L Hanane

S Hebib

H Aubert

N Fonseca

Compact Printed Quadrifilar Helix Antennas for Stratospheric Balloons Telemetry

Introduction

Printed Quadrifilar Helices (PQH) antennas have found application in L-band telemetry for meteorological stratospheric balloons. The PQH antenna, patented by the CNES [START_REF] Auriol | Helix-type antenna and its manufacturing process[END_REF], is relatively simple to manufacture and low cost. Such an antenna has good circular polarization coverage with excellent axial ratio over a wide range of elevation angle. However the reduction in size of modern stratospheric balloon payloads asks for more compact PQH antennas.

Consequently, the challenging problem consists of reducing the axial length of conventional PQH antennas with a minimum impact upon their overall performances. In the literature, meander lines [START_REF] Chew | Meander line technique for size reduction of quadrifilar helix antenna[END_REF][START_REF] Letestu | A size reduced configurations of printed quadrifilar helix antenna[END_REF] and pre-fractal (space-filling) curves [START_REF] Cohen | NEC 4 analysis of a fractalized monofilar helix in an axial mode[END_REF] were applied to the arms of helix antennas in order to reduce its length. Compact PQH antennas with meander lines have been reported in [START_REF] Letestu | A size reduced configurations of printed quadrifilar helix antenna[END_REF] but the performances of the proposed antennas in term of the axial ratio (which are of crucial importance in our application) are not compared with those of conventional PQH antennas. In [START_REF] Cohen | NEC 4 analysis of a fractalized monofilar helix in an axial mode[END_REF] pre-fractal curves have been used to reduce the axial length of monofilar helices antennas but, from a practical point of view, the extension to quadrifilar helices appears to be highly problematic.

In this communication, the four arms of quadrifilar helices antennas are prefractal and printed on the cylindrical surface of the antenna. Very few of such prefractal PQH antennas are found to achieve the technical requirements for L-band stratospheric balloons telemetry. We present in this paper a solution with a 33% axial length reduction when compared to the original PQH antenna. The obtained axial ratio is lower than 2 dB for elevation angle between -80° and 80°.

Design of pre-fractal Printed Quadrifilar Helixes antennas

Based on the Iteration Function System (IFS) algorithm [START_REF] Jurgens | Chaos and Fractals: New Frontiers of Science[END_REF], a specific software has been developed to generate the pre-fractal profile of PQH antennas. The total length of such profiles is adjusted in order to obtain the same operating frequency (1.85GHz) for each studied PQH antenna and to achieve the technical requirements in terms of radiation pattern (radial mode) and input impedance (close to 50Ω). The axial ratio is required to be lower than 2 dB over elevation angle range as large as possible. In order to achieve circular polarization, the four arms of the PQH antennas are excited with the following classical phase law: 0°, 90°, 180° and 270°.

The pre-fractal profiles with interesting characteristics are shown in Figure 1. These profiles are printed on a thin low-permittivity dielectric substrate (Figure 2) and wrapped around a cylindrical support. The Figure 3 shows the resulting PQH antennas. The design and the simulation of these antennas are performed using IE3D software based on the Method of Moments. The PQH-F1 and PQH-F2 antennas reduce the axial length of the conventional PQH antenna by 33% and 38%, respectively. The Figure 4 displays the simulated LHCP and RHCP directivity patterns of these two compact antennas at the desired operating frequency. In term of the LHCP gain pattern, these two antennas will be slightly out of the requirements in some radiating directions (the desired minimal LHCP gain patterns are displayed in the figure). However, the axial ratio of the PQH-F1 antenna is lower than 2 dB for elevation angle between -70° and 70°. Moreover, with printed line widths of 1mm, the input reflection coefficient is found to be close to -16 dB for the PQH-F1 antenna while this coefficient is close to -22.5dB in the case of the PQH-F2 antenna with line widths of 0.8mm. Very few pre-fractal PQH antennas are found to achieve the technical requirements for L-band stratospheric balloons telemetry, especially in term of co-polarized field. In the generation of the pre-fractal profile, as the order of iteration increases in the IFS algorithm, the resulting pre-fractal PQH antenna seems to enhance the axial mode to the detriment of the desired radial mode of radiation. Moreover, according to the electromagnetic simulations, we have observed that classical sinus-type profiles offer analogous performances to prefractal PQH-F1 and PQH-F2 antennas in terms of directivity patterns and size reduction.

Conclusion

Two pre-fractal Printed Quadrifilar Helices antennas have been presented. These compact antennas offer good compromises between size and performances. The designs introduced in this paper reveal the feasibility of an axial length reduction between 30 to 40% without significant cross-polarization degradation. Experimental validations will be presented at the conference.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Pre-fractal profiles: (a) at the first-order iteration; (b) at the second-order iteration with α=30° and (c) at the second-order iteration with α=45°.

Figure 4 .

 4 Figure 4. The simulated radiation patterns for : (a) the PQH-F1 antenna and (b) the PQH-F2 antenna.

Table 1

 1 summarizes the characteristics of the PQH, PQH-F1 and PQH-F2 antennas.

		Conventional PQH	PQH-F1	PQH-F2
	Antenna axial height	340 mm	227 mm	211 mm
	Total wire length	380 mm	322 mm	341 mm
	Operating frequency	1.85 GHz	1.85GHz 1.85 GHz
	Size reduction	0 %	33 %	38 %
	Input reflection coefficient	-25 dB	-16 dB	-22.5 dB
	width of the printed lines	5.5 mm	1 mm	0.8 mm

Table 1 .

 1 Characteristics of the PQH, the PQH-F1 and PQH-F2 antennas.

Acknowledgement

The authors would like to thank Errazi Rachid for his helpful development of the IFS-based software for the generation of the pre-fractal profiles.


Jean-Yves Franceschi

Mike Gartrell

Dos Ludovic

Thibaut Santos

Emmanuel Issenhuth

Mickaël De Bézenac

Alain Chen

Rakotomamonjy

Tristan Alice Oh

Amir Naumann

Kate Globerson

; Saenko

Moritz

Unifying GANs and Score-Based Diffusion as Generative Particle Models

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

Unifying GANs and Score-Based Diffusion as Generative Particle Models J.-Y. Franceschi, 1 M. Gartrell, 1 L. Dos Santos, 1, * T. Issenhuth, 1,2, * E. de Bézenac, 3, * M. Chen, 4, * A. Rakotomamonjy 1, * 1 Criteo AI Lab 2 LIGM, Ecole des Ponts, Univ Gustave Eiffel, CNRS 3 SAM, D-MATH, ETH Zürich 4 Valeo.ai

Our Contributions

• We unify gradient flows, score-based diffusion models, and GANs in a single framework. • We represent generated data as moving particles.

A model is defined by: • a gradient vector field that the particles follow either at inference or training time; • the possibility of incorporating a generator that smooths this movement. • This suggests the existence of hybrid models:

• a generator trained with diffusion guidance (Score GANs); • a GAN trained without a generator (Discriminator Flows). • We experimentally verify our findings.

GANs vs Diffusion

Traditional opposition in the literature.

GANs → Generator trained by discriminating true vs fake data.

• Generator (manifold learning).

• Close to SOTA performance.

• Harder to optimize.

• Fast inference.

Diffusion → Learns to progressively reverse a data degradation process.

• No generator (on the data space).

• SOTA performance.

• Easier to optimize.

• Slow inference.

From PMs to Int-PMs

• We assign to each generated particle x = g θ (z) the same loss as in PMs: L gen (θ) = -E z∼p z h ρ t g θ (z) . • We do not take into account the dependency of ρ t w.r.t. θ t , to mimic PMs: ρ = StopGradient(g θ ♯p z ). • Continuous-time gradient descent:

dθ t dt = -η∇ θ t L gen (θ t ) = η∇ θ t E z∼p z h ρ t g θ t (z)
= ηE z∼p z ∇ θ t g θ t (z)∇h ρ t g θ t (z) .

• Evolution of particles:

dg θ t (z) dt = ∇ θ t g θ t (z) ⊤ dθ t dt = ηE z ′ ∼p z ∇ θ t g θ t (z) ⊤ ∇ θ t g θ t z ′ ∇h ρ t g θ t z ′ .

Particle-Based Framework

Generated particles x t ∼ ρ t follow a gradient vector field ∇h ρ t , i.e. optimize an objective h ρ t .

Wasserstein Gradient

-∇ W F(ρ t ) = -∇ ∂F(ρ ) ∂ρ t Log Ratio Gradient α t ∇ log p data ⋆ k σ(t) RBF -β t ∇ log ρ t Discriminator Gradient -∇ c • f ρ t
where f ρ t discriminates ρ t from p data

Particle Models (No Generator)

• At generation / inference time t:

x 0 ∼ π = ρ 0 , dx t = ∇h ρ t (x t ) dt.
• Independently moving particles.

• Each x t individually follows a gradient ascent path on h ρ t (x t ). • h ρ is usually a predefined functional approximated with neural networks.

Wasserstein Gradient Flows

• Gradient descent for functionals over distributions F (Santambrogio, 2017).

Score-Based Diffusion

dx t = α t ∇ log p data ⋆ k σ(t) RBF (x t ) dt + 2β t dW t ⇔ -β t ∇ log ρ t dt.

Discriminator Flows

• Particles directly follow the discriminator gradient. • The discriminator is simultaneously trained and used to generate data.

Interacting Particle Models (Generator)

• Training with the same loss:

L gen (θ) = -E z∼p z h ρ t g θ (z) .

• At training time t:

dg θ t (z) = η A θ t (z) ∇h ρ t dt.
• Generalization of PMs where particles interact with each other.

Stein Gradient Flows

• Stein gradient flows (Liu, 2017) are kernelized Wasserstein gradient flows:

dx t = E x ′ t ∼ρ t k x t , x ′ t ∇h ρ t x ′ t dt.
• Int-PMs under mild hypotheses (generalization of Durr et al. ( 2022)). • Hint towards the same h ρ being used in a PM and an Int-PM.

Score GANs

GANs

• Gradient descent-ascent on the minmax objective yields the generator loss:

L GAN (g θ ) = E z∼p z c • f ρ g θ (z) .

Smoothing Operator

• A θ t (z) is a linear operator on vector fields (kernel integral operator):

A θ t (z) (V ) ≜ E z ′ ∼p z k g θ t z, z ′ V g θ t z ′ , k g θ t z, z ′ ≜ ∇ θ t g θ t z ′ ⊤ ∇ θ t g θ t (z).
• k g θ t is the generator's matrix Neural Tangent Kernel (NTK, Jacot et al., 2018).

• Special case: k g θ t z, z ′ = δ z-z ′ I d (generator with infinite capacity).

• No interaction between particles:

A θ t (z) (V ) = V g θ (z) .
• dg θ t (z) = ∇h ρ t g θ t (z) dt: we retrieve PMs.

• General case: A θ t represents the parameterization of ρ as a manifold.

• A θ t smooths the original vector field ∇h ρ t by convolving it with k.

• Particles interact with each other through generator parameterization.

Other Models & Flows

Score GANs in Practice

• Two practical issues:

• sliced score matching to train s ρ ϕ ; • scheduling σs w.r.t. training time t.

• We randomly sample σ and also noise the particles:

∇h ρ = ∇ log[p data ⋆ k σ RBF ] -∇ log[ρ t ⋆ k σ RBF ], ≡ ∇h ρ (•, σ) = s p data ψ (•, σ) -s ρ ϕ (•, σ). • Generator update:
• few-step training of s ρ ϕ with denoising score matching; • gradient descent step:

θ ← θ + η E σ∼p σ ,ε∼N (0,σI D ),z∼p z ∇ θ g θ (z) ∇h ρ g θ (z) + ε, σ .

Discr. Flows in Practice

• Discriminator loss:

L d (f ; ρ, p data ) = E ρ [a • f ]-E p data [b • f ]+R(f ; ρ, p data ).
• Naive training: successive f ρ t trainings and ρ t updates.

• For efficiency purposes, we simultaneously learn all timeparameterized discriminators:

f ρ t = f ϕ (•, t).
• Training step: (•, t) to discriminate between x t and p data .

• sample t ∼ U [0, 1] , x 0 ∼ π; • compute x t = -η t 0 ∇ c • f ϕ (•, s) (x s ) ds; • train f ϕ
• Generalization of some gradient flows.

Links

Article

Code and samples

• Code for all models and baselines. • Animated samples.

Experimental Results

• Hybrid models are viable, support theory. • EDM: diffusion (Karras et al., 2022).

Properties

• Discr. flows learn a path to the data distribution, unlike diffusion.

• PMs vs Int-PMs: Int-PMs are prone to mode collapse but are faster than PMs at inference and have better latent space properties.

Perspectives

• Our work paves the way for new hybrid models.

• Model improvements: Score GANs for score distillation, Discr. Flows for generation efficiency.

•

  Int-PMs and Stein (generalization of Durr et al. (2022)): k g θ t (z), g θ t z ′ = k g θ t z, z ′ in the NTK regime.• Langevin diffusion(Song et al., 2019) is a KL flow.

• Under some hypotheses, GANs are Stein flows

(Franceschi et al., 2022; Yi et al., 2023)

: KL flow for f -divergence GANs, squared MMD for IPM GANs. • As a consequence, under similar hypotheses, Discriminator Flows with the same losses are Wasserstein flows. • Many methods use neural networks to approximate the flow (Alvarez-Melis et al., 2022; Heng et al., 2023).


Guérin

Katia Guérin

Optimized

Charlotte Gervillié

Marc Dubois

Malika El-Ghozzi

Sandrine Berthon-Fabry

Aurélie Boisard

Julien Labbé

Optimized electrode/electrolyte interface of MWCNT-SnO 2 composite through gas-solid fluorination

Optimized electrode/electrolyte interface of MWCNT-SnO 2 composite through gas-solid fluorination

K.

The benefit of enriching Solid-Electrolyte Interface with fluorine atoms through the use of fluorinated additives into the electrolyte composition has recently gained popularity for anode materials used in secondary lithium-ion battery [1]. Another strategy is to provide these fluorine atoms via surface fluorination of the electrode material, particularly for MWCNT-SnO 2 based composites where fluorination must act selectively on SnO 2 . Our study presents two methods of surface fluorination applied on MWCNT-SnO 2 , one using F 2 (g) and the other XeF 2 (s). These fluorinating agents are known for their different particle penetration depths. An ultra-thin and very dense fluorinated layer achieved by the action of F 2 (g) allows to form a very stable interface leading to gravimetric capacities of 789 mAh.g -1 after 50 cycles. A thin and porous fluorinated layer made by XeF 2 (s) action favors the formation of a new Sn-based fluorinated phase never reported in the literature which also stabilizes capacities over 50 cycles. In any case, the value of adding fluorine atoms to the surface of the electrode material to improve cycle stability is demonstrated [2].

Scheme 1 .

 1 Scheme 1. Selective fluorination of Tin oxide in front ot carbon nanotube through the use of molecular fluorine


S Hebib

H Aubert

O Pascal

N Fonseca

L Ries

J M Lopez

Pyramidal multi-band antennas for GPS/Galileo/MicroSat application

Introduction

There is a constant increase of interest for multi-band antennas, mainly driven by the objective to reduce the number of onboard and ground antennas by integrating several applications on a single radiating element. In the framework of the Galileo satellite navigation system, the French Space Agency (CNES) proposed to study the possibility of combining GPS, Galileo and MicroSat telemetry (TM) applications on the same multi-band antenna. The GPS / Galileo bands used here include for example ARNS as well as high precision applications. This communication introduces a novel topology of trap-loaded multi-band antenna based on pyramidal structures [START_REF] Hebib | Multi-band antennas for GPS/Galileo applications[END_REF]. The experimental results confirm the good performances observed during the electromagnetic simulations. The multi-band behavior and the required circular polarization characteristic of the proposed pyramidal antenna are validated experimentally.

Antenna design

Two interesting configurations can be considered to obtain circularly polarized antennas from linearly polarized ones. The first configuration uses quadratic phase excitations placed at the center of the structure [START_REF] Ben Abdillah | Cross shaped fractal antenna: a compact circularly polarized radiating element[END_REF] while for the second configuration, the quadratic phase excitations are located at the border of the antenna [START_REF] Rao | Triple-band GPS trap-loaded inverted L antenna array[END_REF]. According to electromagnetic simulations, the latter configuration provides higher directivity with wider bandwidth as compared to the first one. Furthermore, the four feeding ports in this second configuration are all disjointed, making it easier to feed. However, this configuration suffers from a spurious interference effect which is an array effect induced by the non homothetic antenna shape. In addition to this, for our application, it presents insufficient radial directivity at high frequencies.

A solution to overcome these two drawbacks involves the use of the axis perpendicular to the antenna surface. The resulting pyramidal antenna (figure 1) provides a good radial radiation, hence possible improvement in the radial directivity. Furthermore, with this configuration, the feeding ports are brought closer to each other, leading to a reduction or even suppression of the cumbersome array effect. A pyramidal inclining angle of 45 degrees presents a good trade-off between the expected radial and axial radiation performances. The multi-band behavior of this antenna is obtained using trap-loads. These loads can be lumped [START_REF] Rao | Triple-band GPS trap-loaded inverted L antenna array[END_REF] or distributed [START_REF] Ben Abdillah | Distributed constant antennas for compact dual-band applications[END_REF][START_REF] Gianvittorio | Fractal Yagi antennas: design, simulation, and fabrication[END_REF] elements. In order to simplify the process of antenna design and to reduce the computation time, the trap-loads used in the electromagnetic simulations are considered as ideal ON/OFF switches. The design and the simulation of the proposed antenna are performed using IE3D software based on the Method of Moments.

Antenna manufacturing

According to IE3D simulations results, the best impedance matching is obtained when the four feeding ports are located at the vicinity of the circular central hole of the ground plane. However, in practice, it is not convenient to place the SMA connectors at the edge of this hole. A solution is to locate the SMA connectors at a more convenient position and to use 50 Ω microstrip lines to connect them to the radiating elements, as shown on figure 1. The outer radius of the circular ground plane is chosen in order to reduce the edge radiation produced by the surface current on the ground plane. The four radiating elements that constitutes the antenna are printed with copper (width = 1 mm) on a relatively lowpermittivity substrate (relative permittivity = 2.08 and thickness = 762 µm). The same substrate is used for the realization of the 50Ω-microstrip lines.

Antenna measurements

The input return losses and the bandwidth performances of the antenna with ideal trap-loads are presented in Table 1. Measurements of input reflection coefficients were performed using the vector network analyzer WILTRON 37269A. It can be seen that the impedance matching in all bands is quite good, particularly for the second and the third bands (around ---18dB). A weaker impedance matching is obtained in the first frequency band (---13.11dB): post-simulations using CST Microwave studio software have shown that this low impedance matching is caused by the metallic cylinder placed beneath the ground plane to reduce rear radiations (this post-simulations have confirmed that this cylinder has a little impact on the return losses of the two other frequency bands). Optimization of the full antenna using CST Microwave studio software is under way. The radiation specifications are satisfied in the GPS/Galileo frequency bands (centered at 1.197 GHz and 1.575 GHz) and slightly out of the technical requirements in some radiating direction for TM frequency band (centered at 2.245 GHz). Some minor adjustments can be proposed to improve radiation performances in this frequency band: for instance adjusting the inclination of the four radiation monopoles. From these experimental results we conclude that the multi-band behavior and the circular polarization of this antenna with ideal traploads have been validated experimentally.

First band (GPS/Galileo

Conclusion

A novel solution based on pyramidal structures with traps was designed and tested experimentally. The measurements results confirm the good performances obtained from the electromagnetic simulations. The solution suggested in this communication has been developed for a tri-band application but, it could also be advantageously applied for applications in multiple frequency bands. Moreover the exploitation of available volume offers new degrees of freedom for the design of the antennas such as the angle of inclination of the pyramid and the radius of the circular hole bored in the ground plan as well as the length of the cylinder beneath. The proposed multi-band antenna is easy to design and is flexible. It is a good candidate for other multi-band applications.

Figure 1 .

 1 Figure 1. Pyramidal triple-frequency trap loaded antenna: (a) the practical realization and (b) the simulated model

Figure 2 .

 2 Figure 2. The measured radiation patterns (RHCP : -; LHCP : ••• ; Minimum required RHCP : -) for the multi-band antenna at: (a) 1.197 GHz, (b) 1.575 GHz and (c) 2.245 GHz

Table 1 .

 1 ) The measured return losses and bandwidths for the multi-band antenna

	Second band	Third band
	(GPS/Galileo)	(MicroSat)

Acknowledgement

The authors would like to thank José DaBenta and Olivier Pigaglio for their contributions to the manufacturing of the antennas and Lise Feat, Mael Ferret and Daniel Belot for their contributions to the measurements of the various prototypes.


Nelson J G Fonseca
email: nelson.fonseca@cnes.fr

Hebib Sami

Hervé Aubert

L-Band Compact Printed Quadrifilar Helix Antenna with 'Iso-Flux' Radiating Pattern for Stratospheric Balloons Telemetry

Introduction

Quadrifilar helix antennas have very interesting characteristics. For instance, by selecting properly the height and number of turns of the helix, one can achieve a radiation pattern of so-called 'iso-flux' shape with high gain at low elevation. Such a pattern enables to improve the link budget for stratospheric balloons telemetry as the gain of the antenna compensate for the free space propagation losses. The French Space Agency (CNES) has been working on the topic for years and has patented a simple to manufacture and low-cost Printed Quadrifilar Helix (PQH) antenna with integrated feeding network [START_REF] Auriol | Helix-Type Antenna and its Manufacturing Process[END_REF], particularly adapted to short missions with no material reuse.

More recently, CNES has worked with Systems Analysis and Architecture Laboratory of the French Research Agency (LAAS-CNRS) on the axial length reduction of the PQH antenna with 'iso-flux' pattern since balloons payload improvements were asking for antenna improvements too. Various size-reduced helix antennas are presented in the literature, but they present mainly hemispherical patterns and the cross-polarization degradation induced by the sizereduction technique is usually not addressed [START_REF] Chew | Meander Line Technique for Size Reduction of Quadrifilar Helix Antenna[END_REF][START_REF] Letestu | A Size-Reduced Configuration of Printed Quadrifilar Helix Antenna[END_REF]. The authors previously proposed to use pre-fractal and quasi-sinusoidal curves which led to sizereductions between 33% and 38 % [START_REF] Hanane | Compact Printed Quadrifilar Helix Antennas for Stratospheric Balloons Telemetry[END_REF][START_REF] Hanane | Compact Printed Quadrifilar Helix Antenna with sinusoidal profile for Stratospheric Balloon Telemetry[END_REF], but the achieved co-polarization patterns have some non-conformities that needed to be improved.

In this communication, we propose two new designs based on sinusoidal profiles. Antenna height reduction ranges from 33 to 39 % with no significant degradation of the main performances. Cross-polarization level remains similar to the reference antenna performances and co-polarization pattern is now fully compatible with stratospheric balloons telemetry 'iso-flux' specifications.

Antennas design description

The PQH antenna is composed of 4 straight wires printed on a thin substrate that is then rolled to form the helix. The feeding network produces the same amplitude at each wire input and a phase progression of 90°. Such a configuration results in good circular polarization. The previously developed software [START_REF] Hanane | Compact Printed Quadrifilar Helix Antennas for Stratospheric Balloons Telemetry[END_REF][START_REF] Hanane | Compact Printed Quadrifilar Helix Antenna with sinusoidal profile for Stratospheric Balloon Telemetry[END_REF] has been adapted to include basic curves defined by the superposition of N sinusoidal functions according to the following formula:

T x T x A T x A y N k k k ≤ ≤       +       = ∑ - = 0 , 2 sin 2 sin 1 1 0 πσ π (1) where 0 A A k
is the amplitude ratio for the k th sinusoidal function k σ 1 is the period ratio the k th sinusoidal function A basic curve is defined over one period of the so-called 'fundamental' sinusoidal function, characterized by the longer period. Depending on the period and amplitude ratios, various basic curves can be analyzed as illustrated in fig. 1. A radiating wire of the PQH antenna is then composed of the repetition of basic curves, the period being scaled so that the total length of the 'unfolded' wire is somewhat similar to the reference one. Mathematical transformations are then applied to the points defining the wires to incline them and produce the cylindrical shape. Basic curve repetition ranges typically from 1 to 20 and the number of combined sinusoidal functions remains lower than 2 or 3 to keep the number of points defining the radiating wires compatible with a parametric analysis process in terms of computation time.

Two profiles were finally selected for their interesting radiating patterns. They are referred to as SP-PQH 1 and 2 (Sinusoidal Profile PQH antenna). The planar layouts of the proposed SP-PQH antennas are compared to the reference one in fig. 2. SP-PQH1 is characterized by a single sinusoidal basic curve whereas SP-PQH2 is the combination of two sinusoidal functions with a period ratio of 2. The basic curve of each antenna is repeated 10 times. Further geometrical characteristics are given in table

Simulation results and discussion

The proposed PQH antennas were analyzed using the Method of Moments based commercial tool ASERIS-EMC2000© (EADS CCR). The dielectric substrate supporting the printed wires was not considered since its thickness is small compared to the wavelength. The design frequency is 1775 MHz. Simulation results presented in fig. 3 reveal that the proposed SP-PQH antennas have wider bandwidth operation that conventional PQH antenna. For instance, with a specification of -10 dB, the bandwidth is respectively 2.3, 3.2 and 3.8 % for the reference PQH, the SP-PQH1 and the SP-PQH2 antennas. Simulated radiation patterns of the SP-PQH antennas are compared to the reference one in fig. 4. One can note that the maximum directivity is a bit lower than that of the reference antenna. As we reduce the height of the antenna the maximum directivity at low elevation always decreases and the main beams become wider. This behavior makes it particularly difficult to design compact helix antennas with 'iso-flux' patterns. Nevertheless, the co-polarization patterns are fully compatible with the 'iso-flux' specification. In the case of SP-PQH1, the cross-polarization level is even improved, as well as the rear radiation.

Manufacturing is now under process for the SP-PQH antennas. Good agreement was found comparing EMC2000© and measurements for the reference antenna. Hence, we can feel confident on the presented results.

Conclusion

Two sinusoidal profile compact printed Quadrifilar helix antennas have been presented. Particular care has been given to the co and cross-polarization patterns during the parametric design process to produce antennas with performances very similar to the conventional one in those aspects. A size reduction ranging from 30 to 40% is confirmed. Experimental validation will be presented at the conference.

Fig. 1 -Fig. 2 -Fig. 3 -Fig. 4 -

 1234 Fig. 1 -The basic curve can be either (a) a single sinusoidal function or the superposition of two sinusoidal curves with (b) high period ratio or (c) low period ratio

  1.

		Reference PQH	SP-PQH1	SP-PQH2
	Axial length	293 mm	196 mm	178 mm
	Wire length	329 mm	351 mm	329 mm
	Inclination angle	63°	54°	61°
	Size reduction	-	33,1%	39,3%

Table 1 -Geometrical characteristics of SP-PQH antennas compared to reference antenna

 1

Acknowledgment

The authors would like to thank C. Grevet, R. Harbi, B. Monteillet and M. Pascal for the improvements brought to the sinusoidal profile generation software.


Sami Hebib
email: sami.hebib@gmail.com

Hervé Aubert

Olivier Pascal

Nelson J G Fonseca

Lionel Ries

Jean-Marc E Lopez

Trap-Loaded Pyramidal Tri-Band Antenna for Satellite Applications

Introduction

In recent years, several researchers have devoted large efforts to develop radiating devices that satisfy the demands of the satellite telecommunication industry for improved performances in terms of multiple frequency bands and miniaturization. Multi-band antennas are often considered on satellite systems to reduce the number of onboard or ground antennas, combining several applications on the same antenna. Recently, a circularly polarized tri-band GPS/Galileo/TM MicroSat antenna based on a pyramidal structure was presented by the authors in [START_REF] Hebib | Pyramidal multi-band antennas for GPS/Galileo/MicroSat applications[END_REF][START_REF] Hebib | Multi-band antennas for GPS/Galileo applications[END_REF]. In this previous report, the design and measurement have been performed considering ideal trap-loads, that is, loads replaced by short-or open-circuits.

Here the trap-loads of the pyramidal tri-band antenna are characterized by their measured S-parameters and the resulting measured frequency performances and radiation patterns are presented and discussed.

Pyramidal tri-band antenna description

The antenna was required to operate simultaneously in the E5a, E5b and L1 frequency bands of the Galileo and GPS positioning systems and in the MicroSat Telemetry (TM) frequency band. Hence, the frequency plan of the antenna is the following:

• E5a/E5b: 50 MHz bandwidth centered at 1.197 GHz.

• L1: 24 MHz bandwidth centered at 1.575 GHz.

• MicroSat TM: 90 MHz centered at 2.245 GHz.

Return loss lower than -10 dB is required at the input port of the antenna and radiation characteristics are also specified for the three previously mentioned operating frequency bands. Figure 1(a) shows the original pyramidal tri-band antenna proposed recently by the authors [START_REF] Hebib | Pyramidal multi-band antennas for GPS/Galileo/MicroSat applications[END_REF]. It is composed of four printed wires forming a pyramid with a base angle of 45°. The ground plane is circular with a hole in the center, which was found to improve the return loss of the radiating wires. For mechanical constraints, four 50 Ohms microstrip lines are used to shift the feeding points of the antenna away from the central hole. Finally, a metallic cylinder is placed beneath the ground plane in order to reduce the rear radiation through the hole. The design process of the pyramidal tri-band antenna (see [START_REF] Hebib | Multi-band antennas for GPS/Galileo applications[END_REF]) considers ideal trap-loads, that is, loads replaced by short-or open-circuits depending on the considered frequency. Here the measured S-parameters of these loads replace the ideal equivalent circuit and are taken into account in the design.

LC f c π 2 1 =
. These trap-loads are designed to produce an open-circuit at the considered frequencies, thus defining the length of the wire contributing to the radiation at a given frequency. MuRata chip capacitors (C) and inductors (L) are chosen here for their compactness and reliability. The design process of the trap-loads is performed as follows:

• First, using the resonant frequency formula of a LC-parallel circuit and the nominal values of the different components given by MuRata, relevant couples (L,C) are selected for obtaining resonant frequencies close to the desired operating frequencies. • Then, the chips are mounted on small boards (Figure 1(b)) and the Sparameters of the trap-loads are experimentally obtained. • Finally, from the rejected band of the measured trap-loads, the configuration given in table 1

Trap-loaded antenna measurements

The obtained input return loss is depicted in Figure 2. The highest and intermediate operating frequencies of the tri-band antenna, that is, frequencies related to our choice of the trap-loads, are very close to the expected ones. By reducing the total length of the radiating wires it is possible to finely adjust the lowest operating frequency at the desired value (1.197GHz). Complementary simulations revealed that this frequency shift can be anticipated since it is predicted by the simulations results. The shift is due to the fact that the total length of the wires was defined considering ideal traps. Nevertheless, the presented results reveal the potential of this antenna. The measured bandwidths are respectively 53, 43 and 55 MHz. If a generic design is required, the higher bandwidth needs to be improved. But the MicroSat TM application requires actually a very low bandwidth inside the allowed bandwidth, which means that the problem may be overcome by 2 or 3 generic designs covering different portions of the TM band. The measured radiation patterns are in good agreement with the nominal required specifications in the first and second frequency bands (i.e., GPS/Galileo bands).

In the highest frequency band (TM MicroSat), the patterns are slightly out of the technical requirements in some radiating directions. This can be improved by adjusting the base angle of the radiating wires.

Conclusion

A novel multi-band circular polarization antenna based on pyramidal structure and trap-loads was designed and tested experimentally. The measured Sparameters of trap-loads have been taken into account in the design for obtaining the technical requirements of the antenna. The measurement results confirm the tri-band behavior of the antenna in the GPS/Galileo and TM MicroSat frequency bands. The proposed radiating structure can also be adapted to combine other satellite applications, like S-band Digital Multimedia Broadcasting.

Figure 1 -

 1 Figure 1 -(a) Top of the trap-loaded pyramidal tri-band antenna and (b) board for the measurement of the trap-loads S-parameters

Figure 2 -Figure 3 -

 23 Figure 2 -Input return loss of the trap-loaded pyramidal tri-band antenna Figure 3 displays the measured Right Handed (RH-) and Left Handed (LH-) Circular Polarization (CP) directivity patterns of the antenna at the three operating frequencies.

Table 1 -Trap-loads components for TM MicroSAT and L1 GPS/Galileo operating frequency bands

 1 is finally chosen.

		Component	Value	Reference number
	Trap-load components for	inductor	4.3 nH	LQW18AN4N3C00
	TM MicroSat band	Capacitor	1.2 pF	GQM1885C2A1R2CB01
	Trap-load components for	inductor	12.0 nH	LQW18AN12NG10
	L1 GPS/Galileo band	Capacitor	0.75 pF	GQM1885C2AR75CB01

Acknowledgement

The authors would like to thank D. Kitenge, Murata Electronique S.A.S., France, for offering the chip components used in the frame of this study.


Camille Dupont
email: camille.dupont@cea.fr

Yanis Ouakrim

Quoc Cuong Pham

UCP-Net: Unstructured Contour Points for Instance Segmentation

Fig. 1: Segmentation results of UCP-Net with only two user clicks on the object contour. The model is trained on SBD [START_REF] Hariharan | Semantic contours from inverse detectors[END_REF] but is able to perform well for unseen classes such as ground-markings (right).

Abstract-The goal of interactive segmentation is to assist users in producing segmentation masks as fast and as accurately as possible. Interactions have to be simple and intuitive and the number of interactions required to produce a satisfactory segmentation mask should be as low as possible. In this paper, we propose a novel approach to interactive segmentation based on unconstrained contour clicks for initial segmentation and segmentation refinement. Our method is class-agnostic and produces accurate segmentation masks (IoU > 85%) for a lower number of user interactions than state-of-the-art methods on popular segmentation datasets (COCO MVal, SBD and Berkeley).

I. INTRODUCTION

As deep learning gains popularity, the need for large amounts of annotated images has never been greater. Annotating images is a tedious and time consuming task, especially in the field of image segmentation where human annotators have to draw complex polygons around all sorts of objects. Interactive image segmentation aims to reduce the workload required to extract objects or regions from images. It relies on sparse user interactions such as clicks or scribbles to produce dense binary masks that precisely encompass the desired regions. It is often an iterative process, where users interact with the algorithm both to initialize and adjust the generated segmentation masks. To be considered effective, an interactive segmentation algorithm must comply with three main requirements: i) meet high-quality standards, i.e. 80-90% intersection over union (IoU); ii) be less timeconsuming than manual segmentation; and iii) be robust to variation in user interactions. It is also usually expected to be robust to domain or category shift.

Although most approaches rely on positive and negative clicks [START_REF] Xu | Deep interactive object selection[END_REF], [START_REF] Li | Interactive image segmentation with latent diversity[END_REF], [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF], recent studies have shown that extreme clicks [START_REF] Papadopoulos | Extreme clicking for efficient object annotation[END_REF], [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF] can be effectively used to give scale information and indicate precisely points that belong to the object thus removing ambiguities. In particular, the scale information allows the crop of the original image and therefore a higher resolution which significantly increases the performance compared with the full image [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF]. However, such an interaction requires users to click at exact object locations, a time-consuming task which is prone to user inattention mistakes, and to click 4 times regardless of the object complexity, which can either be insufficient at times and dispensable at others. Our method aims to extend extreme clicking toward generic contour clicking by removing its two main constraints: the fixed number of clicks and the need for specific click location. The key contributions of our work can be summarized as follows:

• We design a novel interactive segmentation pipeline suitable for consuming unconstrained contour clicks, hence relaxing the strong cognitive load of extreme points while maintaining the benefits of enclosurebased interactions such as a higher resolution and scaleinformation. • We show how such a pipeline can be trained to perform satisfactory segmentation from unstructured contour points as few as two.

• We conduct an extensive study of main enclosure based interaction types with human annotators. The resulting model is able to perform segmentation in real-time directly in a web browser (53 ms for 128 x 128 instances through WebGL) with no need for a dedicated GPU. We believed that it will constitute a more realistic solution in comparison with the standard deep learning frameworks that require standalone graphics cards.

II. RELATED WORK

a) User interaction types: Early approaches to interactive segmentation rely on low-level image features such as pixel color to infer boundaries, thus requiring samples of the foreground and background pixels [START_REF] Greig | Exact maximum a posteriori estimation for binary images[END_REF], [START_REF] Mortensen | Intelligent scissors for image composition[END_REF]. This often translates into scribble interactions on both foreground (positive) and background (negative) pixels or rough drawing around the target. This information is then fed to a heuristic algorithm to produce a segmentation. The arrival of deep neural networks able to extract higher-level features enabled for sparser interactions such as simple clicks. While most approaches use positive and negative clicks [START_REF] Xu | Deep interactive object selection[END_REF], [START_REF] Li | Interactive image segmentation with latent diversity[END_REF], [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF], recent studies have shown that extreme clicks [START_REF] Papadopoulos | Extreme clicking for efficient object annotation[END_REF], [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF] can be effectively used to give scale information and indicate precisely points that belong to the object thus delivering valuable information. As users must click on the left-most, right-most, top and bottom points of the object they want to segment, the interaction is also more consistent and reliably reproducible. Unlike positive and negative clicks, extreme points have not been extended to an iterative refinement training scheme. b) Interaction simulation: In addition to the interaction effectiveness, the mechanism behind the automatic simulation of extreme clicks is a confounding factor for both training and evaluation. Maninis et al. [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF] observe in the case of extreme clicks a decrease of up to 5% of the mean IoU between the simulated and real clicks evaluation. We briefly present commonly used simulation strategies to mimic human behavior. Foreground clicks are usually constrained to cover the central area by using a margin from the object boundary or by applying k-medoids [START_REF] Jang | Interactive image segmentation via backpropagating refinement scheme[END_REF], whereas negative clicks are either peripheral to the object or on negative objects [START_REF] Xu | Deep interactive object selection[END_REF], [START_REF] Liew | Regional interactive image segmentation networks[END_REF], [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Li | Interactive image segmentation with latent diversity[END_REF], [START_REF] Liew | Multiseg: Semantically meaningful, scale-diverse segmentations from minimal user input[END_REF], [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF]. Stricter interaction policies such as bounding boxes and extreme points simply include noise by perturbing the corners of the perfect coordinates up to a certain pixel amount [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], [START_REF] Benenson | Large-scale interactive object segmentation with human annotators[END_REF], [START_REF] Shahin | Fairs -soft focus generator and attention for robust object segmentation from extreme points[END_REF] or scale percentage [START_REF] Wang | Object instance annotation with deep extreme level set evolution[END_REF].

c) Embedding User Interactions: User interactions being sparse, they require an effective pre-processing so as to be fully perceived and exploited by the segmentation network. A popular pre-processing consists in encoding the interactions into a 2d-image that can be fed to the convolutional network. Clicks are usually turned into Euclidean [START_REF] Xu | Deep interactive object selection[END_REF], [START_REF] Liew | Regional interactive image segmentation networks[END_REF], [START_REF] Hu | A fully convolutional two-stream fusion network for interactive image segmentation[END_REF], [START_REF] Li | Interactive image segmentation with latent diversity[END_REF], [START_REF] Jang | Interactive image segmentation via backpropagating refinement scheme[END_REF] or Gaussian [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Li | Interactive image segmentation with latent diversity[END_REF], [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Forte | Getting to 99% accuracy in interactive segmentation[END_REF] distance maps. The authors of [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], [START_REF] Benenson | Large-scale interactive object segmentation with human annotators[END_REF] observed that Gaussians yield better results than distance transforms. Three other transforms led to an improvement over Gaussians: binary disks [START_REF] Benenson | Large-scale interactive object segmentation with human annotators[END_REF], superpixels [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF] and multifocal ellipses [START_REF] Shahin | Fairs -soft focus generator and attention for robust object segmentation from extreme points[END_REF], but no comparison between them was provided.

In 2016, Xu et al. [START_REF] Xu | Deep interactive object selection[END_REF] proposed the first interactive segmentation pipeline relying on a Fully Convolutional Network (FCN) encoder-decoder taking the concatenation between the RGB image and the embedded user interaction as input. Most modern approaches to interactive segmentation follow this lead [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], [START_REF] Benenson | Large-scale interactive object segmentation with human annotators[END_REF], [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF], [START_REF] Liew | Regional interactive image segmentation networks[END_REF], [START_REF] Liew | Multiseg: Semantically meaningful, scale-diverse segmentations from minimal user input[END_REF], [START_REF] Shahin | Fairs -soft focus generator and attention for robust object segmentation from extreme points[END_REF]. While the majority use the whole image as input [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Majumder | Content-aware multi-level guidance for interactive instance segmentation[END_REF], [START_REF] Liew | Regional interactive image segmentation networks[END_REF], [START_REF] Liew | Multiseg: Semantically meaningful, scale-diverse segmentations from minimal user input[END_REF], [START_REF] Forte | Getting to 99% accuracy in interactive segmentation[END_REF], [START_REF] Jang | Interactive image segmentation via backpropagating refinement scheme[END_REF], recent architectures based on object enclosure [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], [START_REF] Wang | Object instance annotation with deep extreme level set evolution[END_REF], [START_REF] Shahin | Fairs -soft focus generator and attention for robust object segmentation from extreme points[END_REF], [START_REF] Benenson | Large-scale interactive object segmentation with human annotators[END_REF], [START_REF] Zhang | Interactive object segmentation with inside-outside guidance[END_REF], [START_REF] Sofiiuk | f-brs: Rethinking backpropagating refinement for interactive segmentation[END_REF] feed image crops to the FCN to achieve speed-up and preserve object details. The approach proposed by [START_REF] Sofiiuk | f-brs: Rethinking backpropagating refinement for interactive segmentation[END_REF] takes the whole image as input and exploits the predicted mask boundaries to obtain a crop of the image, which is subsequently fed into a refinement model. Instead of using image patches, Liew et al. [START_REF] Liew | Regional interactive image segmentation networks[END_REF] crop the feature maps around the input clicks to infer local predictions which are reassembled afterwards.

In order to learn deep features for images and interaction maps individually, the authors of [START_REF] Hu | A fully convolutional two-stream fusion network for interactive image segmentation[END_REF], [START_REF] Forte | Getting to 99% accuracy in interactive segmentation[END_REF] use two separate encoder streams: one for the image and another one for the interactions, leading however to a heavier model.

In comparison with negative and positive clicks, extreme clicks have the advantage of being less ambiguous and enable to reduce the search space by extracting an RoI around the object. However, such methods require users to click at exact object locations which is more constraining than positive and negative clicks. Moreover, they require users to click at least 4 times regardless of the object complexity. To solve these two main limitations, we propose a novel interactive segmentation approach that exploits unconstrained contour clicks ranging from 2 to n. This increased flexibility enables the unified approach to generate masks with different precision levels. We demonstrate that our method is able to deliver high-quality results with a lower number of clicks than the current state of the art of interactive segmentation.

III. METHOD

Our network is built upon both approaches based on extreme clicks and those based on positive negative clicks. Exploiting the contour clicks representing the target object enables us to crop the original image and benefit from a higher resolution. Similar to [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF], the crop is concatenated with its corresponding click heatmap and then fed to a binary segmentation network (Figure 2). However, unlike extreme clicks methods and similar to positive-negative methods, we choose to investigate a much broader range of number of clicks with unconstrained locations in an iterative fashion. This flexibility speeds up the interaction process even further and adapts well to both coarse and fine objects. Indeed, we observed that, in most cases two unconstrained user clicks provide enough information for a model to predict an accurate segmentation mask (Table I). In some cases, complex objects or situations can lead to the two clicks being insufficient for the model to correctly segment the object (Figure 6). In regard of this observation, we propose an iterative approach where correction clicks are added until a satisfactory segmentation mask is predicted by the model. Therefore, the number of clicks fits the complexity of the setup, thus speeding up the annotation process.

From a user's perspective, our interactive segmentation pipeline can be summarized as follows: first the user clicks on two locations of the object contour, then they can add additional contour clicks to correct or refine the mask (Figure 2). a) Simulating user interactions: Simulating user interactions is a challenge in the field of interactive segmentation. We propose a novel online iterative training scheme, during which our model is trained with a combination of three strategies to simulate human contour clicks. When asking 5 annotators to draw a few clicks on object contours on the Berkeley data set (100 instances), we observe that they instinctively distribute them to best represent the targeted object breadth. In particular for n = 2 contour clicks, we measure that the distance ratio between clicked pair points and the furthest ground truth pair points is approximately distributed as a normal random variable with mean 1 and standard deviation 0.03 (Figure 3). The interaction can therefore be simulated by selecting pairs producing a distance following this distribution, both during training and testing.

We describe here the other two simulation strategies for n > 2 as illustrated in Figure 4. Let C gt be the set of ground truth contour pixels.

• Geometric strategy: gradually refines salient regions of the target. We denote C geo the contour pixels resulting from the conversion of the n-1 points set into polygon boundaries. The n th click is then obtained sequentially as the furthest ground truth pixel from C geo so as to mold the clicks to the shape of the target:

p n = arg max p∈C gt min q∈C geo p -q , n > 2 (1)
• Corrective strategy: relies upon the prediction of the interactive segmentation network from n -1 clicks. We note C pred its corresponding contour pixels. The n th click is defined as the furthest ground truth pixel from the prediction:

p n = arg max p∈C gt min q∈C pred p -q , n > 2 (2)
Fig. 5: Mean IoU between ground truth mask and itself when cropped using the smallest-circle method enlarged with expansion ratios ranging from 1 to 1.9. The n = 2 clicks are simulated using max-distance ratio of 0.95. We choose the cut-off value r opt = 1.4.

Batch of ∆n new clicks can be added at once by partitioning the erroneous areas and applying the strategy to each blob. The first aims to best represent the targeted object by gradually refining salient regions. The second aims to simulate human correction to the network errors by selecting contour clicks furthest from the prediction contours. The corrective strategy applies natively to multi-region objects or objects with holes as it is based on euclidean distance from contours regardless of the contours hierarchy. The extension of the geometrical strategy to multi-regions is defined using a coarse-to-fine policy by prioritizing exterior hull coverage and subsequently interior regions as shown in Figure 4.

b) Region of interest: Similarly to [START_REF] Mahadevan | Iteratively trained interactive segmentation[END_REF], we feed the network with a crop of the original image to benefit from a higher resolution. While extracting a region of interest is straight-forward in the case where provided clicks give a good approximation of the shape of the targeted object, it can be more difficult in the case of very sparse contour clicks (under four). As described previously, we conducted a human experiment that showed an innate distribution of the clicks to best represent the breadth of the targeted object. To ensure full enclosure of the targeted object, we therefore extract the RoI by solving the smallest-circle problem. To do so, we rely on Welzl's algorithm [START_REF] Welzl | Smallest enclosing disks (balls and ellipsoids)[END_REF]. It corresponds to the diagonal's circle and the circumscribed circle for two and three points respectively (Figure 2). In order to reckon the users' interaction fluctuation, guarantee object enclosure and have context information, we expand the circle's diagonal by 1.4 (Figure 5). The crop generated by this cut-off expansion ratio ensures a negligible mean loss (<1%) on more than 20K instances in the SBD train set [START_REF] Hariharan | Semantic contours from inverse detectors[END_REF] using simulated pair clicks of 0.95 fraction.

c) An iterative training scheme: The training first consists of a warm-up phase with two contour clicks as input. These clicks are simulated geometrically as described in the previous section. During a second stage, we aim to cover a wider range of click numbers and randomly pick n add additional geometric contour clicks to each sample. Experimentally, we observe that a range n add ∈ [0, 8] allows for precise segmentation masks (Figure 7).

IV. EXPERIMENTS A. Datasets

We evaluate our model across five publicly available segmentation datasets. To compare our model with other segmentation methods, we use the mean number of clicks necessary to reach the typically used 85-90% IoU threshold, known as the Number of Clicks metric (NoC @x%). Forte et al. [START_REF] Forte | Getting to 99% accuracy in interactive segmentation[END_REF] argue this widely used metric fails to characterize the ability of models to progress over a wider range of clicks, particularly useful for applications with high-quality requirements such as image editing. They recommend the additional use of accuracy score across a range of clicks. We use the SBD dataset [START_REF] Hariharan | Semantic contours from inverse detectors[END_REF] to train the proposed model. It includes 8,498 training images and 2,857 test images, corresponding respectively to 20,164 and 6,671 instances.

To simulate user clicks during evaluation, we first generate 2 clicks on the target object and then apply the corrective strategy to refine the prediction. To compute the NoC@x% metric, the refinement is limited to the targeted IoU threshold. To compute the mIoU for progressive n clicks, the refinement is limited to n clicks.

B. Comparison of user interactions

To compare contour clicks with traditional enclosure interactions, we conducted an experiment with five human annotators. Annotators had to label the 100 images of the Berkeley dataset [START_REF] Martin | A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics[END_REF] using bounding boxes, extreme clicks, as well as three free contour clicks and two free contour clicks.

The user guidelines for each interaction types are shown in Figure 10. To both designate the object of interest in the image and prevent the users from anticipating their cursor

COCO MVal @85% VOS-Wild* [START_REF] Benard | Interactive video object segmentation in the wild[END_REF] [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF]) and unconstrained contours clicks using either simulated clicks or real clicks on the 100 Berkeley images [START_REF] Martin | A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics[END_REF]. * Re-implemented using a EfficientNet-B6 backbone, so that only the user interaction varies. position, a miniature of the image with the ground truth mask of the targeted object is briefly displayed during two seconds.

Then the miniature is replaced with the full resolution image on which the user can draw a box or click on contour points. Figure 11 gives an overview of the annotation interface. While click precision was not mentioned in the guidelines, we calculated the accuracy with respect to the groundtruth box to ensure fairness in time comparison between extreme points and bounding boxes and found no significant difference in standard deviation (3.2% vs 3.6%).

Results are shown in Table II. Two user-clicks proved to be almost three times faster than extreme clicks, while also being significantly faster than simple bounding boxes. Note that this finding is contradictory with the results of Papadopoulos et al. [START_REF] Papadopoulos | Extreme clicking for efficient object annotation[END_REF] who observed that extreme points (7.2s) were significantly faster than bounding boxes (34.5s).

C. Implementation details a) Architecture and hyper-parameters: Like many previous interactive segmentation methods [START_REF] Bredell | Iterative interaction training for segmentation editing networks[END_REF], we use a U-Fig. 9: Examples of predictions on the Berkeley dataset [START_REF] Martin | A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics[END_REF] with their corresponding input clicks.

Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] architecture. We replace the VGG backbone with an EfficientNet-B6 [START_REF] Tan | Efficientnet: Rethinking model scaling for convolutional neural networks[END_REF] which has become the backbone of choice for many deep learning tasks and is at the top of the ImageNet classification leader-boards. After a pre-training on ImageNet, we train on SBD train (20,172 instance images; 8,498 images) and use the SBD val for validation (6,671 instance images). Simulated user clicks are represented as Gaussian distance functions and fed to the model as a fourth image channel. Unless specified otherwise, the results given in this report were obtained while evaluating on SBD val. We use the dice coefficient as our loss function as our experiments demonstrated that it enables a slightly higher mean IoU than binary cross entropy alone and binary cross entropy and the dice coefficient combined. We use a learning rate of 1e-5, that is reduced to 1e-6 when the loss has not been improving for the last 15 epochs. Training stops after 7 epochs without improvement of the loss function. We use a batch size of 12 as it gave better results than batch sizes of 8 and 16. We resize images to 256*256 as it enables to obtain a better IoU than resizing the images to 128*128 or 512*512. We set dropout to 0.5.

b) Data augmentation: As genericity is a critical component in annotation assistance systems, we apply a substantial variety of image augmentations to our images during the training phase. We rely on the ImgAug [START_REF] Jung | imgaug[END_REF] library to apply noise (drop out, coarse drop out, Gaussian noise, weather changes...), color changes (gama contrast, temperature...) and geometric transformations (perspective, vertical and horizontal flips...) with default parameters. In terms of user interaction, we add Gaussian noise to the simulated clicks as shown in Figure 3.

D. Evaluation

Table I provides a comparison of UCP-Net against previous interactive segmentation methods. We reach standard benchmark IoUs with lower numbers of clicks on SBD and Berkeley while getting close to state of the art on GrabCut. Moreover, we conducted an ablation study to evaluate the accuracy gain between extreme and unconstrained contour points. Following DEXTR's training protocol [START_REF] Maninis | Deep extreme cut: From extreme points to object segmentation[END_REF] with 4 extreme points using our architecture, we observe that two unconstrained contour clicks allow for a similar accuracy (-1.4%) while being more than twice as fast (Table II, III). We also observe experimentally a robustness to click location variation (Figure 8), which further validates unconstrained clicks as a flexible and cognitively easy option for interactive segmentation. Qualitatively, our approach seems robust to object shape variation, occlusion and dense scenes (Figure 9). Figure 7 gives a comparison of the ability of our model to improve segmentation masks with an increase number of user clicks with other methods. Our pipeline is able to continuously improve IoU with an increasing number of clicks. We observe a larger gap against other methods on SBD [START_REF] Hariharan | Semantic contours from inverse detectors[END_REF] which may be due to bias as its train and test set are most resembling. Note that we do not include the GAIS method in the curve comparison as they use a synthetic dataset for training.

When compared against other contour based methods, UCP-Net enables for a significant drop in the number of needed user clicks to achieve a satisfactory segmentation on SBD, GrabCut and COCO MVal.

V. CONCLUSION

With our generic contour based approach we have shown that unconstrained contour clicks enable for faster and more accurate segmentation thanks to fewer user clicks. We set a new state of the art of interactive segmentation on SBD, Berkeley, and COCO MVal. Our method is suitable for annotation purposes, enabling to label datasets requiring only a handful of user interaction. Moreover, it is also perfectly suitable for image editing applications as our iterative scheme makes it possible to reach a very high accuracy. In future work, investigating the contour clicks' embedding might prove relevant to best exploit this interaction as it was found for extreme clicks [START_REF] Wang | Object instance annotation with deep extreme level set evolution[END_REF]. Moreover, the usage of the previously predicted segmentation yields significant improvement in iterative positive and negative interaction approaches [START_REF] Benard | Interactive video object segmentation in the wild[END_REF], [START_REF] Forte | Getting to 99% accuracy in interactive segmentation[END_REF] and may be equally applicable for unconstrained clicks. Given the nature of contour clicks, they could also be further exploited to simultaneously segment or correct objects which are close to one another or which overlap as they share common boundaries.

Fig. 2 :

 2 Fig.2: Method overview. Unconstrained user clicks (green dots) are used to crop a Region of Interest, calculated to ensure the object enclosure by solving the smallest-circle problem on SBD train set[START_REF] Hariharan | Semantic contours from inverse detectors[END_REF]. Like interactive segmentation methods relying on extreme clicks, the crop is then fed as a fourth image channel to a CNN, illustrated here by U-Net which was used in our experiments. Through a unified approach, UCP-Net supports additional corrective clicks (orange dot) which can be used to refine the predicted segmentation mask.

Fig. 3 :

 3 Fig. 3: User pair clicks distance distribution for N = 5 annotators on the Berkeley dataset [21] (top). Visual examples of clicks pairs corresponding to 0.95 and 1 distance ratios with respect to the maximum distance (bottom).

Fig. 4 :

 4 Fig. 4: Visual example of two strategies for contour clicks simulation. Geometrical simulation (a) aims to gradually refine salient regions of the target (white line). Corrective strategy (b) simulates an iterative user-like behavior where the user clicks on the contour further (red dots) from the previous prediction (yellow line).

Fig. 6 :

 6 Fig. 6: Two example cases where a corrective click is added: target ambiguity (top) and model failure (bottom).

Fig. 7 :

 7 Fig. 7: Curves of mean IoU scores after n clicks for Grabcut [23] (a), Berkeley [21] (b) and SBD [1] (c) test sets. Note that we excluded the out-performing method [18] on Grabcut which uses additional synthetic data during training.

Fig. 8 :

 8 Fig. 8: Location noise during training allows for a robustness to user variation.

Fig. 10 :

 10 Fig. 10: Annotation visual guidelines given during the time comparison experiment for (a) bounding box, (b) extreme points, (c,d) free contour clicks.

Fig. 11 :

 11 Fig. 11: Experiment interface. The target object is shown briefly during 2s (left), with a reduced image size to prevent the user from anticipating the cursor position. Afterwards, the image is displayed at full resolution (right).

TABLE I :

 I Comparison table. mIoU is specified for methods which did not reach the @x%. *Methods relying on contour clicks. **Using different types of interactions, the authors gave a NoC equivalent of their result.

TABLE II :

 II

	Interaction type	NoC Simulated clicks Real user clicks
	Extreme clicks [7]*	4	89.1	87.7
	Free contour clicks	2	87.0	86.3

Interaction time for extreme clicks, bounding boxes and unconstrained contours clicks on the 100 Berkeley images [21] (N = 5 annotators).

TABLE III :

 III mIoU comparison between extreme clicks (DEXTR