Thomas Padois

Franck Sgard

Olivier Doutres

Alain Berry

Acoustic source localization using a polyhedral microphone array

Keywords: acoustic source localization, spherical microphone array, generalized cross-correlation, reverberant environment

Introduction

Each year, millions of workers are exposed to excessive noise levels. In Québec, between 400,000 and 500,000 of the 2,5 million workers are exposed daily to noise levels likely to generate hearing impairment. Hearing loss is by far the most recorded occupational disease [START_REF] Duguay | Statistiques sur les maladies professionnelles au Québec[END_REF] and its total cost to the society is the highest [START_REF] Lebeau | Maladies professionnelles : impact économique au Québec[END_REF]. Therefore noise control solutions have to be implemented to continue prevention efforts. To reduce noise levels at the workstation, direct noise sources and their reflections by the environment have to be detected.

Microphone array techniques have become widespread for noise source localization [START_REF] Johnson | Array Signal Processing: Concepts and Techniques[END_REF][START_REF] Brandstein | Microphone Arrays: Signal Processing Techniques and Applications[END_REF][START_REF] Benesty | Microphone Array Signal Processing[END_REF][START_REF] Bai | Acoustic Array Systems: Theory, Implementation, and Application[END_REF].These techniques are based on the calculation of the propagation delay between a pair of microphones in the time domain or the phase shift in the frequency domain. An accurate assessment of a source location requires several microphones. Commonly, microphone array measurements lead to an acoustic image or noise source map coded with colors to highlight the noise source locations [START_REF] Lanslots | Selecting sound source localization techniques for industrial applications[END_REF]. Depending on the situation, the microphone array processing, the number of microphones and the array geometry may differ. Detecting aeroacoustic sources, speakers in a meeting room or noise sources in industrial halls does not involve the same constraints and challenges.

For transportation applications, like cars, trains or aircrafts, there is no ambiguity on the source location with respect to the microphone array.

Therefore a planar acoustic array geometry is preferred. Today, the most common planar geometry corresponds to several spiral arms which provide an acoustic image with moderate side lobes and operate over a broad frequency range [START_REF] Underbrink | Circularly symmetric, zero redundancy, planar array having broad frequency range applications[END_REF]. The microphone array technique commonly used is the conventional beamforming in the frequency domain based on the cross-spectral matrix of the microphone signals [START_REF] Michel | History of acoustic beamforming, 1 st Berlin Beamforming Conference (BeBec)[END_REF]. Due to the poor resolution of the acoustic image provided by beamforming, deconvolution techniques or inverse problems are used to clean up the noise map [START_REF] Brooks | A deconvolution approach for the mapping of acoustic sources (DAMAS) determined from phased microphone arrays[END_REF][START_REF] Sijtsma | Clean based on spatial source coherence[END_REF][START_REF] Suzuki | L1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources[END_REF][START_REF] Padois | Inverse problem with beamforming regularization matrix applied to sound source localization in closed wind-tunnel using microphone array[END_REF].

Microphone array techniques are also used in speech processing to detect speakers in a meeting room [START_REF] Dmochowski | A generalized steered response power method for computationally viable source localization[END_REF][START_REF] Do | SRP-PHAT methods of locating simultaneous multiple talkers using a frame of microphone array data[END_REF]. In this case, the microphone array involves few microphones and is located either at the center of the room on the table or on a wall [START_REF] Velasco | Source localization with acoustic sensor arrays using generative model based fitting with sparse constraints[END_REF][START_REF] Brutti | Multiple source localization based on acoustic map de-emphasis[END_REF]. The source is the human voice and the goal is to track the speakers. The main constraints are a high background noise and a reverberant environment. The common microphone array technique used is the beamforming, also called the steered response power based on the Generalized Cross-Correlation (GCC) of the microphone signals [START_REF] Knapp | The generalized correlation method for estimation of time delay[END_REF].

In workplaces such as an industrial hall, the dimensions of the rooms are very large and the reverberation time may be high (more than one second). The sound sources are usually broadband and may come from any direction therefore spherical microphone arrays are preferred. A 32-spherical microphone array associated to eigenbeam beamforming processing is used to localize a main source and its reflections [START_REF] Sun | Localization of distinct reflections in rooms using spherical microphone array eigenbeam processing[END_REF]. The obtained noise source maps allowed for a correct source localization. However, the processing had to be done at each frequency which is time consuming for broadband sources, moreover the number of microphones is high. Time-domain algorithms based on the GCC can be used to create a noise source map showing the main sources and potential reflections from the walls, floor or ceiling. However, the noise source map obtained may not be accurate due to the presence of large side lobes or high background noise and inverse problems have to be used to improve the resolution [START_REF] Padois | Comparison of acoustic source localization methods in time domain using sparsity constraints[END_REF]. Noël et al. [START_REF] Noël | A new temporal method for the identification of source directions in a reverberant hall[END_REF] developed a time domain technique associated with an inverse problem to detect source positions in complex industrial environments. Despite a correct source localization, the computation time of the inverse problem is very high. Moreover, their microphone array geometry is not well adapted for omnidirectional localization due to the absence of microphones at the top and bottom of the array.

The objective of the paper is to propose a fast signal processing technique with few microphones to localize acoustic sources in a reverberant environment. First, instead of using post-processing techniques to improve the noise source maps through the solution of associated inverse problems, the focus is rather put on generating a clean initial noise source map. Each microphone pair leads to a Spatial Likelihood Function (SLF) [START_REF] Aarabi | The fusion of distributed microphone arrays for sound localization[END_REF]. The noise source map is then obtained by summing up all the SLFs. Two criteria, based on the SLF energy or geometry of the microphone array and scan zone, are proposed to discard the microphone pairs which do not bring useful information. Then a polyhedral microphone array geometry with a small number microphones is proposed. The 14-microphone array is compared to the spherical microphone array developed by Noël et al. [START_REF] Noël | A new temporal method for the identification of source directions in a reverberant hall[END_REF]. The main originality of this work is that the proposed technique does not operate on the a posteriori noise source map but acts before generating the noise source map by removing SLFs with useless information. Moreover, by removing useless SLFs and using few microphones, the computation time and complexity is not increased.

Section 2 presents the source localization method and criteria used to compute the noise source map. Then, numerical data are used to assess the proposed microphone array geometry and criteria in Section 3. Finally, the performances of the microphone array geometries and criteria are confirmed by experiments carried out in a fully reverberant room (section 4).

Source localization method

Acoustic signal model

The objective of this section is to present the theoretical formulation of the source localization technique. The acoustic pressure source signal s(r s , t) is generated by an omnidirectional point source at location r s and recorded by a set of M free-field microphones at locations r m . The acoustic pressure signal x m recorded by the microphone m is given by

x m (t) = α m (r s )s(r s , t -∆t ms ) + v m (t), (1)
where t represents time, α m (r s ) is the geometrical attenuation due to the propagation between the source and the microphone and v m (t) is an uncorrelated additive noise due to background or sensor noise. The term ∆t ms corresponds to the propagation delay between the source and the microphone, called Time of Flight (ToF), and is defined by the Euclidean distance

∆t ms = 1 c 0 r m -r s 2 , (2)
where c 0 is the sound speed and • p is the l p -norm of a vector or a matrix.

In a real scenario, the microphone signals are sampled at a frequency f s and the processing is performed on discrete signals. The acoustic pressure microphone signal is then divided into segments of N points and the source localization technique presented in the following section may be performed frame by frame.

Conventional Beamforming

The main idea behind most source localization techniques is to compensate the time delay between each microphone. For a given sound speed, the ToF between the microphones and a set of L virtual sources at location r l is computed. Each microphone signal is delayed by the corresponding ToF, which corresponds to steer the microphone array in the direction of the virtual source. When the sum of the delayed microphone signals is maximized the source is localized. This technique is known as delay-and-sum beamformer and its output y l (t) can be expressed for the virtual source l location as

y l (t) = M m=1 x m (t + ∆t ml ), (3)
where ∆t ml is the time delay which steers the beamformer into a virtual source location. The beamformer output power Y BF for a virtual source location l is given by

Y BF l = E{y 2 l (t)} = M m=1 M n=1 R xm,xn (∆t ml -∆t nl ), (4)
where E{•} is the mathematical expectation and R xm,xn the cross-correlation function between the signals x m and x n defined by

R xm,xn (τ ) = E{x m (t)x n (t + τ )}, ( 5
)
where τ is the time lag. The beamformer output power is obtained after the summation process over all microphones. The estimated source position r e is provided by the peak value of the beamformer among all virtual source locations

r e = arg max l (Y BF l ). (6)
The set of virtual source locations is called a scan zone and may be in one, two or three dimensions. In this study, the scan zone is a plane and the result obtained is a two dimensional image called noise source map. The noise source map is composed of a main lobe (source position), side lobes and spurious lobes due to the microphone array geometry. Commonly, the computation of the beamformer output is performed over the M p = M (M -1)/2 microphone pairs due to the symmetry of the cross-correlation matrix (redundant information). Moreover, the auto-correlation terms (auto-correlation of microphone signals) are removed because they do not bring any information to the noise source map. These terms are known as "DC" component or self-noise. Usually, the beamformer output is computed thanks to the Generalized Cross-Correlation (GCC) [START_REF] Knapp | The generalized correlation method for estimation of time delay[END_REF], which is a weighted cross-correlation function, therefore the noise source map obtained is called GCC in the following.

Truncated cross-correlation

To obtain the beamformer output power, the time delay (∆t ml -∆t nl ) between a virtual source location and a microphone pair has to be computed.

Then, the cross-correlation of the microphone pair is estimated. Finally the value of the cross-correlation corresponding to the time delay is picked up and added to the source map. For a large number of virtual source locations and number of microphones the computation time may be intractable. Rather than searching the time delay for each virtual source location, one by one, the time delays between all the virtual source locations and a microphone pair (m, n) are computed and stored into a time lag vector τ m,n

τ m,n = |∆t m1 -∆t n1 | , . . . , |∆t ml -∆t nl | , with l = 1, ..., L, (7)
with |•| the absolute value. This vector corresponds to the time delay between all the virtual source positions and the microphone pair (m, n). Then, the peak value of the time lag vector is looked up. This time lag corresponds to the largest time delay possible for the considered microphone pair and all the virtual source positions. Therefore, the time delays of the crosscorrelation exceeding this maximum time lag are removed because they cannot be reached. A truncated cross-correlation function referred to as Rxm,xn is introduced,

if |τ | < max(τ m,n ), Rxm,xn (τ ) = R xm,xn (τ ), (8)
Rxm,xn is a vector corresponding to the N t allowed time delays. Now, the goal is to match each truncated cross-correlation value (with size [1 × N t ]) to the time lag vector (with size [1 × L]). However, the size of the time lag vector and the truncated cross-correlation are different. Therefore, the truncated cross-correlation vector is interpolated over the time lag vector which means that for each virtual source location a truncated cross-correlation value is assigned. The result is called the Spatial Likelihood Function (SLF) [START_REF] Aarabi | The fusion of distributed microphone arrays for sound localization[END_REF] for a microphone pair. Theoretically, the maximum of SLF is a hyperboloid in three dimensions and a hyperbola in two dimensions. However, in real situations, the hyperbolas are spread out and blurred and rather represent hyperbolic areas [START_REF] Velasco | Source localization with acoustic sensor arrays using generative model based fitting with sparse constraints[END_REF], called hyperbolas in the following. These hyperbolic areas can be narrow or wide according to the microphone positions. Finally, the processing is repeated for all the microphone pairs. The number of SLF is thus equal to the number of microphone pairs. To create the noise source map, all the SLFs are summed up. The peak values of the noise source map, which are the locations where the hyperbolas intersect, correspond to the source positions.

Examples of Spatial Likelihood Function

The SLFs are investigated for three microphone pairs called vertical, diagonal and collinear configurations (see Figure 1.d-f, considered microphones are plotted as red circles). The source generates a broadband signal. For each case, the cross-correlation is shown in (Figure 1.a-c). The SLF is shown in three dimensions and a slice is cut in the plane of the source (scan zone).

The vertical case corresponds to microphones at the same position but with a different z position. The source location is at equal distance from both microphones therefore the time delay is zero and the resulting SLF is a line as expected. In the case of the diagonal configuration, the time delay is not zero.

This leads to a hyperboloid in three dimensions and a hyperbola in the scan zone plane. In the case of several microphone pairs, the intersection between the hyperbolas yields the source location. In the collinear configuration, the first microphone is in front of the second microphone, i.e. the first microphone is between the source and the second microphone on the same axis. In this case, the time delay is always negative because the acoustic waves always reach the first microphone before the second (for a source located in the scan plane). Therefore for the considered scan zone, the time delays between the scan points and the microphone pair are almost similar (very low variance).

The resulting SLF is a cone in three dimensions and a large main lobe in two dimensions due to the intersection of the scan zone with the cone.

The SLF for each configuration are shown in the scan zone than the SFLs with a large main lobe. Criteria are discussed in the following to reject the SLF which provides inaccurate source localization.

Geometrical criterion (GC)

A Geometrical Criterion (GC) based on the vectors formed by a scan point and a microphone pair to improve the resolution of the noise source map obtained with GCC is proposed. Consider a scan point coordinate r l and a microphone pair defined by points r m and r n . Two vectors from the scan point to the microphones can then be defined. If the l 2 -norm of the normalized cross product of these two vectors is small, the angle θ between the two vectors is small and an inaccurate SLF for the localization, similar to the collinear configuration, may result,

a) b) c) d) e) f)
----→ r m -r l ∧ ----→ r n -r l 2 ----→ r m -r l 2 ----→ r n -r l 2 = sin(θ). (9)
The GC criterion is presented as a spatial weighting function W mn (r l ) multiplying the SLF (Eq. 8). When the angle θ is lower than β GC , the value of the SLF (corresponding to a scan point location) is set to zero

W mn (r l ) =    1 if θ > β GC 0 otherwise. ( 10
)
The GC criterion depends on a scan point and a microphone pair, therefore some scan points of a SLF or the whole SLF may be discarded. In the following, this method is called GCC-GC.

a) b) c) d) e) f)

Energy criterion (EC)

An alternative Energy Criterion (EC) is proposed and called GCC-EC.

As shown in figure 2.a-c the pattern of the SLF depends on the microphone locations. The noise source map is obtained by summing all SLFs, thus a SLF with large main lobe does not provide accurate information about the source position but contains a high energy (due to the size of the main lobe).

Therefore SLFs with a high energy may be removed. The energy of the SLF can be obtained by the l 2 -norm operation (root mean square value of the SLF for all the scan points). Therefore, removing the SLF given by a microphone pair with energy higher than a threshold β EC should improve the resolution of the final noise source map. The main difference between the criteria is the computation. With the GCC-GC the value of the angle θ is computed for all the scan points and microphone pairs whereas the GCC-EC is computed for each SLF,

Rxm,xn (τ ) =      Rxm,xn (τ ) if 10 log 10 Rxm,xn (τ ) 2 min Rxm,xn (τ ) 2 < β EC 0 otherwise. ( 11
)
3. Numerical source localization

Numerical set-up

The performances of the GCC associated to the two criteria are first investigated from synthetic data. The acoustic signal is generated by a broadband omnidirectional point source in free-field conditions. The acoustic point source is located at (x = 0, z = 0) at 1 m from the microphone array center at the same z position. The geometry of the microphone array is discussed in Section 3.2. The acoustic time signal is sampled at f s = 44 kHz. The scan zone, where the source is searched, is a square with side equal to 0.6 m. The distance between the microphone array and the scan zone is 1 m. It was verified through numerical simulations that a small error on this distance (less than 10%) leads to a correct source position with a similar noise source map.

A larger error provides a correct source position detection but with higher spurious lobes levels. The scan zone is discretized with 101 scan points along each direction which leads to a total number of scan points L = 10, 201. The cross-correlation is computed using the inverse Fourier transform of the crossspectrum between microphone pair signals. Commonly the cross-spectrum is whitened by the PHAse Transform (PHAT) filter, which removes its magnitude. This technique enhances the cross-correlation estimation because only the phase information is used to compute the inverse Fourier transform [START_REF] Knapp | The generalized correlation method for estimation of time delay[END_REF].

Microphone array geometries

In the context of acoustic imaging various microphone array geometries can be used depending on the configuration (planar, circular...). In an industrial hall, the acoustic energy may come from all the directions, therefore spherical microphone arrays are preferred. The distribution of the microphones on the sphere has to be correctly chosen. Polyhedral discretization of a sphere has been discussed theoretically in [START_REF] Hu | Geometrical arrangement of microphone array for accuracy enhancement in sound source localization[END_REF]. In the present study, a polyhedral geometry is proposed with 14 microphones arranged on the ver- teria should improve the noise source map. However, both criteria require defining a tuning factor (β GC or β EC ). To get the best value of the tuning factor, the width of the main lobe in both directions is picked up for several values of the tuning factor. The main lobe width is defined by the length of the main lobe at -3 dB. The number of scan points is increased up to L = 361, 201 (one point per millimeter) in order to accurately estimate the main lobe width. β EC varies from 0 dB up to 8 dB and β GC from 0 ˚up to 23 ˚. The main lobe width versus tuning factor is displayed in Figure 5 for both microphone array geometries. With β EC = 8 dB and β GC = 0˚, the noise source maps obtained correspond to the GCC source map (without criteria). In this case, the main lobe width along the x-axis is similar for both microphone array geometries. However, the main lobe width along the z-axis is larger with the ISIT microphone array as shown in Figure 4.d. Note that the main lobe width is similar in both directions with the CUBE array due to the symmetry of the geometry. With both arrays, if β EC > 3 dB the main lobe width is not improved by the criterion. For lower values, the main lobe width is enhanced until it reaches a minimum for the CUBE and ISIT (z-axis). With the CUBE array, the smallest main lobe width is reached when β EC is in the range [0.6; 1] dB. With the ISIT array, the main lobe width along the x-axis decreases as β EC decreases but at the expense of a larger main lobe width along the z-axis (larger than without criterion). For β EC < 1 dB, the main lobe width along the z-axis is large because too many SLFs are removed and only SLFs with a vertical line are kept (which explains the small main lobe width along the x-axis). Therefore a trade-off has to be made. In order to compare the noise source maps provided by both microphone array geometries with the GCC-EC, a value of β EC = 1 dB is chosen.

This allows for the best main lobe width with the CUBE array and a small main lobe width along the z-axis with the ISIT array is achieved. As for the GCC-EC, when β GC < 10˚, the main lobe width is not clearly improved for both microphone array geometries. With the CUBE array, the optimal main lobe width is reached when β GC is in the range [18˚; 20˚]. With the ISIT array, the trend of the main lobe width is similar to GCC-EC, the x main lobe width decreases with β GC but the z main lobe width increases.

The optimal values chosen for both criteria are β GC = 20˚and β GC = for the CUBE and ISIT array, respectively. The noise source map obtained with both microphone array geometries and above optimal values of the criteria, are plotted in Figure 6. The CUBE array provides a narrower, more symmetric main lobe than the ISIT array for which the main lobe is blurred with side lobes in the vertical direction. The best noise source map is given by the CUBE array with GCC-EC which exhibits a narrow main lobe and a) b)

Influence of background noise

The previous noise source maps have been generated in the case of microphone signals without additive noise (or background noise). Now, an uncorrelated white noise with zero mean is added to each microphone signal (see Eq. 1). In the case of a workplace, the background noise can be electrical or due to undesirable noise sources. The electrical noise depends on the quality of the acquisition system and is considered of low amplitude as compared to the main sources. However, the amplitude of the acoustic background noise such as the heat and ventilation air conditioning can be high. To determine the amount of noise added to the microphone signals,

the Signal to Noise Ratio (SNR) criterion is used. The previous noise source maps have been generated without noise, therefore the SNR is equal to +∞.

An SNR= 0 dB is chosen to generate the noise source maps which correspond to a source and a noise with the same level (see Figure 8). Without criteria, the noise source maps obtained with both microphone arrays are very similar. With the CUBE array, the side lobes in the horizontal and vertical directions are more extended but the main lobe size is slightly narrower.

With the ISIT array, the noise source map keeps the same pattern with side lobes slightly more extended. Therefore, even with background noise added to the microphone signals, the source can be located and the noise source maps are almost the same as without background noise. Using the criteria, the noise source maps are improved. With the ISIT array, the noise source maps obtained are almost the same as Figures6.b-d. With the CUBE array the noise source maps are slightly different but the spurious lobes are still removed. Finally, even with a high background noise (SNR= 0 dB), the source can be located and both criteria still improve the noise source maps. In the following, the background noise amplitude is set to zero to only investigate the performances of both arrays and criteria.

Influence of source-array distance

The numerical set-up of Section As expected, the best result is obtained when the source-array distance is well estimated. However, even with biased source-array distances, the source position is located. The main difference is the number and level of spurious lobes. Figure 10 shows the noise source maps for a smaller bias of the source-array distances ([0.95; 1; 1.05] m). If the source-array distance is estimated with a small error, the noise source maps are very similar. Therefore, if the source-array distance can be experimentally estimated, with a small error, the source position will be correctly estimated.

Commonly, the source-array distance is an input into the microphone array processing and can be quite accurately estimated experimentally. If the source-array distance cannot be estimated, the alternative way is to use a plane wave formulation.

Three acoustic sources with different source levels

In this section the performances of the microphone arrays associated with the criteria are compared in the case of three sources with different levels The noise source maps are shown in Figure 11 for the horizontal source configuration. In all the cases, the source positions are correctly detected.

However with GCC, the detection of the source with the weakest level is difficult due to the spurious lobes. The criteria allow for a better detection of the source positions. In this configuration the ISIT microphone array provides a noise source map with few spurious lobes due to its lower side lobes level along the x-axis. To get a better insight into the noise source maps, slices along the x-direction are presented in Figure 12. Both criteria improve the main lobe width and reduce the background noise of source maps. For both microphone array geometries, the GCC-EC provides the best results with low side lobes level and narrow lobes. Moreover, the GCC-EC better estimates the noise source levels. The GCC-GC is less efficient with the CUBE array and under-estimates the weakest source level with the ISIT array.

As discussed in Section 3. array is poor due to the smaller z-dimension of the microphone array, thus inaccurate noise source maps may be expected in the vertical axis. The three acoustic sources, previously set horizontally, are now along the z-axis.

The noise source maps are shown in Figure 13 for both microphone array geometries and criteria. Without any criterion, the noise source maps exhibit a high side lobe level and the detection of the weakest source is difficult. Both criteria improve the noise source maps by removing side lobes and narrowing the main lobe. However, the noise source map based on GCC-GC and ISIT still exhibits a very poor vertical main lobe width whereas this artifact is not present in the noise source map based on the GCC-EC and GCC-GC with the CUBE array. The slices along the z-direction are presented in Figure 14.

When GCC-GC is used, the ISIT array shows a large side lobe. The best main lobe width is provided by the GCC-EC which leads to the best estimation of the source level. To set-up the microphone arrays, two similar frames have been designed.

Each frame was composed of a sphere of radius 3.81 cm supported by a tripod. Holes were drilled in the sphere according to each microphone array geometry pattern. Rods with 20 cm length were inserted into the holes and the microphones were mounted at the end of the rods (see Figure 15) scan points, i.e. one scan point by centimeter). For both microphone arrays, the GCC with and without criteria was applied.

to
The noise source maps are shown in Figure 16 for both microphone array geometries and detection algorithms. The GCC with the ISIT array exhibits two large spots at source positions with a vertical main lobe width larger than the horizontal main lobe width. The noise source map is enhanced when the criteria are applied. The GCC-GC and GCC-EC remove the spurious lobes and decrease the size of the main lobes. With the CUBE array, the noise source map, obtained with GCC, exhibits two main spots with a smaller main lobe width than the ISIT array in the vertical direction. The GCC-GC workers and to avoid slowing down the production, the computation time

Conclusion

In this study, the performance of spherical microphone arrays, combined For both geometries, the microphones were distributed on a sphere with a radius of 0.25 m. An Energy Criterion (GCC-EC) and a Geometrical Criterion (GCC-GC) were proposed to select a subset of relevant microphone pairs in Cross-Correlation estimations, and improve the noise source map. The noise source maps provided by both microphone arrays and criteria were assessed using numerical data in free-field and experimental data obtained in a reverberant room.

The case of a single source, three horizontal sources and three vertical sources with different sound levels were studied through numerical simulations. The best noise source map in terms of main lobe width and side lobes is provided by the CUBE array with the GCC-EC. Even with background noise, both criteria are efficient and lead to clean noise source maps.

Then, the performances of both microphone arrays were compared in the case of experimental data. Two loudspeakers were set in a reverberant room.

The CUBE array associated to the GCC-EC clearly detected the two source positions with the best resolution.

Finally, it has been shown that the smallest GCC computation time is achieved for the CUBE array (due to it is low number of microphone pairs).

Moreover, the GCC-EC is faster than the GCC-GC.

This study demonstrated that the CUBE array is more efficient than the ISIT array and that the GCC-EC allows for improving the noise source map with a weak increase of the computation time.

Usually in acoustic imaging, inverse problems can be used to achieve a high resolution. The input of the inverse problem is the noise source map and the computation time may be long due to the iteration process. The next step of this work is to study how the improved noise source map obtained with the CUBE array combined with the GCC-EC criterion affects the resolution of inverse problems.

Figure 2 .

 2 a-c).The final noise source map is obtained by summing all the SLFs provided by the microphone pairs, Figure2.d-f). Owing to the last comment, some microphone pairs do not provide accurate information about the source location, such as the collinear configuration (Figure2.e-f). The sum of SFLs with a narrow hyperbola area provides a more accurate localization (Figure2.d)

Figure 1 :

 1 Figure 1: Cross-correlation between a microphone pair signal (top) and SLF (bottom) for three microphone pair configurations, a-d) vertical, b-e) diagonal and c-f) collinear. The microphone array center is at y = 0 m and z = 0 m. The filled red dots represent the microphone pair of interest. The black circles are the other microphone positions. The scan zone is the black square at y = 1 m and the blue circle is the real source position. The shaded surface is the hyperboloid.

Figure 2 :

 2 Figure 2: Spatial Likelihood Function (SLF) for three microphone pairs configurations, a) vertical, b) diagonal and c) collinear. Sum of the (SLF) d) vertical + diagonal, e) vertical + collinear and f) diagonal + collinear. The white circle is the source position.

Figure 3 :Figure 4 :

 34 Figure 3: a) Spherical 14-microphone array (called CUBE). b) Spherical 15-microphone array (called ISIT). The large black dot is the source position. The dashed gray lines represent circles of radius 0.25 m.

Figure 5 :Figure 6 :Figure 7 :

 567 Figure 5: Main lobe width in both directions (x-axis and z-axis) versus tuning factor, a) GCC-EC and b) GCC-GC. The main lobe width is divided by the diameter of the spherical microphone array and expressed in %.

3 . 1

 31 Figure 9.

[ 0 ;Figure 8 :Figure 9 :

 089 Figure 8: Noise source maps in the case of a Signal to Noise Ratio (SNR) equal to 0 dB . a) CUBE array with GCC, b) ISIT array with GCC, c) CUBE array with GCC-EC, d) ISIT array with GCC-EC, e) CUBE array with GCC-GC and f) ISIT array with GCC-GC. The black circles are the source positions.

Figure 10 :

 10 Figure 10: Noise source maps for three source-array distances with CUBE array and GCC, a) 0.95 m, b) 1 m and c) 1.05 m. The black circles are the source positions.

Figure 11 :Figure 12 :

 1112 Figure 11: Noise source maps in the case of three horizontal acoustic sources with different sound levels ([0; -3; -6] dB). a) CUBE array with GCC, b) ISIT array with GCC, c) CUBE array with GCC-EC, d) ISIT array with GCC-EC, e) CUBE array with GCC-GC and f) ISIT array with GCC-GC. The black circles are the source positions.

4. Experimental source localization 4 . 1 .

 41 Experimental set-upIn order to confirm the above findings on array geometries (CUBE and ISIT) and criteria (GCC-EC and GCC-GC), experiments were conducted in a reverberant room. The reverberation time based on the TR60 is about 3 s at 1 kHz which leads to a reverberation radius of 0.5 m.

Figure 13 :Figure 14 :

 1314 Figure 13: Noise source maps in the case of three vertical acoustic sources with different sound levels ([0; -3; -6] dB). a) CUBE array with GCC, b) ISIT array with GCC, c) CUBE array with GCC-EC, d) ISIT array with GCC-EC, e) CUBE array with GCC-GC and f) ISIT array with GCC-GC. The black circles are the source positions.

Figure 15 :Figure 16 :

 1516 Figure 15: Photograph of the experimental set-up.

Figure 17 :Figure 18

 1718 Figure 17: Slices of the noise source maps in the case of the loudspeakers at z = 0 m, a) CUBE array and b) ISIT array.

  with the Generalized Cross-Correlation (GCC) technique, to detect broadband point sound sources was investigated. The objective of the paper was to propose a fast signal processing technique to generate a clean noise source map with few microphones. A geometry based on the compound of a cube with an octahedron (called CUBE) and comprising 14 microphones has been proposed. This geometry has been compared with another 15 spherical microphone array used previously in the literature and called ISIT by the authors.


Introduction: Belgian education systems

An important feature of the Belgian context is that, since 1989, education has been within the competence of the three language-based communities. These communities (French-, Flemish-and Germanspeaking) manage similar but completely independent education systems. Therefore, a truly in-depth analysis would result in three independent NESET reports: one for each of the three education systems. However, these systems have a common history and face similar equity-related challenges. In this report, we will focus on what they have in common, although some differences, primarily between the Flemish Community (Flanders) and the Federation Wallonia-Brussels (FWB), will be discussed.

In Belgium, schooling is compulsory and free of charge between the ages of 6 and 18. Preschool (3 years from the age of 2.5 years) is optional, and is referred to, together with primary education (6 years), as 'fundamental education'. Secondary education (6 years) is made up of three 'tiers', the first comprising (theoretically at least) a common structure for all pupils. Starting in the second tier, secondary education is divided into curricula (general, technical and vocational) with different objectives and opportunities. Higher education is organized by 'universities', 'hautes écoles / hogescholen' and 'arts colleges', and divided into three cycles: Bachelors, Masters and Doctorate. Except for a few specific programmes for which an entrance examination is required (engineering, medicine), access to higher education, whatever the institution, is only conditioned by the acquisition of a secondary education diploma.

Freedom of education is proclaimed in the Belgian Constitution of 1831 and remains at the core of educational policy in Belgium. It means:

• Freedom provided to pupils and their families to choose the educational institution that suits them. This, combined with the public funding of schools according to the number of pupils they enrol, leads to a school quasi-market. • Freedom to organise schools. This leads to the organisation of the education system into various networks (public, public grant-aided and private grant-aided; see annex 4). The schools receive public funding on the same per-capita basis whatever their network.

Section 1. Main equity-related policy challenges

To structure the discussion of the main equity-related policy challenges in Belgium, we use the conceptions of equity adapted by [START_REF] Demeuse | Efficiency and equity[END_REF] from [START_REF] Grisay | Quels indicateurs pour quelle réduction des inégalités scolaires[END_REF]. According to these authors, there can be several levels of equity, depending on which type of equality is pursued: equality of access; equality of treatment; equality of achievement; equality of realization.

1.1.

Equality of access Equality of access regarding compulsory education can be considered as realized in Belgium, with a gross participation rate of nearly 100% between the ages of 3 and 17 (Fédération Wallonie-Bruxelles & [START_REF]Les indicateurs de l'enseignement[END_REF]. The main equity challenges regarding compulsory education occur rather at the related dimensions of equality of treatment and equality of results.

Not unexpectedly, equality of access is more of a problem in higher education. Access rates to higher education have undergone a constant increase since the end of the 1980s, with approximately 75% of holders of a secondary education diploma accessing higher education in FWB in 2008 (Fédération Wallonie-Bruxelles & ETNIC, 2012). However, studies show that access to higher education in Belgium is still unequal (OCDE, 2012) and linked with various variables [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF]) such as socio-economic status, handicap and the type of curriculum attended in secondary education.

1.2.

Equality of treatment At least since the idea of school vouchers was first introduced by the Catholic minister Schollaert as early as 1911 [START_REF] Desmed | Le projet de loi Schollaert et le bon scolaire (1911)[END_REF], the dominant idea regarding compulsory education funding in Belgium can be expressed by the formula '1 child = 1 child'. With this idea as their point of departure, the Catholic school network argued for the equality of treatment for the children attending their schools. The 'school pact ' andthe ensuing law in 1959 (Belgique, 1959) ratified this idea, leading to the school quasi-market.

Studies have shown that the quasi-market functioning of the education systems in Belgium fosters several types of segregation between schools, resulting in the creation of 'ghetto' schools and 'sanctuary' schools (see [START_REF] Demeuse | School segregation in the French Community of Belgium[END_REF] for a synthesis). With [START_REF] Delvaux | Ségrégation scolaire dans un contexte de libre choix et de ségrégation résidentielle[END_REF], we define segregation as the expression of social differences in space, appearing as soon as individuals classified by society into distinct social categories are separated in space and thus do not mix with each other. Hence, segregation can be characterized by two factors: the social categories and the type of spatial separation. We identified three possible social categories (socioeconomic, academic and ethnic), and three possible types of separation (between schools, between curricula and within schools) resulting in 9 types of segregation, about which we have varying amounts of information [START_REF] Demeuse | School segregation in the French Community of Belgium[END_REF]. In the FWB, a major part of the research and political attention is focused on socioeconomic segregation between schools in secondary education, that is to say the separation of pupils between schools according to their socioeconomic status. We generally refer to this type of separation when we use the term "segregation" in the context of the FWB. There is a lack of data about ethnic segregation in the FWB as a consequence of the philosophical position of the government that ethnic and immigration categorization is not desirable (Friant et al., 2008;Jacobs et al., 2009b). On the other hand, Flanders is more prone to use "ethnic" categorization, with the widespread use of the term "allochtone" to refer to immigrant inhabitants (Jacobs et al., 2009b). As a consequence, there is in Flanders much more research and political attention regarding ethnic segregation between schools than in the FWB (see e.g. [START_REF] Sierens | The desegregation policy in Flemish primary education: is distributing migant students among schools a good solution[END_REF][START_REF] Agirdag | Segregatie in het basisonderwijs: geen zwart-witverhaal[END_REF][START_REF] Poesen-Vandeputte | Balans van het evaluatieonderzoek van het gelijke nderwijskansenbeleid in Vlaanderen (Onderzoeksrapport[END_REF]. When using the term "segregation" in Flanders, we generally refer to socio-economic and ethnic separation between schools.

There are great socio-economic disparities between schools related to the type of curriculum they offer (see annex 1). Technical/vocational schools are more often chosen by families from lower socioeconomic backgrounds. Moreover, the 'waterfall system' adds its effect to this: pupils from the academic curricula with non-satisfactory school results tend to switch to technical or vocational curricula, and these pupils are more often those with lower socioeconomic status (Friant et al, 2008). Thus a certain hierarchy of curricula is established according to a social status linked to school success for some and school failure for others. As each school does not offer all curricula, such a mechanism creates segregation between schools. Technical/vocational schools draw pupils with a lower socioeconomic status that have in this way been pushed out of general education (Friant et al, 2008). In addition, schools are in competition with each other to attract pupils, as the pupils have not only a financial value, because their numbers determine the subsidies awarded to each institution, but also a peda-gogical value based on their more or less desirable personal traits [START_REF] Delvaux | Hiérarchie scolaire et compétition entre écoles: le cas d'un espace local belge[END_REF]. This competition results in increased socioeconomic and academic segregation between schools.

Equality of results

Studies (e.g. [START_REF] Dupriez | Inequalities in school systems: effect of school structure or of society structure?[END_REF][START_REF] Monseur | Composition académique et sociale des établissements, efficacité et inégalités scolaires : une comparaison internationale[END_REF] have shown that social and academic segregation in education systems generally results in significant inequalities in school results. Indeed, peers play an important role in a pupil's learning, be it by influencing the process of learning in the class or by the fact that teachers adapt the demands of the curriculum and the evaluation to the composition of the group (see e.g. [START_REF] Thrupp | School composition and peer effects[END_REF]. Such a school composition effect is suspected to play a great role in Belgian education systems. However, recent studies in Flanders using longitudinal data (e.g. [START_REF] Vandecandelaere | Invloed van de etnische en sociale samenstelling en diversiteit van de schoolpopulatie op de prestaties en leerwinst voor wiskunde in het eerste leerjaar[END_REF] did not show any significant effect of school composition on pupils' progress, raising debates about the extent to which segregation plays a role in school inequalities in Flanders.

PISA assessments from OECD assessing 15-year-old pupils' competencies show quite different results between language communities; Flanders often shows some of the best results of the OECD countries, while the FWB is below average overall. However, both communities have in common a strong score discrepancy between low-SES and high-SES pupils [START_REF] Baye | Les compétences des jeunes de 15 ans en Communauté française en sciences, en mathématiques et en lecture. Résultats de l'enquête PISA[END_REF]Jacobs et al, 2009;[START_REF] Overheid | Leesvaardigheid van 15-jarigen in Vlaanderen: De eerste resultaten van PISA[END_REF]. These assessments also underline the importance of the average socioeconomic level of the schools themselves on differences in pupil performance. This situation is problematic in terms of equity: depending on the children's SES and on the composition of the school they attend, their results can differ significantly (Jacobs et al., 2009a). However, studies in Flanders show that while pupils' results vary according to school composition, there is no significant effect of school composition on pupils' progress (e.g. [START_REF] Vandecandelaere | Invloed van de etnische en sociale samenstelling en diversiteit van de schoolpopulatie op de prestaties en leerwinst voor wiskunde in het eerste leerjaar[END_REF]. Some studies using PISA data [START_REF] Jacobs | Performances des éleves issus de l'immigration en Belgique selon l'étude PISA: une comparaison entre la Communauté française et la Communauté flamande[END_REF]Jacobs et al., 2009a) also show that the immigrant origin, strongly linked to socio-economic status, can play a role in the observed difference of pupil performance in Flanders and the FWB.

Studies in Flanders monitoring pupils' course of study have shown that a significant proportion (around 14% in 2010) of pupils still leave school without obtaining any qualification [START_REF] Van Landeghem | Vroege schoolverlaters in Vlaanderen tot 2010: Een analyse van de invloed van de financieel-economische crisis van 2008[END_REF], 2013). These early dropout rates are linked with variables such as the parents' level of education, language spoken in the home and gender. Some geographical disparities are also observed [START_REF] Van Landeghem | Vroege schoolverlaters in Vlaanderen in 2010: Indeling volgens locatie, opleidingsniveau van de moeder en moedertaal (Onderzoeksrapport[END_REF].

Using other statistics (the EU labour force survey), Chenu and Blondin (n.d.) have shown that early school leaving rates were higher in 2011 in the FWB (14,7% in Wallonia and 18,9% in according to their statistics) than in Flanders (9,6% according to their statistics). Moreover, the trend towards a decrease of early school leaving rates is stronger in Flanders than in the FWB. The situation of Brussels is the most preoccupying. Some discrepancies are also observed between curricula; early leaving rates being notably higher in vocational curricula than in general ones (Chenu and Blondin, n.d.).

At the higher education level, studies show an effect of several variables on achievement, adding their effect to the fact that some groups have a reduced access rate to higher education. Socio-cultural variables such as the parents' level of education (OCDE, 2012) or income [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF] play an important role in student achievement. Other influential variables are related to the previous course of study, but also to the school attended while in secondary education.

Section 2. Main relevant policy initiatives, reforms, measures; assessment

While carrying out sociological studies in the 1960s and 1970s, researchers and stakeholders in Belgium came to the conclusion that access to schooling opens to the masses , but that not all children are equal when it comes to schooling: some children need more attention to obtain the same results as others. In this sense, there are still no equal opportunities of school success and social realization.

Acknowledging these inequalities, targeted compensatory policies have emerged since the end of the 1980s. These policies, inspired by the French and English area-based policies that emerged since the 1970s, were based upon the simple assertion 'to give more to those who have less'. The idea, which replaces strict equality of treatment, consists in re-establishing a balance by giving pupils from underprivileged backgrounds supplementary means, not only on an individual basis, which until then was the rule with the attribution of individual grants, but on a collective basis, by enhancing the funding given to schools enrolling those pupils. See [START_REF] Friant | Priority Education Policies in Belgium: Two Modes of Regulation of the Effects of a Market Logic[END_REF] for an extended review of these compensatory policies.

More recently, another line of action has been implemented, which is to reduce school segregation. There are still debates in the public opinion, especially in Flanders, about the real effects of school segregation on inequalities of results and the reasons why there should be desegregation [START_REF] Poesen-Vandeputte | Balans van het evaluatieonderzoek van het gelijke nderwijskansenbeleid in Vlaanderen (Onderzoeksrapport[END_REF]. However, there is a consensus that segregation results at least in inequalities of treatment and that desegregation could be an instrument of social cohesion. Reducing school segregation in Belgium involves regulating the enrolment process, whether making such regulation a part of the compensatory policy, as in Flanders, or separate from it, as in the FWB.

2.1.

Compensatory policies

In the FWB

Considering the characteristics of our education systems, which emphasize freedom of choice regardless of the distance travelled by pupils, basing an educational priority policy on zones is not a good idea.

In the FWB, a compensatory policy was set up in 1998 under the term 'positive discrimination' (it has since 2009 undergone some modification and is now called 'encadrement différencié' -ED1 ). This educational priority policy was also the occasion for setting a new goal for the education system as a whole: to ensure equality of social realization. In the education system of the FWB, 'positive discrimination' means a 'distinction drawn to the advantage of primary or secondary schools on the basis of social, economic, cultural or pedagogical criteria' (Gouvernement de la Communauté française, 1998).

The mechanism of positive discrimination or ED consists in a modulated allocation of means to schools according to the socioeconomic origin of the pupils attending them. This allocation of extra means to those schools targeted as enrolling an underprivileged population is done mechanically by ranking schools according to an objective criterion, the socioeconomic index (SEI), and by allocating extra funds to the less privileged schools according to this criterion.

The targeting operates on the basis of the SEI of each pupil according to the characteristics of the area in which he lives (unemployment rate, average revenue, comfort of the houses, etc.). The SEIs of all pupils are averaged at the school level. Schools are targeted on the basis of their population and not on the basis of the area in which they are located because of the free choice of school: pupils do not automatically attend the school of their area and school populations can change from year to year.

Identification on the basis of the actual school population has thus been chosen because it allows taking these constraints into account and adapting to changes in the schools' population, thus avoiding a definitive labelling of schools [START_REF] Demeuse | Analyse critique des fondements de l'attribution des moyens destinés à la politique de discrimination positive en matière d'enseignement en Communauté française de Belgique[END_REF]. Moreover, such a method (calculating a SEI on the basis of the pupils' area of residence and targeting schools according to their population, not their area of implantation) is supported by results of prior scientific studies in Belgium and other countries [START_REF] Demeuse | Analyse critique des fondements de l'attribution des moyens destinés à la politique de discrimination positive en matière d'enseignement en Communauté française de Belgique[END_REF][START_REF] Poesen-Vandeputte | Balans van het evaluatieonderzoek van het gelijke nderwijskansenbeleid in Vlaanderen (Onderzoeksrapport[END_REF] showing that an indirect indicator of socioeconomic status predicts educational attainment as accurately as variables directly collected from families.

Schools benefitting from ED consist of approximately 25% of all pupils in the FWB, for each level of studies. The targeted schools benefit from additional means amounting to 62 million euros, or 1.35% of the education budget. These targeted schools are split into five classes according to their average SEI, each class being given a weighting index for the allocation of extra means, in such a way that the more their public is socioeconomically underprivileged, the more extra means a school receives.

These extra resources are of three types (Gouvernement de la Communauté française de Belgique, 2009):

• Extra teachers;

• Financial means allowing to purchase equipment, to organize cultural and sports activities, or to convert rooms; • Other human resources (non-teaching staff) such as educators, social workers, childcare workers, etc.

How these extra resources are used is not determined a priori. Currently, identification of potentially targeted schools is automatic, but schools only receive extra resources if they introduce an action project, and if this project is accepted. Every five years, schools must introduce a project describing pedagogical actions to be taken to 'ensure all pupils equal opportunities of social emancipation' (differentiated pedagogy, smaller groups, school dropout prevention, etc.). It must present concrete actions foreseen over a five-year duration and must include the allocation and distribution of the extra means. These pedagogical actions are to be frequently evaluated. A 'phasing-out' procedure is also foreseen, with a progressive reduction of the extra means allocated.

In addition to these extra means arising from positive discrimination are extra means arising from 'positive differentiation', i.e. extra financial means with the aim of improving the material conditions of schools, consisting in a reallocation of extra funds obtained by the FWB. These means are allocated according to a progressive formula linked to the schools' average SEI.

An evaluation of the effectiveness or efficiency of compensatory policies in the FWB is still lacking. The evaluation of other dimensions [START_REF] Bouchard | La qualité : Mieux la définir pour mieux la mesurer[END_REF]) of these policies is, however, better documented. One of these dimensions is targeting. While the FWB has not taken the same options as Flanders in targeting, both have strong arguments to support their choices.

The FWB targets schools according to a SEI characterizing the pupils' district of residence. This SEI takes into account no variables referring to nationality, ethnicity, language or migrant origin. From a scientific point of view, these other variables have been set aside by the inter-university team in charge of calculating the index because they add no additional information than targeting by socioec-onomic status alone [START_REF] Demeuse | Analyse critique des fondements de l'attribution des moyens destinés à la politique de discrimination positive en matière d'enseignement en Communauté française de Belgique[END_REF]. Moreover, these variables were deliberately ruled out by the legislators to avoid stigmatization of populations of immigrant origin. Some more recent research results [START_REF] Jacobs | Performances des éleves issus de l'immigration en Belgique selon l'étude PISA: une comparaison entre la Communauté française et la Communauté flamande[END_REF]Jacobs et al., 2009a), however, would support a compensatory policy which took into account such variables in targeting, but current political thinking apparently does not agree.

Other criticisms of ED targeting concern the somewhat artificial divide between 'classes' of schools and determining how many extra means they will receive. ED schools, or schools of the same class, do not form a homogeneous whole by their population or context, and do not take in pupils that are clearly more underprivileged than do other schools with a nearly equal SEI [START_REF] Bouchat | Discrimination positive et mobilité scolaire[END_REF]. Moreover, an in-depth study of the situation of some schools at the limit of targeting [START_REF] Demeuse | Behind the positive discrimination in French Community of Belgium: central criteria vs. local actions[END_REF] shows that the schools' population possibly comes from non-homogeneous districts and does not disperse randomly throughout the districts. These criticisms of current ED targeting would support an addition of pedagogical criteria to the targeting (e.g.: late enrolments, high absenteeism, high rates of pupils lagging behind). This should, however, be examined cautiously, given the risk of fostering a logic of offloading by selective schools of pupils with difficulties towards schools that would be rewarded to treat these difficulties. Indeed, such reasoning is supported neither by the government nor by a scientific agreement on its effectiveness.

In Flanders

Many similarities still persist between the education systems of Flanders and the FWB. Some major differences can be noted concerning the issue of equity in education in Flanders, compared to the FWB:

• A history of integrating variables such as a command of the Dutch language and immigrant background (the latter often referred to with the widespread term 'allochtone') in the targeting of compensatory policies. • A direct collection of disadvantage indicators by a registration system.

• A tradition of scientifically evaluating the measures to a much greater extent than in the FWB. • A progressive mainstream integration into regular educational legislation and funding of compensatory policies and measures aimed at creating equal opportunities.

The first compensatory policies to have been implemented in Flanders targeted pupils from immigrant background and pupils who had a poor command of the Dutch language [START_REF] Friant | Priority Education Policies in Belgium: Two Modes of Regulation of the Effects of a Market Logic[END_REF]. They were followed by an 'extended care' policy similar to the positive discrimination policy of the FWB, mainly targeting schools enrolling pupils from underprivileged background. These policies were merged in 2002 into a single, more ambitious framework, which is still operational at the time of writing: the Equal Education Opportunity Act (referred to as GOK, from its Dutch name 'Gelijke Onderwijskansen').

Like ED in the FWB, GOK is an indirect policy: the final target-group of these policies are the underprivileged pupils, but governmental actions are directed towards schools (Poesen-Vandeputte & Nicaise, 2012). Extra means are given to schools according to the concentration of underprivileged pupils they enrol (see annex 2). The resource targeting is based on objective, measurable criteria indicating the socioeconomic background of the pupils: poorly educated mothers, jobless households, travelling households, children placed in institutional or foster care and non-Dutch-speaking households. These indicators are collected using an extensive registration and control system at the pupil level including questionnaires for parents. The total amount of extra funding allocated this way approaches 4% in basic education [START_REF] Friant | Priority Education Policies in Belgium: Two Modes of Regulation of the Effects of a Market Logic[END_REF].

In contrast with the FWB, where evaluation is lacking, there is an evaluation of many dimensions of the GOK policy in Flanders (see Poesen-Vandeputte & Nicaise, 2012 for a comprehensive synthesis). At the level of targeting, an a priori evaluation [START_REF] Bollens | Zorgverbreding in het basis-en secundair onderwijs: een zoektocht naar financierigscriteria[END_REF] showed that an individual registration system, even if it is rather complex, is more accurate in targeting resources than the use of geographical or approximate indicators. This way of targeting is, however, not perfect, as social background questionnaires can be perceived as intrusive by parents, schools can complain about the burden of paperwork, and a risk of fraud exists. An a posteriori evaluation of the accuracy of targeting by Poesen-Vandeputte & Nicaise (2010) showed that the GOK criteria can correctly identify pupils at risk of failure, but miss approximately 15% of underprivileged pupils who are socio-emotionally at risk.

There are several evaluations of the effectiveness of the GOK policy in Flanders, although evaluating such a policy is methodologically extremely difficult. Keeping in mind that the main goal of the GOK policy is to improve the quality of schooling in such a way that the results of pupils of the target group approach the average, an overall conclusion of these evaluations is prudently positive (Poesen-Vandeputte & Nicaise, 2012). For example, a research by [START_REF] Ooghe | De "gelijke onderwijskansen (GOK)" -finaneciering: Werkt ze? Voor wie? En wat kunnen we eruit leren?[END_REF] showed a positive effect of the GOK funding on the cognitive results of targeted pupils. However, pupils with learning disabilities at the beginning of their school career are helped little, if at all, by the GOK funding. Another goal of the GOK policy is to act upon the school career of underprivileged pupils: with the GOK policy, the government hopes to reduce grade repetition, the 'waterfall system' and orientation towards specialized education. These effects have not yet been studied as such. However, monitoring indicators show an increase in reorientation towards specialized education (Van Landeghem & Van Damme, 2001; see annex 3), a result which could be interpreted as a failure of the GOK policy to reduce these negative effects (Poesen-Vandeputte & Nicaise, 2012).

Regulation of enrolment procedures

Compensatory policies alone do not seem to solve the problem of the important inequalities that persist in Belgian education systems, as well in the FWB as in Flanders, where partially similar measures are taken. Indeed, studies on segregation in Belgium show just how much each of these two education systems is segregated, and encourage taking seriously the differences that can exist between schools, both concerning the inequalities of results and the socioeconomic composition [START_REF] Agirdag | Segregatie in het basisonderwijs: geen zwart-witverhaal[END_REF][START_REF] Baye | Un ensemble d'indicateurs pour mesurer l'équité des 25 systèmes éducatifs de l'Union européenne[END_REF].

School segregation is considered, by the scientific community as well as by the government, as a major problem that has to be tackled. From a philosophical point of view, it is not desirable to have an education system that separates children according to social group, be it socioeconomically or ethnically defined. What would be the attitude of these children towards life in society when they have completed schooling? From a pedagogical point of view, there is scientific consensus on the negative effects of segregation. Numerous studies have shown that peers play an important role in a pupil's learning, concentrating children with difficulties thus has an aggravating effect [START_REF] Thrupp | School composition and peer effects[END_REF].

In Flanders, however, some studies show mixed results on the effects of segregation, possibly because segregated schools are also those receiving extra means from the GOK policy, which possibly improves their performance [START_REF] Poesen-Vandeputte | Balans van het evaluatieonderzoek van het gelijke nderwijskansenbeleid in Vlaanderen (Onderzoeksrapport[END_REF].

Assuming that free school choice is one of the parameters contributing to segregation, it should be possible to regulate this free school choice by altering school enrolment policy. The regulation of school enrolment procedures has consequently been applied, in different ways, in both the FWB and in Flanders.

In the FWB, acknowledging the extensive socioeconomic segregation existing in the education system, the Government set out to encourage social mixing within secondary schools, in particular through the 'Contrat pour l'Ecole' (Gouvernement de la Communauté française de Belgique, 2005).

The motivation was to ensure that all parents receive truly identical treatment (setting up an enrolment record in all schools, managing enrolment according to common and identical rules avoiding favouritism) not assured before.

The regulation of enrolment procedures began in 2007. It was followed by a 3-year period of turmoil with the promulgation of a new decree each year. This was the consequence of the bad reception by a part of public opinion of any measure they interpreted as an unacceptable reduction of their freedom of choice. The first idea was to apply a 'first-come, first-served' principle. The secondary schools had to keep a register of available spots and requests for enrolment, keeping track of each request in order of arrival, starting from a date known to everyone. This 'enrolment law', produced spectacular effects in the media, analysed in depth by [START_REF] Delvaux | Débat sur la régulation des inscriptions scolaires en Belgique francophone: où se situent les désaccords? Les Cahiers de Recherche en Éducation et Formation[END_REF]. A 'social mixing decree' was applied the following year, introducing, in the few highly popular schools in which demand exceeded offer, some priority rules according to SEI and distance travelled, plus a random draw for the extra demand. This idea of random drawing fuelled a feeling of injustice for some parents. Moreover, strategies of multiple registrations caused major problems and dramatically reduced the chances of satisfying parents' preferences. The enrolment procedure that is in application at the time of writing was set up in 2010. In order to correct the problems of the previous version, random drawing was abandoned. Parents' preferences are maximised by asking them to rank several schools, and enrolment management is centralized by a commission to avoid multiple registrations. These procedures are still contested by some parents, but its application since the start of the school year 2010-2011 has been carried out without major problems.

Unfortunately, as seems too often the case in the FWB, there is an obvious lack of evaluation of the effects of these measures on desegregation. It can be argued that it is too soon to evaluate these effects. However, given the modest scope of these measures, one should not expect a spectacular desegregation effect to be observed.

The application of a regulation of enrolment in Flanders is interlocked with the GOK policy. As in the FWB, it has undergone a certain number of modifications since its implementation. Beginning in 2002, there were only two categories of pupils with a priority at registration: siblings and Dutchspeaking pupils in Brussels. In 2005, a priority period of registration for indicator-pupils was implemented. Finally, a new decree regarding enrolment procedures was promulgated in 2012. Schools from the same area must work together in a 'local consultation platform' (LOP), which regulates school enrolment in order to achieve desegregation. To do so, a system of 'double quota' is implemented: according to their status (indicator-pupil or not), pupils are registered in two different contingents. In each school, a certain number of spaces are reserved to each contingent of pupil so as to achieve a more even repartition of privileged and underprivileged pupils among schools in the same LOP (Poesen-Vandeputte & Nicaise, 2012). For example, if an area is constituted of 30% underprivileged pupils and 70% privileged pupils then each school of this area should reserve 30% of their available spaces for underprivileged pupils and 70% of their available spaces for privileged pupils.

It is difficult to evaluate the exact effect of the GOK policy on school desegregation, because it has undergone a certain number of changes since its beginning. However, a monitoring of segregation in Flanders over a period of 10 years (2001-2002 to 2011-2012) [START_REF] Wouters | De evolutie van schoolse segregatie in Vlaanderen[END_REF] shows an increase in segregation of indicator-pupils between schools rather than a decrease. This could be interpreted as a failure of the GOK-policy to reduce segregation up until now. An examination of the evolution of segregation in areas where a central registration procedure resembling the 2012 rules was implemented also showed mixed results in terms of desegregation [START_REF] Wouters | De evolutie van schoolse segregatie in Vlaanderen[END_REF]. A reexamination of the evolution of segregation in the future should show how much the new registration rules have had an effect on desegregation.

Promoting access to higher education

There is a strong political will in Belgium to promote access to higher education to all categories of the population. In this regard, financial assistance is available to individual students according to their (or their parents') income. Moreover, if the registration fee in 2013 for a year of study at the university in the FWB is a maximum of 835 euros for mainstream students, it is free for students from lowincome families fulfilling the conditions to obtain financial aid. The latter category of students is far from insignificant, ranging between 11% and 25% at the university level according to the institution [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF]. These students also receive the mandatory course hand-outs for free.

These measures, however, are not sufficient to reduce the association between access to higher education and variables such as socioeconomic status, handicap and the type of curriculum followed in secondary education [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF]OCDE, 2012). Inequality of results also adds its effects to this inequality of access, academic success being linked with these latter variables [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF].

Adult education

In Flanders and in the FWB, adult education falls under the competence of various institutional levels (federal state, community or region) and several ministries (education, work, agriculture). The institutions are quite heterogeneous, giving formal adult education, non-formal adult education and prison education (Vermeersche & Vandenbroucke, 2009). All these policy initiatives aim at answering the needs of employers but also giving adults better chances of social and professional inclusion and promoting personal accomplishment.

Formal adult education falls within the competence of the ministry of education of each community. Its main component is "social advancement education" (now called "continuing education" in Flanders). Vermeersche and Vandenbroucke (2009) give a good description of this type of adult education "This is a broad and varied type of education for all interested adults. It aims at imparting knowledge, improving skills and attitudes. Most of the issues covered by this form of education are oriented towards people's profession (business related courses, vocational courses), although a lot of them are also leisure-related or focused on functioning in society, or are both (like language courses). Social advancement education is the largest sector within the Flemish adult education sector (De Meyer, 2006). There are over 250 000 course participants each year. Before they can enrol, they must have finished full-time compulsory education." (p.11) "Second chance education" is a part of social advancement education enabling adults to obtain a diploma of secondary education they missed out by leaving compulsory education (Vermeersche & Vandenbroucke, 2009, p.12).

Moreover, there exist in Flanders a number of centres for adult basic education focusing on semi-or unskilled adults missing the competences taught in primary or secondary education. All courses are free of charge. They are mostly followed by low-educated immigrants learning Dutch as a second language, but other courses are also offered (Vermeersche & Vandenbroucke, 2009, p.12).

Section 3. Proposals for reforms and specific measures

Flanders and the FWB being two distinct education systems, it is difficult to propose reforms and specific measures that could apply to both. Both try to promote more equity by applying reforms that are sometimes similar, but not always with the same timing.

Flanders is now at the beginning of a new period with the integration of the former GOK policy into the mainstream educational legislation. This means that, beginning in the school year 2013-2014, the redistribution of resources is automatically integrated into the general funding of education. The pupil registration rules have also changed with the introduction of the 'double quota' procedure for the school year 2013-2014. Moreover, an extensive reform of secondary education has been debated during the last few years. From an equity point of view, this reform proposes measures solving the problem of the 'waterfall system' at the core of many equity issues. For that problem, the reform proposes a comprehensive first-level school qualification, with the first choice of course of study delayed until the age of 14. In addition, it is proposed to break down the dividing walls between general, technical and vocational curricula by the introduction, starting in the second stage, of five cross-domains of study (science and technology; language and culture; economics and organisation; art and creation; welfare and society). Each school would have to propose, for at least one domain, curricula that until now belong to general, technical and vocational education. This would be an important measure to reduce academic as well as socio-economic segregation between schools.

The negotiations for the reform of secondary education in Flanders ended in June 2013 with the production of a 'master plan' (Vlaams Parlement, 2013) paving the way for the reform. This 'master plan', however, does not seem to be as ambitious as the first propositions were. The comprehensive first degree until the age of 14 is, in fact, challenged by the choice of a basic option at 13 and the logic of 'domains' breaking down dividing walls between curricula has not been totally adopted, leaving to the schools the freedom to be more 'technical-vocational' or more 'general'.

This reform of secondary education should improve equity in the Flemish system, although we think the reforms first proposed by the Flemish minister of education Pascal Smet (2010) were more promising in this regard. Future reform proposals in the FWB education system could take inspiration from the Flemish example, with the relative advantage (for the implementation of reforms) that, while the education system of the FWB is known to be under-performing, there is a more widespread consensus that it must be improved. For example, an application of the 'double quota' registration system could also be considered for the FWB, especially since a reflection on school catchment areas was carried out some years ago with, until now, no political follow-up [START_REF] Delvaux | Les bassins scolaires: de l'idée au projet. Propositions relatives aux domaines d'intervention, aux instances et aux territoires[END_REF].

Especially in the FWB, we have found a lack of evaluation of the effects of the measures taken to enhance equity of the education system. At the moment of writing, there is no evaluation of the effectiveness of the compensatory policies implemented in the FWB, nor is there any assessment of the desegregation effects of the regulation of enrolment procedures. There is also a great need to better understand 'what works' in terms of pedagogical actions that could be implemented in ED-schools.

Setting up scientific evaluations of these policies would, in this respect, be an important measure in itself.

Finally, measures improving access to and success in higher education should also be implemented. In this respect, a change in the funding of higher education institutions in the FWB according to the so-cioeconomic status of their students has been examined [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF]. However, these measures are dependent on what happens at the level of secondary education, as it is known that, depending on the curriculum followed and the school attended, access and success in higher education can vary greatly [START_REF] Demeuse | Etude interuniversitaire portant sur le financement complémentaire et différencié des institutions de l'enseignement supérieur en Fédération Wallonie-Bruxelles[END_REF].

Section 4. Conclusions

Belgian education systems have a common history and many common traits. They face partially similar challenges to which they give partially similar solutions. Equity issues in compulsory education are mainly treated by compensatory policies modulating the allocation of resources to schools according to their socioeconomic composition and by the regulation of enrolment procedures aimed at reducing socioeconomic segregation between schools. However, few measures have until now addressed the 'waterfall system' in place in secondary education, which is at the core of the creation of equity issues in both systems. The future reform of secondary education in Flanders will head in this direction, although not as much as was first foreseen.

Other future challenges include the consideration of equity issues in higher education. Access to higher education has widely opened since the last decades, but still remains unequal. Moreover, as success in higher education is strongly linked to socioeconomic variables, a resource reallocation on the model of the compensatory policies taking place in secondary education could be foreseen.

Annex 1.

Friant, Derobertmasure and Demeuse (2008) showed the following repartition of schools in FWB (Table 1). The first row of table 1 shows the proportion of pupils concerned. The second row shows the average socioeconomic index (SEI) of each type of school.

The socioeconomic index is based on the student's district of origin (the notion of district is a statistical division of the territory (Demeuse, 2002, p. 219). A synthetic socioeconomic index score is assigned to each district in Belgium, on the basis of 11 variables within the framework of six domains (income per inhabitant, level of the certificates, unemployment rate, employment rate and proportion of people receiving welfare, professions, comfort of housing). Thus, each student is assigned the socioeconomic index score of the district where he lives and somehow brings this index score to the level of the institution. From a statistical point of view, this is a normal distribution metric variable that varies between 3.5 and 3.5. It is recalculated every 3 years on the basis of the latest statistics available.

Annex 4 .

 4 Distribution of pupils accross networks in the FWB and in Flanders Distribution of pupils accross networks in Flanders and FWB (adapted from Flemish Ministry ofEducation and Training, 2013 pp. 12 & 18 and Fédération Wallonie-Bruxelles & ETNIC, 2012, p.77)

Table 1 -

 1 Average SES according to the type of school inFWB (2005FWB ( -2006) )

		Academic Mixed Technical/vocational
	Percentage of pupils 27,3%	60,1% 12,6%
	SEI	0,38	-0,04	-0,23

There is no adequate English translation of this expression ED. It approximately means 'differentiated funding', although it has a broader meaning, including pedagogical aspects.

ACKNOWLEDGEMENTS

The author would like to thank Mayke Poesen-Vandeputte (HIVA -KU Leuven) and Sally Power (Cardiff University) for their very helpful comments and Hugh Parker (UMONS) for his proofreading of my English. Annex 3. Percentage of pupils of age 11 attending special education in Flanders according to the year of birth (Van Landeghem & Van Damme, p. 3). J = percentage of the boys' cohort M = percentage of the girls' cohort J+M = percentage of the total cohort

Annex 2.

Number of extra GOK-teachers per school according to the proportion of GOK-pupils in the school during the first GOK-cycle (2002GOK-cycle ( -2005) ) in fundamental education (Ooghe, 2011, p.2)


玛瑙科研组 玛瑙科研组 是什么? 是什么?

 Joint team

[

  Two deformation fields  Deform gradients & images  Deform brush footprints TEAM [Vergne et al. -SIGGRAPH 2012] Based on new relief analysis  Non-local: features in neighborhood  Multi-direction: better anisotropy / filtering  Multi-scale: feature size [Ammann et al. -EGSR 2012] Visualization of underground pipelines in video streams  With visually correct occluding order  Without 3D geometry of the real environment Artistic painting on a street Kalkofen et al. 2007] [Zollmann et al. 2010] Video segmentation [Zhong et al. 2009]  Separation of front and back faced surfaces To preserve the context continuity  Smooth outside using Gaussian filter  Smooth inside using cross bilateral filter [Eisemann et al. 2004] Better visualization of occluding order  Do not require 3D geometry of the real environment

AR Conclusion LaBRI LP2N Our approach: beyond Computer Graphics

	Real World		Process	Virtual World
		Optics	Digital	Digital Scene
	3D real scene +	Acquire / Model
	Human user	Render / Display

 Goals  Study, model, acquire interactions between light, shape and matter  Take into account observers (humans or sensors)  4 axes  Analysis and Simulation  Acquisition and Display  Rendering, Visualization and Illustration  Creation and Edition TEAM Ex. TEAM A

global view but specialized of processes

 Real World:  Physics and Optics laws  Human abilities  Virtual World: models &

algorithms Conclusion Ex. AR Our approach: beyond Computer Graphics A global view but specialized of processes  Real World:  Physics and Optics laws  Human abilities  Virtual World: models & algorithms Acquire / Model Render / Display TEAM Real World

	Members
	Xavier Granier Inria Research Scientist		Pascal Barla Inria Research Scientist
				Gael Guennebaud
				Inria Research Scientist
		Process	Virtual World
		Optics	Digital	Digital Scene Romain Pacanowski
				CNRS Research Engineer
	3D real scene
	+
	Human user
	Ex. AR	Conclusion

Christophe Schlick

Professor @ Univ. Bordeaux

Jannick Rolland

Professor @ Rochester & Optics Institute

Patrick Reuter

Assistant Professor @ Univ. Bordeaux

http://manao.inria.fr http://www.cad.zju.edu.cn/