Victor Désangles

Guillaume Bousselin

Alexandre Poyé

Nicolas Plihon

Rotation and shear control of a weakly magnetized plasma column using current injection by emissive electrodes

The evolution of the radial profile of the rotation of a weakly magnetized plasma column is investigated experimentally in a radio-frequency Argon plasma at low pressure when a strong electron current is emitted by large emissive cathodes. Current injection from large emissive cathodes over a background plasma column (with a plasma density of a few 10 18 m -3 ) is characterized. Radial scans of the ion-velocity show that a continuous control of the rotation profile may be obtained using two spatial configurations for the locations of the emissive cathodes (either in the center or at the edge of the plasma column). The rotation profile results from the electric drift velocity, damped by drag exerted on the ions. We demonstrate that the evolution of the rotation profile with the injected current is then controlled by the modification of the plasma potential profile in the presence of strongly emissive cathodes.

Introduction

Understanding and controlling the rotation in plasmas has a tremendous importance for an extended variety of plasma regimes. In the context of astrophysical plasmas, rotation and shear are essential ingredients in the context of the dynamo instability [START_REF] Rincon | Dynamo theories[END_REF] or the magneto-rotational instability [START_REF] Lesur | Magnetohydrodynamics of protoplanetary discs[END_REF]; the control of the rotation profile is thus a key ingredient in experiments dedicated to study basic astrophysical processes [START_REF] Forest | The Wisconsin Plasma Astrophysics Laboratory[END_REF][START_REF] Flanagan | Weakly Magnetized, Hall Dominated Plasma Couette Flow[END_REF][START_REF] Plihon | Flow dynamics and magnetic induction in the von-Kármán plasma experiment[END_REF][START_REF] Terasaka | Flow structure formation in an ion-unmagnetized plasma: The HYPER-II experiments[END_REF]. In the context of technological plasmas, it has been known for a long time that sheared poloidal rotation leads to turbulence reduction in fusion devices [START_REF] Biglari | Influence of sheared poloidal rotation on edge turbulence[END_REF][START_REF] Burrell | Effects of E × B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices[END_REF]. At smaller scales, the effect of E × B rotation has an impact on several promising technological fields, such as plasma propulsion and plasma processing [START_REF] Kaganovich | Physics of E ×B discharges relevant to plasma propulsion and similar technologies[END_REF], or centrifugal separation [START_REF] Zweben | Plasma mass separation[END_REF].

A large number of studies have been dedicated to study how boundary conditions may change the rotation profile in plasmas. Most of these studies focused on the influence of the biais of cold limiters, concentric rings or grids on the rotation profiles and on the rotation shear profiles of plasma columns or plasma torii [START_REF] Hooper | Nonambipolar radial particle transport in a tandem mirror[END_REF][START_REF] Severn | Experimental studies of the rotational stability of a tandem mirror with quadrupole end cells[END_REF][START_REF] Tsushima | Control of radial potential profile and nonambipolar ion transport in an electron cyclotron resonance mirror plasma[END_REF][START_REF] Gueroult | Initial experimental test of a helicon plasma based mass filter[END_REF][START_REF] Schaffner | Turbulence and transport suppression scaling with flow shear on the Large Plasma Device[END_REF][START_REF] Desjardins | Dynamics of flows, fluctuations, and global instability under electrode biasing in a linear plasma device[END_REF][START_REF] Brochard | Transition from flute modes to drift waves in a magnetized plasma column[END_REF][START_REF] Terasaka | Flow structure formation in an ion-unmagnetized plasma: The HYPER-II experiments[END_REF]. Fewer studies investigated the effect of emissive cathodes on the control of the velocity profile and on the rotation-shear profile. Following the pioneering studies in the late 1980's [START_REF] Intrator | The virtual cathode as a transient double sheath[END_REF][START_REF] Taylor | H-mode behavior induced by cross-field currents in a tokamak[END_REF], the community showed recently a renewed interest in this topic [START_REF] Moon | Control of electron temperature and space potential gradients by superposition of thermionic electrons on electron cyclotron resonance plasmas[END_REF][START_REF] Plihon | Flow dynamics and magnetic induction in the von-Kármán plasma experiment[END_REF][START_REF] Jin | Plasma flows generated by an annular thermionic cathode in a large magnetized plasma[END_REF]. In this article, we investigate in detail the scheme proposed in [START_REF] Plihon | Flow dynamics and magnetic induction in the von-Kármán plasma experiment[END_REF] where a background radio-frequency plasma column is stirred using large emissive cathodes inserted in the plasma column.

This article shows that current emission over a background plasma is an efficient way to continuously control the plasma rotation profile. We show that the rotation profile is set by the local value of the electric drift and that current injection modifies the plasma potential profile. Several recent theoretical models have been developed to understand how biased electrodes modify the potential distribution in strongly or weakly magnetized plasma columns [START_REF] Curreli | Cross-field diffusion in low-temperature plasma discharges of finite length[END_REF][START_REF] Gueroult | A necessary condition for perpendicular electric field control in magnetized plasmas[END_REF][START_REF] Poulos | Model for the operation of an emissive cathode in a large magnetizedplasma[END_REF][START_REF] Liziakin | Negative electric potential in a cylindrical plasma column with magnetized electrons[END_REF]. Our experimental investigation provides a set of experimental data in the weakly magnetized regime, which complements the work of [START_REF] Jin | Plasma flows generated by an annular thermionic cathode in a large magnetized plasma[END_REF] in strongly magnetized regimes.

The experimental setup and the plasma diagnostics used is this article are detailed in section 2. Section 3 first presents the operation of the large emissive cathodes over the background radio-frequency plasma column. The ability to continuously control the plasma rotation using strong current emission is then shown. The experimental rotation profiles are then analyzed in section 4 in the framework of plasma drifts perpendicular to the magnetic field, strongly damped by collisions. The azimuthal dependence of the rotation profile and the effect of the central anode are discussed in section 5. Finally, concluding remarks are given in section 6.

Experimental setup

Experimental apparatus

The experimental setup consists of a magnetized plasma column, described in details in [START_REF] Plihon | Flow dynamics and magnetic induction in the von-Kármán plasma experiment[END_REF], and whose main characteristics are recalled here. The plasma is created by a radio-frequency inductive source made of a 3-turns helicoidal coil wrapped around a 11-cm inner diameter borosilicate bell jar. The antenna is powered by a 3.3 kW radio-frequency (r.f.) power supply running at 13.56 MHz through a manual L-type matching box [START_REF] Lieberman | Principles of Plasma Discharges and Materials Processing[END_REF].The plasma then enters a 80 cm long, 20 cm in diameter grounded stainless-steel cylinder -the z-axis being defined as the axis of the cylinder, while x is the horizontal axis and y the vertical axis (see Fig. 1). Argon gas is injected through a puffed valve at the top of the experiment, close to the source, in the plane z = 16 cm and is pumped down by a primary pump and a turbo-molecular pump located on the side of the experiment, further away from the source, in the plane z = 49 cm. Working pressures are in the milliTorr range, while base vacuum is routinely below 10 -6 Torr (1.4 ×10 -4 Pa). The plasma is confined by an axial magnetic field generated by a set of three Bitter coils located around the vessel in the planes z = 3, z = 29 and z = 69 cm. Each coil is composed of one hundred copper rings of 26 cm inner diameter and 58 cm outer diameter, generating a 50 turns coil of thickness 11 cm. All coils are powered by the same constant current and produce a field up to 1500 G along the axis of the experiment. All results presented in this article were obtained for typically 1kW of r.f. power, magnetic fields of the order of 100 G, and pressure around 1 mTorr, leading to plasma columns with densities of a few 10 18 m -3 electron temperature of a few eV and radial extension R of typically 5 cm (see section 2.2). In this context, the electrons are fully magnetized, while the ions are weakly magnetized -which is why we call theses regimes weakly magnetized. Indeed the ion Larmor radius is of the order of 2 cm (i.e. 0.4 R) and the ion-neutral collision frequency is of the same order of magnitude as the ion cyclotron frequency.

The goal of this article is to investigate and demonstrate the ability to control the rotation profile of the plasma column when inserting large emissive cathodes in the plasma column. The operation of the emissive cathodes is detailed in section 3.1; it consists of a tungsten filament heated up to 2650 K and negatively biased to emit a few amperes in the plasma. The emissive cathodes may be inserted in the center of the plasma column or at mid-radius. One configuration studied here consists of a single cathode in the center (see Fig. 1 g)) and the other consists of two cathodes located at x = ±3 cm and an anode in the center (see Fig. 1 h)). The electrical boundary conditions of the end plates of the cylinder are chosen insulating: an alumina ring (110 mm inner diameter, 197 mm outer diameter) is installed at z = 0 cm and a borosilicate disk (195 mm outer diameter) is installed at z = 80 cm. The current flows in the presence of strong electron emission from the cathodes are discussed in Section 5, but we summarized here the overall picture. The electrons emitted by the cathodes are strongly magnetized and lead to the formation an axial electron beam radially and azimuthally localized at the cathode location. The cathode current is thus balanced by an ion current, driven towards the cathode. In the presence of a single cathode, this means a radially inward current. In the configuration with two off-centered cathodes and an anode this corresponds to a radially outward current in the central region, and a radially inward current in the outer region (for radii larger than the location of the cathodes).

To keep the whole apparatus in a steady thermal state, the operation of the plasma is pulsed: the plasma is sustained over typically 1 second, during which data are acquired, with a repetition period of typically 30 s. Note that when emissive cathodes are used, the heating power supplies are always kept on, which maintains a high temperature of the tungsten filaments. The biasing power supplies are powered only when the plasma has been fired by the r.f. power supply. The whole experiment is fully automated to allow high repeatability and reproducibility of the plasma. The level of shot to shot reproducibility was ±0.6% for the ion saturation current of a Langmuir probe, with a standard deviation of 0.2% (estimated from a series of 40 shots) and ±50 mV for the plasma potential from an emissive probe, with a standard deviation of 13 mV (estimated from a series of 20 shots). The probes are inserted in the measurement plane at z = 49 cm, either along the x or the y-axis using motorized translators. Diametrical scans of the plasma parameters are acquired sequentially: each spatial point has been acquired during one plasma-pulse, and the probe is translated between two pulses.

Experimental methods

Plasma parameters reported in this article were measured using electrostatic probes: plasma density and electron temperature from Langmuir probes, plasma potential from emissive probes and ion velocity from Mach probes [START_REF] Désangles | Forçage à grande échelle d'une colonne de plasma faiblement magnétisée: influence d'une cathode émissive de grande taille[END_REF]. The Langmuir probes are composed of a single tip made of a 1 mm long 0.2 mm tungsten wire enclosed in a single alumina probe shaft of 1.5 mm outer diameter and 0.8 mm inner diameter. The current-voltage characteristics [START_REF] Chen | Lecture Notes on Langmuir probe diagnostics[END_REF] are measured using a National Instrument Source and Measure Unit PXIe-4139. The Langmuir probes were not r.f. compensated, but previous studies showed that, in the range of parameters used for this study, r.f. compensated Langmuir probes [START_REF] Sudit | Rf compensated probes for high-density discharges[END_REF] showed similar results to uncompensated Langmuir probes. The plasma density is computed following the method proposed in [START_REF] Chen | A floating potential method for measuring Ion density[END_REF]. The emissive probes [START_REF] Sheehan | Emissive probes[END_REF] are made of a 8-mm long loop of 0.2 mm diameter tungsten filament held by a two bore alumina shaft 6 mm outer diameter. The filament is made emissive by Joule heating: a home-made constant-current controller delivers up to 8 A from a 12 V battery. The heating current is controlled with an uncertainty of ± 0.1 A, leading to a ± 0.25 V uncertainty on the measured plasma potential. The heating current is evaluated for each set of experimental parameters following the method proposed in [START_REF] Kemp | Plasma potential measurements by electron emissive probes[END_REF] and is kept constant for a diametrical scan. The Mach probes are made of two 4 mm diameter and 0.1 mm thick Tantalum disks back to back to each other, embedded in a 8 mm diameter ceramic head, following the design described by [START_REF] Weisberg | Pursuing the Plasma Dynamo and MRI in the Laboratory : Hydrodynamic Studies of Unmagnetized Plasmas at Large Magnetic Reynolds Number[END_REF]. The probe head is held by a two-bore ceramic shaft of 4 mm outer diameter. Both Tantalum disks are biased at -60 V with respect to the grounded vessel by two independent DC power supply, and the flowing ion saturation current is measured using shunt resistors. The ion flow velocity is then obtained from the logarithm of the ratio of the ion saturation current density measured on the collector facing the ion flow (J sat,up ) to the ion saturation current density measured back to the flow (J sat,dn ) [START_REF] Chung | Mach probes[END_REF] as

V i = C s K m ln J sat,up J sat,dn
, where C s is the sound speed (assessed for the different plasma conditions in the experiment and taken uniform over the plasma and equal to 3500 m.s -1 ) and K m is a calibration factor taken from PIC and fluid simulation results available in the literature [START_REF] Chung | Mach probes[END_REF]). In the case of unmagnetized ions (ion Larmor radius greater than the probe dimension) and cold plasma (T i < 3T e ), we use the recommended and commonly used [START_REF] Chung | Mach probes[END_REF][START_REF] Collins | Stirring unmagnetized plasma[END_REF]) value is 1.34. The other sources of uncertainties on the estimate of the ion velocity by Mach probes are respectively the evaluation of the collection area, the probe angular position relative to the azimuthal flow, the influence of an eventual axial flow [START_REF] Shikama | Practical formula for Mach number probe diagnostics in weakly magnetized plasmas[END_REF]. The influence of the collection area is corrected by a systematic procedure averaging two 180 degrees symmetric measurements (one face facing the flow, and then back to the flow). The second issue is mitigated by the development of a protractor on the probe mechanical feedthrough flange. From calibration measurements, we estimate the uncertainties over the measured velocity to be smaller than 100 m.s -1 for our experimental setup. We adopt here a conservative approach and chose to keep errorbars of 100 m.s -1 , including uncertainties related to drift of plasma conditions, probes conditions and probes perturbations. We note that, due to different geometries of our probes, the spatial averaging of the measurements varies from 1 mm for the plasma density and electron temperature to 4 mm for the plasma potential and the ion velocity.

Typical background plasma parameter profiles

Figure 2 displays diametrical scans of the plasma density n, electron temperature T e and plasma potential Φ p , measured along the x-axis in the plane z = 49 cm, for a typical set of experimental control parameters (120 G, 1 kW and 1 mTorr), showing a plasma column with a typical radial extension R ∼ 5 cm. This configuration is the reference plasma background case, over which we investigate the effect of current injection from large emissive cathodes. This reference background plasma case will be labeled 0-K in the remaining of this article, for no-cathode present in the plasma column. We note a weak hollow center on the plasma density, which is likely to be a skin-depth effect of the ionization by the r.f. inductive source [START_REF] Chabert | Physics of radio-frequency plasmas[END_REF]. A slight asymmetry is observed on the plasma parameters profiles, whose origin lies on the geometry of the r.f. antenna (which is not perfectly axisymmetric) and the disturbances due to the presence of intrusive probes †. In the remaining of the article, we analyze the experimental results in a framework where we assume axisymmetric plasma parameters; we therefore introduce a procedure which symmetrized the experimental plasma parameters with respect to the center of the vessel. The experimental data points X(x) are first interpolated and smoothed as X i (x) (the original experimental data points are filtered using a 7-points, first order Savitzky-Golay filter, before being linearly interpolated every 1 mm), and an axisymmetric field X s (r) is computed as

X s (r = a) = 1 2 X i (x = a) + X i (x = -a)
. The steps of this procedure are shown in Fig. 2, resulting in the symmetrized fields shown as dashed lines. All experimental measurements displayed in the remaining of this article have been symmetrized.

Control of the rotation profile using large emissive electrodes

Characterization of current emission by a large emissive electrode

Let us first describe the experimental operation of the large emissive cathodes inserted within the background plasma column in order to drive and control the rotation profile. The large emissive cathode is a 0.508 mm diameter tungsten wire rolled up on itself over 6.25 turns (see Fig. 1 c)). The legs of the filament are mechanically locked in 4 mm diameter copper rods (insulated from the plasma by alumina tubes) which feed the current to the cathode. The cathodes' filaments were bought from Union City Filament (custom design ref. . The cathodes can be inserted in the plasma radially from ports in the z = 16 cm plane. The principle of operation is the following: the filaments (i) are Joule-heated up to 2650 K in order to become strongly emissive, using a heating DC power supply and (ii) are negatively biased with respect to the plasma potential using a biasing DC power supply, typically down to -40 V with respect to ground, in order to emit an electronic current of about 10 A in the plasma. Two different experimental arrangements have been used for the purpose of this communication: one cathode in the center of the plasma (configuration 1K in Fig. 1 g)) and two cathodes off-centered at x = ±3 cm with a grounded anode in the center of the plasma, located at z = 70 cm (configuration 2K in Fig. 1

h).

A strongly emissive regime is obtained when flowing a heating current I h within the filament, typically reaching 20 A (resulting in a voltage drop U h of the order of 18 V, i.e. 360 W of heating power). Both the current I h and the voltage U h of the heating power supply are measured in vacuum and in the absence of plasma. The temperature of the tungsten filament can then be estimated using the calibrated tungsten resistivity [START_REF] Desai | Electrical Resistivity of Selected Elements[END_REF]. This estimate is in excellent agreement with measurements using an optical pyrometer (Raytek RAYMR1SCSF), with uncertainties lower than 10 K. Note that we chose to control the heating of the tungsten filament imposing the voltage of the heating power supply, although, at first sight, the current seems to be the most accurate experimental control parameter. Indeed, when the cathode is in contact with a plasma and left floating (as it occurs for each shot during the ignition phase of the plasma), the voltage drop within the filaments drives currents to and from the plasma, which do not significantly contribute to the Joule heating. In short, this can be understood from the fact that, in the presence of a plasma, only the center of the emissive filament floats at the plasma potential. Half of the filament is at a potential larger than the plasma potential (drawing electrons from the plasma) and half of the filament is at a potential lower than the plasma potential (emitting electrons to the plasma); these extra currents add up to the heating current when the voltage is kept constant, but do not contribute to heating. We checked, from measurements using the pyrometer, that the temperature of the emissive cathode does not increase when the plasma is ignited, supporting our choice for the control of the temperature of the emissive cathode.

During one shot, once the plasma has been ignited, the cathode is biased negatively at voltage U b with respect to ground, using a biasing DC power supply. The voltage bias of the cathode Φ c is defined as the averaged potential over the length of the filament:

Φ c = U b + U h 2 .
The evolution of the bias current I b fed by the biasing power supply to the emissive cathode as a function of the cathode bias is reported in Fig. 3 a) for several values of the cathode temperature. As expected, the bias current is controlled by the temperature of the tungsten filament T and the cathode bias relative to ground Φ c . This current significantly increases as the temperature increases, and exceeds 10 A when the temperature exceeds 2600 K (the ion saturation current of the cold cathode being 280 mA). The emitted current is introduced as

I em (∆Φ, T ) = |I b (∆Φ, T ) -I b (∆Φ, T = 285K)
| with ∆Φ being the potential of the cathode relative to the unperturbed plasma potential (i.e. when the cathode is left floating) ∆Φ = Φ c -Φ p,Iem=0 . The evolution of I em as a function of ∆Φ is displayed in Fig. 3 b). An empirical evolution of the emitted current I em as a function of the cathode temperature T and the bias ∆Φ is well captured by Richardson's law [START_REF] Richardson | Electron Emission from Metals as a Function of Temperature[END_REF], introducing an effective emission area of the filament A eff (∆Φ) as: The effective emission area A eff (∆Φ) takes into account the current of electrons from the plasma, collected at the cathode, which increases as ∆Φ increases, allowing for an empirical prediction of the current delivered by the biasing power supply and injected into the plasma. We stress here that the evolution of the emitted current following Eq. 3.1 does not take into account the shift of the central plasma potential Φ p (r = 0) towards negative values when the cathode is strongly emissive and negatively biased (i.e. Φ c 0). The modification of the central plasma potential Φ p (r = 0) in the presence of strongly emissive cathodes will not be discussed further in this article, but it is worth noting that the shift can reach -14.5 V for a cathode biased at -40 V and emitting 12 A.

I em = A eff (∆Φ) A G T 2 exp - e W k b T , ( 3

Control of the plasma rotation profile

In this subsection, we demonstrate that large current emission from the cathodes allows for the control of the azimuthal flow. As previously introduced, three configurations are detailed in this article. The reference case (labeled 0-K ) corresponds to the background plasma created by the r.f. source for a 120 G magnetic field, a 1 kW absorbed r.f. power, at pressure 1.0 mTorr, whose plasma parameters are displayed in Fig. 2. Two configurations in which the plasma flows of the background plasma are modified by current emission from large cathodes are analyzed here: one configuration in which one cathode located at the center of the plasma column injects current to the vessel wall (referred to as the 1-K configuration in Fig. 1, for one single cathode inserted in the plasma column) and one configuration in which two off-centered cathodes drive current to the vessel wall and to an anode located in the center of the column (referred to as 2-K configuration in Fig. 1, for two cathodes inserted in the plasma column). The emissive cathodes are located in the z = 16 cm plane, while plasma parameters reported in this section were measured in the z = 49 cm plane (heat radiation and high energy electrons emission by the cathodes spoil measurements in the z = 16 cm plane, which are not discussed here).

The background plasma column displays radial gradients of the plasma potential and of the plasma pressure and a rotation profile is expected to emerge from drift velocities. Indeed, a strong azimuthal flow measured using Mach probes, is observed for the reference configuration (0-K ), as displayed in Fig. 4 a) (open black circles). The velocity profile is strongly sheared with a clockwise flow for r < 3.5 cm and a counter-clockwise flow for r > 3.5 cm. We will show in next section that the features of this flow profile is understood from the local electric drift. Inserting floating hot cathodes does not modify the azimuthal plasma flow, as displayed in Fig. 4 a) for the single centered cathode configuration and the two off-centered cathodes configuration respectively labeled 1-K -off and 2-K -off. These flow measurements confirm that floating hot cathodes indeed behave similarly to emissive probes and that, despite the voltage drop U h across the cathode (due to finite resistivity and Joule heating) our large emissive cathodes float at a potential close to the local plasma potential, and do not affect the global plasma equilibrium.

In contrast with floating cathodes, the azimuthal velocity profile is drastically modified for large current emission by the cathodes. Let us first focus on the azimuthal velocity profile in configuration 1-K, for 12 A of emitted current I em , displayed in Fig. 4a) (upper orange triangles). When a large electron current is emitted at the center of the plasma column, the azimuthal velocity is now positive everywhere in the plasma column, i.e. the whole column rotates in the counter-clockwise direction. Electron current injection at the center of the plasma column thus leads to a reversal of the rotation in the center of the column. An opposite situation as been observed in the 2-K configuration: the central part of the plasma column rotates in the clockwise direction (similarly the 0-K configuration), but the amplitude of the flow has been strongly increased, as observed in Fig. 4a) (lower red triangles) when the each of the two cathodes emit 5 A. This shows that the direction of rotation of the ions in the central part of a plasma column can be efficiently controlled by strong emission of electrons from emissive cathodes at specific locations. Surprisingly, the velocity profile in the outermost region of the plasma column is affected similarly, i.e. the counter-clockwise outer rotation is slightly increased by current emission with respect to the 0-K reference configuration. The origin of this effect is still unclear, but, as shown in Section 5, this effect is absent in the vertical plane. A possible explanation could be the interaction, in the horizontal plane, of the large cathode shafts, which are partially grounded at large radii, with the current injection by the cathodes.

In order to quantify the influence of the emitted current, the evolution of the peak velocity V max i,θ for r < 3.5 cm is displayed as a function of the cathode current I K in Fig. 4b) (V max i,θ

is the velocity at zero radial shear, i.e. the maximum velocity for a profile of positive values of V i,θ , such as for the 1-K configuration, and the minimum velocity for a profile of negative values of V i,θ , such as for the 0-K configuration). As a convention, the cathode current is positively defined in the 1-K configuration (i.e. I K = I em ), and negatively defined in the 2-K configuration (i.e. I K = -I 1 em = -I 2 em , where I 1 em is the current emitted by cathode 1). The origin

I K = 0 A corresponds to the 0-K configuration, for which V max i,θ = -200 m.s -1 . As I K increases, V max i,θ
continuously increases, and exceeds 600 m.s -1 when I K = 15 A (upper orange triangles). On the other hand, when I K decreases, V max i,θ continuously decreases (lower red triangles). The scan in emitted current I K reported in Fig. 4b) was obtained with constant heating of the cathode (2650 K) while varying the amplitude of the bias U b typically from -20 to -40 V; i.e. it was obtained following one of the constant-temperature curve displayed in Fig. 3 a). The detailed effect of the ion magnetisation, through the evolution of the amplitude of the magnetic field B is left for future studies, however Fig. 4 c) shows that current injection in the 1-K configuration allows to reverse the rotation profile for several values of the magnetic field B for I K = 5 A. For all amplitudes of the magnetic field, the value of peak velocity V max i,θ (I K = 0) in the reference 0-K configuration is negative (displayed as blue circles in Fig. 4 c)), while the value of peak velocity V max i,θ (I K = 5) in 1-K configuration is positive (displayed as upper orange triangles).

Drift velocity controlled by current emission

Drift velocity damping by collisions

In this section, we now show that the modifications of the azimuthal flow profile can be attributed to the modification of the plasma potential profile. The analysis is developed assuming axisymmetry and thus applied to the 0-K and 1-K configurations, however, a similar approach seems applicable to the 2-K configuration, as discussed in Section 5. Assuming axisymmetry of the plasma column, the momentum equation for the ions leads to an azimuthal ion drift velocity involving an electric drift term V E = (E × B)/B 2 and an ion diamagnetic drift term V D = -(∇P i × B)/(neB 2 ) expressed as:

V i,θ = 1 K (V E + V D ) = 1 K - E r B z + k B T i neB z ∂n ∂r , (4.1)
where K is a factor accounting for the drag exerted on ions. The drag factor K may be expressed as [START_REF] Chen | Introduction to Plasma Physics and Controlled Fusion[END_REF], where ν m is the macroscopic momentum transfer frequency [START_REF] Hagelaar | Modelling methods for low temperature plasmas[END_REF], which reads ν m = ν in + ν iz , and which takes into account momentum drag from ion-neutral collisions through the ion-neutral collision frequency ν in and the creation of ions through the ionization frequency ν iz †

K = 1 + (ν m /ω ci ) 2 (
The ion-neutral collision frequency is evaluated as n n σ in v th,i , where n n is the neutral gas density, σ in is the momentum exchange cross section between an ion and a neutral and v th,i the most probable thermal speed equal to 8kT i /πm i . The values of K have been estimated assuming an ion temperature T i equal to 0.2 eV for the 0-K configuration and equal to 0.32 eV for the 1-K configuration (a value estimated from Laser Induced Fluorescence of the 442.6 nm ArII line [START_REF] Bieber | Measurements on argon ion by tunable diode-laser induced fluorescence in a low magnetic field helicon configuration reactor[END_REF]) and thus the cross-section σ in at 0.2 eV and 0.32 eV [START_REF] Phelps | Cross Sections and Swarm Coefficients for Nitrogen Ions and Neutrals in N 2 and Argon Ions and Neutrals in Ar for Energies from 0.1 eV to 10 keV[END_REF][START_REF] Phelps | The application of scattering cross sections to ion flux models in discharge sheaths[END_REF] . The theoretical estimate of the damping † The additional collision term νiz v in the momentum equation is usually not taken into account when the plasma density is assumed to be constant. Inserting the continuity equation ∂n/∂t + ∇ • (n v) = nνiz in the first-order moment of the Boltzmann equation leads to the additional friction term νiz v for the momentum equation ∂ v/∂t factor K assumes a flat neutral density profile (estimated from neutral pressure measured at the wall), and involves the plasma density averaged between r = 0 and r = 4 cm (using Langmuir probe measurements) and a constant ion temperature over the plasma column. The ionization frequency is estimated from the functional form ν iz = n n K iz , with K iz = 2.34 10 -14 T 0.59 e e -17.44/Te m 3 s -1 [START_REF] Lieberman | Principles of Plasma Discharges and Materials Processing[END_REF]. Assuming a neutral temperature of 350 K and an average electron temperature T e = 4.6 ± 0.2 eV, this leads to values K 0K = 7.2 ± 1 for the 0-K configuration and K 1K = 7.3 ± 1 for the 1-K configuration when the emissive cathode emits 12 A. We stress here that, for the plasma parameters investigated here, the ion-neutral collision frequency ν in and the ionization frequency ν iz are of the same order of magnitude, and thus contribute equally to the damping of the flow (i.e. even if there were no charge exchange collisions, the flow would be strongly damped). We also stress that the value of the drag factor K depends on the exact value of the electron temperature, ion temperature and the collisions crosssections, with an extreme sensitivity on the electron temperature. We now show in next subsection that our experimental results may be interpreted from a damped electric drift.

Local drift computation

Figure 5 a) displays the relative plasma potential profiles V p measured from emissive probes and Fig. 5 b) show the density profiles for configurations 0-K and 1-K for 12 A of current emitted by the cathode. To increase readability, the relative plasma potential V p is defined as V p (r) = Φ p (r) -Φ p (r = 0), with values of the plasma potential at the center equal to Φ p (r = 0) = -1 V for the 0-K configuration and to Φ p (r = 0) = -15.5 V for the 1-K configuration at 12 A of emitted current. Strong electron current emission from a negatively biased cathode at the center thus shifts negatively the plasma potential of the plasma column (the cathode bias was set to U b = -40 V). In addition to the global shift of the plasma potential, the injection of electron current in the center also strongly modifies the shape of the plasma potential profile. The plasma potential profile of the background plasma column (0-K configuration) decreases from the center outward, reaches a minimum around r = 3.5 cm and increases on the outward. The plasma potential profile is in strong contrast for the 1-K configuration: it continuously increases outward, with a localized drop of the potential near the cathode. This leads to a reversal of the local electric field, and thus a reversal of the electric drift velocity between the 0-K and 1-K configurations. Electron emission also strongly modifies the plasma density profiles as can be seen in Fig. 5 b): ionisation from the beam of primary electrons in the central part of the column strongly increases the plasma density in the central part of the plasma column (r 2 cm), which also leads to a reversal of the diamagnetic drift velocity between the 0-K and 1-K configurations.

The computation of electric drift and the ion diamagnetic drift velocities from the experimental profiles of the plasma parameters shows that the electric drift velocity clearly exceeds the diamagnetic drift velocity (see Fig. 5c) and d)). Moreover, the total drift velocity profile is strongly correlated to the experimental ion flow profiles displayed in Fig. 4a). An empirical drag factor K e is introduced by the minimization of the function

f (K e ) = V i,θ -(V E + V D ) /K e .
The experimental ion velocity profiles and the damped drift velocities including the minimization factor K e are displayed in Fig. 5c) and d) for the 0-K configuration (with K 0K e = 6.7) and the 1-K configuration respectively (with K 0K e = 8.9). A good agreement is found between the measured velocity profile and the sum of damped drift velocities, which is dominated by the electric drift velocity. The electron current injected by large emissive cathodes allows to control the profile of the plasma potential and, in turn, the azimuthal velocity profile: large emissive cathodes are thus a very efficient mean to achieve rotation profile control. While the empirical and )

Mach probe V E /8.9

V D /8.9

(V E +V D )/8.9 d) 1-K con guration theoretical values of the drag factor K are of the same order of magnitude their small discrepancy is most probably due to one of the following reasons: an overestimate of the the electric field when measuring the plasma potential profile with the emissive probe (the probe heating current is kept constant over the plasma column radius which likely leads to an overestimate of the plasma potential gradient) or the uncertainty on the renormalizing factors used in the Mach probe signal analysis.

We note here that the ion Larmor radius is of the order of the plasma potential gradient length, and that the conditions for the application of the E ×B drift theory is not strictly fulfilled. The agreement observed between the experimental results and the computed drift velocity calls for the application of the fluid drift theory, though its validity should be confirmed from kinetic or PIC simulations in the presence of collisions.

5. Discussion: 2-K configuration and influence of the central anode 5.1. Azimuthal dependence of the plasma flow in the 2-K configuration Diametral profiles of the ion velocity and of the plasma potential measured along the horizontal axis and the vertical axis are displayed Fig. 6 for several conditions in the presence of two cathodes, inserted in the horizontal plane at location z = 16 cm. As the central symmetry is preserved the symmetrisation procedure was applied to the measurements. The reference case, referred to as 2K-Off, consists of two hot unbiased cathodes in the presence of an anode in the center and is displayed using blue bullets. The 2-K configuration introduced in the previous sections, with two hot, negatively biased cathodes, in the presence of a central grounded anode is shown using red lower triangles and is labeled in this section 2K-On Anode. In the central part of the column (i.e. radial positions lower than 5 cm), the velocity profiles are of similar amplitude along the vertical and horizontal axes. The first observation is that, for the 2K-On Anode case, a counter-clockwise flow larger than the 2K-Off reference case is observed in the central part, along both axes. Although the cathodes are inserted in the horizontal plane, they are efficient to drive an azimuthal flow everywhere in the plasma column. However the central counter-clockwise velocity peak increases from 200 m.s -1 in the 2K-Off reference case to about 400 m.s -1 on the horizontal axis and to only 300 m.s -1 on the vertical axis in the 2K-On Anode case. The plasma velocity increase due to current injection is higher in the horizontal plane than in the vertical plane and the axisymmetry is broken under this current injection geometry. As for the 0-K and 1-K configurations discussed before, the features of the flow are consistent with a strongly damped E × B flow and with the measurements of the plasma potential shown in the lower panels of Fig. 6. The central plasma potential gradient increases from 7.6 V.m -1 in the 2K-Off reference case to 12.5 V.m -1 along the horizontal axis and only to 8.75 V.m -1 along the vertical axis in the 2K-On Anode case. Similarly to the observations made in section 4, a large increase in the plasma velocity at large radius is observed only on the horizontal axis, whose origin may speculatively be attributed to the presence of the large cathode shafts along the horizontal axis.

The radial location at which the electric field corresponds to the radial location at which the azimuthal velocity is zero. Due the coils positions and the ripple of the magnetic field lines in our experiment, the magnetic field line crossing r = 3 cm at the cathode plane (z = 16 cm) crosses r = 3.8 cm at the measurement plane (z = 49 cm). However, the assumption that plasma parameters remain invariant along a magnetic field line does not strictly hold (the plasma parameters at (r, z) = (3, 16) cm correspond to those at (r, z) = (3.5, 49) cm). We thus expect a minimum for the plasma potential for radius around 3.5 cm, which is in fairly good agreement with the data shown in Fig. 6.

Influence of the central anode on the flow

The ion velocity and plasma potential profiles in the presence of two hot biased cathodes in the absence of an anode are also shown in Fig 6 as yellow diamonds, and referred to as 2K-On No Anode. In this case, all the current emitted by the cathodes is collected at the grounded vessel, while 30 % is collected at the central anode in the 2K-On Anode configuration. The first observation is that ion flow in the 2K-On No Anode case is strongly reduced in the central part of the plasma column (at radial positions below ∼ 3.5 cm) as compared to the 2K-Off reference along both the vertical and horizontal axes. Once again, the flow features are in good agreement with the plasma potential profiles. In particular, the plasma potential profile is strongly flattened along the horizontal axis. For radial location larger than 4 cm, the effect of the central anode is weaker. The effect of the central anode can be interpreted as follows: the current of the primary electron beam emitted by the cathodes is balanced by (i) a ion current directed inward from the grounded vessel, at radii larger than 3.5 cm, and (ii) a ion current directed outward from the anode, at radii lower than 3.5 cm, leading to local minimum of the plasma potential around 3.5 cm. In the absence of the anode, only the first contribution of the current leads to the modification of the electric field and of the flow.

In the 1-K configuration, the cathode is located at the center of the plasma column and the current emitted by the cathode is collected at the grounded vessel walls. Since the primary electron beam is strongly magnetized, the global radial current flow likely consists of an ion flow. This leads to a local minimum of plasma potential at the center of the column (see Fig. 5). We also investigated a configuration for which a grounded anode was inserted in the center of the plasma column at location z = 70 cm. In this configuration, 40% of the current was collected at the anode. Surprisingly, for the same current driven by the cathode, the differences measured for the velocity profile and for the plasma potential profile (not shown) in the presence or the absence of the central anode remain lower than the uncertainty of the measurements. The authors believe that more detailed spatial measurements of the plasma potential and modeling are required to provide a detailed understanding of these results.

Conclusions

Current injection from large emissive cathodes, over a background weakly magnetized plasma column generated by a radio-frequency source, was demonstrated to be an efficient way to control the rotation profile and rotation shear of the ion flow. In the range of plasma parameters investigated in the present article, we show that the azimuthal ion flow is effectively controlled by the local electric drift damped by a drag exerted on the ions. The large negative bias of the large emissive cathodes strongly modify the local plasma potential, their operation was analyzed to follow a modified thermionic emission law, allowing to precisely control the amount of injected current. This injected current strongly modifies all plasma parameters, and in particular the plasma potential profile. We showed that the plasma potential profile can be continuously modified by current injection -this allows to continuously control the rotation profile of the ion flow, and the natural background plasma rotation may be reversed or enhanced depending upon the location of the emissive cathodes and the intensity of the injected current. Two physical effect contribute to the damping of the flow on nearly equal grounds: the ion-neutral charge exchange collisions, but also the creation of ions from volume ionization.The efficiency of the ion stirring using emissive cathodes could be increased at lower base pressure, thus requiring the design of optimized radiofrequency source to create high density plasmas below the mTorr range. This work also calls for predicting capabilities of the equilibrium plasma parameter when locally injecting current in order to better understand the driving mechanisms, for instance extending the recent works done for magnetized plasmas to moderately magnetized plasmas [START_REF] Poulos | Model for the operation of an emissive cathode in a large magnetizedplasma[END_REF][START_REF] Liziakin | Negative electric potential in a cylindrical plasma column with magnetized electrons[END_REF][START_REF] Gueroult | A necessary condition for perpendicular electric field control in magnetized plasmas[END_REF]. Beyond the present investigations in quiescent regimes, the influence of large-scale, low-frequency fluctuations of the plasma parameters usually observed in plasma columns on the efficiency of the plasma flow drive is also a crucial question related to the self-organization in plasmas.

Figure 1 .

 1 Figure 1. Experimental setup: a) top-view, b) end-port view. A large emissive electrode modifies the plasma parameters: c) photograph of the emissive filament, and glowing emissive filament when heated up to around 1500 K d) close up, e) when the plasma is off and f) when the plasma is on. Electrical configurations with g) one cathode, and h) two cathodes inserted. See text for details.

Figure 2 .

 2 Figure2. Diametrical scan of n, Te and Φp for a 120 G, 1 kW and 1 mTorr plasma: raw measurements X (open symbols), interpolated data X i (solid line) and symmetrized fields X s (dashed line).

Figure 3 .

 3 Figure 3. a) Evolution of the bias current I b as a function of the bias voltage Φc for various values of the cathode temperature T , b) thermionic emitted current as a function of T for various bias voltages ∆Φ, the inset shows the evolution of the effective area A eff as a function of ∆Φ. See text for details.

  .1) with A G = 6.0 10 5 A.K -2 .m -2 the Richardson constant (Bernhard 1995; Gale & Totemeier 2004), W = 4.54 eV the work function of Tungsten, and k b the Boltzmann constant.

Figure 4 .

 4 Figure 4. a) Radial profiles of the azimuthal velocity V i,θ measured using Mach probes: reference case (0-K ), configuration with a single cathode in the center (1-K ) emitting 12 A and configuration with two off-centered cathodes (2-K ), each one emitting 5 A. Floating hot cathodes configurations are labeled off and emissive cathodes are labeled on. b) Amplitude of the peak velocity peak V max i,θ as a function of the emitted current IK (see text for details). c) evolution of V max i,θas a function of the magnetic field amplitude B for the 0-K configuration (blue circles) and the 1-K configuration (upper orange triangles) for a 5 A emission current.

Figure 5 .

 5 Figure 5. a) Plasma potential (relative to the plasma potential at r = 0) and b) plasma density profiles for the configurations 0-K and 1-K (emitting 12 A). Experimental and computed drift velocities profiles for the c) 0-K and d) 1-K configurations.

Figure 6 .

 6 Figure 6. (left) Horizontal and (right) vertical scans of the (top) ion velocity and (bottom) plasma potential for the three cases in the presence of two cathodes. The cathodes were biased to -27 V and emitting 10 A (5 A per cathode) for the Anode and No Anode cases. See text for details.

† Email address for correspondence: nicolas.plihon@ens-lyon.fr

† This effect is particularly pronounced on the plasma potential scans from the emissive probe. Indeed, the emissive probe shaft is large (5 mm in diameter) and its insertion from one side of the experiment (say x = -10 cm) has a dramatic effect on the measurements made on the other side (x > 0).

Acknowledgements.

The authors are grateful to M. Moulin and M. Tanase for technical support and thank T. Carter, C. Forest, and D. Weisberg for fruitful discussions.

Funding. This work was supported by French National Research Agency under contract ANR-13-JS04-0003-01.

Declaration of interests.

The authors report no conflict of interest.

Data availability statement.

The data that support the findings are available upon reasonable request fom the corresponding author.

Author ORCID.

V. Désangles, 0000-0001-7557-2271; A. Poyé, 0000-0002-0239-0888; N. Plihon, 0000-0001-8874-3674

Author contributions.

V.D and G.B. performed the experiments, V.D, G.B, A.P. and N.P. contributed to analysing data and reaching conclusion. V.D. and N.P. wrote the paper.


Marco Marcon

Massimiliano Pierobon

Augusto Sarti

Stefano Tubaro

Stefano Tubaro 3d Markerless

Andrea Cavallaro

Hamid Aghajan

3D Markerless Human Limb Localization through Robust Energy Minimization

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Gesture tracking and posture estimation require the localization of the human body in the scene and the estimation of each limb position during motion. This process can be considered as a combination of two major components, namely, Model Definition and Pose Estimation. Model definition aims at the moulding of the human body model that best fits to the specific shape and size of the tracked human subject, whereas pose estimation is devoted to the proper model adaptation to the postures and the body joint configurations during the motion evolution [START_REF] Choo | People tracking with hybrid monte carlo[END_REF]. Only a few human motion tracking approaches use images from multiple cameras in order to obtain cues on 3D information. On the other hand, a broad range of applications is based on a single monocular acquisition device,e.g. [START_REF] Bregler | Tracking people with twists and exponential maps[END_REF]. Motion tracking solutions can be parsed into three main classes: marker-based, model-based and model-free. Our aim is the realization of a markerless system able to estimate the human posture evolution exploiting visual features such as colors, edges, silhouettes and textures. The output of such a system is a set of angles relating each limb to each other, submitted to appropriate constraints for each joint (articulations differ in possible rotation angles and angular extensions). Various approaches that explicitly model the human body as an assembly of rigid parts can be found in the literature [START_REF] Ioffe | Probabilistic methods for finding people[END_REF].Most of them adopt a two-stage strategy: a bottom-up detector is first applied on the image in order to extract the candidate parts, then, a top-down procedure is used to properly infer about the joint configuration and to find the assembly that best fits; Dynamic Programming is also frequently used to solve the same problem with greater efficiency; e.g. Lee and Cohen [START_REF] Lee | Proposal maps driven mcmc for estimating human body pose in static images[END_REF] accurately estimate the human 3D pose though the adoption of a data-driven Markov Chain Monte Carlo (MCMC) framework. Image observations of different cues are used to infer possible positions of body joints. They translate these inferences into pose hypotheses though the use of the 'proposal maps' as an efficient way of consolidating the evidence and generating 3D pose candidates during the MCMC search, anyway the need of a proper detection of non-frontal postures requires a good face detection algorithm. Moreover, the computational cost is quite high. In the work of Mori et al. [START_REF] Mori | Recovering human body configurations: combining segmentation and recognition[END_REF], Normalized Cuts algorithms are used to detect salient human body parts. Brute-force approaches are also applied to solve the body parts assembly problem but they need to store templates for all possible configurations, as in an exemplar-based approach. Unfortunately this approach will dramatically increase the computational cost. On the other hand, Ren et al. [START_REF] Ren | Recovering human body configurations using pairwise constraints between parts[END_REF] detect the candidate body parts in a bottom-up fashion through the use of parallel cues, assembled together into body configurations using various pairwise constraints between human body parts. Actually most of the works presented in literature require an initialization phase to define the body geometry of the tracked person and the problem of recovering human body configurations without assuming an a priori knowledge of the scale, pose or appearance becomes extremely challenging since it demands the use of all possible sources of information: The self-occlusion is one of the most hard-to-solve problems in a monocular environment. Poppe et al. [START_REF] Poppe | Towards real-time body pose estimation for presenters in meeting environments[END_REF] use a computer vision-based approach to estimate the body pose of a presenter in a meeting environment. They extract a 2D silhouette and match it against a planar projection of a 3D human body model with 16 Degree of Freedom (DoF). They use skin color to locate hands and head. The algorithm is able to cope with low resolution image sequences from a monocular device. The constraints imposed by Poppe are:

1. the person has to face the camera all the time 2. the presenter is supposed to wear short sleeve attire . In [START_REF] Siddiqui | Robust real-time upper body limb detection and tracking[END_REF] Siddiqui and Medioni describe an efficient system for the detection and tracking of the human limbs. The human model consists of a collection of 2D part models related to the lower and upper limbs, the head and the torso. The individual parts are organized into a tree structure, having the head at its root. The detection of proper visual features is made easier through the assumption that the users wear short sleeve shirts, thus leaving their forearms exposed. The main focus is on the tracking of image regions related to the hands and the forearms rather than on a complete articulated object fitting. Capo et al. [START_REF] Capo | Automatic human body modelling for vision-based motion capture[END_REF] present a computer vision algorithm able to automatically model the human body skeleton. The body is decomposed into its main parts through the computation of the curvature of a B-Spline coming out of a parametrization of the human body contour. They rely on the assumption that the user stands in a predefined pose during a calibration/initialization phase. Our aim is the release of most of the aforementioned constraints estimating body posture from a 3D model obtained from a multi-camera set-up frame-by-frame.

The acquisition set-up

The acquisitions of 3D body models with their temporal evolution were made at our laboratories where a controlled environment is monitored using eight synchronized and calibrated cameras. We adopted the Running Gaussian Average algorithm, directly derived from the work by Wren et al. [START_REF] Wren | Pfinder: real-time tracking of the human body[END_REF], in order to provide a segmentation of the actor silhouette from the image background. This solution stems from a statistical description of the foreground and the background obtained from a collection of the previous frames; This approach provided the best trade-off for accuracy and fast frame processing; obviously, for real environments, especially in outdoor scenes, more complex approaches may be required for accurate model definition. Once several silhouettes of the same subject are simultaneously extracted from different viewpoints, it is possible to provide a reconstruction of the actor volume, or at least an approximation of it. Every pixel within the silhouette can be traced back from the image plane to the 3D environment, exploiting the information on the optical center and the viewpoint direction of the corresponding camera. Thus, the set of all these lines that connect the silhouette to the volume is a cone with the silhouette as its basis. The intersection of all cones coming from different viewpoints is a volumetric object named Visual Hull (VH, in the following), and it is supposed to enclose the actor body (examples are given in Fig. 1. The closeness of the VH to the actor volume

Human Model definition

The posture tracking problem requires the definition of a human body model and its proper adaptation within the actor volume. The human model gives to the algorithm the opportunity of exploiting the a priori information about the human body structure and, therefore, the search space related to possible body part configurations can be reduced through the definition of a set of constraints, such as human body proportions, limb connections and their possible relative motion. The skeleton model defined for our experiments comes as simplified representation of the human skeleton, named stick figure, where the joints are modeled as spheres and the bones as cylinders. Moreover, we used a flesh figure that extends the stick figure with truncated cones and ellipsoids, as shown in Fig. 2, making the model closer to the real human shape. The aim of our work stems in the realization of a robust system able to track human body without making any assumption on the initial actor position. In this situation the skeleton size and the definition of volumes for each limb in the flesh model becomes a challenge. We tackled these problem through the application of the following approach. Starting from the head, whose shape can be clearly distinguished from the rest of the body, the other parts detection proceeds with the torso, the shoulders and the hips. Subsequently, the procedure estimates the positions of legs and then arms, which are often partially or completely adjacent to the torso. The knowledge about the position and the orientation of the other body parts offers some clues about the configuration of arms and legs, thus allowing to cope with adjacency problems.

Anchor points localization

Most of the body parts are localized starting from a geodesic description of the VH surface: the first step is the determination of center of mass C of the VH,it is usually localized in the middle of the torso and is simply computed with the classical center of mass formula C i =

x,y,z iV (x,y,z)

x,y,z V (x,y,z) where i is x, y or z the sum is over the whole Voxel-Set and the function V is 1 if the voxel is inside the VH and 0 otherwise. The next step is the analysis of the surface curvature. In order to obtain an accurate estimation of it the vectors normal to the surface must be accurately computed: due to the discretization of the voxel-set the surface requires a filtering step before normal computation. The approach we followed is based on 3D Sobel filtering applied on the whole voxel-set: The filter is a 3D matrix (a 3 × 3 × 3 cube) where the planes are defined as:

S 1 =   1 2 1 2 4 2 1 2 1   , S 2 =   0 0 0 0 0 0 0 0 0   , S 3 =   -1 -2 -1 -2 -4 -2 -1 -2 -1   (1)
The application of this filter gives the amount of variation (first derivative) in a direction orthogonal to the matrix planes. Defining two other 3D matrices obtained by a 90 degrees rotation along two orthogonal axes of the previous matrix ( 1) is then possible to obtain for each surface voxel the 3 components of a vector normal to the surface itself. The resulting vector is normalized to become a "unit vector": a result is shown in Fig. 3 . The curvature is then approximated for each surface voxel as the average angular displacement of the normals in a neighborhood of the voxel from its normal. If each voxel in the nearest neighborhood would lay on the same plane of the considered voxel then all voxels would have the same normal and the curvature would be 0. The following step is the determination of face; it is easily located since it shows a high variability of the curvature in almost all of its shape and, in particular, in the frontal part. These considerations allow an easy identification of the head and of its frontal part as shown in Fig. 4. We further underline the fact that our algorithm do not use any information about face color and, in general, about textures making this approach robust to illumination changes, actor race and clothing color. Once the face and the center of mass is defined (the two main anchor points in our approach) it is possible to define a map-subdivision of the whole surface based on the geodesic distance from the center of mass. The definition of the 'geodesic distance' we used is derived from the graph theory where the graph G(V, E) is defined with the vertex set V and edge set E, with n = |V | and m = |E|. Each edge e ∈ E has an associated cost (or weight), cost G (e), which is a non-negative number. An xy shortest path P x,y (G) = e 1 , e 2 , ..., e k is a collection of k edges of G forming a shortest path from x to y. The path P x,y (G) can also be defined as a sequence of nodes lying on the path. The length (total weight) of P x,y is denoted by the geodesic distance d G (x, y); further details can be found in [START_REF] Bouttier | Geodesic distance in planar graphs[END_REF]. Examples of the application of this distance definition are given in Fig. 1(right). Good results are obtained also in complex configurations, as shown below, even if it needs to be pointed out that this method suffers from the closed loop geodesic distance problem: in fact, when an arm gets in contact with the torso, the distance obtained from one point belonging to the torso and the distance of the tip of the hand from the center of mass will most likely be equivalent to the euclidean distance, since those two points would be directly connected (see, e.g., Fig. 1(right)). This problem, even if unsolved in the geodesic distance definition is correctly tackled in the model fitting part.

Degrees of

The stick and flesh figure adopted

In Fig. 2 we gave the representation of the stick and flesh figures we adopted that are mainly derived from the pioneer works of prof. Johansonn [START_REF] Johanson | Visual perception of biological motion and a model for its analysis[END_REF] and further developments; the stick figure (in the following SF) is not sufficient to correctly tackle complex poses without any initialization with a reference pose, but since we do not want to add constraints, a second layer based on a flesh figure (in the following FF) is used (similar approaches were followed by [START_REF] Mikic | Human body model acquisition and tracking using voxel data[END_REF]and [START_REF] Magnor | M3: Marker-free model reconstruction and motion tracking from 3d voxel data[END_REF]). We described each articulation using one of these three shapes: a frustum of cone with circular bases (3 DOF, 1 for each radius and 1 for its height) a cylinder with elliptical bases (3 DOF, the major and minor axes and its height) and a sphere (1 DOF, its radius, used just for the head). In table 1 we report the DOF for each articulation. The proposed approach requires a set of assumptions (heuristics) about limbs articulation, flesh and cloth deformation and movement constraints; the main problem can be stated as: the pose detection is the search in the space of possible configurations of the FF where the best fitting with the voxels is achieved. The best fitting will correspond to the minimization of an energy defined as:

E (θ) = voxel-set (V V H ⊕ V F F (θ)) voxel-set V V H (2)
where the sum is made over each voxel of the voxel-set and V ( V H) represents the VH: it is '1' if the voxel belongs to the VH and 1 otherwise. Many constrictions must be enforced to reduce the minimum search in the 43dimensions space. It follows a list of the different types of constrictions we applied to the search and their major effects: distance of joints:

V ( F F )
1. The lengths of each bone must be inside a predefined range which is scaled to the head length detected for the subject. The standard human body proportions are used. This is the base starting point for the search of each joint. 2. Every pair of symmetric bones or muscles is considered with the same size. 3. Inclusion in the voxel set: each bone must fully included in the voxelset.

Assuming the characteristic of the VH to contain the entire volume of the captured subject, a bone which even partly laying outside has an extra highpenalty in the Energy value. 4. Angle checks: shoulders, hips and knee joints implement articulations limits to account for real human motion range. 5. Penetration check: bones defined by the flesh figure should not penetrate each other. This constriction add a further energy penalty to these configurations.

Detection sequence

To reduce computational time and to avoid local minima in the optimal parameters search we followed a branched fitting sequence, starting from the Torso and Head and then moving towards the peripheral 'leafs'. The Head/Face localization is performed using the surface curvature as described above, the next step is the fitting of a sphere within those voxels, this is done following locally an energy minimization approach similar to the one previously defined in [START_REF] Bregler | Tracking people with twists and exponential maps[END_REF] but applied only to this part. The radius of estimated sphere gives a first raw approximation of the skeleton size that must be used in the global fitting. The next step consists in the accurate determination of the Torso: we used 6 DOFs for the Central Spine, 3 for the Pelvis and 2 for the Neck bone, this allowed us to deal with a Torso capable of 'twist and bend' action. This approach is quite different from the previous model of Trivedi [START_REF] Mikic | Human body model acquisition and tracking using voxel data[END_REF] reported in Fig. 5(left) and allows us to tackle complex configurations as shown in Fig. 5(right). The first rough estimation of the Torso position is coaxial with the segment joining the center of the head with the VH barycenter and further refinements are based on the previously described approach for local energy minimization. The next step concerns the lower body limb detection, in particular, starting from the lower part of Torso we will look for knees: we found them analyzing the curvature variations in a sphere centered at the lower part of the Torso and with radius equal to the femur; the center of mass of these high curvature zones is recognized as the Knees. Ankles are estimated using the same approach based on a sphere centered at the knee and with radius equal to the Tibia. These approaches based on local curvature could also be strengthened identifying local maxima in the geodesic distance from a reference point: knees and ankles, besides their curvature, present smooth local maxima of geodesic distance from a generic surface points, furthermore their slow decreasing behavior in the neighborhood of the maximum allows us to identify a wide maximum region discarding local curvature and/or distance maxima due to clothing or ouliers. The foot bone is then identified looking for the principal direction of the surface voxels farthest than the ankle. The localization of knee, ankle and feet is shown in Fig. 6 Fig. 6. From left to right: the localization of the knees, ankles and the identification of the feet bone based of the principal direction of farthest voxels.

Higher body Limbs detection

Elbows and hands detection follows a process similar to the lower body part: starting from shoulders geodesic distance is evaluated and elbows usually represent wide local maxima and hands represent absolute maxima. Both of them can be obtained with an exhaustive search in spheres respectively centered on shoulders and elbows with radii of humerus length and radius length. Anyway this kind of articulations present a lot of ambiguous situations when elbows or hands are in contact with torso or legs originating seamless VHs. In these cases arms or hands in the FF are assumed in contact with the torso. An example of higher body limbs localization is shown in Fig. [START_REF] Poppe | Towards real-time body pose estimation for presenters in meeting environments[END_REF].

global refinement

After the rough estimation of the limbs position described below we can provide the energy functional described in (2) with a good guess of the SF and of FF; hopefully close to the global minimum. Further minimization is then acquired using an improved version of the simplex algorithm described by Nelder and Mead [START_REF] Mckinnon | Convergence of the nelder-mead simplex method to a nonstationary point[END_REF].

Experimental results

Our algorithm as been widely tested on numerous real world data acquired in our lab of different people also with complex configuration; The good results validated our heuristic approach for robust limb localization. They are examined through visual feedback and through the analysis of three dimensional paths of the articulations during a performed actions. Visual analysis allows an immediate gross evaluation of the results, as well as the individuation of critical poses. The plot of the three dimensional paths followed by the articulations allow detecting discontinuities in the movements. In Fig. [START_REF] Capo | Automatic human body modelling for vision-based motion capture[END_REF] we show the SF fitting for 6 frames while in Fig. [START_REF] Wren | Pfinder: real-time tracking of the human body[END_REF] the head position is shown for 66 consecutive frames. In Fig. we give some examples of correct fitting for complex configurations. We presented a novel approach to robust markerless human pose estimation. The presented system uses a VH obtained by 8 digital video cameras and does not require any assumption on the starting pose of the subject or on its physiognomy. Furthermore, there is no demand upon post processing of all frames to produce a reliable result since each frame is processed independently and the algorithm can be parallelized on different frames. The accuracy achieved in the estimate of the joints positions is not yet suited for a biomedic research and movement analysis, being lower than what such systems usually demand. It is on the contrary perfectly suited for the use in all those applications, which require an absence of restrictions imposed by the system and that ask for precision within 5cm in order to grasp the action. Actually there is no analysis between consecutive limbs estimations in different frames but further developments will implement these aspect to strengthen the localization with noisy VH.

Fig. 1 .

 1 Fig. 1. (left)Visual Hull reconstruction from intersection of reprojection cones from silhouettes. (right)Two examples of Visual hull reconstruction; different colors relates to different geodesic distances from the model centroid

Fig. 2 .

 2 Fig. 2. The stick figure represents a human skeleton, defined by connections and bounds on angles. The image shows the possible axis of rotations and the DOF of rotation (left). The flesh figure extends the stick figure with volumes around bones (right).

Fig. 3 .

 3 Fig. 3. Determination of normal vectors using Sobel filters on voxel-set slices

Fig. 4 .

 4 Fig. 4. curvature radius of the VH: points with lower radius (high curvature) are represented in blue and are mainly localized in the facial region while all the other colors represent bigger radii and points with neutral color represents very high radii (surface almost flat)

  is a sampling of the Flesh Figure in the Voxel-set and is '1' if the considered voxel belongs to the FF and '0' otherwise; the parameter θ indicates the values of the 43 DOFs. The operand ⊕ indicates the XOR logical operation and the denominator normalizes the whole sum to the VH volume. The energy definition we used is then a normalized Hamming distance between the VH and the FF and its minimization corresponds to the search for the optimal θ: θ = min θ (E (θ)).

Fig. 5 .

 5 Fig. 5. (left) The skeleton model adopted bi Trivedi (right)some twisted and blended configurations that our model can honor

Fig. 7 .

 7 Fig. 7. Arms and hand configuration in complex configuration where Elbows are in contact with the Torso

Fig. 9 .

 9 Fig. 9. 4 complex positions correctly recognized

Fig. 10 .

 10 Fig. 10. Head 3D position during action performing

Table 1 .

 1 Degrees of Freedom related to each model feature of the union of both Stick Figure and Flesh Figure; the Central Spine gives the relative reference of the backbone with the viewing system.

			Freedom
	Feature	Rot. Trans. Length Radii DOF
	Joints
	Central Spine 3	3		6
	Neck bone	2			2
	Shoulder(2)	3			2 x 3
	Elbow (2)	1			2 x 1
	Pelvis	2			2
	Hip (2)	3			3
	knee (2)	1			2 x 1
	Ankle (2)	2			2 x 2
	Flesh descriptors
	Head			1	1
	High Torso		1	2	3
	Humerus (2)		1	2	3
	Radius (2)		1	2	3
	Femur (2)		1	2	3
	Tibia (2)		1	2	3
	Total				43

M2SFA2 2008: Workshop on Multi-camera and Multi-modal Sensor Fusion


Alexandre Alahi

Michel Bierlaire

Murat Kunt

Andrea Cavallaro

Oct Hamid Aghajan

Object Detection and Matching with Mobile Cameras Collaborating with Fixed Cameras

A system is presented to detect and match any objects with mobile cameras collaborating with fixed cameras observing the same scene. No training data is needed. Various object descriptors are studied based on grids of region descriptors. Region descriptors such as histograms of oriented gradients and covariance matrices of different set of features are evaluated. A detection and matching approach is presented based on a cascade of descriptors outperforming previous approaches. The object descriptor is robust to any changes in illuminations, viewpoints, color distributions and image quality. Objects with partial occlusion are also detected. The dynamic of the system is taken into consideration to better detect moving objects. Qualitative and quantitative results are presented in indoor and outdoor urban scenes.

Introduction

Low-cost digital cameras and progress in processing large data sets such as digital videos have promoted the installation of cameras on fixed and moving platforms.

Cameras are now integrated into many devices such as phones or vehicles. The use of data provided from all cameras capturing a given scene, leads to a better understanding of the objects of interest. Mobile cameras (e.g. a camera held by a pedestrian or placed in a car) benefit from their proximity to the objects of interest to capture high resolution features.

Many car manufactures and institutions are interested in detecting potential collision of cars with pedestrians in urban areas. For that purpose they have mounted cameras in cars. Expensive systems exist such as stereo cameras combined with other sensors [START_REF] Suard | Pedestrian Detection using Infrared images and Histograms of Oriented Gradients[END_REF]. Low-cost systems, e.g. using a single low resolution camera (for example 320 × 240), are not performing well enough in such application. In a classification framework, only a restricted number of features such as shape [START_REF] Gavrila | Pedestrian detection from a moving vehicle[END_REF], histogram of oriented gradient [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF][START_REF] Suard | Pedestrian Detection using Infrared images and Histograms of Oriented Gradients[END_REF], or covariance matrices [START_REF] Tuzel | Human Detection via Classification on Riemannian Manifolds[END_REF], can be used to detect a pedestrian in a single image. These systems suffer from high false positive rates and from the restriction to only detect objects present in their training data.

Alahi et al. in [START_REF] Alahi | A master-slave approach for object detection and matching with fixed and mobile cameras[END_REF] propose a system to cope with the limitations of the previous systems. Features extracted from fixed cameras are used to detect objects Fig. 1. Left column: objects of interest highlighted in a fixed camera.Right column: objects detected and matched by the proposed approach in a mobile in mobile cameras 1 . An object descriptor based on a cascade of grids of region descriptors is presented. They obtain higher performance than approaches considering a region with a single descriptor. They compare the covariance descriptor proposed by [START_REF] Tuzel | Region covariance: A fast descriptor for detection and classification[END_REF] with histograms of color information.

In this paper, we compare several object descriptors with the proposed cascade of descriptors. We study the impact of describing an object with various grids of region descriptors. The covariance descriptor is compared with the extensively used histograms of oriented gradients [START_REF] Suard | Pedestrian Detection using Infrared images and Histograms of Oriented Gradients[END_REF]. The covariance of various feature sets are considered. In addition, a preprocessing step is added comparing the proportion of edges between two regions to enhance the performance of the approach both qualitatively and quantitatively. Finally, the dynamics of the objects are considered. Several observations are kept to describe a moving object instead of a single observation as in [START_REF] Alahi | A master-slave approach for object detection and matching with fixed and mobile cameras[END_REF].

Experiments show that objects are successfully detected even if the cameras have significant change in image quality, illumination, and viewpoint. Figure 1 presents two examples of the detection and matching of the approach presented in this paper. Partial occlusions are also handled.

The paper is structured as follows: first, an overview of the two region descriptors used in this work is given. Then, after a presentation of the proposed object descriptor, the detection and matching process is presented. In section 5, the performances of different descriptors are evaluated on challenging data sets. Quantitative and qualitative results are given.

Region Descriptors

Covariance matrix

Covariance matrices are a very attractive descriptor first used by Tuzel et al. [START_REF] Tuzel | Region covariance: A fast descriptor for detection and classification[END_REF], [START_REF] Porikli | Covariance Tracking using Model Update Based on Lie Algebra[END_REF], [START_REF] Tuzel | Human Detection via Classification on Riemannian Manifolds[END_REF]. For each pixel, a set of features is extracted. Alahi et al. in [START_REF] Alahi | A master-slave approach for object detection and matching with fixed and mobile cameras[END_REF] use the grayscale intensity, I, and the norm of the first order derivatives with respect to x and y, I x and I y :

f n = (x, y, I, I x , I y ) (1)
Other features such as the R,G,B values or the second order derivatives, the gradient magnitude, mg, and its angle, θ, can also be used. The pixel coordinates, x and y, are integrated in the feature vector to consider the spatial information of the features. Finally, the covariance of a region is computed as:

C i = 1 N -1 N n=1 (f n -m)(f n -m) T ( 2
)
where N is the number of points in the region, and m the mean vector of all the feature vectors. With covariance matrices, several features can be fused in a lower dimensionality without any weighting or normalization. They describe how features vary together.

Similarity between two regions B 1 and B 2 is given by the following distance proposed by [START_REF] Forstner | A metric for covariance matrices[END_REF]:

σ r (B 1 , B 2 ) = i ln 2 λ i (C 1 , C 2 ) ( 3
)
where λ i (C 1 , C 2 ) are the generalized eigenvalues of the covariance matrices C 1 and C 2 .

Histogram of Oriented Gradients

Histograms of Oriented Gradients (HOG) are efficient to compute descriptors based on the first order derivatives with respect to x and y of the image intensity (denoted by I x and I y ). From these two derivatives, a gradient field is computed assigning to each pixel a magnitude mg(x, y) and an angle θ(x, y):

mg(x, y) = I 2 x (x, y) + I 2 y (x, y) (4)
θ(x, y) = arctan

I y (x, y) I x (x, y) (5)
The angle values θ ∈ [0, 360[ are quantized to N discrete levels θ i . A histogram is formed where each bin is the sum of all magnitudes with the same orientation θ n in a given region.

The Bhattacharyya distance [START_REF] Comaniciu | Real-time tracking of non-rigid objects using mean shift[END_REF] or the L 2 norm can be used to compute the distance, σ r , between the histograms.

Object Descriptor

A Collection of Grids of Descriptors

In this work, a descriptor is created for each observation x i of an object, referred to as an object descriptor (OD). An observation correspond to the rectangular region bounding the object of interest in the fixed camera at a given frame.

An object descriptor (OD) is used taking into account local and global information. It is a collection of grids of region descriptors (see figure 2). Each grid segments the object into different number of blobs of equal sizes. Grids of finer blob size describe local information whereas grids of coarse blob size describe a more global behavior.

Similarity Measurement

Similarity between grids of descriptors is computed by generating a distance map representing the distances between corresponding blobs. If several observations are available for the same object, the minimum distance, σ r , between each blob is selected among all observations (see figure 3).

Finally, since many objects do not have a rectangular shape and some can be partially occluded, only the most similar distances are kept. Thereupon, blobs belonging to the background can also be discarded. The sum of the smallest distances in the distance map is the final similarity measurement σ.

Object Detection and Matching

Problem Formulation

Given a set of observations {x 1 , x 2 , ..., x n } of an object O in a fixed camera, we wish to locate it in the image plane of a mobile camera. No additional training data should be used.

OD1 OD2 Region in a mobile camera Distance Map Min σ 1 σ 2 σ 2 Min σ 9 σ 10 σ 9 • • • • • • OD1 OD2 Region in a mobile camera Distance Map Min σ 1 σ 1 σ 2 σ 2 σ 2 Min σ 9 σ 9 σ 10 σ 10 σ 9 • • • • • •
Fig. 3. Generation of the distance map between a set of observations of an object from a fixed camera and a region in the mobile camera.

The Approach

Given the ODs of an object, all possible regions in the image plane of a mobile camera are compared with the ODs. A window of size proportional to the object bounding box scans the image plane of the mobile camera at different scales.

For each region, its similarity with the ODs is computed to find the region with highest similarity. Each region is translated by 15% of its width or height, and scaled by 25% (6 scales are considered in this work).

Preprocessing: Edge Filtering

Some regions in the mobile camera do not need to be compared with the ODs. They can be discarded with a simple preprocessing. The difference between the proportion of edges in two regions can give a quick indication about their similarity. If the proportion of edges is not similar, the region is discarded. As a result, fewer regions remain to be analyzed and it increases the likelihood to detect the right object by reducing the search space.

Cascade of Coarse to Fine Descriptors

Some regions can be easily discarded without knowing the local information.

Therefore, an approach similar to a cascade of classifier is proposed. "Easy regions" are discarded with coarse grids (i.e. grids with small number of blobs). More challenging regions require the use of finer grids (i.e. more number of blobs). The detection process is divided into several stages. At each stage, a finer grid is used. After each stage, only the best candidates, i.e. regions with highest similarity (top ρ% of the evaluated regions), remain (see figure 5). The percentage (ρ) of regions to keep after each stage can be fixed, or adaptive such that after each stage, the same percentage is kept:

N r × ρ Ns = 1 (6)
where N r is the total number of regions in the mobile camera to compare with the object descriptor, and N s is the total number of stages to use.

ρ = N -1/Ns r (7)

Updating the Observations

An object moving in a scene can have different appearances across time even from a fixed viewpoint. A set of relevant observations should be kept to detect the same object with a mobile camera at all time.

In order to cover the most different appearances of an object, the most dissimilar observations are kept. As a result, if an object does not have a similar appearance in the mobile camera with the current observation, it might have a better similarity with an older observation.

Let D be the set of observations of an object, and m the number of observations to keep:

D = {OD i , OD 2 , ..., OD m } (8)
We define the "set similarity" operator as the sum of all distances between the ODs of a set:

σ set (D) = ∀k,l∈D σ(OD k , OD l ) (9)
Initially, the set D correspond to the m first observations of the object. Then, given a new observation OD n , m + 1 choices of the set D are possible, referred to as D p :

D p = {D 1 , ..., D m+1 } = {{OD n , OD 2 , ..., OD m }, {OD 1 , OD n , ..., OD m }, ..., {OD 1 , OD 2 , ..., OD n }, {OD 1 , OD 2 , ..., OD m }} (10)
The set with the most dissimilarity (highest σ set ) is kept:

D u = arg max ∀Di∈Dp σ set (D i ) (11)
where D u is the new updated set of observations.

5 Performance Evaluation

Data Sets

Indoor and outdoor data sets have been used [11]. Each data set is composed of video sequences captured concurrently by a fixed and a mobile camera from the same scene. Fixed cameras are located at a height equivalent to the first floor of a building. Mobile cameras are held by pedestrians walking in the scene. The images are recorded at 25fps with a resolution of 320 × 240. Figures 1 and11 presents an example of images captured by the cameras.

The data sets used have meaningful changes in viewpoint, illumination, and color distribution between fixed and mobile cameras. Sensing devices are also different. Indeed, mobile cameras have a cheap capturing device and hence provide noisy images.

Experiments

Thousands of frames and objects are selected within the fixed cameras to find correspondence in mobile cameras. In the first data set, only pedestrians are of interest. In the second one, random rigid objects in the scene are selected to prove generalization of the approach to any objects of interest. Only objects present in the view of the mobile camera are selected in the fixed camera. Hence, the performance of the system is quantitatively measured by computing the percentage of correct detected and matched objects in the mobile camera, %TP. It is clear that the false positive rate is simply its complementary, hence does not need to be reported.

Region Descriptors

First, each object is described with a single region descriptor to select the best ones for the remaining evaluation. The following region descriptors are evaluated:

-Covariance of:

-(x, y, I, I x , I y ): as in [START_REF] Alahi | A master-slave approach for object detection and matching with fixed and mobile cameras[END_REF] show that it degrades the performance.

Figure 6 presents the %TP over all the descriptors on both data sets. Interestingly, when pedestrians are considered, the HOGs perform as good as the best covariance descriptors and even slightly better with 16 number of bins. On the second data set, for rigid objects, it is not the case.

Three regions descriptors based on the covariance matrix and the three HOGs are selected to continue the evaluation process:

-Covariance of:

-(x, y, I, I x , I y ): since it gave the best performance in [START_REF] Alahi | A master-slave approach for object detection and matching with fixed and mobile cameras[END_REF].

-(x, y, I, I x , I y , mg, θ): since it gave the best performance on both data sets when 7 features are selected.

-(x, y, I, I x , I y , I xx , I yy , mg, θ): since it gave the best performance among other features set. -Histogram of Oriented Gradient with 8, 12, and 16 bins.

Detection and Matching Process

In average, 85% of the regions are filtered out with the proposed preprocessing step without removing the true positive regions. In addition, without such preprocessing, the performance of the descriptors are decreased by 23% in average. Reducing the search space, increases the likelihood to find the right region. Considering a region with a single descriptor is not enough. Local information is lost in the global behavior. Figures 7 and8 present 3 strategies: first, an object is described by a single grid (first graph). Various number of blobs per grid are considered. Increasing the number of blobs, increases the performance over all descriptors reaching a limit. Second, an object is described by a collection of grids. The final similarity measurement is the sum of the measurements over all the grids. With covariance matrices, considering several grids does not give better performance than simply considering the grid with higher number of blobs, although, for HOG, it is the case. The proposed cascade of grids leads to very similar performance with much lower computation cost. The number of descriptors to compute is much less than the previous two approaches. Figure 9 presents the performance of the cascade of descriptors for various ρ with respect to the number of region descriptor computed. Figure 10 presents the performance of the approach if several regions in the mobile camera are kept as matching the object of interest. Considering two or three regions is enough to increase the performance. Further work could classify those candidate regions as matching or not the object of interest by evaluating the posterior probability: checking if those regions match the same object in the fixed camera.

Finally, considering several observations increases the performance of the system. It is not relevant to give a quantitative results since it depends on the behavior of the objects. Nevertheless, by keeping three observations the performance increases by 7%. Moving objects are much better detected.

Figure 11 presents the output of our proposed system (5 stages cascade of HOG of 8 bins) on both data sets.

Conclusions

A system is presented to detect and match any objects detected by a fixed camera in the image plane of a mobile camera. The performance of various object descriptors are measured both quantitatively and qualitatively. The proposed approach based on edge filtering, and the cascade of region descriptors outperform other approaches or lead to similar performance with much less computation cost, making it feasible for a real-time application. Although, the object descriptor based on HOG have slightly lower performance than those based on the covariances, they are much faster to compute and compare. Indeed, even with the fast implementation proposed by [START_REF] Tuzel | Region covariance: A fast descriptor for detection and classification[END_REF] to compute the covariance matrices, they are still expensive to measure similarity if many features are used. Future work will combine those descriptors to evaluate the posterior probability of the detected regions.

Fig. 2 .

 2 Fig. 2. A collection of grids of descriptors

Fig. 4 .Fig. 5 .

 45 Fig. 4. A three stages cascade of coarse to fine descriptors. At each stage, a finer grid is filtering out remaining regions

  [5] -(x, y, I x , I y ): to measure impact of the intensity value -(x, y, I xx , I yy ): the 2 nd order derivatives -(x, y, mg, θ): gradient magnitude and angle -(x, y, I, I x , I y , I xx , I yy ): the grayscale values, 1 st and 2 nd order derivatives -(x, y, I, I x , I y , mg, θ): the grayscale values, 1 st order derivatives and gradient magnitude with angle -(x, y, I, I xx , I yy , mg, θ): the grayscale values, 2 nd order derivatives and gradient magnitude with angle -(x, y, I, I x , I y , I xx , I yy , mg, θ): set of all features -Histogram of Oriented Gradient with 8, 12, and 16 bins Color features are not considered since Alahi et al. in

Fig. 6 .

 6 Fig. 6. %TP for various region descriptors on data set 1 (left-side), and data set 2 (right-side).

Fig. 7 .

 7 Fig. 7. %TP on the 1st Data set (pedestrians only) for various region descriptors based on 3 Object descriptors: Left hand-side:A single grid of n blobs (here n=1,4,9,16,25). Middle column: collection of grids. Right hand-side: Cascade of grids.

Fig. 8 .

 8 Fig. 8. %TP on the 2nd Data set (rigid objects only) for various region descriptors based on 3 different Object descriptors.

Fig. 9 .

 9 Fig. 9. %TP with respect to the number of region descriptors needed

Fig. 10 .

 10 Fig. 10. %TP with respect to the number of best match kept on data set 1 (left-side), and data set 2 (right-side).

Fig. 11 .

 11 Fig. 11. Random Examples of the proposed system. 1st and 3rd column: objects of interest seen in fixed camera. 2nd and 4th column: corresponding detected objects in the mobile camera (output of the proposed approach)

Indeed, a very large number of fixed cameras have been installed in major cities (e.g. in

2002, approximately four millions just for the UK[START_REF] Mccahill | Cctv in london[END_REF]).