annotation process.

I. INTRODUCTION

The first approaches in image retrieval are the text-based image retrieval, where images are annotated by experts and then retrieved using the annotated keywords. Due to the exponential growth of the quantity of images, assigning relevant text keywords to images is too tedious and time-consuming. To overcome this problem, Content-Based Image Retrieval approaches (CBIR) were developed. In this case, images are represented and retrieved by their visual content, such as color, texture, and shapes. Thus images are extracted without using semantic information describing their contents. However, in CBIR, most systems were only able to interpret images based on low level features and not able to automatically describe images with semantic representation. In addition, recent studies have shown that there is a significant semantic gap between low-level image features and high-level semantic concepts. To overcome this problem and to bridge the semantic gap between low level image features and semantic concepts, the third category of approaches of image retrieval has been introduced. These approaches focused on Automatic Image Annotation. Image annotation consists of automatically assigning relevant text keywords to any given image that reflect its visual content. The main goal of automatic image annotation is to improve image retrieval. Despite the large amount of research works in the image annotation area, two main problems persist: [START_REF] Deng | What does classifying more than 10,000 image categories tell us?[END_REF] visually supporting the image annotation process and (2) mapping visual and semantic features are still a challenging issues. In this paper, we propose a visually supporting image an-notation framework based on visual features and ontologies. The idea is to visually assist the image annotation process by : (1) extracting and classifying visual features into general categories, (2) building ontologies, and (3) combining the results of classification and relevant concepts associated to the feature classes. The remainder of this paper is organized as follows. Section 2 presents an overview of the related research, along with our motivations and objectives. Section 3 describes our image annotation framework and its different components. In section 4, a case study illustrating the functionality of the proposed framework as well as the application results are presented. Finally, section 5 concludes this paper and proposes directions for future works.

II. OVERVIEW AND MOTIVATIONS

In image retrieval area, Automatic Image Annotation (AIA) is an important issue aiming to bridge the gap between low level features and high level semantic information. According to the large number of regions in images, techniques for image annotation and retrieval become increasingly important. In this context, several image annotation and retrieval methods based on various learning techniques have been applied [START_REF] Tian | Support Vector Machine for Automatic Image Annotation[END_REF] and [START_REF] Li | Hybrid Learning Framework for Large-Scale Web Image Annotation and Localization[END_REF]. Moreover, image annotation could be presented as a classification problem when the goal is to improve image classification and annotation accuracy [START_REF] Mairal | Convolutional kernel networks[END_REF], [START_REF] Vanetti | Unsupervised Feature Learning using Self-Organizing Maps[END_REF] and [START_REF] Wang | Unsupervised Joint Mining of Deep Features and Image Labels for Large-scale Radiology Image Categorization and Scene Recognition[END_REF]. Several works have focused on scene recognition and image classification using features learning with Convolutional Neural Networks (CNNs) [START_REF] Zhou | Learning deep features for scene recognition using places database[END_REF], [START_REF] Kang | Object detection from video tubelets with convolutional neural networks[END_REF] and [START_REF] Paulin | Local convolutional features with unsupervised training for image retrieval[END_REF]. In addition, several works have been focused on comparing features and supporting image retrieval, in [START_REF] Medeiros | Coordinated multiple views to support image retrieval[END_REF] an approach based on multidimensional visualisation and coordination techniques is proposed. In this work, the coordination techniques are used to perform image retrieval methods. In [START_REF] Kobayashi | A Visualization Technique to Support Searching and Comparing Features of Multivariate Datasets[END_REF], a visual analysis tool is developed to support searching and comparing features of multivariate datasets. In [START_REF] Vanetti | Unsupervised Feature Learning using Self-Organizing Maps[END_REF], a novel model based on the Self-Organizing Map (SOM) neural network has been proposed. The aim is to learn features useful for the problem of automatic images classification. In particular, in this work, the SOM model is used to learn single-layer features from the extremely challenging CIFAR-10 data-set. Several other methods based on HMAX architecture have been used for improving image classification [START_REF] Kean | A HMAX with LLC for visual recognition[END_REF], [START_REF] Hu | Sparsity-regularized HMAX for visual recognition[END_REF] and [START_REF] Theriault | Extended coding and pooling in the hmax model[END_REF]. In [START_REF] Theriault | HMAX-S: deep scale representation for biologically inspired image categorization[END_REF], a novel method of feature learning based on HMAX architecture for image classification has been proposed. The purpose of this work is to build complex features with richer information to improve image classification. In addition, a large number of ontological techniques have been applied along with a great deal of research efforts [START_REF] Srikanth | Exploiting ontologies for automatic image annotation[END_REF], [START_REF] Antonio | Using Multimedia Ontologies for Automatic Image Annotation and Classification[END_REF] and [START_REF] Isabelle | Semantic, Automatic Image Annotation Based On Multi-Layered Active Contours and Decision Trees[END_REF]. For instance, [START_REF] Srikanth | Exploiting ontologies for automatic image annotation[END_REF] have proposed a novel method to use a hierarchy defined on the annotation words derived from text ontology to improve automatic image annotation and retrieval. The hierarchy is used in the context of generating a visual vocabulary for representing images and as a framework for the proposed hierarchical classification approach for automatic image annotation. In [START_REF] Antonio | Using Multimedia Ontologies for Automatic Image Annotation and Classification[END_REF], a complete framework to annotate and categorize images has been proposed. This approach is based on multimedia ontology's organized following a formal model to represent knowledge. In the literature, we remarked that the proposed approaches for image annotation and retrieval have a key problem: the semantic gap between the visual features and the richness of human semantics is not well reduced to improve image annotation and retrieval results. However relations between visual and semantic informations are not well exploited. In particular, most approaches do not exploit both visual and semantic features in a dependence manner. Therefore, they are not expressive and they cannot be efficiently used for automatic image annotation and retrieval. In parallel, several image annotation approaches have been proposed to solve semantic gap problem by using ontologies which could improve image annotation accuracy. Moreover, annotation tasks are generally carried out without any visual support. Starting from these remarks, we propose a visually supporting image annotation framework that has four main characteristics: (i) it allows extracting invariant and complex visual features; (ii) it allows to learn classification of features; (iii) it is based on ontology which is built integrating feature classification results and semantic concepts; and, (iv) it allows annotating image by combining both visual and semantic similarities.

III. IMAGE ANNOTATION FRAMEWORK BASED ON VISUAL FEATURES AND ONTOLOGIES

In this section, we detail the proposed image annotation framework and its components. As depicted in Figure 1, the visual image annotation is performed on two main phases: training phase and testing phase. The training phase is supported by two components: (1) extraction and classification of features and (2) ontology's building. The testing phase is performed by image annotation component. This phase is composed of three main steps: feature extraction (Figure1 Step (3.1)), image classification (Figure 1 Step (3.2)) and image annotation (Figure 1 Step (3.3)). These components will be detailed in the following subsections.

A. Training phase 1) Extraction and classification of features:

The extraction and classification of features component consists, firstly, in extracting features of training images; secondly, in classifying the features. To extract visual features from training images, we use a HMAX architecture; in particular we adopt the HMAX model proposed by [START_REF] Theriault | Extended coding and pooling in the hmax model[END_REF]. The reason for which we use the HMAX model is to provide complex and invariant visual information and to improve the discrimination of visual features in order to obtain a good classification during the training phase. The HMAX model follows a general 4 layer architecture. Below we describe the operations of each layer. Simple ("S") layers apply local filters that compute higher-order features and complex ("C") layers increase invariance by pooling units.

•

Layer 1 (S1 Layer): In this layer, each feature map is obtained by convolution of the input image with a set of Gabor filters g s,o with orientations o and scales s. In particular S1 Layer, at orientation o and scale s, is obtained by the absolute value of the convolution product given an image I [15]:

L1 s,o = |g s,o * I| (1)
• Layer 2 (C1 Layer): The C1 layer consists in selecting the local maximum value of each S1 orientation over two adjacent scales. In particular, this layer partitions each L1 s,o features into small neighborhoods U i,j , and then selects the maximum value inside each U i,j .

L2 s,o = max Ui,i∈L1s,o * U i,j (2)
• Layer 3 (S2 Layer): S2 layer is obtained by convolving filters α m , which combine low-level Gabor filters of multiple orientations at a given scale.

L3 s,m = α m * L2 s (3)
• Layer 4 (C2 Layer): In this layer, L4 features are computed by selecting the maximum output of L3 m s across all positions and scales.

L4 = max (x,y),s L3 1 S (x, y), ..., max (x,y),s L3 M S (4)
After extracting visual features from training images, the layer 4 feature vector for each image is used to train a classifier.

2) Ontology's building component: The ontology's building component consists, firstly, in selecting the closest concepts of a concept associated to a given feature class, and extracting taxonomic and semantic relationships between them using BabelNet 1 , and then, creating the extracted relationships; secondly, in adding features of concepts of the corresponding level to the current feature class, and then, by the use of the concepts, reclassifying all updated features. This process is repeated in a recursive manner until all concepts are treated and all relationships between them are created, where each features class and its corresponding concept are the input of a new ontology level creation process. In last level, relations between concepts and features are added in order to improve the exploitation in both visual and semantic information. In particular, in the extracting taxonomic and semantic relationships phase, if the target concept has many senses according to BabelNet (Babel synset), a semantic disambiguation task is performed using BabelFy 2 . Let Θ be the ontology to be built, Dc denote the original concepts which are extracted from the meta data of our image database. Let consider: -Dc = Dc 1 , Dc 2 , ..., Dc M : a set of the original concepts; -Lr : a lexical resource ; Fig. 1: Framework's Architecture -F c : is the feature class related to the current concept; -C : is the current concept that is the root of the ontology which we will build. We summarize the ontology building process according to the algorithm 1. After building ontology of each concept and its corresponding features class, semantic relationships between all root nodes of each ontology, are extracted, and created in order to provide an integrated exploitation and view of both the related semantic concepts and visual features.

B. Testing phase

The testing phase includes three main steps which are: features extraction, image classification and image annotation (Figure1 ). To achieve the testing phase we need to use similarity measures in order to select the annotation concepts that represent the given image.

1) Similarity measures :

To perform the image annotation process, both visual and semantic similarities between concepts are computed. Visual similarity between concepts: the visual similarity between concepts consists on estimating the visual correlation between two concepts. In the field of image annotation and retrieval, recent approaches have been proposed to measure this similarity between concepts using several methods like the confusion matrix [START_REF] Deng | What does classifying more than 10,000 image categories tell us?[END_REF], Kullback-Leibler (KL) divergence [START_REF] Fan | Mining multilevel image semantics via hierarchical classification[END_REF] and the common features shared across the classes. In our work, we propose a simple method for estimating the visual correlation between concepts using the euclidean distance between feature vectors associated to each concept. The visual similarity between two adjacent concepts C i and C j is:

V isualSim(C i , C j ) = d(v(C i ), v(C j )) (5)
The visual similarity between two not adjacent concepts C i and C j is: U pdateΘ : add(T axonomicRelations)

8:

U pdateΘ : add(SemanticRelations)

VisualSim(C i , C j ) = d(v(C i ), v(CM 1 )) * n k=1 d(v(CM k ), v(CM k+1 )) * d(v(CM k ), v(C j )) where • V (C) : is the feature vector related to the concept C. • d(v(C i ), v(C j )) : is the euclidean distance between v(C i ) and v(C j )).
• C M : is the intermediate concept between C i and C j in the ontology. Semantic similarity between concepts: In ontology-based image annotation and retrieval, many semantic similarity measures can be used. In this context, several studies used semantic similarity measures to improve the image annotation and retrieval [START_REF] Patwardhan | Using WordNet-based context vectors to estimate the semantic relatedness of concepts[END_REF]. In our context, semantic similarity between concepts is computed according to the following formula.

SemanticSim(C j , C k ) = η(C j , C k ) = w C j w C k ||w C j ||.||w C k || (6)
where wC k : is the concept C k vector defined in the words space.

2) Image annotation: First, a test image is introduced and features are extracted using HMAX architecture. Then, the class with maximum probability, which is generated by the classifier, is selected as the concept of the test image. Finally, giving this concept, we find the closest concepts in the ontology. The annotation concepts are found using both visual and semantic similarities between concept that is found in the image classification step (Figure 1: 3.2) and nearest concepts that are defined in the ontology. The annotation is generated using the concepts that have a high annotation score which is computed by combining both visual and semantic similarities. The steps of image annotation process are detailed in the algorithm 2. During the annotation image process (Figure 1 Step (3.2)), visual and semantic similarities are used in order to compute annotation score between the given image and the closest concepts that are defined in ontology. The annotation Add AnnoScore (I, Ct i ) in V s 10: end for 11: bestConcepts←Select the top-k concepts from V s 12: Add bestConcepts in V c 13: return V C score is performed by a formula that combines the visual and semantic similarities. The both visual and semantic similarity measures that are used will be presented in the next subsection.

IV. EXPERIMENTAL EVALUATION

In order to show that our proposal framework can have a great interest and that can contribute to improve the image annotation task, we are interested, firstly, in conducting case study; secondly, in developing a prototype to show that the proposed framework can improve the performance image of annotation. We implemented the prototype using Matlab and JAVA programming language. In this section, we first present the experimental setup, then we present the case study and finally we show the obtained experimental results.

A. Experimental setup

To evaluate our approach, we used the Image Caltech 101 data-set. This data-set contains 9144 images from 102 categories. The number of images per category varies from 31 to 800. Most images are of medium resolution (about 300 x 300 pixels) and well aligned with some variability. In our case, we use 7 categories (faces, ibis, car, airplanes,camera, lotus, elephant) with 20 images for each categories. Also we use 10 and 15 training examples for each category and 35 images are used as testing set. In order to evaluate the proposed image annotation method, we used the average precision as evaluation metric.

B. Case study

Throughout this section, we illustrate a case study of the proposal framework. Figure 3 illustrates the different steps with a specific example related to the given image. Let's consider a test image composed of the three "man". So this image represents three "faces" of three "persons". As depicted in Figure 3, during the testing phase, when a test image is submitted, a HMAX features are extracted (Figure 3 Step (3.1)), after that, this image is classified aiming at affecting a concept to the input image (Figure 3 Step (3.2)). When our system detects the concept that represents the input image, visual and semantic similarities between this concept and all the closest concepts that are defined in the corresponding ontology, are combined and computed in order to determine score annotation for each pair "input imageclosest concept" (Figure 3 Step (3.3)). As shown in Figure 3, the concept "face" is detected when the classification of the input image is achieved. Using this concept "face" and its corresponding features, the system extracts the top ranked concepts that can represent the input image according to their score annotation. During the training phase, image features are extracted using HMAX architecture and a learning classification consists in training one-vs.-all SVM to operate in the feature space. In particular, features is classified into two classes and the concepts "camera" and "face" are associated to them. The extracted visual features and their classes are visualized (Figure 3 Step (1)). After that, for each features class and its corresponding concept, ontology is built. In particular, when relationships between the concept which is associated to the features class and their closest concepts, are extracted and created, the class of features is updated and reclassified using SVM classifier (Figure 3 Step (2.1) and Step (2.2)). As shown in Figure 3, concepts "photographic camera", "flash camera" and "TV camera" are found, thus taxonomic relationships between these concepts and "camera" are created. In parallel, concepts "face mask", "person" and "face pack", are also selected and taxonomic relationships between them are created. Thus, features of concept "person" are reclassified into two classes that represent concepts "employer" and "man". Part of the built ontology is represented in Figure 4. When our input image is submitted to our system, visual features are extracted and concept "face" is detected. After that, annotation score is computed by combining both visual and semantic similarities between this concept and the nearest concept that are extracted from the ontology. Thus, as depicted in Figure 3, according to the annotation score, relevant annotation concepts which represent semantic content of the test image like "person", and "employer" are returned. An example of image annotation results is visualized in Figure 5.

C. Experimental results

In order to evaluate the results improvement of image annotation we define two image annotation strategies. The first strategy is based on extraction and classification of visual features (ECVF) and the second strategy is focused on combining the visual features classification with ontologies (VFCO) and using visual and semantic similarities. The evaluation results shown in Table 1 represent the average precision obtained according to the strategies. The strategies VFCO and ECVF use the HAMAX features to annotate images. Compared to a classical image annotation strategy, we remarked that our strategy VFCO outperforms them. We observe that combining visual features classification and ontologies improves the average precision by 5.55% and 4.41% when using respectively 10 training images per category and 15 training images per category. V. CONCLUSION This paper presents a visually supporting image annotation framework based on visual features and ontologies. Our contribution can be summarized in: [START_REF] Deng | What does classifying more than 10,000 image categories tell us?[END_REF] visually support image annotation process, (2) combining feature classification results to semantics in order to build ontologies, (3) providing an integrated exploitation and view of semantics and Hmax features. The case study and the experiments that have been carried out highlight an improvement of the image annotation results. Currently, we integrate big data technologies to the framework in order to experiment it on ImageNet.

Algorithm 1

 1 Summarized Algorithm of building ontology Input: F c: feature class, C: Concept, ID: image database Output: ontology 1: Initialization (Θ:ontology, C: root concept) 2: Dc ← ExtractOriginalConcepts(ID) 3: Cp ← ExtractRelatedConcepts(C, Lr) 4: for each Cp i in Cp do

Fig. 2 :

 2 Fig. 2: Case study: illustrated process for a given image query

Algorithm 2

 2 Image annotation Input: I: test image, Θ : ontology Output: annotation concepts 1: Initialisation: annotation concepts vector V c = ∅ 2: FeaturesVector ← feature extraction(I) 3: Classify(featuresVector) 4: C ←concept of result class 5: Ct ← ExtractClosestConceptOfC(C,Θ) 6: Generate a empty vector of annotation score V s 7: for each Ct i ∈ Ct do 8: AnnoScore(I,Ct i ) =visSim(C,Ct i ) * semSim(C, Ct i ) 9:

Fig. 3 :Fig. 4 :

 34 Fig. 3: Visualization of extracted features and their classes

Fig. 5 :

 5 Fig. 5: Image annotation results

  SubF eaturesClasses ← classif y(F c, Cp) 14: for each Cp i ∈ Cp do

	11:	end if
	12: end for
	13: 15:	if (Cp i isLeaf N ode()) then
	16:	ConFeatRelation←CFRelation(Cp i , SubF eaturesClasses)
	17:	end if
	18: end for
	19: U pdateΘ : add(ConF eatRelation)
	20: return ontology

9:

if (Cp i / ∈ Dc) then 10:

U pdateF c : add(features of nearset concept of Cp i )

TABLE I :

 I Image annotation results evaluation

	Strategy	Hmax parameters	Average precision
		scale	orientation	10 training images	15 training images
	ECVF	8	12	0.54	0.68
	VFCO	8	12	0.57(+5.55%)	0.71(+4.41%)

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