E Vanhove
email: emilie.vanhove@onera.fr.

T Tondu

J F Roussel

Delphine Faye
email: delphine.faye@cnes.fr.

Pascale Guigue
email: pascale.guigue@cnes.fr.

In Situ Real-Time Quantitative and Qualitative Monitoring of Molecular Contamination

The quantitative and qualitative monitoring of contamination is an important issue for the mitigation of the risks induced by contamination. In situ and real-time measurements of contamination levels are currently performed with good accuracy by using quartz microbalances. However, they have to be completed by chemical analyses to identify the nature of the contaminants. Unfortunately, in situ techniques are limited to a very rough characterization. A transfer of the samples is then required, which prohibits real-time monitoring and may lead to the partial degradation of the samples. To tackle this challenge, an experimental technique, coupling thermogravimetric analysis and mass spectrometry, has been developed at ONERA. This method takes advantage of a preseparation of the species through the thermogravimetric analysis. A numerical tool was moreover developed to process automatically experimental thermogravimetric analysis/mass spectrometry data. It enables determination of the contribution of each species (deconvolution of thermogravimetric analysis measurements species by species, both for quartz crystal microbalance measurements and mass spectrometry spectra) and extraction of the mass spectrum of each of these species. The results of this analysis are presented for the characterization of an adhesive widely used for space applications. The deconvolution in species matches very well the experimental data. Nomenclature dmt∕dt = total mass reemission rate in 10 -8 g • cm -2 • s -1 M j t = mass spectrometry measurement for mass-to-charge ratio j arbitrary unit m i t = dimensionless mass reemitted for chemical species i m∕z = mass-to-charge ratio in u m 0i

= initial mass of the chemical species i in 10 -8 g • cm -2 s ji = component of mass spectrum of species i corresponding to mass-to-charge ratio j in arbitrary units TGAt = thermogravimetric analysis experimental measurement in 10 -8 g • cm -2 • s -1

I. Introduction

M OLECULAR contamination can seriously compromise the objectives of a mission. It can indeed significantly degrade the performance of measuring instruments and solar panels, as well as thermal control systems. To mitigate this risk, a number of tests are systematically performed on ground during the phases of design, manufacture, and validation of the satellite [START_REF] Tribble | Fundamentals of Contamination Control[END_REF][START_REF]Standard Practice for Preparation of Aerospace Contamination Control Plans[END_REF].

The most widely used test to characterize this contamination consists of monitoring the mass of deposited contaminants per unit area by using quartz microbalances [START_REF]Standard Test Method for Total Mass Loss and Collected Volatile Condensable Materials from Outgassing in a Vacuum Environment[END_REF][START_REF]Kinetic Outgassing of Materials for Space[END_REF][START_REF]Standard Test Method for Contamination Outgassing Characteristics of Spacecraft Materials[END_REF]. This measurement is both very reliable and very sensitive [START_REF] Vashist | Recent Advances in Quartz Crystal Microbalance-Based Sensors[END_REF][START_REF] Wallace | New Generation of Miniaturized, High-Mass-Sensitivity Quartz Crystal Microbalances (QCMs) for Space Applications[END_REF]. However, this technique does not allow determination of the chemical nature of each of the contaminants nor its relative proportion in the deposit. To complement this measurement, various chemical analyses can thus be carried out, such as in situ mass spectrometry, gas chromatography coupled to mass spectrometry, Fourier transform infrared spectroscopy, etc. [START_REF] Anderson | Mass Spectrometry of Spacecraft Contamination Using Direct Analysis in Real-Time Ion Source[END_REF][START_REF] Mandrile | Direct Detection and Quantification of Molecular Surface Contaminants by Infrared and Raman Spectroscopy[END_REF][START_REF] Pang | Real-Time Molecular Contamination Monitoring During Spacecraft Development[END_REF][START_REF]Detection of Organic Contamination of Surfaces by Infrared Spectroscopy[END_REF][START_REF] Guyt | Detection of Organic Contamination on Surfaces by Infrared Spectroscopy[END_REF]. Unfortunately, all of these techniques have severe limitations.

To begin with, a large part of them in fact require a transfer of samples. This transfer is undesirable for two reasons. First, a transfer is highly likely to irremediably deteriorate samples (pressure or temperature changes, spontaneous evolution of samples over time such as reemission or phase change, etc.). This would raise doubts extremely hard to clear up, for example, the extent to which the quartz crystal microbalance (QCM) measurements can really be compared with the results of the chemical analysis.

The second reason is that this transfer prevents the chemical characterization from being performed in real time. The time evolution information is thus definitively lost. This information is, however, of particular interest. On the one hand, it allows a much better correlation between the quantitative measurements (the deposited mass) and the chemical analyses (nature of contaminants). On the other hand, it enables the kinetic study of contamination phenomena (outgassing, transport, reemission, etc.). Some of the most recent physical models are indeed based on the individual behavior of each chemical species of a mixture of contaminants [START_REF]Kinetic Outgassing of Materials for Space[END_REF][START_REF] Roussel | Progress on the Physical Approach to Molecular Contamination Modeling[END_REF]. The same is true for models of contamination-UV synergy [START_REF] Tondu | New Mechanism for VUV Fixation of Contamination[END_REF][START_REF] Roussel | Ultraviolet Fixation of Molecular Contamination: Physical Model, Numerical, Implementation and Validation[END_REF]. As of today, however, common experimental measurements only monitor the total contaminant deposit. In the future, a real-time analysis able to quantitatively separate the contributions of each species would, on the other hand, thus enable 1) a much better assessment of contamination mechanisms at work, 2) a much more realistic extraction of model parameters and a much better characterization of the kinetic properties of each contaminant, and 3) a more relevant and comprehensive analysis of tests performed on ground.

Some techniques, such as Fourier transform infrared spectroscopy and mass spectrometry (MS) can, however, be operated in situ.

Unfortunately, it can be pretty hard to implement them with the required sensitivity and, above all, to interpret the measurements, because they result from a complex mixture of a priori unknown contaminants. As a consequence, these analyses are generally not quantitative and are often limited to a very rough characterization.

To meet this challenge, ONERA has developed an analytical technique for the real-time and in situ qualitative (nature of each deposited contaminant) and quantitative (deposited mass of each species) monitoring of molecular contamination by coupling the thermogravimetric analysis (TGA) and MS analyses [START_REF] Tondu | Mixture Effects in Contaminant Reemission[END_REF]. In the first part of this study, the experimental setup, the measurements, and a preliminary analysis of these data are presented. The method is applied to the characterization of a real contaminant, the Scotch-Weld EC-2216, an adhesive frequently used in the aerospace industry. Although TGA results in a kind of rough species separation, this separation is incomplete. As a result, the mass spectrum measured is still the one of an unknown mixture of contaminants. Because such spectra are very complex, the analysis of experimental data as shown in the first part requires a great deal of expertise and is unreasonably time consuming. Furthermore, it does not allow the extraction of the mass spectra of each one of the chemical species. ONERA therefore upgraded its numerical tool COMPEX to enable the automatic analysis of the TGA/MS experimental data. The second part briefly describes this tool and presents the results of this digital processing.

II. Coupling of TGA and MS Analyses

In this first part, the experimental setup, the protocol used, the experimental data, and their analysis are explained.

A. Experimental Setup

Contamination photons synergy is the experimental facility dedicated to the study of molecular contamination at ONERA. An effusion cell (20-200°C) generates a controlled molecular beam of contaminants toward a collection plate (steel plate of typically 10 cm 2 ) and a QCM (Maxtek 6 MHz), both individually temperature controlled from -100 to 100°C (cooling with liquid nitrogen and resistance heating, system developed by ONERA). During the TGA, contaminants reemitted from the collection plate are analyzed using a mass spectrometer (Bruker). QCM frequencies are sensitive to temperature. This dependence has been characterized and subtracted to TGA measurements.

B. Experimental Protocol

The protocol used was specifically designed for the characterization of real contaminants. It includes four steps of outgassing. At the end of each step, a TGA/MS measurement is performed.

The four outgassing steps were performed at 75, 100, 125, and 150°C. Each step lasted about 20 h. The contaminants were collected on the collection plate at -80°C. The temperature profiles of the effusion cell and of the plate are given in Fig. 1. A TGA was performed at the end of each step at the heating rate of 2°C∕ min. Reemitted contaminants were then analyzed by mass spectrometry. The TGA/MS data recorded after the first outgassing step at 75°C were not exploited because the amount of deposited contaminant was too low.

C. Experimental Data

ATGA/MS experiment consists of one TGA and 250 mass signals.

For each m∕z between 1 and 250, the intensity is measured as a function of time, and thus as a function of temperature, because the experiment carried out is a TGA.

Figure 2 shows the three TGAs monitored after the outgassing steps at 100, 125, and 150°C (i.e., total mass reemission rate from the QCM). By way of illustration, the measurements obtained for the mass 47 for the three outgassing steps are given in Fig. 3.

D. Experimental Data Analysis: Deconvolution 1

Although TGA performs some species separation, it remains incomplete. Furthermore, peak emissions partly overlap. The issue of the deconvolution is therefore to use mass spectrometry data to separate the contributions of the different chemical species and to identify them (Fig. 4). However, several species contribute to each mass signal monitored by mass spectroscopy, making the interpretation of experimental data quite difficult.

As a consequence, the deconvolution was performed by identifying the masses that stem from one single species. Such an identification was based on the following criteria:

1) A mass signal having a unique and very narrow peak (e.g., mass 47, Fig. 3) most likely corresponds to a single species. 2) When masses separated by at least several unities have identical complex signals (several peak emissions), they are very likely to be emitted from a single species. By contrast, isotopes and, in particular, carbon-13 lead to M 1 and M 2 masses that have identical signals but may well correspond to several species.

3) The heaviest masses have a lower probability to correspond to several species. 4) Finally, the temperatures that correspond to a peak or a shoulder of the TGA performed after the step at 150°C were identified. The analysis thus focused on the masses that show a sharp peak for these temperatures.

These masses were called characteristic masses and were used to identify the species. The TGA, measured by the QCM, is the total mass reemission rate. It can be described as the sum of the masses of each species. It is therefore a linear combination of the characteristic masses of these species. It was thus finally possible to reproduce the experimental TGAs with only five main contaminants, for which the characteristic masses were the masses 106, 76, 109, 86, and 212 (Fig. 4). The mass 76 saturates for the outgassing step at 150°C. However, as the masses 47 and 76 were proportional for all the outgassing steps (Fig. 5), the mass 47 was used instead of the mass 76 for the TGA deconvolution. A very satisfying fit of experimental data was thereby obtained for the three outgassing temperatures, although the reemission profiles recorded after each temperature step differ widely. In this first analysis, the less abundant contaminants were deliberately neglected. Thus, for instance, for the outgassing step at 150°C, a contaminant, emitted at approximatively -45°C, seems to be lacking.

The first part of this paper described how to determine in situ and in real time the contribution of each species of a contaminant mixture during a TGA experience by coupling the TGA and MS analyses. This TGA deconvolution enables for each identified species a first estimation of its reemission properties as well as of its total deposited mass at the end of each outgassing step. Based on this deconvolution, thanks to the masses identified as characteristic of a single species, it is also possible to determine the contribution of each species to the deposit during the outgassing step. This technique thus provides new information that could be exploited to validate contamination models (outgassing and reemission) and to extract their parameters. However, this method has two limitations: First, the interpretation of experimental data is very tedious, and second, it is not possible to extract in this way the mass spectrum of each species to identify them. This is why the numerical tool COMPEX developed by ONERA was enhanced to enable the automatic processing of TGA/MS data.

III. Numerical Processing of TGA/MS Data A. Numerical Model

The available experimental data are the TGA measurements, on the one hand, and the mass spectrometry data, on the other hand. A TGA (total mass reemission rate) can be described as the sum of the contributions of each species i.

TGAt dmt dt X i m 0i dm i t dt (1)
In the same way, we can break down the mass spectrometry measurement M j t monitored for each mass j:

M j t X i s ji m 0i dm i t dt ( 2
)
The unknowns are then the initial mass and the mass spectrum s ji of each species.

A higher weight (w > 1, here 50) is, moreover, given to the TGA. The error function is thus

w X i m 0i dm i t dt -TGAt 2 X j X i s ji m 0i dm i t dt -M j t 2 (3)
At each step, the optimum spectra s ji opt are computed using the least-squares method, the masses being considered fixed. Current spectra s ji n are replaced at the step n 1 by spectra defined by Eq. (4):

s ji n 1 s ji n s ji opt 2 (4)
Equation ( 2) being linear in s ji , the error decreases. The spectra are then fixed and the masses are treated by the same method. Because the error is reduced with each iteration, the algorithm converges and a local minimum is found.

B. Simulation: Deconvolution 2

The TGA performed immediately after the outgassing step at 150°C is simulated. Ten species are used for this simulation. To evaluate the ability of our numerical tool to process TGA/MS data, we compare the results of the experimental data analysis described in the first part of this paper (deconvolution 1) with those provided by the numerical tool (deconvolution 2). In particular, it is important to assess whether or not the chemical species showing up in the two deconvolutions are identical. To this end, we use the masses (masses monitored by mass spectrometry) that had been identified as characteristic of a chemical species. These are the masses resulting from the contribution of a single species, or at least for which one species is predominant. Thus, for the sake of simplicity, because no other information is at first available, the chemical species are named after their characteristics masses: For instance, the species which is the (quasi) exclusive contributor to the mass 76 (Fig. 3) is called S76.

TGA

Figure 6 shows, at the bottom, the COMPEX simulation (deconvolution 2) of the TGA performed after the outgassing step at 150°C and, at the top, the deconvolution 1 of this TGA. Overall, these two deconvolutions are very similar, which is a very satisfying result. The simulation perfectly fits the experimental TGA. The weights of each species (masses initially deposited, S76, S86, S109, and S212) are very close to the ones of deconvolution 1. The main differences are slightly different reemission parameters for the species S109 (remission occurs at a lower temperature in the simulation) and the appearance of some additional species (A, B, C, D, E, F), which globally correspond to missing masses in deconvolution 1.

Indeed, although deconvolution 1 is robust (three outgassing temperatures were properly described with a small number of species) and, as a consequence, reliable, this deconvolution relies on a number of approximations (modest contributions are neglected, etc.). As a result, deconvolution 1 is not an absolute reference but rather a good indication of the likelihood of the results.

Characteristic Masses

The masses that had been identified as characteristic of a single (or at least predominant) species were the masses 47 (signals of mass 47 and 76 are quasi identical), 109, 86, and 212. These masses are shown in Fig. 7. Again, a really good fit of experimental data is obtained for these characteristic masses (Fig. 7) as well as for all of the monitored mass signals (not shown).

The masses 47 and 212 result almost exclusively from the contributions of the species S76 and S212, respectively, and the species S86 and S109 predominantly contribute to the masses 86 and 109, respectively. The species S76, S212, S86, and S109 were thus properly identified. The contributions of the species S86 and S109 are a bit difficult to distinguish from each other because they have close reemission parameters and mass spectra.

Mass Spectra

The advantage of the automatic data processing is that it now allows extraction of the mass spectrum of each species. The proper identification of these chemical species would, however, require further data treatment, including the comparison of the spectra with a database and or gas chromatography (GC)/MS data. Nevertheless, typical fragment patterns can yet be observed. For example, in the spectrum of the species S109 (Fig. 8), C n H 2n-3 fragments clearly appear, which could point at S109 being an alkyne.

C. Conclusions

The results of this simulation are very promising: They are selfconsistent and in line with the ones of the previous deconvolution. The main species of the mixture of contaminants are properly identified. Further data processing, including the comparison of the spectra with a database, is, however, required to more precisely determine their chemical nature. It would, moreover, be very interesting to compare these spectra with the GC/MS analysis of the EC-2216. Processing a complete data set (i.e., comprising several TGA performed at different outgassing temperatures) would as well enable a further validation and a more accurate evaluation of the results (initial masses, reemission properties, and mass spectra).

IV. Conclusions

This paper presented the implementation of the coupling of the TGA and MS analyses and the treatment of the experimental data thus generated. This in situ and real-time characterization method allows the analysis of complex mixtures of contaminants with the objective of determining the nature, quantity, and outgassing and reemission properties of each chemical species of the deposit. Analyzing TGA/ MS experimental data is, however, fastidious and unreasonably time consuming. To overcome this difficulty, a numerical tool able to automatically process such data was developed. tool enables the species-by-species deconvolution of a TGA experiment and the extraction of the mass spectrum of each identified species. The estimation of reemission properties is also greatly facilitated. Ultimately, the determination of these mass spectra would also allow the deconvolution of the contaminant emitted at each step species by species (characterization of the outgassing properties of each species). The method has been applied to the characterization of an adhesive widely used in space, the Scotch-Weld EC-2216. The results are very promising because the deconvolutions obtained are globally consistent and the simulation fits very well experimental data (TGA and MS data). Further data processing, including the comparison of the spectra with a database, is, however, required to more precisely determine the chemical nature of the species.

Fig. 1

 1 Fig. 1 Temperatures of effusion cell and collection plate.

Fig. 2

 2 Fig. 2 TGA measurements, outgassing steps at 100, 125, and 150°C.

Fig. 3

 3 Fig. 3 TGAs performed after the outgassing steps at 100, 125 and 150°C , m∕z 47.

Fig. 4

 4 Fig. 4 Species-by-species deconvolutions of TGA measurements, outgassing steps at 100, 125, and 150°C.

Fig. 5

 5 Fig. 5 TGAs performed after the outgassing steps at 100, 125 and 150°C, m∕z 47 and 76.

Fig. 7

 7 Fig. 7 Species-by-species deconvolution of m∕z 47, 86, 109, and 212.

Article in Advance / VANHOVE ET AL. Downloaded by ONERA on January 6, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.A33505

Downloaded by ONERA on January 6, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.A33505

Article in Advance / VANHOVE ET AL.

Acknowledgments

The results obtained at ONERA were funded by Centre National d'Etudes Spatiales Research and Technology and ESA Technology Research Programmes, for which the ONERA authors are very grateful.


Thomas Tondu

Emilie Vanhove

Jean François Roussel

Delphine Faye

Mixture Effects in Contaminant Reemission

The deposit of a pure contaminant or of contaminant mixtures may exhibit complex behavior. This impacts the possible in-flight reemission of these deposits as well as the interpretation of thermogravimetric analyses. These effects were studied, first on theoretical grounds, and then experimentally on controlled mixtures of pure contaminants or uncontrolled mixtures stemming from a real material outgassing. Several effects were clearly identified, such as phase segregation and various mixture behaviors, corresponding to quick or slow diffusion of the contaminants within the mixture.

Nomenclature c 1

= contaminant 1 concentration in fraction of a monolayer c bulk;i = bulk concentration of contaminant i in fraction of a monolayer c dep;i = concentration of contaminant i in the deposit in fraction of a monolayer c surf;i = surface concentration of contaminant i in fraction of a monolayer D = diffusion coefficient in monolayers per time unit dm∕dt = total evaporation rate in monolayers per time unit dm i ∕dt = evaporation rate of contaminant i in the mixture in monolayers per time unit dx dep ∕dt = speed of the surface of the evaporating deposit in monolayers per time unit m 2 = contaminant 2 mass in monolayers v pure;i = evaporation rate of contaminant i in a pure system in monolayers per time unit x = distance from the deposit surface in monolayers x dep = thickness of the evaporating deposit in monolayers x p = thickness of contaminant beyond which the contaminant concentration is its bulk concentration in monolayers I. Introduction I N-FLIGHT spacecraft contamination is driven by four main phenomena: contaminant generation (outgassing, propulsion, etc.), transport, reemission, and fixation by space radiation [START_REF] Tribble | Fundamentals of Contamination Control[END_REF][START_REF] Roussel | Progress on the Physical Approach to Molecular Contamination Modeling[END_REF]. No correct in-flight contamination assessment can be produced if one of these phenomena is neglected. This paper focuses on the reemission phenomenon and, more specifically, on the interactions between the contaminants deposited on a surface. Contamination is composed of a high number of contaminants generated by a large number of materials, each outgassing several chemical species. Within a deposit, the interactions between contaminants affecting reemission are not yet totally established.

Evaporation of a pure contaminant can be simply described. Thick film deposits have an order 0 evaporation rate at a given temperature. It is given by the Langmuir law. Temperature dependence for pure contaminant evaporation is given by the Clausius-Clapeyron law. As a result, the evaporation rate of a pure contaminant is almost an Arrhenius law characterized by an activation energy and a preexponential factor [START_REF] Tribble | Fundamentals of Contamination Control[END_REF][START_REF] Roussel | Progress on the Physical Approach to Molecular Contamination Modeling[END_REF]. We previously showed that this simple description can be insufficient to describe reemission of a deposit generated by vacuum deposition, for two main reasons. The deposit can evolve into clusters, which exhibit a different vacuumcontaminant interface than a film. Furthermore, contaminants can be either amorphous or crystallized, with different evaporation parameters. Vacuum deposition tends to form amorphous deposits at very low temperature. This amorphous deposit can undergo crystallization. This transformation has a complex kinetic driven both by nucleation and crystal growth.

Contaminant mixtures can condense on cold surfaces in a crystallized or amorphous deposit. The possibility for two different contaminant molecules to crystallize together in a single phase is almost null. On the other hand, amorphous homogeneous mixtures can develop when molecular mobility is low in the deposit. The formation of several phases and molecular mobility in the deposit are of high importance in the contaminant reemission process.

Thermogravimetric analysis (TGA), performed by measuring the evaporation rate of a deposit that is heated at constant rate, is a classical characterization method for reemission kinetics. TGA can be applied to deposits generated by real space material outgassing [START_REF]Kinetic Outgassing of Materials for Space[END_REF][START_REF]Standard Test Method for Contamination Outgassing Characteristics of Spacecraft Materials[END_REF]. For all the aforementioned reasons, the interpretation of these TGA experiments is not easy. In this paper, we focus on identifying the physical processes that govern evaporation of a mixture of contaminants during a TGA experiment. In the first part, we treat theoretical aspects of contaminant evaporation in binary systems. In the second part, we present evaporation experiments of controlled mixtures of two and three contaminants. The experimental results are discussed and modeled. In the third part, we present TGA experiments of outgassing products of the adhesive Scotchweld EC2216. These TGAs are monitored by mass spectrometry.

II. Theoretical Aspects of Mixture Evaporation

We consider a homogenous system composed of two contaminants (contaminants 1 and 2). At the experiment temperature, each contaminant i is characterized by its evaporation rate in a pure system v pure;i . For simplification, we express the rates in monolayers per time unit. We also assume that one monolayer of each contaminant corresponds to the same amount of contaminants.

Only contaminants with access to vacuum can evaporate. We assume that each contaminant has the same affinity for other contaminants as for itself. With these assumptions, the evaporation rate of each contaminant is proportional to its surface concentration (expressed as a fraction of a monolayer, hence a dimensionless number smaller than 1) and to its own evaporation rate in a pure system:

dm i dt -c surf;i :v pure;i (1)
In the absence of diffusion, surface concentrations evolve, leading to an enrichment in low-volatility contaminant and impoverishment in high-volatility contaminants.

The contaminant i concentration variation in the last monolayer is described by Eq. (2):

dc surf;i dt dm i dt -c bulk;i X j dm j dt ( 2
)
where dm i ∕dt is the evaporation of contaminant I, and -c bulk;i • dm i ∕dt is the uncovering of contaminant i molecules due to the evaporation of contaminant j.

In the steady state, dc surf;i ∕dt 0. As a result, the flux of each contaminant is proportional to its bulk concentration:

dm i dt c bulk;i dm dt (3)
and for a binary mixture:

dm 1 dt -c bulk;1 v pure;1 v pure;2 v pure;1 c bulk;2 v pure;2 c bulk;1 (4)
which allows to deduce the total evaporation rate for a binary mixture∶ dm dt -v pure;1 v pure;2 v pure;1 c bulk;2 v pure;2 c bulk;1 [START_REF] Anderson | Mass Spectrometry of Spacecraft Contamination Using Direct Analysis in Real-Time Ion Source[END_REF] At a given temperature, evaporation rates of different contaminants can vary over several orders of magnitude, and the probability of similar evaporation rates for two contaminants is very low. For very different evaporation rates, the total evaporation rate is driven by the evaporation of the contaminant with the smallest volatility, which evaporates as if it were pure:

if v pure;1 c bulk;2 ≫ v pure;2 c bulk;1 dm dt - v pure;2 c bulk;2 (6)
This phenomenon is illustrated by Fig. 1, where a TGA of a homogeneous deposit containing 75% of contaminant 1 and 25% of contaminant 2 is simulated using Eq. ( 2). The evaporation rates of each contaminant in the mixture, and as pure contaminant, are presented. In this simulation, contaminant 1 is much more volatile than contaminant 2. Emission of contaminant 1 is observed around 50°C. This emission corresponds to the transition from a homogeneous deposit to a deposit impoverished in contaminant 1 in the surface (contaminants that have access to vacuum evaporate). After that, contaminants are emitted in proportion to their bulk concentrations (three times more contaminant 1 than 2). Contaminant 2 evaporates as if it were pure. The main TGA peak is 4 times the contaminant 2 peak. This is also equivalent to a temperature shift.

We now consider the opposite case with a very rapid diffusion within the contaminant deposit. This means that surface composition always equals bulk composition. We consider the case of a volatile contaminant (contaminant 1) in solution with a nonvolatile contaminant (contaminant 2). The contaminant 1 concentration (and correlated evaporation rate) is governed by the following differential equation:

dc 1 dt d dt m 1 m 1 m 2 - ν pure;1 m 2 c 1 1 -c 1 2 (7)
If c 1 is small, the concentration decreases exponentially. Figure 2 presents the shapes of TGA peaks for the same amount of volatile contaminant diluted at three concentrations in a nonvolatile contaminant. The higher the dilution is, the higher the emission temperature is. This simulation was performed with an activation energy of 100 kJ∕mol for the contaminant evaporation. It leads to a temperature shift of less than 20°C in peak position, when the pure contaminant gets diluted to 10%.

The rapid diffusion, however, raises questions because it supposes a high molecular mobility. In this case, two contaminants at solid state would tend to crystallize separately.

On the other hand, mobility can be small without being null. In this case, the volatile contaminant evaporation rate follows a classical t -1∕2 law, whereas the second contaminant remains condensed.

We showed previously that, in the absence of diffusion, evaporation of the high-volatility contaminant is controlled by the emission of the low-volatility contaminant. In the case of slow diffusion, the decrease of the concentration gradient close to the surface, caused by diffusion, can be counterbalanced by the lowvolatility contaminant evaporation. In the referential following the moving deposit surface, which is in translation because of the deposit thickness decrease, the high-volatility contaminant profile c 1 x; t is governed by the following Lagrangian diffusion equation:

dc 1 dt dx dep dt dc 1 dx D d 2 c 1 dx 2 (8)
In this equation, the first term, dx∕dtdc 1 ∕dx, is due to the displacement of the deposit surface caused by evaporation, and the second term, Dd 2 c 1 ∕dx 2 , is due to diffusion. In the steady state, dc 1 ∕dt 0, and for a binary system,

dm dt - v pure;1 v pure;2 v pure;1 c dep;2 v pure;2 c dep1 (9) if v pure;1 c dep;2 ≫ v pure;2 c dep;1 dm dt - v pure;2 c dep;2 - dx dep dt d 2 c 1 dx 2 - v pure;2 Dc dep;2 dc 1 dx c 1 c surf;1 exp -v pure;2 D1 -c dep;1 x c dep;1 1 -exp -v pure;2 D1 -c dep;1 x c 1 ≈ c dep;1 1 -exp -v pure;2 D1 -c dep;1 x (10)
This stationary solution only rigorously exists for an infinitely thick deposit. In practice, the deposit concentration is only modified from its bulk concentration over a thickness x p . Figure 3 shows this thickness and the stationary phase (thick profiles) of the evaporation, between the first stationary profile and the last stationary profile. Thin lines show the initial and final transient phases.

The evaporation regime indeed remains stationary as long as the deposit keeps larger than x p , which is given by

x p 1 -c dep;1 • D∕v pure;2 (11)
Actually, the stationary assumption remains valid as long as the contaminant concentration at the bottom of the deposit remains equal to the initial bulk concentration.

The main difference between no diffusion and slow diffusion is that the stationary regime is reached in the absence of diffusion when volatile contaminant of the first contaminant monolayer get evaporated, whereas it is reached when the stationary profile has established on several monolayers in the case of slow diffusion.

Furthermore, in TGA conditions, x p variations depend on relative activation energies of D and of the low-volatility contaminant evaporation rate. If x p remains constant with temperature (same activation energies), the TGA is similar to Fig. 1, except for the fact that the first peak area is proportional to x p (x p 1 in the absence of diffusion). If x p increases with temperature, the emission of the highvolatility contaminant increases more rapidly than the emission of the low-volatility contaminant and inversely. The stationary regime stops when x p x dep .

III. Experiments

Characterization of contaminant evaporation was performed in ONERA-The French Aerospace Lab's COPHOS facility (from "contamination photon synergy") dedicated to simulating contamination processes, such as outgassing, reemission kinetics, and photofixation (see Fig. 4).

The setup is based on an effusion cell (20-200°C) for molecular beam generation and on four independently temperature-controlled Quartz crystal microbalances (QCMs) (Maxtek 6 MHz) for deposit monitoring. The QCMs are in direct view of the effusion cell. This assembly is surrounded by a shroud that can be either cooled down to cryogenic temperature to stick any contaminant and prevent indirect contamination on QCMs or heated up above effusion cell temperature to reevaporate any contaminant. In this second hot configuration, contaminants collected by the QCMs have been condensed and reevaporated several times on the shroud. This second configuration allows the use of a mass spectrometer for analysis of the outgassed contaminants or of contaminants reemitted by QCM heating.

We also used temperature-controlled contaminant collectors for contaminant reemission characterization by TGA. In this configuration, plates of typically 10 cm 2 have been contaminated and decontaminated by heating at constant temperature rate. The evaporated contaminants could be thus characterized by mass spectrometry.

QCM frequencies depend on temperature. This dependence has been characterized and subtracted from TGA measurements.

We generated a controlled mixture of up to three contaminants. The simultaneous deposition of contaminants was managed by introducing up to three crucibles containing pure contaminants in the effusion cell. The crucibles are closed by plates with a hole. The hole sizes were adapted to tune each contaminant flux. It is very difficult to find molecular contaminants with similar evaporation rates. The tuning of the hole sizes allowed generating similar contaminant fluxes even for volatility ratios between contaminants as high as 1 to 1000. We chose bisphenol A (BPA), octadecan-3-one (OD), and triphenylmethane (TPM) as pure contaminants. These contaminants have been chosen for their compatibility toward the generation of a similar flux with the three crucible strategy. They are also expected to have significantly different mass spectrometry responses.

IV. Results and Discussion

A. Pure Contaminant

Each contaminant was first separately characterized by measuring the outgassing rate (open crucible conditions) as a function of temperature. Reevaporation rates were also measured, by applying temperature steps (the temperature is kept constant, and the resulting constant reevaporation rate is measured for each temperature step) or temperature ramps (classical TGA for each pure contaminant) to the QCMs.

Two series of evaporation rates can be observed, depending on whether the deposit is crystallized or amorphous. Figure 5 presents the case of TPM evaporation rate measurement. Here, both TGAs and two of the step measurements are characteristic of amorphous deposit, whereas the six other step measurements exhibit the characteristic of crystallized deposits. Crystallized deposit at low temperature was only observed after heating the deposit above 10°C.

B. Binary Mixture

Several TGAs of the BPA/TPM mixture were performed. Figure 6 presents a typical experiment. The TGA of the BPA/TPM mixture is compared to the TGA of pure contaminants and to a simulation. Three peaks appear; the first one is consistent in position with pure TPM, but it only corresponds to a fraction of the TPM present in the deposit. The last peak is consistent with the evaporation of BPA (position and area). The intermediate peak at approximately 15°C is attributed to TPM (for mass conservation reason) and is observed when BPA evaporation starts. Extra experiments were performed to help interpreting this experiment and are represented in Figs. 7 and8.

Figure 7 compares two compositions (BPA 60%-TPM 40% and BPA 35%-TPM 65%) and two amounts (350 and 450 10 -8 g∕cm 2 ) of the mixture BPA/TPM that correspond to a comparable amount (210 and 160 10 -8 g∕cm 2 ) of BPA, whereas Fig. 8 compares two compositions (BPA 60%-TPM 40% and BPA 35%-TPM 65%) and two amounts (350 and 290 10 -8 g∕cm 2 ) of the mixture BPA/TPM that correspond to a comparable amount (140 and 190 10 -8 g∕cm 2 ) of TPM. As expected, for the same amount of BPA in the mixture Fig. 7, the BPA peak remains unchanged. More surprisingly, the first TPM peak clearly depends on the TPM concentration and not on the total amount of TPM. Indeed, for a comparable amount of TPM Fig. 8, the first peak is much smaller with the 40% TMP mixture than with the 65% TPM mixture. The TGAs of Figs. 6-8 can thus be interpreted by the formation of two phases: a pure TPM phase and a homogeneous TPM/BPA phase. A total of six experiments with the TPM/BPA mixture showed that the concentration of TPM in the mixture after the total evaporation of the first peak can be assessed to be 40%. This concentration is considered to be the limit of solubility of TPM in BPA (in solid phase). The dissolved TPM is released when the BPA evaporation starts. Figures 7 and8 show that this emission can be extremely sharp and is incompatible with a classical TGA interpretation. Finally, these TGAs where simulated (Figs. 678) assuming slow diffusion [Eq. ( 8)] and c surf;TPM ≪ 1. As it can be seen in these figures, simulations fit the experimental curves very well.

The evaporation of this phase was also studied by measuring the evaporation rate at a constant temperature of a 40% TPM mixture rapidly heated up to 4.25°C after its deposition. Figure 9 presents the evaporation rate at constant temperature as a function of time. The 4.25°C temperature is above the first peak evaporation (cf. Fig. 6), and so this evaporation must be interpreted as the evaporation of the homogeneous BPA/TPM mixture. A constant evaporation rate can be observed during the first 45 min of evaporation. Then, the evaporation rate slowly decreases down to the pure BPA evaporation rate. The initial evaporation rate indicates that TPM evaporation cannot be explained by rapid diffusion. Otherwise, evaporation rate would follow an order 1 law. On the other hand, the fact that the final deposit is compatible with pure BPA indicates that some diffusion occurs.

These first 45 min can indeed be explained by the steady-state evaporation rate and concentration profile given in Eq. (10). The end of steady-state evaporation is reached when the moving steady concentration profile reaches the substrate (Fig. 3). Then, the evaporation rate continuously decreases down to the BPA evaporation rate, which is reached when all TPM is evaporated. From this experiment, and using Eq. ( 11), a diffusion coefficient of TPM in BPA at 4.25°C close to 10 -16 cm 2 ∕s was deduced. This is a very low diffusion coefficient but is sufficient to allow TPM diffusion within thin TPM/BPA films.

As a conclusion on Sec. IV.B, we can say that the TPM/BPA TGA experiments are quite well explained by phase segregation due to limited solubility of TPM in BPA. The pure TPM phase evaporates like a pure TPM thin film. ¶ After evaporation of this TPM phase, the mixture evaporates like a homogeneous deposit with slow diffusion, as described previously. The very sharp second TPM peak observed in Figs. 6-8 can be explained by a high diffusion activation energy.

C. Ternary Mixture

A third contaminant, OD, was added to the binary BPA/TPM mixture. Figure 10 presents the influence of adjunction of OD (40% in the deposit) to a BPA 40%-TPM 60% mixture.

In the ternary mixture, the first TPM peak disappears, whereas another peak quite similar to OD evaporation, but higher in intensity (or shifted to lower temperatures), appears. For mass conservation reasons, the OD-like peak must also contain TPM evaporation. This explains the fact that evaporation rate is higher than that for pure OD. This observation is compatible with the formation of a TPM/OD phase and a BPA phase. The evaporation of the TPM/OD phase is compatible with the evaporation in absence of diffusion (or very limited diffusion) described previously. Simulation, based on Eq. ( 2), thus satisfyingly fits the experimental curves.

For confirmation of these hypotheses, a similar experiment was then performed using a collecting plate in the hot shroud configuration (reevaporation of all contaminants reaching the shroud). The deposit was collected on the plate and then reevaporated at a constant temperature rate (TGA). The reevaporated contaminants were simultaneously monitored using a cold QCM (-75°C) and mass spectrometry. For each contaminant, a mass, specific to this contaminant, was monitored during the plate heating ramp at 2°C∕ min.

Figure 11 presents the deposition rate on the QCM compared to the mass deposition rate deduced from the mass spectrometry signal. An excellent correlation between QCM and mass spectrometry measurements is observed. Looking now at each mass, it clearly appears that the TPM is mainly emitted simultaneously with the OD. Nevertheless, a fraction of TPM is released slightly before the emission OD, whereas a second fraction is released at the beginning of the BPA evaporation. OD and BPA are almost emitted like pure contaminants. The TGA and mass spectrometry experiment thus clearly indicates that the deposit demixes into two phases, composed of OD/TPM and TPM/BPA mixtures, respectively. For each phase, the emission of TPM is limited by its slow diffusion.

D. Outgassing Products from a Real Material

Finally, experiments were conducted on the deposit obtained from real material outgassing (Scotchweld EC2216 adhesive). We made four successive outgassing steps (75, 100, 125, and 150°C), each one lasting approximately 20 h. During each of the four steps, the deposit was collected on cold plates (-75°C) and then reevaporated during a TGA experiment at 2°C∕ min. Contaminant reevaporation was monitored in the hot shroud configuration using a cold QCM and a mass spectrometer. Contaminant collection after outgassing at 75°C was small, and mass spectrometry data were not treated. The following figures compare TGA and mass spectrometry measurements for the three next outgassing steps. Figure 12 shows the TGA performed after each temperature step (100, 125, and 150°C).

The difficulty that we have highlighted, with controlled contaminant mixtures, is that one TGA peak is not systematically characteristic of one contaminant (TPM with OD), and one mass spectrometry mass can be characteristic of several contaminants [START_REF] Anderson | Mass Spectrometry of Spacecraft Contamination Using Direct Analysis in Real-Time Ion Source[END_REF]. Furthermore, mass spectrometry response is not directly correlated to the contaminant mass flux. We nevertheless tried to interpret these data using mass spectrometry measurements performed during the TGAs.

Figure 13 presents the mass signals for mass 76 a.m.u (atomic mass unit). and mass 47 a.m.u. during the three TGA. The signals of these two masses are proportional whatever the temperature (except small differences at -50°C). This clearly shows that these two masses correspond to the same contaminant, outgassed at the three temperature steps. The comparison to Fig. 12 shows that the 76/47 doublet emission peaks are highly correlated with TGA peaks (total reevaporation rate). This means that the contaminant with characteristic peaks 76 and 47 is a main contaminant.

The same observation is made for the doublet 110/118 (Fig. 14). However, the behavior of these two contaminants is different. The 76/47 contaminant peak is sharp, but its position depends on the studied TGA, hence the mixture composition. The outgassing of this contaminant is thus probably controlled by other contaminants in a mixed phase. On the other hand, the contaminant 110/128 has a wide peak, but with unchanged emission law for the three TGAs. This is typical of a pure contaminant behavior (or of the dominant contaminant of a mixed phase).

Figure 15 finally presents the second reemission peak of the TGA performed after the 150°C temperature step (peak shown in Fig. 12). The behavior of four different contaminants, monitored during this TGA by mass spectrometry is also shown. The intensity of the reemission peak of each contaminant very difficult to assess because relative abundances of ions in the mass spectrum obtained for a mixture do not necessarily reflect the proportions of the compounds in the mixture. Because we are interested in the position of these peaks but not their intensity, they are normalized so that the maximum intensity of the peak is 1. Masses 79 and 110 present doublet behavior (79/108 and 110/128) and are supposed to be representative of two contaminants. Masses 239 and 109 are characteristic of two different outgassing products, identified by gas chromatography (unpublished). It can thus be concluded that this TGA peak actually corresponds to at least four different contaminants, which are emitted almost simultaneously. The reevaporation of the contaminants is thus probably limited here by diffusion (no or slow diffusion).

V. Conclusions

Contamination generated by spacecraft material outgassing can be analyzed by thermogravimetric analysis (TGA), but its interpretation is not easy. The formation of several phases of different composition is highly probable. In each phase, diffusion is often slow, so that during TGA, emission of the most volatile contaminant is limited by diffusion and is triggered by the evaporation of the less-volatile contaminant. This has been clearly demonstrated with controlled mixture of selected materials. In the case of deposit generated by real material outgassing, species separation was only partially achieved thanks to mass spectrometry. Behaviors typical of those identified in the controlled mixtures were identified.

The next steps of these activities shall consist of actually separating the species present in complex deposits coming from the outgassing of real materials. When studying more materials, an important question will be whether the nontrivial mixing effects unraveled here are dominant or, on the contrary, might be neglected in many real situations.

Fig. 1

 1 Fig.1TGA simulation, homogeneous deposit containing 75% of contaminant 1.

Fig. 2

 2 Fig.2TGA simulation, contaminant diffusing rapidly in a nonvolatile contaminant, volatile contaminant initial concentrations: 10, 20, and 100%.

Fig. 3

 3 Fig. 3 Evolution of the concentration of the volatile contaminant during the evaporation.

Fig. 4

 4 Fig. 4 Schematic view of the COPHOS facility.

Fig. 6

 6 Fig. 6 TGA of 290 10 -8 g∕cm 2 of 40% BPA and 60% TPM.

Fig. 7

 7 Fig.7TGA of BPA/TPM mixtures: comparable amount of BPA.

Fig. 8

 8 Fig. 8 TGA of BPA/TPM mixtures: comparable amount of TPM.

Fig. 5

 5 Fig. 5 TPM evaporation rate measurement for two TGAs and for temperature steps.

Fig. 10

 10 Fig. 10 TGA of contaminant mixtures and pure contaminants.

Fig. 11

 11 Fig. 11 TPM/OD/BPA mixture TGA monitored by mass spectrometry and cold QCM.

Fig. 12

 12 Fig.12TGA performed after the 100, 125, and 150°C outgassing steps.

Fig. 13

 13 Fig. 13 Masses 47 and 76 during TGAs performed after the 100, 125, and 150°C outgassing steps.

Fig. 14

 14 Fig. 14 Masses 110 and 128 during the three TGAs.

Fig. 15

 15 Fig. 15 TGA performed after the 150°C outgassing step: total mass and various mass signals.

Downloaded by ONERA on January 6, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.A33507

Article in Advance / TONDU ET AL. Downloaded by ONERA on January 6, 2017 | http://arc.aiaa.org | DOI: 10.2514/1.A33507

Acknowledgments

The results obtained at ONERA-The French Aerospace Lab were funded by the Centre National d'Études Spatiales (CNES) Research and Technology Program, for which the ONERA authors are very grateful to the CNES.


Guillaume Noyel
email: guillaume.noyel@ensmp.fr

Jesus Angulo
email: jesus.angulo@ensmp.fr

Dominique Jeulin
email: dominique.jeulin@ensmp.fr

Jesús Angulo

Classification-driven stochastic watershed. Application to multispectral segmentation

Keywords: Classification-Driven Stochastic Watershed: Application to Multispectral Segmentation Stochastic Watershed, multispectral images, regionalized random balls, classification-driven stochastic watershed, marginal probability density function

Introduction

Watershed transformation (WS) requires, for image segmentation, a function to flood, generally the norm of a gradient (i.e. a scalar function), and seeds (markers) for each region of interest [START_REF] Beucher | The Morphological Approach to Segmentation: The Watershed Transformation[END_REF]. This powerful approach is a deterministic process which tends to build irregular contours. The stochastic watershed was proposed in order to regularize and to produce more significant contours [START_REF] Angulo | Stochastic watershed segmentation[END_REF]. The initial framework was then extended to multispectral images [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF].

The aim of this paper is to introduce improvements of the stochastic watershed and to compare them with the segmentations obtained with the deterministic WS for multispectral images.

The standard stochastic watershed starts from uniform random point markers to flood the norm of a gradient, in order to obtain associated contours to random markers. After repeating the process a large number of times, a probability density function of contours (pdf) is computed by the Parzen kernel method. In our previous works, this pdf was segmented by hierarchies based on extinction values (according to dynamics, surface and volume) in order to select the most significant minima of the pdf. The selected minima were used as the markers for the watershed [START_REF] Meyer | An overview of Morphological Segmentation[END_REF]. In the case of multispectral images, a pdf is built for each channel of the image and the flooding function is the weighted sum of the channels pdf. This function is called a weighted marginal probability density function mpd f [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF].

In this paper, we generate the pdf using the results of a prior classification. First, we compute a spectral classification of the multispectral image by unsupervised approaches such as "k-means" or "clara" [START_REF] Kaufman | Finding Groups in Data. An Introduction to Cluster Analysis[END_REF]. After filtering each class, we obtain some seeds s used as markers to segment the flooding function. This function is a pdf in the stochastic case, or a multivariate gradient in the deterministic one [START_REF] Noyel | Morphological Segmentation of hyperspectral images[END_REF].

The main contributions of this paper are the new algorithm to build the pdf conditionally to the classification, and the segmentation of the pdf with seeds (i.e. markers) obtained by the classification. Finally, we propose a full treatment chain for multispectral images with a robust parameter: the number of classes for the classification.

The method presented here can be applied in various multispectral image fields: remote sensing, microscopy images, medical images [START_REF] Noyel | Filtering, segmentation and region classification by hyperspectral mathematical morphology of DCE-MRI series for angiogenesis imaging[END_REF], thermal images, temporal series, multivariate series, etc.

Multispectral image space (MIS) vs. factor image space (FIS)

Multispectral images are multivariate discrete functions with typically several tens or hundreds of spectral bands. In a formal way, each pixel of a multispectral image is a vector with values in wavelength, in time, or associated with any index j.

To each wavelength, time or index corresponds an image in two dimensions called channel. In the sequel, we use only the term of spectrum and spectral channel. The number of channels depends on the nature of the specific problem under study (satellite imaging, spectroscopic images, temporal series, etc.). Let

f λ : E → T L x → f λ (x) = f λ 1 (x), f λ 2 (x), . . . , f λ L (x) (1)
be an hyperspectral image, where:

• E ⊂ R 2 , T ⊂ R and T L = T × T × . . . × T • x = x i \ i ∈ {1, 2, . . . , P} is the spatial coordinates of a vector pixel f λ (x i ) (P is the pixels number of E) • f λ j \ j ∈ {1, 2, . . . , L} is a channel (L is the channels number) • f λ j (x i ) is the value of vector pixel f λ (x i ) on channel f λ j .
Due to the redundancy of channels, a data reduction is usually performed using Factor Correspondence Analysis (FCA) [START_REF] Benzécri | L'Analyse Des Données[END_REF]. We prefer a FCA in place of a Principal Component Analysis (PCA), because image values are positive and the spectral channels can be considered as probability distributions. As for PCA, from selected factorial FCA axes the image can be partially reconstructed. The metric used in FCA is the chi-squared, which is adapted to probability laws and normalized by channels weights. FCA can be seen as a transformation going from image space to factorial space. In factorial space, the coordinates of the pixels vector, on each factorial axis, are called pixels factors. The pixels factors can be considered as another multispectral image whose channels correspond to factorial axes:

ζ : T L → T K / K < L f λ (x) → c f α (x) = c f α 1 (x), . . . , c f α K (x) (2)
A limited number K, with K < L, of factorial axes is usually chosen. Therefore FCA can be seen as a projection of initial vector pixels in a factor space with a lower dimension. Moreover, as it is shown below, FCA can be used for multispectral images to reduce noise [START_REF] Green | A Transformation for Ordering Multispectral Data in terms of Image Quality with Implications for Noise Removal[END_REF][START_REF] Noyel | Morphological Segmentation of hyperspectral images[END_REF]. Consequently, we have two spaces for multivariate segmentation: the multispectral image space (MIS) and the factor image space (FIS). Figure 1 gives an example of a five bands satellite simulated image PLEIADES, acquired by the CNES (Centre National d'Etudes Spatiales, the French space agency) and provided by G. Flouzat [START_REF] Laporterie-Déjean | Thematic and statistical evaluations of five panchromatic/multispectral fusion methods on simulated PLEIADES-HR images[END_REF], and its corresponding FCA representation. Its channels are the following: f λ 1 blue, f λ 2 green, f λ 3 red, f λ 4 near infrared and f λ 5 panchromatic. The panchromatic channel, initially of size 1460 × 1460 pixels with a resolution of 0.70 meters, was resized to 365×365 pixels. Therefore, the resolution is 2.80 meters in an image of 365 × 365 × 5 pixels. In order to represent a multispectral image in a synthetic way, we have created a synthetic RGB image using channels f λ 3 red, f λ 2 green and f λ 1 blue. Figure 1 shows FCA factor pixels c f α of image "Roujan".

f λ 1 f λ 2 f λ 3 f λ 4 f λ 5 RGB Figure 1. Channels of multispectral image f λ "Roujan" ( c CNES): f λ 1 blue, f λ 2 green, f λ 3 red, f λ 4 near infra-red, f λ 5 panchromatic, synthetic RGB representation. c f α 1 c f α 2 c f α 3 c f α 4

Pre-processing and spectral classification

As shown by Benzécri in [START_REF] Benzécri | L'Analyse Des Données[END_REF] and by Green et al. in [START_REF] Green | A Transformation for Ordering Multispectral Data in terms of Image Quality with Implications for Noise Removal[END_REF], some factor pixels on factor axes contain mainly noise, and others signal information. In order to choose relevant axes containing information (i.e. signal), we introduce a new method based on a measurement of signal to noise ratio SNR. For each factorial axis α k , the centered spatial covariance is computed by a 2D FFT (Fast Fourier Transform) on the pixels factors:

g α k (h) = E[c f α k (x)c f α k (x + h)], with c f α k (x) = c f α k (x) -E[c f α k (x)
]. The covariance peak, at the origin, contains the sum of the signal variance and the noise variance of the image. Then, the signal variance is estimated by the maximum (i.e. value at the origin) of the covariance g after a morphological opening γ, with a structuring element of size 3 × 3 pixels: Var(signal) = γg α k (0). In fact, one property of the morphological opening is to remove peaks on images. The noise variance is given by the residue of the opening of the covariance at the origin: 3). The signal to noise ratio is defined for a factor axis as: By observation of the factor pixels and their signal to noise ratios, which are higher for axes 1, c f α 1 , and 3, c f α 3 , than for axes 2, c f α 2 , and 4, c f α 4 , the axes 1 and 3 are retained. In figure 4, we notice that axis 3, which is selected, has a lower inertia than axis 2, which is rejected. Therefore, SNR analysis makes possible to describe relevant signal, more than inertia.

Var(noise) = g α k (0) -γg α k (0) (fig.
SNR α k = Var(signal) Var(noise) = γg α k (0) g α k (0) -γg α k (0) (3)
g α 1 (h) γg α 1 (h) g α 2 (h) γg α 2 (h)
After the data reduction and the spectral filtering stage by FCA, a spectral classification κ by clara [START_REF] Kaufman | Finding Groups in Data. An Introduction to Cluster Analysis[END_REF] is performed on the factor space. We have to stress that a correct classification, used later for constructing the pdf, requires factor pixels without noise. The classification algorithm uses a euclidian distance which is coherent with the metric of the factor space [START_REF] Noyel | Morphological Segmentation of hyperspectral images[END_REF]. The unique parameter is the number of classes, which is chosen in order to separate more the classes. Here, for this example, 3 classes are retained (fig. 5). The classification κ is then filtered class by class, in order to reduce their area. A closing by reconstruction after an erosion by a structuring element (se) of size 5 × 5 pixels, followed by an erosion by a se of 3 × 3 pixels are applied. The filtered classification is noticed κ.

RGB κ κ

Two reasons are available for a such filtering. First we prevent random markers from falling on the boundary of a class. In fact, during the pdf building process, in case of a leak on the channel gradient, two regions could be aggregated by a marker on the bounds of a class. The second reason is that the classes are used as seeds (i.e. markers) for the segmentation of the pdf. If all the image space E is completely full of seeds, the limits of the segmented zones are the limits of the seeds. Then, the pdf is useless. Therefore, filtering classes introduces a necessary degree of freedom for the watershed on the pdf.

Regionalized random balls markers

Regionalized random balls markers are used to build the pdf. The novelty of the paper is to condition the markers by the filtered classification κ.

Given D = {D l }, a partition of disjoint classes of the image space E ⊂ R 2 . Each class D l of the partition is composed of connected components C p : i.e. D l = ∪ p C p . Then the point markers µ are drawn conditionally to the connected components C p of the filtered classification κ. To do this,the following rejection method is used: the point markers are uniformly distributed. If a point marker µ is inside a connected component C p of minimum area S and not yet marked, then it is kept, otherwise it is rejected. These point markers are called regionalized random point markers.

Moreover to decrease the probability of the small, textured and low contrasted contours regions, we use random balls as markers. The centers of the balls are the regionalized random point markers and the radii r are uniformly distributed between 0 and a maximum radius Rmax: U [1, Rmax]. Only the intersection between the ball B(µ, r) and the connected component C p is kept as marker. These balls are called regionalized random balls markers.

The algorithm 1 sketches the process. We notice that N is the number of markers to be drawn. The effective number of implanted markers is less than N.

The marker image mrk(x) is the union of retained markers B(µ, r) ∩C p .

Algorithm 1 Regionalized random balls markers

Given N the number of markers to be drawn, S and Rmax for all centers µ between 1 and N do if (C p such as µ ∈ C p is not marked) AND (area

(C p ) ≥ S) then r = U [1, Rmax] keep B(µ,

Probability density function

In the examples illustrating this paper, we use the weighted marginal probability density function with regionalized random balls mpd f balls on the image space MIS with 5 channels [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF]. It would also be possible to work in the factor space FIS with a reduced number of channels. We choose to work in MIS to show that our method is not limited by the number of channels. Nevertheless, the factor space is useful for computing a correct classification used to generate the regionalized random balls markers. In the sequel, in place of using uniform random markers as in [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF], regionalized random markers are thrown. The mpd f balls is computed as follows:

• For the morphological gradient of each channel ρ( f λ j ), j ∈ [1, . . . , L], throw M realizations of N regionalized random balls markers, i.e. the markers {mrk • Obtain the weighted marginal pdf mpd f balls (x) = ∑ L j=1 w j pd f j (x), with w j = 1/L, j ∈ [1, . . . , L] in MIS and w j equal to the inertia axes in FIS. Some markers and their associated realizations of contours are presented in figure 6. The pdf mpd f balls is shown in figure 7.

Segmentation

For segmentation, we compare a deterministic and a stochastic approach on multivariate images (fig. 7).

First step : For both cases, an unsupervised classification κ (kmeans or "clara") is processed in factor space FIS and filtered κ. Second step :

• For the deterministic approach, a chi-squared metric based gradient ρ χ 2 (f λ ) is computed in image space MIS, as a function to flood [START_REF] Noyel | Morphological Segmentation of hyperspectral images[END_REF]. • For the stochastic approach, a marginal probability density function mpd f balls , with regionalized random balls markers conditioned by the filtered classification κ, is processed, in image space MIS, as a function to flood [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF].

Third step : In both cases, the flooding function is segmented by a watershed (WS) using as sources of flooding the seeds from the filtered classification κ.

The results are images segmented by stochastic WS with seeds from classification W S κ sto.balls and deterministic WS with seeds from classification W S κ det .

Results

In figure 7, are given the results of segmentation by deterministic and stochastic WS for image "Roujan" with seeds coming from filtered classification κ. We observe that the contours are smoother and follows more the main limits of the regions for the stochastic approach than for the deterministic one. The parameters for the stochastic WS with seeds coming from the classification W S κ sto.balls are:

• the number of classes for the classification κ: Q = 3 ;

• the maximum number of random balls markers: N = 50, which corresponds to the same order of the number regions in the image ; • the number of realizations for each channel: M = 100, always the same ; • the minimum area S = 10 pixels for connected classes C p , generally the same ; • the maximum radius of the random balls Rmax = 30, generally the same.

In figure 8, for comparison with a segmentation based on a prior number of regions, other images, similar to image "Roujan", are segmented: "Roujan 0 2 " and "Roujan 1 9". As for image "Roujan", factor axes c f α 1 and c f α 3 are kept. They present both a higher SNR than the other axes. Inertias and SNR for factor axes of images "Roujan X X" are presented on the following tables.

A classification "clara" is computed on the factor pixels of these two axes. The mpd f balls are produced as explained for image "Roujan".

Inertia for factor axes for images "Roujan X X"

Image c f α 1 c f α 2 c f α 3 c f α 4
"Roujan" 84.1 % 8.7 % 6.2 % 1 % "Roujan 0 2" 75.6 % 13.7 % 9.2 % 1.5 % "Roujan 1 9" 77.5 % 12.1 % 9 % 1.4 % SNR for factor axes for images "Roujan X X"

Image c f α 1 c f α 2 c f α 3 c f α 4
"Roujan" 5.10 0.03 2.84 0.47 "Roujan 0 2" 2.66 0.01 2.53 0.32 "Roujan 1 9" 3.15 0 2.90 0.51

To segment these mpd f balls two methods are compared: Filtered classification κ, deterministic approach W S κ det on Chi-squared metric based gradient ρ χ 2 (f λ ) (top) and stochastic approach W S κ sto.balls on mpd f balls (bottom) on image "Roujan". In both cases, the seeds come from κ. For visualization, and for complete segmented images the contours are dilated by a se of size 3 × 3 pixels.

κ ρ χ 2 (f λ ) W S κ det zoom W S κ
• a WS with seeds coming from the filtered classification W S κ sto.balls ; • a hierarchical WS based on extinction values, which allows to select the minima according to a morphological criterion of volume W S vol sto.balls .

In figure 8, we notice that the number of regions, resulting from the segmentation, strongly depends on the image, whereas the number of classes is the same for similar images. In fact, the number of regions for volumic WS, W S vol sto.balls , must be chosen according to the considered image, and cannot be fixed "a priori" (50 here). The number of regions depends on the size and the complexity of the image, while the number of classes depends on the spectral content. Consequently, it is more relevant to use a WS with seeds coming from the classification W S κ sto.balls . Moreover only one parameter is needed for WS with seeds W S κ sto.balls : the number of classes in the classification. This parameter is the same for similar images and can be chosen more easily than the number of regions. Moreover, the number of classes produces a more robust segmentation than the number of regions.

Some other results are presented on image "Port de Bouc", in figure 9. Two factor axes are retained in FIS: c f α 1 and c f α 2 of respective inertias: 60.1 % and 23.4 % and of respective SNR: 18.7 and 3.16. The parameters for the stochastic WS are: Q = 7 classes for the classification κ, N = 100 random balls at maximum, M = 100 realizations, a minimum area of S = 10 pixels for the connected classes C p and a maximum radius of Rmax = 30 pixel for random balls. We notice that contours are more regular for stochastic WS than for deterministic WS.

One of the main artefacts of deterministic watershed is that small regions strongly depend on the position of the markers, or on the volume, i.e. the integral of the gray levels of the catch- ment basin, associated to their minima. In fact, there are two kinds of contours associated to the watershed of a deterministic gradient such as ρ χ 2 (f λ ): 1st order contours, which correspond to significant regions and which are relatively independent from markers; and 2nd order contours, associated to "small", "low" contrasted or textured regions, which depend strongly on the location of markers. Stochastic watershed aims at enhancing the 1st order contours from a sampling effect, to improve the resulting segmentations.

Therefore even with good markers, obtained from classification for multispectral images, the contours of the stochastic WS are more regular than for deterministic WS.

Moreover, we have compared the stochastic WS with regionalized random balls markers with a volume criterion W S vol sto.balls , presented in this paper, to the stochastic WS with uniform random points markers with a volume criterion W S vol sto , presented [START_REF] Noyel | Random Germs and Stochastic Watershed for Unsupervised Multispectral Image Segmentation[END_REF]. The number of regions is R = 8 (fig. 10). We notice that W S vol sto.balls concentrates more on main contours of the image than W S vol sto especially for the part concerning the sea. Therefore, stochastic WS with regionalized random balls markers W S vol sto.balls improves the result of stochastic WS with uniform random point markers W S vol sto .

Conclusions and perspectives

In this paper we have introduced a new way of computing regionalized random markers introducing spectral information in the weighted marginal probability density function mpd f balls . Therefore, mpd f balls contains now spectral and spatial information. Usually the main difficulty is the choice of the number of regions for the segmentation. Here, we have presented a complete treatment chain for segmenting multispectral images with a major and robust parameter: the number of classes of the classification. We have shown that the number of classes for the classification is more robust than the number of regions for the segmentation. Moreover, even with good markers, obtained by classification for multispectral images, the contours of the final segmentation are smoother for the stochastic WS with seeds coming from the classification, than for the deterministic WS with the same seeds. Finally, we have introduced a general methodology for segmenting multispectral images. We are thinking on applying on different fields are numerous: medical images [START_REF] Noyel | Filtering, segmentation and region classification by hyperspectral mathematical morphology of DCE-MRI series for angiogenesis imaging[END_REF], microscopy images, thermal images, temporal series, multivariate series, etc.

Figure 2 .

 2 Figure 2. FCA factors pixels c f α of image "Roujan" on axes 1, 2, 3 and 4 with respective inertias 84.1 %, 8.7 %, 6.2 %, 1 %.

Figure 3 .

 3 Figure 3. 2D covariances for factor pixels c f α 1 and c f α 2 of image "Roujan" before (left) and after opening (right).

Figure 4 .

 4 Figure 4. Inertia (%) and SNR for factor pixels of image "Roujan".

Figure 5 .

 5 Figure 5. Synthetic RGB image, classification κ in 3 classes in factor space formed by c f α 1 and c f α 3 with clara and filtered classification κ.

  .M , generating M × L realizations. Get the series of segmentations, {sg j m (x)} j=1...L m=1...M , by watershed associated to morphological gradients of each channel ρ( f λ j ). • Get the marginal pdf on each channel pd f j (x) = 1 M ∑ M m=1 sg j m (x) * G σ , with G σ a Gaussian convolution kernel (σ = 3 pixels for contours of one pixel width).

Figure 6 .

 6 Figure 6. A few realizations of regionalized random balls markers {mrk j m(x)} j=1 m=1...5 (top) by the classification κ and associated contours of watershed {sg j m(x)} j=1 m=1...5 (bottom).

Figure 7 .

 7 Figure 7.Filtered classification κ, deterministic approach W S κ det on Chi-squared metric based gradient ρ χ 2 (f λ ) (top) and stochastic approach

Figure 8 .

 8 Figure 8. Comparison between segmentations of mpd f balls by stochastic WS with a prior given number of regions R = 50 (W S vol sto.balls ) or with seeds coming from the filtered classification W S κ sto.balls . The results are given for images: "Roujan", "Roujan 0 2", "Roujan 1 9".

Figure 9 .

 9 Figure 9.Filtered classification κ, deterministic approach W S κ det on Chi-squared metric based gradient ρ χ 2 (f λ ) (top) and stochastic approach W S κ sto.balls on mpd f balls (bottom) on image "Port de Bouc". In both cases, the seeds come from κ. For visualization, and for complete segmented images the contours are dilated by a se of size 3 × 3 pixels.

Figure 10 .

 10 Figure 10. Comparison between stochastic WS with regionalized random balls markers with a volume criterion W S vol sto.balls to the stochastic WS with uniform random points markers with a volume criterion W S vol sto . There are R = 8 regions. For visualization, and for complete segmented images the contours are dilated by a se of size 3 × 3 pixels.

Figure 11 .

 11 Figure 11. Complete flowchart for classification-driven stochastic WS with regionalized random balls markers W S κ sto.balls .

Acknowledgments

The authors are grateful to Prof. Guy Flouzat (Laboratoire de Télédétection à Haute Résolution, LTHR/ ERT 43 / UPS, Université Paul Sabatier, Toulouse 3, France) for his collaboration on PLEIADES satellite simulated images in the framework of OR-FEO program (Centre National d'Etudes Spatiales, the French space agency).

Author Biography

Guillaume NOYEL is a PhD student at the Centre de Morphologie Mathématique of Ecole des Mines de Paris. He receives his Master degree in Image processing in 2005 from CPE-Lyon, France and his MSc in Image processing (with honors) in 2005 from University J. Monnet, St Etienne, France. His research fields are segmentation, data reduction of hyperspectral images and mathematical morphology. The applications are in biomedicine, remote sensing and temporal series.

Jesús ANGULO received a degree in Telecommunications Engineering (1999). He obtained his PhD in Mathematical Morphology and Image Processing (2003), from the Ecole des Mines de Paris (ENSMP). He is currently a researcher in the Center of Mathematical Morphology of EN-SMP. His research interests are in the areas of multivariate image processing (colour, hyper/multi-spectral, temporal series, tensor imaging) and mathematical morphology, and their applications to biomedicine and biotechnology. Dominique JEULIN is Director of Research and Professor in Ecole des Mines de Paris. At the head of the "Physics of Heterogeneous Media" group, his main current interest covers the theoretical prediction of physical properties of random media (fracture statistics models, homogenization of mechanical and optical properties of composite materials and of biological tissues), models and simulations of random media, 3D image analysis, applications to Materials Science, Biology and Vision.