B Franzelli

B Fiorina

N Darabiha

A tabulated chemistry method for spray combustion

Keywords: tabulated chemistry, spray combustion, combustion modeling, partially-premixed combustion

A tabulated chemistry method for spray combustion B. Franzelli, B. Fiorina, N.

Information from premixed, partially-premixed and diffusion flames are stored in a 3-D look-up table parametrized as function of the progress variable Y c , describing the progress of the reaction, the mixture fraction Y z , denoting the lo-

Introduction

A complete comprehension of spray combustion is necessary to guarantee flame stabilization and to reduce pollutant emissions in aircraft combustions and internal combustion engines [1]. Spray combustion comprises liquid dispersion into droplets and evaporation and presents a complex chemical structure since the fuel droplet evaporation process causes strong inhomogeneities of equivalence ratio in the fresh gases [2,3]. For these reasons, the numerical prediction of combustion phenomena sensitive to detailed chemistry, such as the pollutant predictions or the flame propagation, is very challenging.

Unfortunately, the use of detailed kinetic mechanisms is prohibitive in turbulent combustion simulation of complex industrial configurations due to their too high computational cost and stiffness. Commonly-used approaches to overcome this issue are flamelet-based tabulated chemistry methods that have initially been developed to introduce detailed chemistry in CFD simulation of gaseous flames at a reduced computational cost. The turbulent flame structure is modeled by an ensemble of single flamelet elements generally assuming a single burning regime. However, this assumption may be too restrictive. Premixed Flamelet Tabulation (PFT) methods [START_REF] Gicquel | Proceedings of the Combustion Institute[END_REF][START_REF] Van Oijen | [END_REF], for example, are based on premixed flamelets and are strictly valid only in premixed combustion regimes while Diffusion Flamelet Tabulation (DFT) techniques rely on diffusion flamelets and are adapted for non-premixed combustion [6,7]. Only recently, multi-regime flamelet methods [8,9,10,11] have been proposed to model the structure of complex gaseous flames where both premixedlike and diffusion-like reactive layers are present such as in multi-injection gas turbines or spray combustors.

Although being attractive, the performances of tabulated chemistry method have never been completely investigated for spray combustion. Hollmann and Gutheil [12] observed that a laminar gas library based on a single combustion regime cannot correctly reproduce the structure of a spray flame since premixed-like, partiallypremixed-like or diffusion-like features could be found depending on the boundary conditions. To capture these complex regimes, they proposed a tabulated chemistry method directly based on spray flamelets. This strategy is consistent but requires a very high-dimensional library as all physical spray parameters have to be varied: droplet diameter, liquid volume fraction, liquid injection velocity,... A more efficient solution would be to tabulate only the chemical subspace effectively accessed by spray combustion. A possible strategy is therefore to identify this subspace from gaseous flame elements as in [START_REF] Gicquel | Proceedings of the Combustion Institute[END_REF][START_REF] Van Oijen | [END_REF]10,13]. This point has already been evidenced by Baba and Kurose [14]

Numerical description of a spray flame

In the following, an axisymmetric mono-disperse counterflow spray flame is considered [15]. Pure fresh air is injected on the left side (identified by superscript ox) whereas spray fuel and gaseous air are injected on the right side of the configuration (superscript f ). The gas and liquid phases at the right inlet have the same temperature T f g = T f l and axial velocity v f g = v f l , where subscripts g and l denote the gaseous and the liquid phase respectively. The same values of temperature and axial velocity are imposed at both injection sides: T ox g = T f g and v ox g = v f g . Accordingly to [16], it could be shown that on the jet axis the mass fraction of the k th species Y k as well as the density ρ g , ρ l , the axial velocity v g , v l and the temperature T g , T l only depend on the axial coordinate x for both gas and liquid phases. The radial velocities depend also on the radial coordinate r: u g = rU g (x)

and u l = rU l (x).

Assuming a constant pressure gradient in the radial direction 1 r ∂p ∂r = -J, the gas phase flow is described by the balance equations for mass, radial and axial momentum, energy and species [15]:

2ρ g U g + ∂ρ g v g ∂x = n l ṁl , (1)
ρ g U 2 g + ρ g v g ∂U g ∂x = ∂ ∂x µ g ∂U g ∂x + J + n l ṁl (U l -U g ) -n l f r r , (2)
ρ g v g c pg ∂T g ∂x = ∂ ∂x λ g ∂T g ∂x - K k=1 h k W k Ωk - K k=1 ρ g Y k V kx c p gk ∂T g ∂x + n l ṁl c p gF (T l -T g ) -n l ṁl q, (3)
ρ g v g ∂Y k ∂x = - ∂ ∂x (ρ g Y k V kx ) + W k Ωk + (δ kF -Y k ) n l ṁl , (4)
where n l is the droplet number density, ṁl is the mass vaporization rate of a single droplet, µ g is the mixture viscosity , f i is the i th component of the drag force modeled by the Stokes law, c p gk and c pg are the heat capacity at local constant pressure of species k and of the mixture respectively, h k , W k , Ωk are the specific enthalpy, the molar weight and the molar chemical production rate of the k th species respectively, V kx is the diffusion velocity of the k th species in the axial direction, q is the heat transfered from the gas to each droplet and δ kF is the Dirac's delta equal to one only for k = F (where subscript F is the index for fuel species).

v l ∂m l ∂x = -ṁl , (5)
m l U 2 l + m l v l ∂U l ∂x = f r r , (6)
m l v l ∂v l ∂x = f x , (7)
m l c p l v l ∂T l ∂x = ṁl (q -L), (8)
2n l U l + ∂n l v l ∂x = 0, (9)
where m l = 4 3 πR 3 l ρ q is the mass of a single droplet (with R l the droplet radius and ρ q the liquid specific mass), L is the latent heat of evaporation and c p l is the constant pressure heat capacity of the liquid species. The system of equations is completed by assuming a constant radial pressure-gradient in the axial direction dJ dx = 0. The mass vaporization rate of a single droplet ṁl and the heat transferred from the gas to each droplet q are modeled by the expression for a spherically symmetric single-component droplet obtained from the film temperature model [START_REF] Kuo | Principles of Combustion[END_REF].

Tabulation methods for counterflow spray flames

Tabulated chemistry is a popular technique to account for detailed chemical effects with a reasonable computational cost [START_REF] Mass | Twenty-Fourth Symposium (International) on Combustion[END_REF]. Among the different strategies to generate chemical look-up tables, some of them are based on physical considerations like the PFT methods [START_REF] Gicquel | Proceedings of the Combustion Institute[END_REF][START_REF] Van Oijen | [END_REF], based on premixed flamelets, and DFT techniques [6,7] relying on diffusion flamelets. These techniques assume that the chemical flame structure is described in a reduced phase subspace from elementary configuration. For instance, PFT and DFT models assume that the chemical trajectories accessed in an adiabatic stratified reactive environment evolve in a 2-D subspace (Y c , Y z ), where Y c and Y z are the progress variable and the mixture fraction respectively. The progress variable Y c evolves monotonically between fresh and burnt gases. An explicit definition is [START_REF] Fiorina | [END_REF]:

Y C = Y CO + Y CO 2 . ( 10
)
The mixture fraction Y z is defined from a linear combination of carbon elements in order to represent the local fuel/air mixing:

Y z = Nspec k=1 n Ck Y k W C W k , (11)
where W C is the carbon element weight and n Ck is the number of carbon atoms of the k th species. This assumption is valid when the flame structure remains close to the single flamelet archetype used to construct the chemical structure. However, as

shown in [10,13], there exists more complex situation where effective dimension of the accessed composition space is higher. Supplementary coordinates such as the scalar dissipation rate for the mixture fraction and/or for the progress variable should be added to capture partially-premixed flames where both premixed-like and non premixed-like reaction zones exist.

In the following, we will first describe flamelet tabulation technique that assumes chemical system evolution in a 2-D subspace. Two formulations are represented where chemistry is tabulated from premixed unstrained flamelets and counterflow non-premixed flamelets, respectively. Next, we present an enhanced tabulated chemistry method called 2PFT that increases the range of validity of the model by adding a coordinate to the chemical look-up table, the mixture fraction scalar dissipation rate, as suggested by [10].

Premixed Flamelet Tabulation (PFT)

PFT methods, such as FPI [START_REF] Gicquel | Proceedings of the Combustion Institute[END_REF] or FGM [START_REF] Van Oijen | [END_REF], assume that the chemical subspace accessed by a flame can be mapped by a collection of 1-D gaseous laminar premixed flames computed using detailed chemistry for various equivalence ratios φ within the range [φ L , φ R ], where φ L and φ R are the lean and rich flammability limits. Any thermo-chemical quantity ϕ is stored in a 2-D look-up table:

ϕ = ϕ P F T [Y c , Y z ],
where ϕ P F T is computed from the collection of 1-D premixed flamelets.

The rich φ R (lean φ L ) flammability limit is defined as the maximal (minimal) possible value of the equivalence ratio of a premixed flame. This approach is accurate when the modeled flame structure remains close to the structure of a premixed flame front but introduces errors when diffusion of mass through iso-equivalence ratio dominates [20].

Diffusion Flamelet Tabulation (DFT)

A possible alternative is to tabulate the chemistry from diffusion flamelets as in the flamelet model [6] or in FPV method [7]. In the DFT method, any thermo-chemical quantity ϕ is obtained from a look-up table built from gaseous strained diffusion flames for different values of the strain rate 0 < a < a ext , where a ext is the extinction limit, by varying the inlet velocities. 1 As in PFT method, thermo-chemical variables can be mapped in the 2-D subspace (Y c , Y z ):

1 In a first approximation, the strain rate a of a counterflow flame is estimated from the inlet velocities and jet distance

H: a = v ox +v f H . ϕ = ϕ DF T [Y c , Y z ].
This approach is dedicated to diffusion flames but is not able to capture the structure and consequently the propagation of premixed flame front.

Partially-Premixed Flamelet Tabulation (2PFT)

In the 2PFT method, it is assumed that the chemical flame structure of a complex flame is mapped by a collection of 1-D gaseous partially-premixed counterflow flamelets characterized by an injection of pure air against a fuel/air mixture for different values of equivalence ratio φ f and strain rate a.

The table is then built by varying the fuel/air stream equivalence ratio between φ f = φ f L and φ f = +∞, where φ f L is the smallest value of the fuel/air stream equivalence ratio for which the counterflow flame is stabilized, and solving the flamelet for different values of the strain rate 0 < a < a ext . The limits of the 2PFT table tend towards PFT and DFT tables respectively. Indeed when φ f = +∞ and 0 < a < a ext the table is filled by diffusion flamelets as in DFT. At the opposite when a = 0 and φ L < φ f < φ R the table is filled with unstrained laminar premixed flames as in PFT. The 2PFT method is then based on different archetypal flamelets to map the subspace accessed by premixed, non-premixed and partiallypremixed flames. This subspace is identified by three parameters: the progress variable Y c , the mixture fraction Y z and the scalar dissipation rate χ * of Y z :

χ * = ρ 0 D 0 |∇Y z | 2 , ( 12
)
where ρ 0 and D 0 are a reference density and diffusion coefficient, respectively. In

ϕ = ϕ 2P F T [Y c , Y z , χ * ].
Other strategies are possible to generate the chemical table adapted to partiallypremixed combustion. Among them, are the REDIM [13] and the multi-dimensional flamelet-generated manifold [10] models. These approaches directly solve a projection of the full system of mass conservation species and energy balance equations in the (Y c , Y z ) subspace. Models are required for the progress variable and the mixture fraction dissipation rates. The 2PFT method proposed here is quite different as the table is built from counterflow partially-premixed flamelet solutions obtained in the physical space. Moreover, compared to other multi-regime flamelet models [8,[START_REF] Fiorina | [END_REF]21] the 2PFT method does not require a flame index, i.e.

a model to distinguish between combustion regimes, since the scalar dissipation rate χ * identifies the combustion regime, i.e. from χ * = 0 for premixed flames through the maximum values correspond to diffusion flames.

Results on spray flames

The performances of PFT, DFT and 2PFT strategies are now investigated in spray flames. The structure of a counterflow spray flame strongly depends on the gaseous flow properties as well as the characteristics of the spray, such as the droplet diameter D l , the liquid temperature T l and the liquid volume frac-

tion α l = 4 3 πn l D l 2
3 . The capability of the previously introduced methods to capture the structure of a kerosene spray flame is investigated here for the cases summarized in Table 1. All spray flames have been simulated with the REGATHcounterflow code [22] using a detailed mechanism for kerosene/air flame comprising N spec = 74 species and N reac = 991 reactions [START_REF] Luche | Elaboration of reduced kinetic models of combustion[END_REF]. To simplify the calculation, kerosene is represented by the C 10 H 22 species, whose liquid charac-teristics are summarized in Table 2, and unity Lewis number is assumed for all species.

A first reference spray flame is computed with the following injection conditions: (in kg/m 3 /s) is extremely important since it incorporates all the chemical information in the tabulation methods. The chemical source term ωYc of the reference spray counterflow flame obtained with the detailed mechanism is plotted in Fig. 3a (continuous line). It presents two peaks. A first reaction region is found for 0 < x < 0.2 cm, where fresh kerosene and air burn in a premixed-like regime.

D f l = 40 µm, α f l = 3.0 10 -3 , v f g = v f l = 0.20 m/s and T f g = T f l = 400 K. The jet distance is H = 0.02 m.
A second reaction zone is observed at x ≈ -0.05 cm where burnt products like CO recombine into CO 2 with fresh air coming from the left side (cfr. Fig. 2). As a consequence, to correctly capture the whole structure of a kerosene spray flame the tabulation method is expected to describe both diffusion-like and premixedlike features.

A priori testing

The performances of the three previously described tabulation methods are evaluated on the reference kerosene spray flame with an a priori test.

The PFT, DFT and 2PFT look-up tables are built from gaseous flamelet solutions obtained with the REGATH package and keeping the same detailed mechanism used for the spray flame calculations. The PFT table is built from a collection of unstrained adiabatic gaseous premixed flamelets for φ L < φ < φ R while the DFT table is based on adiabatic gaseous counterflow diffusion flamelets computed for different values of the strain rate 0 < a ≤ a ext by varying the injection velocity between 0.2 m/s and 10.0 m/s. The 2PFT table is composed by a collection of adiabatic gaseous counterflow flamelets for 10 different values of fuel stream equivalence ratio:

1.6 < φ f ≤ +∞ (0.1 < Y f C10H22 ≤ 1.00
) and for different values of the strain rate by varying the injection velocity within the extinction limit.

In all flamelets, the fresh gas inlet temperature is equal to the injection temperature of spray flames (T = 400 K). In the investigated cases, heat exchanges due to kerosene evaporation between liquid and gas phases impact very slightly the solution. Adiabaticity is therefore assumed to simplify the tabulation procedure.

The performances of the tabulated mechanisms are evaluated through an a priori analysis that compares the tabulated quantities to the reference solution obtained with the detailed scheme. For each point of the detailed mechanism solution, the values of progress variable Ỹc , mixture fraction Ỹz and χ * are evaluated using Eqs. ( 10)-( 11) and (12) The PFT method correctly predicts ωYc in the first premixed-like reaction zone, whereas it is not able to reproduce the recombination zone between CO and CO 2 .

The DFT method globally overestimates ωYc The 2PFT methodology is able to accurately describe the production rate in the whole reaction region characterized by both diffusion and premixed combustion regimes. The CO mass fraction is also extracted from the look-up tables and is compared to the detailed chemistry solution in Fig. 3b.. As already observed for the production rate ωYc , the 2PFT method better reproduce the flame structure over the whole computational domain compared to the classical techniques.

Parametric analysis

The ability of the 2PFT tabulation method to correctly describe the flame structure of a spray flame is also evaluated for the different fuel spray injection conditions of droplet diameter D f l , liquid volume fraction α f l and velocity v f g = v f l . All investigated cases are summarized in Table 1. In the cases DIAMa and DIAMb, the droplet diameter is equal to D f l = 70 µm and D f l = 140 µm respectively while the injected liquid fuel quantity, i.e. the liquid volume fraction α l , is kept constant by modifying the droplet density number n l . The progress variable reaction rates are compared to the reference solution ωYc for D f l = 70 µm (Fig. 4). It is composed by a premixed region and a recombination zone as in the reference case. For a higher droplet diameter (D f l = 140 µm), evaporation is initially slower and the kerosene remains mainly in liquid phase before entering into the flame front where it evaporates rapidly. The flame mainly presents one rich partially-premixing-like reaction zone that the PFT method is not able to reproduce. On the contrary, the DFT and 2PFT methodologies fairly agree with the reference solution.

In ALPHAa and ALPHAb cases, the liquid volume fraction α f l is decreased keeping constant the droplet diameter (D f l = 40 µm). The reconstructed progress variable reaction rates are compared in Fig. 5 to the detailed mechanism solutions.

For α f l = 1.4 10 -3 the second reaction zone observed at -0.1 cm < x < 0.1 cm is characterized by a less intense reaction rate ωYc whereas the intensity of ωYc of the first premixed-like region is higher. For a lower value α f l = 0.68 10 -3 , the evaporation zone is thinner and located closer to the injection (x > 0.6 cm). No second diffusion or partially-premixed reaction zone is found. Once again, the 2PFT method is able to correctly capture the different flame structures.

For VELa and VELb cases, the injection velocity is increased (D f l = 40 µm,α f l = 3.0 10 -3 ) and, as a consequence, the flame strain rate increases too (v f g = v f l = 0.5 m/s and v f g = v f l = 1.0 m/s). For these flames, the evaporation zone overlaps a smaller reaction zone. Both the PFT and the DFT methods mainly capture the production rate ω Yc for the highest value of v f g but the 2PFT method better predicts the flame structure even for smaller strain rate values. In all studied cases, it has been shown that the 2PFT tabulation method based on gaseous partially-premixed flamelets is able to correctly describe the structure of the spray flames which are characterized by different combustion regimes. Nevertheless, the 2PFT method has to be validated on more test cases varying the injection temperature as well as for higher droplet diameters that could eventually pass through the flame front. Moreover, variations of fresh mixture enthalpy are expected to have an important role on spray flames for some inlet conditions and their integration in the 2PFT table has to be deeply investigated. Liquid specific mass ρ q 781 kg/m 3 Latent heat of evaporation L 289.9 kJ/kg Boiling temperature 478.9 K Const. pressure heat capacity c p,l 2.003 kJ/(kg K) Figure 3: a) The production rate of the progress variable ωYc and b) the CO mass fraction of the reference spray flame obtained with the detailed chemistry (black continous line) is compared to the a priori profiles for the three tabulated mechanisms: PFT premixed method (dashed gray line), DFT diffusion method (gray crosses), 2PFT technique (black circles).

Conclusion

An evaluation of tabulation

  flamelets. It is shown that tabulated chemistry methods based either on pure premixed flamelets or on pure non-premixed flamelets fail to capture the structure of spray combustion. The reason is the complexity of the chemical structure of spray flames which exhibits both premixed-like and non-premixed-like reaction zones. To overcome this issue, a new multi-regime flamelet combustion model (called Partially-Premixed Flamelet Tabulation 2PFT) is presented in this paper.

  who mentioned the need of a combustion model for partially-premixed flames to guarantee the prediction accuracy of spray jet flames. The present article discusses the chemical structure modeling of spray flames using tabulated chemistry methods, relying on the assumption that the chemical subspace accessed by a two-phase reactive flow can be mapped by a collection of gaseous flamelets. Different tabulated chemistry strategies will be tested. In Section 2, the investigated configuration, a 1-D axisymmetric conterflow spray flame, is described. Three tabulated chemistry strategies are then introduced in Section 3. The PFT methods, based on premixed flamelets, the DFT approach, based on diffusion flamelet elements, and a new technique called Partially-Premixed Flamelet Tabulation (2PFT). The 2PFT method, based on the tabulation of partially-premixed flamelets, is proposed here to tackle complex chemical spray flame structure. All tabulation techniques are tested in Section 4.1 on the 1-D counterflow spray flame configuration. As the structure of spray flames is highly sensitive to the boundary conditions, the performances of tabulated chemistry methods for spray combustion are finally assessed in Section 4.2 for different values of injection velocity, droplet diameter and liquid volume fraction.

  the present work, they correspond to those of a stoechiometric kerosene/air mixture at atmospheric pressure and temperature T 0 = 400 K. Each flamelet point has a unique representation in the (Y c ,Y z ,χ * ) subspace. Any thermo-chemical quantity ϕ can then be stored in a 3-D look-up table:

Figure 1

 1 plots the temperature and the evaporation source term along the spatial coordinate x. The evaporation source term n l ṁl is high near the right injection of liquid kerosene. It presents a peak near the flame front (x ≈ 0.4 cm), where the gas temperature increases due to the thermal conductivity. Species mass fractions are plotted in Fig.2and show that this high temperature region (-0.4 cm < x < 0.4 cm) is characterized by the presence of intermediate species and products. The burnt products are then diluted by the opposed air jet. The production rate of the progress variable ωYc = W CO ΩCO +W CO 2 ΩCO 2

  . The tabulated chemical source terms are then extracted from the PFT, DFT and 2PFT look-up tables ( ω Yc P F T [ Ỹc , Ỹz ], ω Yc DF T [ Ỹc , Ỹz ] and ω Yc 2P F T [ Ỹc , Ỹz , χ * ] respectively) and compared to the reference ω Yc obtained with the detailed chemistry in Fig. 3a (PFT-dotted line, DFT-crosses, 2PFT-circles).

  technique for spray combustion has been presented in this article. The new chemical 2PFT method has been proposed to enhance the range of validity of tabulation methods to multi-regime combustion. It is based on gaseous premixed, partially-premixed and diffusion flamelets parametrized by the progress variable Y c , describing the progress of the reactions, the mixture fraction Y z , denoting the local equivalence ratio, and the scalar dissipation rate χ * , identifying the combustion regime. Results have been compared to those of the classical tabulated chemistry PFT and DFT methods on spray flames using a priori tests for different values of droplet diameter, liquid volume fraction and injection velocity. In all tested cases, the 2PFT tabulation method better describes the flame structure compared to the classical techniques based on single archetypal flamelets and it is more adequate for counterflow spray flames. It has also been demonstrated that the chemical structure of laminar spray flames could be modeled by a tabulated multi-regime flamelet combustion regime based on gaseous flamelets.

  Evaporation term source [Kg/m 3 /s]

Figure 1 :Figure 2 :

 12 Figure 1: The evaporation source term n l ṁl (continuous line) and the gaseous temperature (dashed line) as a function of the axial position in the reference spray flame.

Figure 4 : 20 -Figure 5 :Figure 6 :

 42056 Figure 4: Production rates of the progress variable ωYc for a) D f l = 70 µm and b) D f l = 140 µm. Lines and symbols are the same as in Fig. 3.

Table 1 :

 1 Different studied cases.

	Name case	D f l [µm]	α f l [-]	n f l [1/m 3 ]	v f g [m/s]
	REF.	40	3.0 10 -3	1.0 10 +10	0.20
	DIAMa	70	3.0 10 -3	1.87 10 +9	0.20
	DIAMb	140	3.0 10 -3	0.23 10 +9	0.20
	ALPHAa	40	1.4 10 -3 4.81 10 +9	0.20
	ALPHAb	40	0.68 10 -3 2.33 10 +9	0.20
	VELa	40	3.0 10 -3	1.0 10 +10	0.50
	VELb	40	3.0 10 -3	1.0 10 +10	1.00

Table 2 :

 2 Liquid kerosene properties.

Acknowledgments

The research leading to these results has received funding from the European Communitys Seventh Framework Programme (FP7/2007-2013) under Grant Agreement # ACP8-GA-2009-234009 (KIAI project). The KIAI project started in May 2009 for a duration of 4 years and addresses innovative solutions for the development of new combustors in aero-engines. It aims at providing low NOx methodologies to be applied to design these combustors.

List of Figures


Weakly Supervised Learning of Deformable Part-Based Models for Object Detection via Region Proposals Yuxing Tang, Xiaofang Wang, Emmanuel Dellandréa, and Liming Chen Senior IEEE Member

Abstract-Successful deformable part-based models (DPM) for visual object detection relies on training images with fully annotated object bounding boxes. In the context of lack of object level annotations, our goal is to propose a model enhancing the weakly supervised DPM by emphasizing the importance of location and size of the initial class specific root filter. To adaptively select a discriminative set of candidate bounding boxes as this root filter estimate, first, we explore the generic objectness measurement to combine the most salient regions and "good" region proposals. Second, we propose the learning of the latent class label of each candidate window as a binary classification problem, by training category specific classifiers used to coarsely classify a candidate window into either target object or non-target class. Finally, we design a flexible enlarging-and-shrinking postprocessing procedure to modify the output of DPM, which can effectively fit it to the approximative aspect ratio of the object and further improve the final accuracy. Extensive experimental results on the challenging PASCAL Visual Object Class (VOC) 2007 dataset demonstrate that our proposed framework is effective for initialization of the DPM root filter, and it also shows competitive final localization performance with the state-of-the-art weakly supervised object detection methods.

Index Terms-Object detection, deformable part-based models, region proposals, weakly supervised learning.

I. INTRODUCTION

O BJECT detection/localization in images is one of the most widely studied problems in computer vision. This task remains challenging mainly due to scale and viewpoint variation, deformation, occlusion, background clutter, intraclass variations and inter-class similarities for the objects in real world images. For most of the existing methods, a fully supervised learning (FSL) approach is adopted [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF], [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Szegedy | Deep neural networks for object detection[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], where positive training images are manually annotated with bounding boxes encompassing the objects of interest. This manual annotation of object location for large-scale image database is extremely laborious and unreliable thought extremely valuable. However, it is usually much easier to obtain weakly labeled data, where image level labels (e.g., user generated image tags on Internet) are presented. As a result, in this paper, in contrast to the traditional FSL, we are interested in weakly supervised learning (WSL) for object detection, where the exact object locations in positive training examples Y. Tang, X. Wang, E. Dellandréa and L. Chen are with LIRIS, CNRS UMR 5205, Ecole Centrale de Lyon, F-69134, France. (e-mail: {yuxing.tang, xiaofang.wang, emmanuel.dellandrea, liming.chen}@ec-lyon.fr)

This work was partially supported by French Research Agency, Agence Nationale de Recherche (ANR), through the Visen project, under the grant ANR-12-CHRI-0002-04, within the framework of the ERA-Net CHIST-ERA.

are not provided, given only the binary labels indicating the presence or absence of the objects of interest.

A. Related work

In recent years, there has been a substantial amount of work in weakly supervised object detection. From weakly annotated examples, the common practice is to jointly learn an appearance model together with the latent object location. The majority of related work treats WSL for object detection as an MIL (Multiple Instance Learning) [START_REF] Maron | Multiple-instance learning for natural scene classification[END_REF] problem. In the MIL framework, one has some positive and negative bags. A bag is positive when it has at least one positive instance, while it is negative if all the instances are negative. The objective of MIL is to train a classifier which can correctly classify a test instance as either positive or negative. MIL problems are usually solved by finding a local minimum of non-convex objective function (e.g., MI-SVM [START_REF] Andrews | Support vector machines for multiple-instance learning[END_REF]). Galleguillos et al. [START_REF] Galleguillos | Weakly supervised object recognition and localization with stable segmentations[END_REF] first use the MIL model to recognize and localize objects based on multiple stable segmentations. [START_REF] Nguyen | Weakly supervised discriminative localization and classification: a joint learning process[END_REF], [START_REF] Siva | Weakly supervised object detector learning with model drift detection[END_REF] use variants of MIL to learn object detectors from weakly labeled images and videos. Cinbis et al. [START_REF] Cinbis | Multi-fold mil training for weakly supervised object localization[END_REF] use multi-fold training procedure for MIL to avoid rapid convergence to poor local optima. Also in order to get rid of bad local minimum, Song et al. [START_REF] Song | On learning to localize objects with minimal supervision[END_REF] initialize the object locations via a discriminative submodular covering method.

Another main strategy for WSL detection is to utilize a category-independent saliency measure to predict whether a given image region belongs to an object or not. For example, Deselaers et al. [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF] propose a fully connected CRF (Conditional Random Field) [START_REF] Lafferty | Conditional random fields: Probabilistic models for segmenting and labeling sequence data[END_REF] which aims to select a candidate window with the highest objectness score [START_REF] Alexe | Measuring the objectness of image windows[END_REF] in each positive training image. Some work cast the WSL problem as a transfer learning (TL) problem. For example, Shi et al. [START_REF] Shi | Transfer learning by ranking for weakly supervised object annotation[END_REF] formulate a TL based on learning to rank, which effectively transfers a model for predicting object location from an auxiliary dataset to a target dataset with completely unrelated object categories. Hoffman et al. [START_REF] Hoffman | LSDA: Large scale detection through adaptation[END_REF] propose an algorithm which can learn the difference between the image classifier and the object detector, and transfers this knowledge to classifiers for categories without bounding box annotated data, turning them into detectors. However, for both of these methods, auxiliary object level annotations for part of the dataset are required.

In addition, Pandey et al. [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] modify the fully supervised DPM to a weakly supervised manner without object level annotations, which learns structural object detectors based on randomly initialized windows in the positive training images. Shi et al. [START_REF] Shi | Bayesian joint topic modelling for weakly supervised object localisation[END_REF] propose a WSL framework based on Bayesian joint topic modelling which localizes object across different classes concurrently. Recently, Wang et al. [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF] propose to learn the latent categories using probabilistic Latent Semantic Analysis (pLSA), and select the target object category by evaluating each latent category's discrimination. Bilen [START_REF] Bilen | Weakly supervised object detection with convex clustering[END_REF] et al. propose to couple a smooth discriminative learning procedure with a convex clustering algorithm, by imposing the similarity among objects of the same class.

B. Motivation and Contribution

Deformable Part-based Models (DPM) [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF] and its variants [START_REF] Girshick | Object detection with grammar models[END_REF], [START_REF] Azizpour | Object detection using strongly-supervised deformable part models[END_REF], [START_REF] Ren | Histograms of sparse codes for object detection[END_REF] have been dominant in supervised object detection on challenging PASCAL VOC datasets [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF] for a long period. The DPM represents an object with a holistic root filter that approximately covers an entire object and several higher resolution part filters that capture smaller local appearances (parts) of the object. It also characterizes the deformations by links connecting different parts. In the standard (fully supervised) DPM framework, the root filter is initialized with the positive ground-truth object bounding box, and it is allowed to move around in its small neighborhood to maximize the filter score. The locations of object parts are always treated as latent information due to the unavailability of object parts annotations upon most occasions. A latent SVM (LSVM) is adopted to learn the deformation of the objects, which can alternate between fixing latent values (part locations) for positive examples and optimizing its objective function.

Pandey et al. [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] modify the fully supervised DPM to a weakly supervised manner without object level annotations, which treats the location of root filter and part filters full latent, and learns structural object detectors based on the entire image. Its root filter's location is initialized randomly based on a window which has at least 40% overlap with the positive training image, and its aspect ratio is initialized roughly to the average of the aspect ratios of positive training examples. However, the specific size and location of the initial root filter, as well as their aspect ratio are indicated to have a significant impact on the final localization result [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF], [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF]. By randomly initialization, the object detector tends to learn spurious models of other classes or background regions, leading to lower accuracy during testing. And to our best knowledge, method for initializing the root filter based on theoretical deduction in weakly supervised DPM, as well as the definition of the aspect ratio of the objects, have not been well studied in [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF].

To make up the performance gap between weakly and fully supervised DPM, in this paper, we are motivated to propose a model that enhancing the weakly supervised DPM by emphasizing the importance of location and size of the initial class specific root filter. To be precise, our goal is to discover a reliable initial set of image windows that are probably going to contain the target objects in the positive training images with only category level annotations, so as to represent the object instances. Hence, our WSL framework incorporates adaptive window selection from class independent object proposals and training of deformable part-based models. In particular, we explore the "objectness" approaches [START_REF] Alexe | Measuring the objectness of image windows[END_REF], [START_REF] Uijlings | Selective search for object recognition[END_REF], which generate class independent object proposals with corresponding scores indicate their probabilities of being object instances, then we adaptively select a reliable set of windows from the derived object proposals for each image as initialization, by fusing visual saliency and "objectness" scores. Two different initialization schemes are developed: single region and multiple regions initilization. The former tends to select one relative larger bounding box which may contain the most salient part in the image, while the latter is much more generalized, which selects a small number of object estimations that can also capture smaller and scattered objects. For multiple regions initialization, the labels of the regions are latent information. We learn the latent class label by framing it as a classification problem, which tries to coarsely classify each region into target object class or nontarget class by some class specific classifiers. The generated object estimations are treated as the initial root filter estimates for training DPM detector.

The main contributions in this work are four-fold: A preliminary version of this work appeared in [START_REF] Tang | Fusing generic objectness and deformable part-based models for weakly supervised object detection[END_REF], which fuses the generic "objectness" with deformable part-based models for WSL detection. This paper includes that work but significantly extends it in the following ways. Firstly, we explore a much more generalized model M-WDPM (multiple regions initialization for weakly supervised deformable partbased models) which tries to select multiple regions, and we learn the latent label information of these regions in an effective way. This model shows its superiority in discovering not

Region Selection

Fig. 1. Illustration of our proposed method to extract the initial object estimations: for an input image (a), object proposals (b) are sampled with corresponding scores to their probability to have object inside by object proposal generating method. (c) is the saliency map derived from (b), and (d) is the reference region obtained by thresholding (c). A coarse set of candidate windows (f) are selected on the sorted proposals (e) by non-maximum suppression (NMS). In the upper image of (g), which indicates the single region selection scheme, the blue window is our initial object estimation obtained by optimizing the overlap between (d) and (f). The bottom image of (g) indicates the multiple regions selection scheme, its color windows with solid lines are multiple finer regions which are assumed to represent the objects in original image. For both images of (g), the green dot line windows are ground-truth bounding boxes for person and horse, respectively. only salient objects but also smaller and scattered objects to S-WDPM (multiple regions initialization for weakly supervised DPM) in [START_REF] Tang | Fusing generic objectness and deformable part-based models for weakly supervised object detection[END_REF]. Secondly, we experiment with advanced region proposals generated by Selective Search [START_REF] Uijlings | Selective search for object recognition[END_REF], and we also adopt the latest deep features to represent the image content. Thirdly, we evaluate our framework on the entire PASCAL VOC 2007 dataset, and compare it with state-of-the-arts. We also analyze the types of error that our detection framework inclines to make.

C. The Organization of the Paper

The rest of the paper is organized as follows: we present our weakly supervised DPM framework in details in Section II, and in Section III we present our experimental results and the comparison with other methods on PASCAL VOC 2007 datasets. In Section IV, we conclude our work.

II. FUSING GENERIC OBJECTNESS AND DEFORMABLE PART-BASED MODELS FOR WEAKLY SUPERVISED OBJECT DETECTION

In this section, we detail our approach of the weakly supervised DPM for object detection. Firstly, we introduce our approach to adaptively select the representative and discriminative regions from the category-independent object proposals. Secondly, we elaborate how to learn the latent class information when multiple regions are selected. Then we briefly describe the weakly supervised learning procedures using the selected regions with DPM and detection rescoring algorithm for testing. Finally we propose our new post-processing method to further refine the predicted object bounding box obtained by weak DPM detector, so as to cover the object more precisely.

A. Object Estimations: Initialization

In the weakly supervised DPM training procedure, a good initialization of the root filter is crucial. Hence, our goal is to discover a reliable initial set of image windows that are probably going to contain the target objects in the positive training images with only category level annotations, in order to represent the object instances.

1) Region extraction: Two general approaches have been proposed for generating class-independent object proposals in recent years: window scoring methods such as Objectness [START_REF] Alexe | Measuring the objectness of image windows[END_REF], BING [START_REF] Cheng | Bing: Binarized normed gradients for objectness estimation at 300fps[END_REF], EdgeBoxes [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF] and grouping methods such as Selective Search [START_REF] Uijlings | Selective search for object recognition[END_REF], Constrained Parametric Min-Cuts (CPMC) [START_REF] Carreira | Cpmc: Automatic object segmentation using constrained parametric min-cuts[END_REF], Multiscale Combinatorial Grouping (MCG) [START_REF] Arbeláez | Multiscale combinatorial grouping[END_REF]). We use Selective Search since it has been used as the proposal generating method by state-of-the-art supervised R-CNN detector [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF]. We also report results using objectness method [START_REF] Alexe | Measuring the objectness of image windows[END_REF] to make comparison with prior detection work [START_REF] Alexe | Measuring the objectness of image windows[END_REF], [START_REF] Tang | Fusing generic objectness and deformable part-based models for weakly supervised object detection[END_REF].

Given an input image I (shown in Fig. 1(a)), we first select top n scored windows W = {w 1 , w 2 , . . . , w n } and corresponding scores, denoted as S = {s 1 , s 2 , . . . , s n }, which indicate the probabilities to cover objects within them, generated by Selective Search (shown in Fig. 1 (b)). To balance a high recall (i.e., covering more objects) and computation efficiency (i.e., small number of region proposals), we set n = min(1000, N) according to [START_REF] Hosang | How good are detection proposals, really?[END_REF], where N is the number of proposals generated by Selective Search.

Based on the fact that the region proposal method is designed to capture all possible objects within an image, we assume that it has the reliability for providing a set of good candidate windows W * ⊆ W which covers the object of interest. However, the windows with the higher scores are not always the effective choices [START_REF] Shi | Transfer learning by ranking for weakly supervised object annotation[END_REF], which usually encompass other noisy background, or locate poorly on object targets (e.g., they may cover only the object parts). To extract a reliable set of object estimations from the pool of n windows, we design a recursive selection scheme shown in Fig. 1 (c)-(g).

2) Salient reference region: For weakly supervised learning, it is obvious the initialization of DPM root filter is significant. It will hurt the detector gravely if it shoots on the background region. Consequently, starting from visually meaningful regions (foreground objects) is imperatively necessary. Inspired by the success of visual saliency applied in salient object recognition, we compute the reference region R (shown in Fig. 1 (d)) by thresholding and merging the saliency map (or heat map) M (shown in Fig. 1 (c)). The value of saliency map M at pixel I(i, j) is obtained by summing up the scores of the windows that cover this pixel:

M(i, j) = n ∑ k=1 M k (i, j) (1)
where,

M k (i, j) = s k , if I(i, j) ∈ w k , ∀w k ∈ W, 0, otherwise. (2)
The reference region R can be one connected (continuous) region or several discrete regions in the image according to the score range and threshold value.

3) Coarse candidate windows pool: It is known that the score given by Selective Search (i.e., objectness score) corresponds with the probability to have target object inside its window to some extent. To take advantage of this auxiliary information, we concurrently select 200 out of n windows that with higher scores as candidates, according to the histogram of n scored windows (shown in Fig. 1(e)). In order to avoid near duplicate candidate windows, we further perform nonmaximum suppression (NMS) to get a finer set of candidates. Contrary to the common practice, which starts the suppression procedure from highest scored window, we randomly choose one, because we observed that the window with the highest score is not necessarily the best. Fig. 1 (f) illustrates the derived smaller set of l confident candidates Ŵ = { ŵ1 , ŵ2 , . . . , ŵl }, and their corresponding scores denoted as Ŝ = { ŝ1 , ŝ2 , . . . , ŝl }.

4) Object invariant estimations: Given the reference region R which implies the most salient region (or regions) within an image, and confident candidate windows Ŵ with scores Ŝ, the overlap between them provides valuable information to find the locations of target objects. We will propose two different schemes to fuse the salient region(s) with the extracted candidate windows.

a) Single region initialization: In [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], the root filter of the DPM is randomly initialized from a single window which covers at least 40% overlap with the original image. To demonstrate our selection scheme is superior than the randomly chosen window, we also filter out only one single window w * from the candidates pool Ŵ. Intuitively, we expect this window estimation to cover as much as the salient reference region R and to have a relative higher objectness score as well. Hence forth, the estimation of the initial object bounding box with objectness score (w * , s * ) (Fig. 1(g), upper image) can be determined by optimizing the following function:

(w * , s * ) = arg max ŵi ∈ Ŵ, ŝi ∈ Ŝ [α ŝi + (1 -α) area(R ∩ ŵi ) area(R ∪ ŵi ) ], i ∈ [1, l]
(3) where α is a parameter used to control the influence of the objectness score s i . In practice, α = 0.2, was selected by a grid search over {0.1, 0.2, 0.3, 0.4} on a validation set, for the purpose of emphasizing the priority of the intersection over union (IoU) overlap between the candidate window and merged salient reference region.

The single region initialization scheme prefer to select a relative large region which may contain the most salient part in the image. It can produce good DPM object detectors in a weakly supervised manner, when very few objects gathering together in an image. For example, by adopting the single region scheme, the blue window in Fig. 1(g) upper image, is used as a positive training example (i.e. DPM root filter initialization) for both horse and person category.

b) Multiple regions initialization: In fact, multiple objects (e.g., 2.5 objects in average for PASCAL VOC2007 trainval dataset) can be scattered anywhere in an image. We can therefore further improve DPM detectors by providing more object estimations as root filter initiliazations, instead of training the object detectors with a single window for each image. For each image, we are motivated to select a small number of object estimations that can also capture smaller and scattered objects, which can better represent the original image. We adopt the similar criteria as the score function Eq. (3). To alleviate the influence of the area of R, we set α to be 0.3. Instead only selecting the maximal scoring window in Eq.

(3), we pick out top Q scored windows W * for each image.

After generating several object estimations from each image, the next step is to approximately identify the class label of each estimation given only the labels of the whole image. For example, in Fig. 1(g) bottom image, the color windows with solid lines are associated with the horse and person labels. However, so far we have no idea which object(s) (or even background) is/are inside each bounding box. We will commit ourselves to solve this problem in the next subsection.

B. Learning Latent Object Classes via Region Classification

For each positive training image, we have generated Q object invariant estimations with the multiple regions initialization scheme. Consider an object category, e.g., horse, which has P positive training images, we can totally obtain z = P * Q object estimations. Obviously, some of these object estimations come from other categories (e.g., person, sheep, object parts or the background regions as well), where the class labels are latent information. In this paper, we frame the latent class learning problem as a classification problem by coarsely classifying these object estimations into either target object category or non-target category (i.e., other classes, object parts or background). Fig. 2. Illustration of our latent class learning framework for the horse category. For each object category, we train a linear SVM classifier with the CNN features (output of CNN's f c6 layer). Object estimations from the positive training images of this category are scored by its SVM. We select the regions with higher scores by thresholding as the representative objects of this category (horse vs. non horse for this example).

[32] CNN with caffe implementation [START_REF] Jia | Caffe: Convolutional architecture for fast feature embedding[END_REF] on the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2012 classification dataset [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF], which contains 1.2 million images of 1000 categories. Then we warp each region into a required fixed pixel size of 227 × 227, and subtract it with the mean RGB image, and forward propogate it through the network.

Finally, we take the output of the fist fully-connected layer (i.e., f c6 layer) to represent the input region. The output of f c6 layer is a 4096-dimensional feature vector. This feature extraction process is similar to R-CNN [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], but it is worth noticing that we do not fine-tune the pre-trained CNN on target dataset, because the object level annotations are assumed not to be available in the weakly annotated data. And we do not pad the region with additional image context around it, as our region estimation is already expected to have a significant coverage of the context information due to our selection schemes in Section II-A3.

2) Region classification: Consider training a horse detector. For all the P positive training images in the horse category, we generate z object invariant estimations. Intuitively, only part of these z regions contain the target horse object, others may have person, sheep, dog or even background. We learn the latent categories in these regions via region classification.

We first train a horse linear SVM [START_REF] Chang | Libsvm: A library for support vector machines[END_REF] classifier using the images labeled with horse as positive training examples and the ones without horses as negative examples. We compute the similar 4096-dimensional CNN feature vector as in Section II-B1 on whole images. We then run the trained horse classifier on the z object invariant estimations in the positive training images. By thresholding the SVM scores, finally we obtain a subset z regions from z estimations (z < z). These z regions are assumed to represent the target horse category, which can be treated as positive training examples of the horse detector.

Suppose we have K categories we want to detect. We train one binary SVM classifier on positive and negative images of each category, and run these K classifiers on their corresponding object estimations. We select high scoring regions for each target category so as to represent the objects of interest. Fig. 2 shows the latent class learning framework using SVM classification on the horse category.

Note that the above latent class learning process is only applied to multiple regions initialization, since for single region initialization, the unique generated window is used to initialize the DPM root filter for any categories appeared in the image.

C. Weakly Supervised DPM Training and Testing Details

We design two different kinds of deformable part based models for weakly supervised object detection according to different initialization schemes in Section II-A.

1) Single region initialization for weak DPM (S-WDPM) detection: Similarly to [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], each root filter hypothesis in a positive training image is initialized with the corresponding derived bounding box from the single region initialization scheme. The size and aspect ratio of the DPM root filter are decided by the average size and aspect ratio of the object estimation boxes (ground-truth bounding box and aspect ratio are used in [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF]). The root filter hypothesis is allowed to move around in a small neighborhood to maximize the filter score to compensate for imprecise bounding box estimation from Section II-A4a. As in [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], we represent an image by a multiscale HOG feature pyramid [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF] of 16 levels. For this DPM model, we use only a single component, since the multiple components is used for detecting objects with different views. We set the number of parts in this DPM to 8 as [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF]). And for negative training examples, we use random negatives from other object categories. For testing, sliding window approach is adopted. This single region initialized weakly supervised DPM detection model is denoted as S-WDPM. We refer the reader to [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF] for more details concerning the DPM training and detection procedures.

2) Multiple regions initialization for weak DPM (M-WDPM) detection: For the M-WDPM (multiple regions initialized weakly supervised DPM), we make it much "deeper" with the DeepPyramid feature [START_REF] Girshick | Deformable part models are convolutional neural networks[END_REF], for the reason that the HOG feature is suboptimal compared to deep features computed by CNN [START_REF] Szegedy | Deep neural networks for object detection[END_REF], [START_REF] Sermanet | Overfeat: Integrated recognition, localization and detection using convolutional networks[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF], [START_REF] He | Spatial pyramid pooling in deep convolutional networks for visual recognition[END_REF], [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF]. The feature map is computed by the fifth convolutional layer (conv5), which has 256 feature channels. We represent each image (or region) with a feature pyramid of 7 levels (v.s 16 levels for HOG pyramid). For training, the selected object estimations from Section II-B2 are treated as positive training examples, and the random windows from negative images are defined as negative examples. We use a DPM with 3 components and 8 parts per component according to [START_REF] Girshick | Deformable part models are convolutional neural networks[END_REF]. The training and testing procedures are similar to S-WDPM above, but we add a simple bounding box rescoring stage with the help of a frontto-end CNN padded with a softmax classifier.

The rescoring function is defined as:

s i det = κs i M-W DPM + (1 -κ)s i cls , i ∈ [1, K] (4)
where, 0 s i M-W DPM 1 is the normalized DPM detection score on a sub-window of the ith detector, and 0 s i cls 1 is the softmax classification score of the corresponding ith category on this sub-window. κ is a hyperparameter used to levarage the two scores, which ranges from 0.6 to 0.9. The final predicted windows are obtained by thresholding the S i det in Eq. ( 4).

In order to train this front-to-end CNN classifier described above, we fine-tune the pre-trained CNN with image level annotations on our training data. We implement it by removing the last 1000-way softmax layer while keeping all the other parameters and adding a new randomly initialized K-way softmax classification layer, and we then fine-tune the entire network based on the image-level labels.

In [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], contextual information is exploited to rescore the bounding boxes. However, it needs object-level annotations to extract the contextual information. Our detection rescoring method does not require the object level annotations, and it leads to a remarkable improvement in the average precision on several classes in the PASCAL VOC 2007 datasets (see Section III-B). An example of our bounding box rescoring procedure is shown in Fig. 3.

D. Bounding Box Post-processing

In many cases, the bounding boxes generated by DPM detectors are too large (resp. small) when detecting very small (resp. large) objects due to the restrictions of the size of the root filter and the scale of the feature pyramid. To improve the localization and to obtain a more precise prediction of the bounding box aspect ratio, we post-process each bounding box by enlarging or shrinking (ES post-processing) it to cover the object as much as possible. This is done using an improved version of the method proposed in [START_REF] Ke | The design of high-level features for photo quality assessment[END_REF] which measures the amount of area that the edge energy occupies. In brief, we first augment the original bounding box w = (x min , y min , x max , y max ) to 120% of the original width and height (i.e., 144% in total Algorithm 1 Bounding box post-processing pipeline.

Input:

Original bounding box: w = (x min , y min , x max , y max ); original image width: w o ; original image height: h o ; maximal expanding rate: β = 1.2; Laplacian filter shape: γ = 0.2.

Output:

Cropped bounding box: w = (x min , y min , x max , y max ). w = (x min , y min , x max , y max ) ← update by expanding bounding box in four directions (-x, -y, x+, y+) from the current centroid (x c , y c ). 29: end while 30: project w into original image: w = (x min , y min , x max , y max ) ← w = (x min , y min , x max , y max ) area, denoted as w aug = (x aug min , y aug min , x aug max , y aug max ). Expanding from the centroid if applicable. Otherwise, stop when reaching the border of the image.), and calculate the absolute values of the gradients L w aug by applying a 3×3 Laplacian filter with γ = 0.2 over the augmented bounding box. To easily calculate the edge spatial distribution, we then resize the gradient magnitude image size to 100 × 100 and normalize the image sum to 1, i.e., L w aug . And we set the values which are less than 10% of the maximum L max to 0. Finally, we expand the bounding box in four directions from the current centroid (x c , y c ) and stop until it contains 98% of the total gradient magnitude (edge energy) in the augmented box. Detailed algorithm is listed in Algorithm 1.

This post-processing technique is not only able to crop out plain background regions, but also can expand to cover the foreground regions which are not encompassed by the original box. However, the cropping method in [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] is probably to fail with the latter. Fig. 4 shows a few examples of our bounding box post-processing results. It is also worth noticing that this post-processing technique works efficiently for the objects with a unique or plain background, but has limited help for those with cluttered or textured background.

III. EXPERIMENTAL EVALUATION

In this section, we present the experimental results of our proposed framework with two different initialization schemes (i.e., S-WDPM using single region initialization and M-WDPM using multiple regions initialization) on the challenging PASCAL VOC 2007 dataset [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF].

A. Experiments with S-WDPM 1) Datasets: Following the protocol of previous works [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF], [START_REF] Siva | In defence of negative mining for annotating weakly labelled data[END_REF], we evaluate the performance of our proposed S-WDPM (single region initialized weak DPM) framework on two subsets from the training and validation set (trainval) of the PASCAL VOC 2007 dataset (VOC07) [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF]: VOC07-6×2 and VOC07-14. The VOC07-6×2 subset contains 6 classes (aeroplane, bicycle, boat, bus, horse and motorbike) with Left and Right views (aspects) of each class, resulting in a total of 12 separating classes. The VOC07-14 subset (same with PASCAL07-all defined in [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF]) consists of 42 class/view combinations covering 14 classes and 5 views (Left, Right, Frontal, Rear and Unspecified). Similar to [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF], [START_REF] Siva | In defence of negative mining for annotating weakly labelled data[END_REF], we remove all the images annotated as difficult or truncated in both training and evaluation steps.

2) Evaluation protocol: To make fair comparisons, we only choose the detection window with highest score per image, although our method can detect multiple instances appeared in the image using sliding window approach. We also report both results for initial and refined localization as [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], [START_REF] Siva | In defence of negative mining for annotating weakly labelled data[END_REF]. A refined localization is obtained by an iteratively trained DPM detector for one/sevral iteration(s) to refine the initial detection using the previous annotations as ground truth. Performance is evaluated with the percentage of training (train + val) images in which an object is correctly covered by the window (i.e. CorLoc [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF]), if the strict PASCAL-overlap criterion is satisfied (intersection-over-union > 0.5).

3) Experimental evaluation:

We compare our S-WDPM with Weak DPM [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], Weak objectness [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF] and Joint topic model [START_REF] Shi | Bayesian joint topic modelling for weakly supervised object localisation[END_REF]. For the Weak objectness approach [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF], the region proposal with the highest "objectnes" score is selected as the [START_REF] Shi | Bayesian joint topic modelling for weakly supervised object localisation[END_REF].

no post-processing with post-processing [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] S-WDPM [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF] 26.00 predicted window. As Table I shows, our method outperforms [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF] and our baseline approach [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] on both datasets. Both [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] and our S-WDPM use the same HOG feature pyramid for the DPM. We present our results using two kinds of object proposal generating methods: objeness (obj) and Selective Search (SS). For obj, our average performance of initial detection before post-processing the bounding boxes on the VOC07-6×2 and VOC07-14 subsets is 38.74% and 21.73% respectively, versus 37.22% and 19.98% for [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF]. These improvements are due to the initial object estimate of our method described in Section II-A4a, which gives a better initialization of the root filter of DPM detectors. We can also observe that both the postprocessing method of cropping [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] (i.e., S-WDPM(crop) in Table I) and our enlarging-or-shrinking (i.e., S-WDPM(ES)) post-processing method steadily improve the average localization accuracy. In particular, our ES method is superior to the cropping method of [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], as our cropped bounding box is not only able to shrink to crop out the background regions, but also capable of enlarging to cover the whole foreground object resulted by incomplete coverage of the original window. An example is shown in the last row of Fig. 5, where the target object (motorbike) is only partially localized by the initial detector (shown in red rectangles in the middle and right images) for both [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] and our method. However, in the final detection (shown in yellow) after post-processing, our method is able to enlarge the bounding box to approximately include the whole object, while [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] tends to crop out both foreground and background regions. Additionally, the rows start with "Refinement" in Table I indicate that localization accuracy can benefit from the iterative refinement process. It is worth mentioning that with a better initialization, our models converge to a steady level of performance after one less round of costly re-training (i.e., 2 iterations for obj vs. 3iterations) than [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF], and achieve slightly better results in the mean time.

The detailed comparisons for our S-WDPM using obj with the state-of-the-arts on the VOC07-6×2 dataset are listed in Table II. The results show that our method outperforms [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] for most of the categories. Especially, our method achieves the state-of-the-art results in some classes where the target object possesses the most salient regions in that category (e.g., aeroplane, bus, horse). Interestingly, even without refinement process, the accuracy for our method with certain category (e.g., aeroplane left) is superior to the competitors with the time-consuming refinement procedure. Fig. 5 visually compares some of our results with those of [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF]. We find that the best detection result using the Selective Search (63.31%) is 3.49% better than the objectness (59.82%) within the same S-WDPM detection model without postprocessing, and is 3.22% better (67.13% vs. 63.91%) with post-processing, on the VOC07-6×2 dataset. This is in accord with the conclusion in [START_REF] Hosang | How good are detection proposals, really?[END_REF]. Moreover, it achieves comparable or slightly better results than the sophisticated joint topic learning models in [START_REF] Shi | Bayesian joint topic modelling for weakly supervised object localisation[END_REF] with running DPM refinement only once. As shown in Table I, the SS also outperforms obj on the VOC07-14 dataset. Consequently, we entirely adopt the Selective Search method ('fast' option) for our next experiments. For the DeepPyramid feature extraction, we use a single NVIDIA GeForce GTX 780 GPU with 3GB memory. And we reduce the resized image resolution from 1713 × 1713 in [START_REF] Girshick | Deformable part models are convolutional neural networks[END_REF] to 1505 × 1505 to avoid running out of memory.

Ground

2) Parameter selection: As discussed in Section II-A4b, we can generate Q region estimations for each image. Q is a parameter which impacts the quality of the positive training examples. If it is too large, there would be an enormous number of noisy samples for latent class learning. If it is set to be very small, the instances in the original image would not able to be comprehensively represented. Therefore, we experimentally vary Q = {3, 5, 10, 15, 20, 30} to see which one performs best on the PASCAL VOC 2007 validation set. We implement this by directly measuring the average annotation accuracy for all the classes, on the generated bounding boxes (Q per image) with the Pascal-overlap criterion. Fig. 6 shows the annotation accuracy for different Q. We find that Q = 10 obtains the best result (34.5% average accuracy). When it is very small (e.g., 3), the performance drops dramatically to 27.0%. This is because some of the "good" region proposals are not selected due to very small Q, while some selected "bad" regions may harm the model. When it goes up from 10 to 30, the performance declines gradually. One explanation for this might be that many object parts or background regions would be included when Q is large. Hence, we set Q = 10 in all of our experiments. Fig. 7 shows three example images and their 10 selected regions. The κ in Eq. ( 4) which leverages the classification and detection scores is set to 0.7 according to cross-validation on a subset of the validation data. 3) Annotation evaluation: We evaluate the same CorLoc [START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF] as in Section III-A2 on the PASCAL VOC 2007 trainval set. Table III reports our experimental results compared with the state-of-the-art WSL methods for object detection.

For our M-WDPM-HOG baseline which computes the HOG features and does not make use of auxiliary training data from ILSVRC 2012 classification task [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF] as [START_REF] Bilen | Weakly supervised object detection with convex clustering[END_REF], [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF], it outperforms most of the previous works [START_REF] Nguyen | Weakly supervised discriminative localization and classification: a joint learning process[END_REF], [START_REF] Andrews | Support vector machines for multiple-instance learning[END_REF], [START_REF] Siva | Weakly supervised object detector learning with model drift detection[END_REF], [START_REF] Siva | In defence of negative mining for annotating weakly labelled data[END_REF], [START_REF] Shi | Transfer learning by ranking for weakly supervised object annotation[END_REF], [START_REF] Shi | Bayesian joint topic modelling for weakly supervised object localisation[END_REF] (ours: 36.8% vs. best of the previous works (Joint topic): 36.2%). Our M-WDPM-HOG shows modest improvement in most of the classes, which proves that our multiple regions initialization method has very discriminative power to select the "good" regions in the original image for training the DPM root filters.

It is also observed that, with the help of auxiliary training data and recently popular deep features, the average accuracy of our M-WDPM-Deep model increases by 4% over the M-WDPM-HOG model. And our detection rescoring method (i.e., M-WDPM-rescore) further improves the performance for most of the categories. The average improvement for detection rescoring on all 20 classes is 2.7% (43.5% vs. 40.8%). Our M-WDPM-rescore method is comparable with the newly invented convex clustering approach [START_REF] Bilen | Weakly supervised object detection with convex clustering[END_REF], but it is worse than the LCL method [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF] on average. Though [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF] achieves the state-of-the-art performance on many classes, it depends on more sophisticated Super-Vector Coding [START_REF] Zhou | Image classification using super-vector coding of local image descriptors[END_REF] of the deep CNN features that tragically increases the feature dimensionality. And it fails on some categories such as boat and table. However, our W-SDPM-rescore exhibits steady agreeable performance on all the categories. Especially, our W-SDPM-rescore works well on categories where target objects are relatively salient. (e.g., aeroplane, boat, bus, cat and table.) Moreover, it achieves the best results for the classes such as aeroplane, boat, and cat. 4) Detection evaluation: Table IV shows the comparison of our M-WDPM and other methods for object detection on the PASCAL VOC 2007 test set. Our M-WDPM-HOG baseline method achieves an mAP of 22.6%, which outperforms [START_REF] Siva | Weakly supervised object detector learning with model drift detection[END_REF] (13.9%) by a big margin, and is slightly better than [START_REF] Cinbis | Multi-fold mil training for weakly supervised object localization[END_REF] (22.4%). Both [START_REF] Siva | Weakly supervised object detector learning with model drift detection[END_REF] and [START_REF] Cinbis | Multi-fold mil training for weakly supervised object localization[END_REF] represent the image windows with SIFT [START_REF] Lowe | Object recognition from local scale-invariant features[END_REF] descriptor. [START_REF] Siva | Weakly supervised object detector learning with model drift detection[END_REF] uses a Bag-of-Words (BOW) [START_REF] Csurka | Visual categorization with bags of keypoints[END_REF] histogram of 2000 dimension, while [START_REF] Cinbis | Multi-fold mil training for weakly supervised object localization[END_REF] use Fisher Vectors (FV) encoding [START_REF] Perronnin | Improving the fisher kernel for large-scale image classification[END_REF] to represent the candidate windows. [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] uses the same HOG pyramid features Among these methods that adopt low level visual features, our M-WDPM-HOG works best. Although [START_REF] Song | On learning to localize objects with minimal supervision[END_REF] utilizes powerful deep CNN features Our detection rescoring method M-WDPM-rescore continues to improve the average precision (mAP = 27.4%) for nearly all the classes except for the motorbike class. It shows a better performance when compared with [START_REF] Song | Weakly-supervised discovery of visual pattern configurations[END_REF], [START_REF] Bilen | Weakly supervised object detection with posterior regularization[END_REF], and it has a competitive performance when compared with [START_REF] Bilen | Weakly supervised object detection with convex clustering[END_REF]. The performance gap (3.5%) between ours and that of [START_REF] Wang | Large-scale weakly supervised object localization via latent category learning[END_REF] might be partly caused by the use different deep feature representations as discussed in III-B3. We achieve the best detection results for the boat, cat, horse and train classes for this dataset.

In addition, we provide the results obtained by popular supervised object detection methods [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF], [START_REF] Girshick | Deformable part models are convolutional neural networks[END_REF], [START_REF] Girshick | Rich feature hierarchies for accurate object detection and semantic segmentation[END_REF] in the bottom lines of Table IV. One can see that there is still a gap between the weakly supervised detection framework and supervised ones, although our weakly supervised DPM yields better results for some classes (e.g., aeroplane, bird, cat, dog, etc.) to the supervised DPM 5.0 [START_REF] Felzenszwalb | Object detection with discriminatively trained part based models[END_REF].

5) Error analysis:

We present an analysis of the types of errors that our M-WDPMs make on the PASCAL VOC 2007 test set in Fig. 8. We use the diagnosis tool of [START_REF] Hoiem | Diagnosing error in object detectors[END_REF] and consider four types of false positive (FP) errors: Loc (poor localizations), Sim (confusion with similar objects), Oth (confusion with other objects, e.g., correctly localize an object but classifying it to a wrong class) and BG (confusion with background or unlabeled objects). Cor indicates correctly located true positives (TP). We visually show the fraction of correct detections (TP) and errors of each kind (FP) among the top ranking T windows in Fig. 8, where T is the number of ground-truth object windows in the test set of PASCAL VOC 2007.

We consider the M-WDPM-HOG as our baseline and show the distribution of TP and each kind of FP in Fig. 8(a). We can see that the majority errors are due to poor localizations (Loc) and confusion with background regions (BG). When adopting the deep features, our M-WDPM-deep encounters less Loc and Oth, but still it suffers from the Sim and BG error (as shown in Fig. 8(b)). In contrast, after detection rescoring, our best performing method M-WDPM-rescore has less error caused by Loc, BG and Oth (Fig. 8(c)), which validates that our rescoring

IV. CONCLUSION

In this paper, we proposed a model enhancing the weakly supervised learning by emphasizing the importance of location and size of the initial class specific root filter of deformable part-based models. We follow the general setup of [START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF] and introduce several substantial improvements to the weakly supervised DPM. The main contributions included a new selection model based on generic "objectnes" (region proposals) and visual saliency to adaptively select a reliable set of candidate windows which tend to represent the object instances in the image, and a latent class learning process by coarsely classifying a candidate window into either target object or non-target class. Furthermore we designed a flexible enlarging-and-shrinking post-processing procedure to modify the output bounding boxes of DPM, which can effectively further improve the final accuracy. Experimental results on the challenging PASCAL VOC 2007 database according to various criteria demonstrate that our proposed framework is efficient and competitive with the state-of-the-arts. Prof. Liming Chen has taken out three patents, authored more than 100 publications and acted as chairman, PC member and reviewer in a number of high profile journal and conferences since 1995. He has been a (co)principal investigator on a number of research grants from EU FP program, French research funding bodies and local government departments. He has directed more than 30 Ph.D. theses. His current research spans from 2D/3D face analysis and recognition, image and video analysis and categorization, to affect analysis in image, audio and video.

1 )

 1 Region representation: We use the deep convolutional neural networks (CNN) features to represent the regions (object estimations). Firstly, we pre-train an eight-layer (five convolutional layers and three fully-connected layers) Alex-Net

1 : 2 , y min +y max 2 ) 2 : 16 :

 122216 centroid: (x c , y c ) = ( x min +x max augmented width: a = β * (x maxx min ) 3: augmented height: b = β * (y maxy min ) 4: if x c -a 2 L w aug = f ilter(image(w aug ), laplacian , γ); 17: L w aug = norm(resize(|L w aug |, [100, 100]), 1); 18: L max = max(L w aug ); 19: for i = 1, 2, . . . , 100 do 20: for j = 1, 2, . . . , 100 do 21: if L w aug (i, j) < 0.1 * L max then 22:L w aug (i, j) end for 26: current centroid: (x c , y c ) ← average energy point of L w aug ; 27: while energy in w < 0.98 * ∑(L w aug ) do 28:

Fig. 3 .

 3 Fig. 3. Illustration of detection rescoring using M-WDPM and CNN softmax classifier. For a testing image, K (number of classes in target dataset) classspecific M-WDPMs are applied on it in sliding window manner. For each sub-window detected by M-WDPM, the normalized detection score is rescored by the softmax classifier of the detected category. In this example, the wrongly detected car and bicycle are finally discarded by the detector after the rescoring stage.

Fig. 4 .

 4 Fig. 4. Examples of bounding box enlarging and shrinking. Boxes before (resp. after) post-processing are shown in red (resp. yellow).

Fig. 5 .

 5 Fig. 5. Examples of localization results of our S-WDPM on PASCAL VOC 2007 images. The left column: ground-truth bounding boxes in green rectangles. The middle and right columns are detection results with [17] and our S-WDPM framework, respectively. Initial detections are shown in red and detections refined by detectors are shown in yellow. Both results are with individual post-processing approach.

Fig. 6 .

 6 Fig. 6. The impact of parameter Q (number of selected regions for each image in multiple regions initialization scheme). The average annotation accuracy on PASCAL VOC 2007 validation is evaluated with different Q.

Fig. 7 .

 7 Fig. 7. Three example images and their 10 selected regions (resized to same squared size for regularity).

Fig. 8 .

 8 Fig. 8. Analysis of top-ranked detections on PASCAL VOC 2007 test set. Pie charts show the distributions of true positive (TP) and false positives (FP)generated by the detection error analysis tool of[START_REF] Hoiem | Diagnosing error in object detectors[END_REF]. Percentage of top T detections (T is the number of whole objects the test dataset) that are correct (Cor), or false positives due to poor localization (Loc), confusion with similar objects (Sim), confusion with other objects (Oth), or confusion with background or unlabeled objects (BG)[START_REF] Hoiem | Diagnosing error in object detectors[END_REF]. The left three charts show the analysis of our methods, the right one is the analysis of the state-of-the-art supervised detection results obtained by NoC[START_REF] Ren | Object detection networks on convolutional feature maps[END_REF].

Yuxing

  Tang received the B.S. and M.S. degrees from the Department of Information and Telecommunication Engineering, Beijing Jiaotong University, Beijing, China, in 2009 and 2011. He is currently pursuing a Ph.D. degree with the Department of Mathematics and Computer Science, Ecole Centrale de Lyon, France. His research interests are computer vision and machine learning; in particular models for visual category recognition and object detection. Xiaofang Wang received the B.S. and M.S. degrees in biomedical engineering from Central South University, Changsha, China. She was awarded the Ph.D. degree in Computer Science from Ecole Centrale de Lyon, France in 2015. Her current research interests include image/video processing , medical image segmentation and analysis, multiple object tracking, and semantic segmentation. Emmanuel Dellandréa was awarded his Master and Engineering degrees in Computer Science from the University of Tours, France, in 2000 followed by his Ph.D. in Computer Science in 2003. He then joined the Ecole Centrale de Lyon, France, in 2004 as an Associate Professor. His research interests include multimedia analysis, image and audio understanding and affective computing, including recognition of affect from image, audio and video signals. Liming Chen was awarded a joint B.Sc. degree in mathematics and computer science from the University of Nantes, France in 1984. He obtained a M.Sc. degree in 1986 and a Ph.D. degree in computer science from the University of Paris 6 in 1989. He first served as associate professor at the Université de Technologie de Compiègne, then joined Ecole Centrale de Lyon as Professor in 1998, where he leads an advanced research team on multimedia computing and pattern recognition. From 2001 to 2003, he also served as Chief Scientific Officer in a Paris-based company, Avivias, specialized in media asset management. In 2005, he served as scientific multimedia expert in France Telecom R&D China. He has been head of the department of mathematics and computer science from 2007.

TABLE I AVERAGE

 I LOCALIZATION ACCURACY (IN %) OF OUR S-WDPM (SINGLE REGION INITIALIZED WEAK DPM WITH HOG FEATURES) COMPARED WITH STATE-OF-THE-ART COMPETITORS ON THE TWO VARIATIONS OF THE PASCAL VOC 2007 DATASETS. "CROP" AND "ES" DENOTE THE CROPPING METHOD FROM [17] AND OUR ENLARGING & SHRINKING POST-PROCESSING. "obj" AND "SS" DENOTE THE OBJECTNESS AND SELECTIVE SEARCH REGION PROPOSAL GENERATING METHOD. "S" AND "G" DENOTE THE SAMPLING AND GAUSSIAN STRATEGY FROM

TABLE II CLASS

 II LEVEL LOCALISATION ACCURACY (IN %) FOR THE VOC07-6×2DATASET FOR OUR S-WDPM(ES) USING objectness PROPOSALS vs.[START_REF] Pandey | Scene recognition and weakly supervised object localization with deformable part-based models[END_REF],[START_REF] Deselaers | Weakly supervised localization and learning with generic knowledge[END_REF],[START_REF] Siva | In defence of negative mining for annotating weakly labelled data[END_REF].

		Initialisation	Refined by detector
		ours [17] [40]	ours [17] [12]
	aero left	65.1 55.8 39.1	69.7 65.1 58.0
	aero right	64.1 61.5 50.0	84.6 82.1 59.0
	bike left	31.3 31.3 28.4	85.4 87.5 46.0
	bike right	42.0 44.0 30.6	54.0 68.0 40.0
	boat left	9.1	4.6 15.1	13.6	2.3	9.0
	boat right	9.3	9.3 20.7	14.0	7.0	16.0
	bus left	23.8 23.8 31.0	42.9 28.6 38.0
	bus right	65.2 52.2 35.1	69.6 47.8 74.0
	horse left	64.6 60.4 48.5	87.5 83.3 58.0
	horse right	73.9 67.4 45.2	76.1 80.4 52.0
	mbike left	64.1 48.7 46.3	87.2 92.3 67.0
	mbike right	70.6 76.5 55.3	82.4 88.2 76.0
	average	48.6 44.6 37.1	63.9 61.1 50.0

TABLE III COMPARISONS

 III OF WEAKLY SUPERVISED OBJECT DETECTORS ON PASCAL VOC 2007 TRAINVAL SET IN TERMS OF CORRECT LOCALIZATION (CORLOC [12], IN %) ON POSITIVE TRAINING IMAGES. ( † INDICATES METHODS USING AUXILIARY TRAINING DATA FROM ILSVRC 2012.)

	method / class	aero bike bird	boat	bottle	bus	car	cat chair cow
	our M-WDPM-HOG bicycle, person
	car, horse, person
	cow

TABLE IV COMPARISON

 IV OF WEAKLY SUPERVISED OBJECT DETECTORS ON PASCAL VOC 2007 IN TERMS OF AP (AVERAGE PRECISION, IN %) IN THE TEST SET. ( † SUPERVISED METHODS USING OBJECT LEVEL ANNOTATIONS.)

	method / class	aero bike bird	boat	bottle	bus	car	cat chair cow
	our M-WDPM-HOG 34.1 41.5 15.2 to represent the discovered object windows, its performance
	(22.7%) is more or less the same with our HOG based
	M-WDPM, which proves the stronger discrimination of our
	windows selection method. When using the deep features with
	additional training data from ImageNet [34], our M-WDPM-
	deep can achieve an mAP of 24.3%. The boost (1.7%) is not as
	much as that of the annotation task (4%, see Section. III-B3),
	it is probably because the use of distinct measuring criteria
	(mean average precision v.s percent of correct localization).