PhD Yael Armangau
email: yael.armangau@univ-tlse2.fr

Julien Figeac
email: julien.figeac@cnrs.fr

Social support networks within transgender Facebook groups: facing a "therapeutic shield" in France. Version

Keywords: Transgender, Medical Discrimination, Social Media, Social Support, Information-Sharing Behavior, Safe Space

This article aims to analyze the sociabilities, information-sharing behaviors, and types of social support among users of French non-mixed trans Facebook groups. First, our national survey (N = 405) reveals that the different uses of these groups (information retrieval, emotional support, etc.) vary according to the age and education levels of their trans users, or according to their progress on the transition pathways. Secondly, we perform a lexical analysis of the messages (N = 70,488) posted, since 2013, in a sample of 24 groups, in order to identify the main topics of discussion. This analysis leads us to emphasize the diversity of social support provided by trans people to one another, via posts and comments. These findings deemphasize the benefits of institutional support because they suggest, alternatively, that trans people are organizing themselves to avoid challenges associated with medical institutions and the French "therapeutic shield". Such individuals use Facebook to this end, sharing information or support in order to create a safe space managed with a transfeminist ethic, and allowing themselves to make gender-related choices more autonomously, far away from normative judgements (in particular those expressed by the medical profession).

Introduction

Since Émile Durkheim's work on social solidarity (Durkheim, 1893), scholars have continued to address the issues raised therein, working to distinguish the main types of social support afforded by liberal democracies; in particular, these include informational, emotional, esteemrelated, networking, and tangible support [START_REF] Cutrona | Controllability of stressful events and satisfaction with spouse support behaviors[END_REF]. The internet and social media have more recently provided new resources to diverse online communities, which allow for the provision of specific forms of social support, especially for the most marginalized people (e.g. HIV-positive people, people with disabilities), for those requiring hitherto-scarce resources (such as people with eating disorders [START_REF] Tubaro | Sociability and support in online eating disorder communities: Evidence from personal networks[END_REF]), or for women victims of domestic violence. Trans people represent another such marginalized population, using digital platforms to access limited resources, and to organize and manage online communities with an ethic of care free of the types of medical discrimination to which they are often subject [START_REF] Malatino | Trans Care[END_REF]. Many scholars have studied the diversity of resources and support available for trans people [START_REF] Johnson | We're the Normal Ones Here": Community Involvement, Peer Support, and Transgender Mental Health[END_REF][START_REF] Chiland | Online support for transgender people: An analysis of forums and social networks[END_REF][START_REF] Selkie | Transgender Adolescents' Uses of Social Media for Social Support[END_REF][START_REF] Austin | It's my safe space: The lifesaving role of the internet in the lives of transgender and gender diverse youth[END_REF], but they often identify health care professionals as the main providers of social support, thus promoting a pathologic representation of the trans experience which requires first and foremost medical assistance.

In this article, we wish to counter this scientific perspective by focusing on sources of social solidarity and mutual aid provided by and for trans people. We investigate trans Facebook groups in France in order to describe the main types of social support to be found in these digital spaces, and to observe which have become more important over time. This article is based on two complementary methods: (1) a national survey (N = 405) studying the uses of Facebook and social media by trans people, and (2) a lexical analysis of message topics (N = 70,488) published within a sample of 24 Facebook groups. Drawing from the survey, the first results section highlights the diversity and the complementarity of the types of social support requested or provided by the Facebook users according to their profiles. Secondly, the lexical analysis describes in greater detail these diversities of social support, and reveals the centrality of medical protocols in the patterns of information-sharing and discussion observed within these groups. Trans people provide each other information and advice in order to overcome or bypass challenges related to doctors, psychiatrists and medical institutions. Faced with the French health care system's "therapeutic shield" [START_REF] Espineira | Le bouclier thérapeutique : Discours et limites d'un appareil de légitimation[END_REF], the Facebook groups allow trans people to provide each other with social support and to share otherwise difficult-to-find information, allowing this marginalized community to create an online safe space and to engage collectively in a process of autonomization based on a transfeminist ethic.

Trans people facing the strengthening of the French therapeutic shield

In 1978, the first French program to manage transgender pathways was introduced. The "Conseil national de l'Ordre des médecins" recommended that three "experts" be involved in trans cases: a psychiatrist, an endocrinologist and a surgeon. Two years later, the "Diagnostic and Statistical Manual of Mental Disorders" (DSM III) codified the psychiatricization of trans pathways by introducing the term "transsexualism". Specialized teams were established in the largest French cities to apply a program that ostensibly distinguished "true" and "false" "transsexuals" according to Robert [START_REF] Stoller | Sex and gender[END_REF]. Such distinctions led hospitals to restrict access to care to those who were considered "truly transsexuals". This protocol continues to define the different phases of contemporary trans medical pathways, including psychiatric evaluation, psychological and endocrinological assessment, "real-life" tests, and "Long Term Affection" designation (allowing reimbursement of care expenses). Together, they progressively constitute a real "therapeutic shield:(...) a high wall that prevents, refutes and 4 discredits in advance any progress and dialogue" [START_REF] Espineira | Le bouclier thérapeutique : Discours et limites d'un appareil de légitimation[END_REF]. Since July 2010, the protocol has been managed by the SoFECT (French Society for the Study and Management of Transsexualism). This association of non-trans doctors has been heavily criticized, especially following the remarks of a previous president who evoked "the epidemic of transsexualism" [START_REF] Bonierbale | Transsexualisme, ce qu'il faut savoir[END_REF] in France, as well as those of an affiliated psychiatrist who likened "transsexualism" to a "delirium of omnipotence" [START_REF] Chiland | Online support for transgender people: An analysis of forums and social networks[END_REF]. Established protocols led the SoFECT to manage trans pathways by taking a psychiatric approach, requiring the psychiatric supervision of trans people for at least two years before allowing access to Hormone Replacement Therapy (HRT). Furthermore, the association still requests the real-life test in spite of its proven dangerousness. In addition to these issues, self-support associations also denounce the gender stereotypes inherent to such protocol, for which it is necessary to correspond to binary gender norms, to be heterosexual and seronegative, to refrain from sex work, etc.

Faced with the severity of this program, trans people have organized themselves by creating alternative and "individualized" pathways; particularly, those which allow them to choose medical institutions and doctors who will provide care while also bypassing those standards imposed by the medical protocol and reimbursed by the French health care system. Such alternative pathways allow, for example, some trans people to access hormonal therapy without also completing psychiatric follow-up. However, this approach can prevent them from benefiting from free care provided by the French medical system, which is granted by the SoFECT if trans people provide a certificate confirming their adherence to psychiatric followup measures for two years.

Faced with these difficulties related to the French program, trans people have created various information-sharing networks and social support communities to assist themselves. Many associations explain the different options available to trans people during the different phases of their transition pathways, and provide assistance to victims of medical violence or transphobic attacks. Over the last ten years, trans people have also used social media to help each other and to exchange information about the transition program itself. Facebook is now central in France because it enables users to create "safe" groups with restricted access. This article examines the sociabilities between members of these non-mixed Facebook groups in order to describe the different forms of social support within such online communities, in particular that of enabling self-organization in the face of various forms of institutional violence perpetuated by the French therapeutic shield.

Social media into the forms of social support between trans people

Many scholars have shown how the internet and social media promote new forms of social support, for example within anorexic communities [START_REF] Casilli | Online networks of eating-disorder websites: why censoring pro-ana might be a bad idea[END_REF]. These online communities provide two main forms of social support, informational and emotional [START_REF] Coursaris | An analysis of social support exchanges in online HIV/AIDS self-help groups[END_REF][START_REF] Coulson | Receiving social support online: An analysis of a computer-mediated support group for individuals living with irritable bowel syndrome[END_REF][START_REF] Preece | Online Communities: Designing Usability, Supporting Sociability[END_REF]. These digital spaces also promote complementary types of social support, such as those for people with disabilities [START_REF] Braithwaite | Communication of social support in computer-mediated groups for people with disabilities[END_REF] or with HIV/AIDS [START_REF] Coursaris | An analysis of social support exchanges in online HIV/AIDS self-help groups[END_REF], allowing users to exchange messages which help to improve their own image and self-confidence. Following the model proposed by [START_REF] Cutrona | Controllability of stressful events and satisfaction with spouse support behaviors[END_REF], we consider that these online communities have provided over time five types of social support: informational, emotional, esteem-related, networking-related, and tangible support. This model could be combined with other findings within Trans Studies that have highlighted how social media renews the practices of trans people [START_REF] Stryker | The Transgender Studies Reader[END_REF][START_REF] Stryker | The Transgender Studies Reader 2: The Transgender Studies Reader 2[END_REF][START_REF] Schilt | The Development of Transgender Studies in Sociology[END_REF], showing for example how trans vloggers [START_REF] Raun | Out Online: Trans Self-Representation and Community Building on YouTube[END_REF], who often present themselves as experts, share their experiences, difficulties and advice [START_REF] Dame | I'm your hero? Like me?": The role of 'expert' in the trans male vlog[END_REF][START_REF] Horak | Trans on YouTubeIntimacy, Visibility, Temporality[END_REF][START_REF] Raun | Out Online: Trans Self-Representation and Community Building on YouTube[END_REF][START_REF] Raun | DIY Therapy: Exploring Affective Self-Representations in Trans Video Blogs on YouTube[END_REF]. In this article, we extend this research by focusing on the social solidarity among trans people using Facebook. This research perspective extends previous work on the social support available to trans people in accessing to limited resources require by trans pathways (medical information, specific material, etc.), avoiding social isolation and discrimination, and helping to combat the high suicide rate related to the trans population [START_REF] Hendricks | A conceptual framework for clinical work with transgender and gender nonconforming clients: An adaptation of the Minority Stress Model[END_REF][START_REF] James | The Report of the 2015[END_REF]. But these studies often depict health care professionals as the main providers of social support. For example, [START_REF] Evans | Understanding Online Resource Use by Transgender Youth and Caregivers: A Qualitative Study[END_REF] identify the online resources used by trans youth and their parents. They distinguish two different patterns of use: parents tend to consult websites they perceive as "secure" because they are managed by health professionals while, on the other hand, trans youth often seek information from "profane" websites managed by trans people. This distinction led the study to warn about the dangers presented to trans youth, who might presumably be exposed to unreliable and inaccurate information. As these online spaces, created by and for trans people, are considered as potentially dangerous, the scholars advocate the creation of institutional and informational websites designed according to the codes of the trans spaces favored by young people. The medical literature on trans online spaces addresses this topic for obvious reasons, primarily because such spaces allow trans youth to attain expert knowledge on transition pathways, while challenging gatekeepers' paternalistic patientphysician model by reversing the status quo.

Like many scholars and transfeminist researchers, we would like to emphasize the importance of safe spaces managed by and for trans people, including, for example, specific events such as trans summer camps [START_REF] Johnson | We're the Normal Ones Here": Community Involvement, Peer Support, and Transgender Mental Health[END_REF]. Recently, many studies have highlighted how online communities have become more and more important in the management of trans pathways, due to their ability to enable empowerment, fight social isolation, and improve wellbeing and hope [START_REF] Johnson | We're the Normal Ones Here": Community Involvement, Peer Support, and Transgender Mental Health[END_REF][START_REF] Chiland | Online support for transgender people: An analysis of forums and social networks[END_REF][START_REF] Selkie | Transgender Adolescents' Uses of Social Media for Social Support[END_REF][START_REF] Austin | It's my safe space: The lifesaving role of the internet in the lives of transgender and gender diverse youth[END_REF]. Finally, these online spaces contribute to trans well-being; they are necessary to prevent the high suicide rates that mark trans experiences. However, even if scholars have provided interesting data on trans communities, their findings have little to do with the content of such community members' online interaction; this is especially so in France, where the subject is very little discussed [START_REF] Pastinelli | Se retrouver entre soi pour se reconnaître: Conceptions du genre et régulation des échanges dans un forum de personnes trans[END_REF][START_REF] Lallet | Les réseaux sociaux numériques et le développement controversé de savoirs d'expérience sur les transidentités[END_REF]. We thus augment previous research by analyzing the main sources of social support on Facebook (as well as their diversity), and finally by identifying those which have grown in size and influence over time as a result of representing an indispensable and situated perspective.

A mixed research method for situated knowledge

For the purpose of studying the types of social support provided by trans people on Facebook, this research used two complementary methods: a national survey and a lexical analysis of the messages published in a sample of trans Facebook groups.

National survey on social support in social media

We used a self-administered online questionnaire between March and August 2020. It included 405 prompts. The survey was distributed on Twitter and within Facebook groups. French LGBTQI+ associations also helped us to share the survey within their networks; in exchange, we are providing them with the study's main findings in order to assist them in their mission. (For example, accounts or evidence of trans-related medical discrimination, which may be used to justify an increase in government subsidies.) The questionnaire allowed us to collect data on patterns of social support, both on and offline, that trans people have experienced along their pathways. It was built upon a foundation of situated knowledge, combining both our transactivist expertise and our academic knowledge, and thus covered broad elements that may 6 be encountered during trans pathways (loss of social relations, discrimination, problems with the care system, etc.). In this article, we will only study the questionnaire data related to social support within Facebook.

In order to identify the different types of social support we used [START_REF] Cutrona | Controllability of stressful events and satisfaction with spouse support behaviors[END_REF] typology, presented earlier. However, we have adapted it to the specificities of the transgender communities and the French context. For example, we have included the "desire to communicate and engage in activist networks" within the "network" field. In the end, the questionnaire allowed us to analyze 8 different types of Facebook usage: Communicating with other trans/inter/queer people; finding new people to talk to; confiding in others, and finding sources of emotional support; sharing experiences; seeking feedback on surgery; searching for caregivers or physicians; finding legal information; sharing information on transgender and transition pathways; and advocating for the rights of transgender people.

More specifically, this survey aimed to analyze the profiles of these users while characterizing their uses and the types of social support those uses provide. Our analysis also takes into consideration three important dimensions: First of all, we seek to identify the manner in which people find these groups. Then, we identify the sociodemographic profiles of the most active users and of those who, on the contrary, use these spaces infrequently. In a third step, we include the phases of respondents' transition pathways, which influence the types of social support sought by trans people. For example, younger people who have not yet changed their civil status to reflect their gender are logically more likely to seek legal information on this issue, compared to an older person who has already done so.

Lexical analysis of the messages of the Facebook publications

To complete our study on the sociabilities and the types of social support in trans groups, we collected and analyzed, using computer-assisted methods, the contents of the messages within. Because these groups are non-mixed spaces reserved for people who self-identify as trans, it is necessary to have been accepted as a member in order to access them. To validate our membership request by the moderators, we used our status as concerned persons; we were already members of some groups, for private use, which facilitated this step. However, being a trans person is not the only pertinent qualification: some groups also make a distinction between gender identity. In order to access the Facebook groups for trans women, we needed the help of a concerned person who was a member of these groups.

We selected a sub-corpus of 24 groups. First, the sampling method was based on the two most active French-speaking ft* groups. Then, following a non-probability "snowball" sampling method [START_REF] Baltar | Social research 2.0: Virtual snowball sampling method using Facebook[END_REF], we identified the 24 main trans-related groups within the French-speaking communities. These groups are mostly non-mixed trans, dedicated to different trans identities (trans women, trans men, non-binary people, mixed); we have excluded from this corpus the groups dedicated to sexual and/or romantic encounters. Our selection includes 3 groups for men, 4 for women, and 17 mixed spaces. The size of these groups varies from 79 to 4,035 members. We collected the messages of 70,488 postings shared in this sample between February 2013 and April 2020. As Figure 1 shows, the volume of postings increased over the period, reaching approximately 1,800 per month in 2019 and 2020.

Figure 1: Monthly volume of publication in Facebook groups

We have used an open-source software (IRaMuTeQ; [START_REF] Smyrnaios | The Charlie Hebdo Attacks on Twitter: A Comparative Analysis of a Political Controversy in English and French[END_REF], in order to analyze the messages of these postings and to identify the topics of discussion. This allowed us to make a lexical analysis that groups together the most co-occurring terms of the dataset under different lexical classes. These classes are represented by the software in the form of a dendrogram. In section 3.2, we interpret the data qualitatively by describing the main topic that emerges from each lexical class. Therefore, our interpretation of the results of the lexical analysis allows us to analyse the main topics of discussion in the trans Facebook groups.

Results

Trans Facebook groups are organized according to the type of social support provided, and to the phases of transition pathways

First, we present the results of the survey in order to analyze the uses of trans Facebook groups. The objective is to identify the main types of social support provided by them, as well as their usefulness with respect to user profiles and transition pathway phases. Among the participants in the survey (N = 405), 62% of them use trans Facebook groups. They are most often trans men (70.5%; cf. Table 2) between the ages of 18 and 25 (57%). Due to the size of this age group, we find a high proportion of students (41%). As some have not yet finished their studies, a significant number of respondents hold a bachelor's degree (35.5%) or a level higher than baccalaureate +2 (46.2%). Participants often discovered trans Facebook groups by themselves using the Facebook search engine (43.7%). Others joined following the advice of their trans friends and acquaintances (34.33%), or trans associations (12.59%). It appears that the frequency of use of these groups varies according to the different stages of the trans pathways. Use is very frequent at the beginning of a user's transition (54.2%), to self-inform on trans pathways and to socialize with other members of these online spaces. Other important moments motivate frequent use, such as preparation for surgery (10.4%) or periods of coming out (12.4%). These steps also correspond to searches for informational support to which people are referred by posts in these groups.

Many users also publish content (83.7%), most often at the beginning of their transition pathways (29.5%). It appears more generally that users most often request social support in relation to medical care, whether for information, caregiver referrals, or emotional support.

Table 3 highlights the main types of uses and social support in these groups. It appears that the search for information related to surgical operations is central (76.89%). Such searches are much more frequent among men (82.5%) due to the large number of transmasculine people who are engaging or wishing to engage in a mastectomy. At the same time, many people, especially younger people, seek instrumental support in finding safe caregivers (66.53%). Many users also seek information about legal procedures (74.1%). All gender identities are concerned here, with an over-representation among younger respondents, resulting from the fact that many older trans individuals have certainly already completed the administrative procedures related to their transitions. These two types of uses, medical and legal, involve the search for informational support obtained in particular by consulting content.

Among the predominant forms of social support, we find those which are provided through the publication of messages. Indeed, many users share their experiences (73.31%) by relating informational examples that can later help others. Along with these messages, users share information on trans-related topics (67.33%). In such cases, users do not have any particular profile; these practices evolve according to the transition pathway itself, especially during the most critical phases when people feel the need to share their experiences.

Social support supplied in the form of networking [START_REF] Cutrona | Controllability of stressful events and satisfaction with spouse support behaviors[END_REF]) is slightly secondary, as 66.93% of users report engaging in these groups to communicate with other trans/inter/queer people. It even appears that only 48.21% of users frequent these online groups in order to find others to talk with. Even fewer (46.61%) come to seek emotional support. It appears, quite logically enough, that these types of networking-related social support generally concern the youngest. However, as the lexical analysis will reveal, it should be noted that older users may indeed provide support and help to younger ones, even if they do not claim here to use these groups to find such support for themselves. It also appears that education level influences behavior: people with higher levels of education (from Baccalaureate +2) use the groups less frequently for the purpose of finding others to talk to. Finally, it appears that just over a third of respondents use the groups to (37.45%) advocate for transgender rights, in a more politically engaged manner of networking. Even if this use is the least frequent, it nevertheless testifies to an important level of commitment of these actors to trans struggles around questions of rights, discrimination or even empowering reform of the pathways (depsychiatrization and self-determination).

Textual analysis of the forms of social support in trans Facebook groups

The questionnaire allowed us to analyze the main types of Facebook group use, before specifying the group's user profiles. This first part was based on an a priori definition of these uses, as well as the forms of social support found in these online communities. To these ends, we found it productive to engage in a more inductive analysis of user practices by studying the messages of user-shared posts. We therefore perform a statistical analysis of the lexical contents of the postings (N = 70,488) within our corpus, presented in the methodological section, and collected from 24 French-speaking trans Facebook groups between February 2013 and April 2020. In order to characterize the main topics of discussion, we have identified 14 lexical classes using IRaMuTeQ. Figure 2 is a dendrogram that shows a hierarchical representation of these classes according to both their thematic proximity and their weight in the corpus. It shows which terms have the most frequent co-occurrence, and how they have been arranged within the different classes. To facilitate the understanding of this data, we have also named each of these classes.

The lexical analysis first reveals an important theme related to Legal Issues (Class 13). This class represents 6.3% of the lexical contents of the corpus. It refers to specific postings focusing on the legal and administrative aspects of trans pathways, following the research on legal advice analyzed in the previous section. This theme is characterized by terms belonging to the legal sphere ("lawyer", "civil status", "hearing", "judgment") and judicial institutions ("court", "TGI" (tribunal de grande instance), "town council"). These posts also include requests for procedural assistance in changing a first name or gender with respect to civil status. Such procedures were reformed in 2016, with the adoption of the "21st century law on the renovation of the justice system", which allowed the re-designation of an individual's sex without first requiring surgery (which had until that point been mandatory), in particular sterilization. Such individuals must, in both cases, provide documents proving the validity of his or her request while waiting for their case to be assessed during a hearing. The various steps required to create case files can be complicated: what documents to attach, what types of testimony to provide, whether or not to include medical certificates, etc. Thus, given that trans people are usually financially unable to acquire the assistance of lawyers, this lexical class refers to the circulation of limited, dynamic resources related to legal knowledge, including the recent changes in the French law. These types of legal support are plural: informational (advice on procedures, for example) or emotional (encouragement for a person whose case file has been rejected, or who is under great stress on their hearing day). There is also instrumental support, as for example the case when a user, who has no support in their own personal network, asks a member of a group to provide them with a certificate as "a close relative" in order to substantiate their application.

Class 11 (6.4%) directly concerns the rules of use of the Facebook groups themselves; it thus reveals a central use within these groups that we were not able to identify using the questionnaire. Indeed, new members are asked to introduce themselves, at the risk of being expelled from the groups, using standardized informal codes by providing their first name(s), their gender ("ftm/mtf"), their progress in the transition pathway ("hormonal", "out", "transition"), their age and place of residence. These self-presentations therefore refer to a specific type of networking performed by trans communities. Classes 9, 4, 1 and 8 refer to the repertory of intimacy. Per the findings of the questionnaire, these classes reflect the centrality of care and social solidarity within these groups. Their overrepresentation within the corpus (30.7% of lexical content) reveals the safe nature of the groups, facilitating confessions and exposure of private life. Class 9 (6.3%) reports more accurately on the sharing of experiences related to positive events. The objective of these testimonies is to provide others with encouragement ("courage"; "strength"; "path"; "don't give up", "hope").

Class 4 refers to critical situations related to mental health. It contains terms from the lexical repertoire of psychiatry ("depression", "dysphoria", "anxiety", "disorder", "anorexia", "TCA" (eating disorder)) and addresses the urgency of the request for assistance ("emergency", "help", "panic", "suicide"). It reveals the collective trust between members of these groups and the intimate nature of the support provided. Class 1 (16.9%) includes a large number of verbs referring to feelings ("to feel", "to suffer", "to express yourself", "to think", "to understand"). The prevalence of this class testifies to the strong presence of intimate stories, feelings and sentiments, expressed especially for the purpose of sharing experiences and helping each other. Class 8 (5.7%) includes requests addressed to other members ("ask", "question", "questioning"). This class also demonstrates the importance of maintaining safe spaces by using polite or apologetic formulas ("sorry"; "disturb"; "delete"; "silly"; "awkward"). These topics reveal these individuals' need for online support, while highlighting at the same time a break with medical institutions. Indeed, health professionals do not appear in this lexical class, despite the fact that mental health is a main topic. Here again, trans people are primarily seeking help among themselves. This class, which generates a high level of participation, also testifies to a specific ethic of care, in which mental health is a central issue. In other words, these trans online spaces promote a depathologization of trans pathways. Here, mental health is not perceived as an inherent trans issue, nor a characteristic of trans nosography. To the contrary, these group members address mental health as a result of their own marginalization, and the fact that medical institutions still perceive their choices as related to mental disorder. In order to bypass these obstacles, such users manage these groups with a collective ethic of care, aimed at supporting and listening to one another, and at creating safe spaces.

Classes 10 and 12 refer to the development of a collective expertise and social support network regarding hormonal therapy; they concern the two uses, identified with the questionnaire, relating to the sharing of experience and information. Class 10 (7.1%) focuses on the effects of HRT with words related to the body ("face", "skin", "thigh", "leg", "belly") and its evolution ("beard", "hair", "voice"). Class 12 (3.7%) refers to a more medical expertise ("rate", "dosage", "mg", "pressure", "injection") based on the different hormonal substitutes available in France ("androcure", "androtardyl", "progesterone", "oestrodose"). This collective expertise allows the community to have knowledgeable exchanges, contra the monopoly of doctors involved in trans pathways (self-medication, blood test reading, rate adjustment). As noted above, some healthcare professionals, following hospital protocols, feel threatened by the expertise that trans people accumulate in online spaces. These lexical classes testify to the autonomization of trans people in face of gatekeepers, and the ways in which social media provides new resources for empowerment.

Classes 6 and 5 are also related to the sharing of information and advice on medical issues, focusing directly on the medical management of trans pathways in France. Class 6 (10.5%) refers mainly to the search for trusted caregivers, as well as strategies for obtaining reimbursements for care and/or access to surgery. Class 5 (8.8%) focuses precisely on surgical operations ("mastectomy", "phalloplasty", "vaginoplasty", "hysterectomy") and their annexed lexicons ("results", "incision", "hospital", "overcharge"). This class also contains many surnames of surgeons who perform these operations. Like the previous classes, classes 6 and 5 promote the empowerment of those on trans pathways. However, they work differently.

Whereas the previous classes focus on the accumulation of expert knowledge related to hormone therapy, these classes have two objectives: the creation of networks of trusted health professionals, and the shaping of strategies related to different surgical procedures (medical cost reimbursement, choice of surgeon and methods of surgery, etc.). We would like to draw particular attention to the creation of trusted caregiver networks, and the practice allowing users to identify both healthcare "allies" as well as those professionals to be avoided. Indeed, users can seek information about safe trusted health professionals using keywords referring to location and medical specialty (e.g.: endocrinologist Paris), as well as specifics about what they are seeking (e.g.: a prescription at the first appointment). This leads users to testimonials containing the names of doctors who may assist in bypassing the prerogatives of the official protocols. Such networking allows users to avoid healthcare professionals taking a pathologizing and psychiatric approach, particularly those associated with SoFECT. Other types of alliances are being created in response to these professionals, too, especially among feminist health professionals. These alternative pathways and care networks publicly undermine the therapeutic shield, as well as its legitimacy. Their preventive measures are shared among the groups in order to provide the most accurate directory of information to trans people at all stages of their pathways, constantly updated and available at all times.

Class 14 (4.1%) includes information on materials related to the transition ("binder", "prosthesis", "packer", "STP"). This class accounts for merchant exchanges, donations, and critical product returns, according to brand, within the groups. It concerns more particularly transmasculine or ft* individuals who use this type of equipment. This instrumental support was invisible in the questionnaire but is nevertheless very important. This type of material is difficult to find in France, and trans people are often obliged to order it on English-speaking sites; this requires the payment of significant custom fees, as well as the ability to transact in English, which may be a problem for less educated users.

Classes C7, C3 and C2 refer to the sharing of resources and information, in social media terms. Class 7 (4.2%) concerns the sharing of information about offline events, usually organized by trans associations. Class 3 (7.2%) represents the sharing of audiovisual resources ("movie", "series", "documentary", "broadcast", "reportage") related to transgender people. Class 2 (11%) refers the sharing of articles ("press", "blogs", "academics") about important transgender issues ("transphobia", "law", "discrimination", "intersex", "law", "violence").

This lexical analysis of the messages contained in Facebook posts therefore allows us to identify the main types of social support among the users of the groups. It highlights the sharing of information and advice on Legal Issues (C13), the codes of self-presentation in these safe spaces (C11) or on medical transition pathways (C6, C5), the centrality of intimacy and care (C8, C9), social support in relation to HRT (C10, C12) and, more generally, the sharing of media resources or information (C7, C3 and C2). The analysis finally reinforces the findings of the survey by highlighting the types of social support in these online groups according to an inductive approach. This leads us to counter the many scholarly findings which emphasize the centrality of health professionals in the providing of support for trans individuals. Conversely, our research shows how online communities managed by and for trans people constitute safe spaces which tend to promote autonomization and empowerment by providing a wide diversity of social support.

Conclusion

Over the years, the transgender pathways managed by French medical institutions have been characterized by restrictive measures, and particularly strict psychiatric follow-up protocols. This medical program now constitutes a "therapeutic shield" [START_REF] Espineira | Le bouclier thérapeutique : Discours et limites d'un appareil de légitimation[END_REF] which discourages many trans people; especially the youngest, who have the least capacity for financial action. This "shield" leads such individuals to organize themselves within online communities, and to create safe spaces in order to negotiate or bypass such institutional obstacles. Trans people have therefore, gradually, created such groups on Facebook, perceiving the platform to be safe, in order to share their experiences and expertise. In this way, these Facebook groups extend the informational and emotional support provided by transgender associations, while promoting networking across many users, especially those who live far from large cities. Our research analyzes the online sociabilities in these groups by showing the centrality, the diversity and the complementarity of the types of social support provided by the users to each other. We have described different types of social support, which are similar to those identified by [START_REF] Cutrona | Controllability of stressful events and satisfaction with spouse support behaviors[END_REF]: informational, emotional, esteem-related, networking, and tangible support. First, our national survey extends previous works by revealing how these types of support vary depending on the sociodemographic characteristics of the users: the youngest generate more demand for support, especially on legal issues, and the least qualified seek more emotional support. Our findings also highlight the multiple dimensions of these solidarities; for example, the networking support category includes not only "looking for people to talk to" and "putting you in touch with safe doctors," but also trading in difficult-to-find trans-related equipment, gaining access to HRT, negotiating health expense reimbursement, and becoming involved in activist networks.

More generally, our analysis of the main topics of discussion within these Facebook groups leads us to emphasize the centrality of the social support provided by other trans people or close friends. This finding extends previous work on the diversity of the resources available for trans people [START_REF] Johnson | We're the Normal Ones Here": Community Involvement, Peer Support, and Transgender Mental Health[END_REF][START_REF] Chiland | Online support for transgender people: An analysis of forums and social networks[END_REF][START_REF] Selkie | Transgender Adolescents' Uses of Social Media for Social Support[END_REF][START_REF] Austin | It's my safe space: The lifesaving role of the internet in the lives of transgender and gender diverse youth[END_REF] by highlighting the secondary role of the healthcare professionals. We have deemphasized the benefits and the value of this institutional support because it appears that, alternatively, French trans people are organizing themselves to avoid challenges associated with medical institutions, and the ostensible "help" of doctors or psychiatrists. We therefore emphasize the growing importance of these online social support networks, provided by and for trans people using Facebook in particular. In a context where the French protocols for managing trans pathways continue to subject individuals to psychiatrization and even dehumanization, trans people gradually took to digital media in order to define safe spaces for sharing information, discussing related matters, and confiding in each other without fear. In these safe spaces, these users create a transfeminist ethic of care, characterized by a collective approach that places great importance on mental health. In contrast to the traditional pathways managed by medical institutions and psychiatrists, these digital platforms provide a tool for knowledge and expertise, allowing greater autonomous management of gender-related choices, while also focusing careful attention on the most marginalized (e.g. sex workers, people with mental illnesses or who have not sufficiently incorporated binary gender expectations, etc.).

Finally, we promote here a transfeminist analysis of social support. We show how these online communities free themselves from institutional protocols (medical and legal in particular) and improve a new trans ethic of care (Marvin, 2018;Malatino, 2019) facing social isolation, transphobia, cissexism and, more broadly, social norms. By providing social support to each other and sharing expert knowledge, trans people challenge norms and institutions, while engaging in strategies and forms of resistance that promote the empowerment of more "individualized" trans pathways [START_REF] Hilário | Contestation, instrumental resistance and strategic conformation within the diagnostic process of gender dysphoria in Portugal[END_REF].

Figure 2 .

 2 Figure 2. The main lexical classes included in the messages shared in the trans Facebook groups

Table 2 : Profiles of participants using trans Facebook group Number of participants Share of participants

 2

	Gender	Women, trans women, mtf	50	19,9%
		Men, trans men, ftm	177	70,5%
		Non-binary	24	9,6%
	Age	< 18	7	2,8%
		18-21	73	29,1%
		22-25	70	27,9%
		26-30	44	17,5%
		31-35	17	6,8%
		36-40	10	4,0%
		41 and more	30	12,0%

Table 3 : Types of usage of Facebook groups Types of usage Share of users

 3

	Seek advice on surgical operations	76.89 %
	Seek legal information	74.10 %
	Share personal experiences	73.31 %
	Share information	67.33 %
	Communicate with other trans/inter/queer people	66.93 %
	Search for caregivers	66.53 %
	Seek people to talk to	48.21 %
	Seek emotional support	46.61 %
	Advocate for the rights of trans people	37.45 %


Justine Duck

Romain Schaller

Frédéric Auber

Yann Chaussy

Julien Henriet

Jean Lieber

Emmanuel Nauer

Henri Prade

Analogy-based post-treatment of CNN image segmentations

Keywords: analogical extrapolation, case-based reasoning, convolutional neural networks, medical image segmentation, kidney cancer

Convolutional neural networks (CNNs) have proven to be efficient tools for image segmentation when a large number of segmented images are available. However, when the number of segmented images is not so large, the CNN segmentations are less accurate. It is the case for nephroblastoma (kidney cancer) in particular. When a new patient arrives, the expert can only manually segment a sample of scanned images since manual segmentation is a time-consuming process. As a consequence, the question of how to compute accurate segmentations using both the trained CNN and such a sample is raised. A CBR approach based on proportional analogy is proposed in this paper. For a source image segmented by the expert, let a be the CNN segmentation of this image, b be its expert segmentation and c be the CNN segmentation of a target image close to the source image. The proposed approach aims at solving the analogical equation "a is to b as c is to d" with unknown d: the solution d of this equation is proposed as a segmentation of the target image. This approach and some of its improvements are evaluated and show an accuracy increase of the segmentation with respect to the CNN segmentation.

Introduction

Convolutional neural networks (CNNs) constitute powerful tools for many tasks, such as image segmentation [START_REF] Litjens | A survey on deep learning in medical image analysis[END_REF]. However, as many techniques of deep learning, they are demanding in terms of the computing time they require for the learning phase. This is particularly true when the dataset is continuously enriched, as it leads to re-run regularly the learning process. By contrast, case-based reasoning (CBR [START_REF] Riesbeck | Inside Case-Based Reasoning[END_REF]) is usually less demanding in terms of computing time and also for the volume of resources (including cases) and it is "naturally" fitted to the continuous enrichment of the case base.

This article studies the issue of using CBR to improve the results of a CNN when few additional data are available, without having to re-train the CNN. This issue is considered for an application of image segmentation of kidney cancer scans. More specifically, a CNN has been run on images segmented by an expert for 14 patients, with about 100 slices per patient. Given new patient's images, the CNN can propose some segmentations, but with an insufficient precision. To increase this precision, the expert manually segments about 10% of these images and then, the goal is to exploit this 10% to improve the precision of the CNN segmentations of the 90% remaining images. For this purpose, an approach called OV 2 ASSION based on re-running the CNN with the additional examples (the 10%), has been studied in previous works. In this paper, an alternative approach to OV 2 ASSION based on CBR methodology and on analogical proportions is studied.

After some necessary preliminaries (Section 2), a general approach is presented (Section 3) explaining how the CNN image segmentation can be modified by retrieval and adaptation of an image manually segmented. The result is a partial segmentation, meaning that some pixels are undecided. Section 4 presents some improvements to the approach, in particular, to make decisions for undecided pixels. Section 5 concludes and describes future directions of work.

Preliminaries

This section introduces the notions and notations that are useful for the article. Section 2.1 presents the issue of image segmentation, in the framework of kidney cancer images. Section 2.2 presents two deep-learning approaches for addressing this issue: one based on a CNN and one which is an improvement of this approach in the context of the study, called OV 2 ASSION. This article proposes another improvement of the approach of the outcome of the CNN that is based on CBR and analogical proportions introduced in Sections 2.3 and 2.4.

Image segmentation and its application to kidney cancer management

Nephroblastoma is one of the most frequently abdominal tumor observed in children (generally 1 to 5-year-old boys and girls). This cancer represents 5 to 14% of malignant paediatric tumors. This tumor is developped in the kidney. Most of the time, its initial diagnosis is based on imaging. Generally, ultrasounds are planned first in order to confirm its existence and approximate its position. Then, a CT-scan provides its position, and the healthy tissues and organs are reached with a higher accuracy. Radiologists and surgeons need 3D representation of the tumor and the border organs in order to plan the surgery (e.g. anticipate vascular risks, choose between a total or partial nephrectomy), and also to inform the family. Image segmentation is a topic of image processing. It consists in associating a single label to each pixel of an image. In the field of health, segmenting a scan consists in defining the anatomical structure to which each pixel belongs. Segmentation is one of the key steps of the construction of 3D representations of all the organs, veins, arteries, cavities and other anatomical elements (such as a tumor). Formally, for an image of m × n pixels, let Dom = {0, 1, . . . , m -1} × {0, 1, . . . , n -1}. An image is a mapping associating to each (i, j) ∈ Dom the code for the color of the pixel. In this paper, only binary segmentations are considered: there are 2 labels, denoted by the Boolean values 0 and 1. More precisely, the segmentation distinguishes pixels associated to the tumor (label 1) from other pixels (label 0). Formally, a segmentation of a tumor is a mapping S : Dom → {0, 1}. For (i, j) ∈ Dom, S(i, j) is denoted by S ij .

Automatic segmentation is one of the actual key challenges of image processing since most of the time, and in the particular case of the segmentation of nephroblastoma in children, surgeons and radiologists must lead the segmentation process manually. The manual segmentation of the images of a kidney is time consuming (it requires about 6 to 8 hours of medical expert time [START_REF] Chaussy | 3D reconstruction of Wilms' tumor and kidneys in children: Variability, usefulness and constraints[END_REF]), hence the usefulness of tools for assisting these experts. The quality of an automatic or semi-automatic segmentation is evaluated comparing it to a reference one given by an expert. In the field of image processing applied to healthcare, the Dice coefficient is usually employed [START_REF] Dice | Measures of the amount of ecologic association between species[END_REF]. It gives a similarity value (on [0, 1]) between two segmentations S1 and S 2 defined by

DICE(S 1 , S 2 ) = 2 × number of (i, j) ∈ Dom such that S 1 ij = S 2 ij = 1 #S 1 + #S 2 (1)
where #S is the number of (i, j) ∈ Dom such that S ij = 1.

If S 1 is the segmentation automatically computed, and S 2 is the desired segmentation (the ground truth, given by the expert), the closest to 1 is DICE(S 1 , S 2 ), the better the segmentation is and the least the expert has additional work to do.

Now, for N images of the same kidney (e.g. N slices as in Figure 1) providing a 3D representation, a segmentation of this collection of images can be defined as S : k ∈ {1, 2, . . . , N } → S(k), where S(k) is a segmentation of the image number k. Now, given S 1 and S 2 two segmentations of the same collection of images, the Dice coefficient of (S 1 , S 2 ) can be computed with a definition similar to [START_REF] Badrinarayanan | Segnet: A deep convolutional encoder-decoder architecture for image segmentation[END_REF]. 1 This is called the 3D Dice coefficient in the following of the paper and provides a global assessment of a similarity between two collections of segmentations (e.g., for a given patient, the predicted collection of segmentations and the expert collection of segmentations).

The final 3D representations are used by surgeons and radiologists in order to plan the surgery, to have a clear vision of the healthy tissues and also to communicate with the children's families [START_REF] Chaussy | 3D reconstruction of Wilms' tumor and kidneys in children: Variability, usefulness and constraints[END_REF]. Fig. 1: 3D representation of a kidney with nephroblastoma, with the horizontal slices of the scanner imaging.

Using a CNN for kidney tumor segmentation

Inside the deep learning paradigm, CNN principles [START_REF] Lecun | Deep learning[END_REF] have been implemented in Fully Convolutional Network (FCN) [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF], SegNet [START_REF] Badrinarayanan | Segnet: A deep convolutional encoder-decoder architecture for image segmentation[END_REF], DeconvNet [START_REF] Noh | Learning deconvolution network for semantic segmentation[END_REF], DeepLab [3], and appear to be high-performance tools for image segmentation.

In medical and biology applications, Thong et al. [START_REF] Thong | Convolutional networks for kidney segmentation in contrast-enhanced CT scans[END_REF] used CNN to perform segmentation of healthy kidneys. U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] performed segmentation of cells in microscopy images. Currently, CNNs obtain accurate results on the recognition of the shape of a healthy kidney, because the shapes and areas are more or less the same from one subject to another. However, when the form of the considered structure is complex and varies a lot from one case to another, the segmentation is still a challenge. Neural networks for segmentation also need many heterogeneous data in order to be able to transcribe reliable results. In particular, pathological kidneys deformed by nephroblastoma have very different forms from one patient to another, with unpredictable shapes and situations. This then has led to find another method to segment more complicated structures with limited data.

Having a sufficiently large volume of data representative of all possible data is essential for training a deep neural network. As manual segmentation is expert time-consuming, at the scale of a hospital, the learning set composed of the entire segmented abdomens of patients may be composed of tens of cases only. This may not be large enough for conventional learning since each tumor and pathological kidney is unique and varies greatly from one patient to another. This is the reason why we have designed a new method for training on a small dataset: the OV 2 ASSION (Overlearning Vector for Valid Sparse SegmentatIONs) [START_REF] Marie | Segmentation of deformed kidneys and nephroblastoma using Case-Based Reasoning and Convolutional Neural Network[END_REF]. As shown in Figure 1, the OV 2 ASSION method is based on the overlearning of some manually segmented slices of the patient, separated by a gap in order to calculate the segmentation of the entire set of unsegmented slices of this patient automatically. Each black line in this figure represents the selected slice for the training of the neural network. The gap between the chosen slices is the same in order to recover information homogeneously at different levels. This method is used in order to train a CNN based on the U-Net architecture.

Case-based reasoning

Let P (resp. S) be a set. An element x of P (resp. y of S) is called a problem (resp. a solution). A relation on P × S is assumed to exist, with the meaning "has for solution". A case is a pair (x, y) ∈ P × S such that x has for solution y. This "has for solution" relation is not completely known to the system. However, it is assumed that some cases (x s , y s ) ∈ P × S are known: they are the source cases and constitute the case base CB.

CBR aims at solving a problem, called the target problem and denoted by x tgt . A classical process model of CBR consists in (1) selecting k source cases relevant to solve x tgt (retrieval step), ( 2) inferring a solution y tgt of x tgt by reusing these source cases (adaptation step). If k = 1, step ( 2) is qualified as single case adaptation. Other steps, not considered here, follow adaptation. On the set U = {0, 1} of the Booleans, the minimal analogical proportion (according to the inclusion of quaternary relations) can be defined by

Analogical proportions

a:b::c:d if b -a = d -c
where the differences take their values in {-1, 0, 1}. Another analogical proportion, called in the following Sheldon Klein's proportion [START_REF] Klein | Analogy and mysticism and the structure of culture (and Comments & Reply)[END_REF], can be defined by |b -a| = |d -c|.

An analogical equation is an expression of the form a:b::c:? where ? is the unknown. For the minimal analogical proportion on Booleans, solving this equation consists in computing b -a + c: if this value belongs to {0, 1} then it is the unique solution. Otherwise, b -a + c ∈ {-1, 2} and the equation has no solution: the triples (a, b, c) such that a:b::c:? has no solution are (0, 1, 1) and (1, 0, 0). By contrast, an equation a:b::c:? based on Sheldon Klein proportional analogy always has a solution. If (a, b, c) = (0, 1, 1) then the unique solution is 0. If (a, b, c) = (1, 0, 0) then the unique solution is 1. Otherwise, the solution is the same as for the minimal analogical proportion, i.e., b -a + c.

Analogical proportions and analogical equations have been used in CBR in (at least) two ways. First, when the problem and solution spaces are not the same (P = S), a process called analogical extrapolation is applied (see e.g. [START_REF] Lieber | Making the best of cases by approximation, interpolation and extrapolation[END_REF]): it consists in retrieving k = 3 source cases whose problem parts are in analogy with the target problem and then in solving the analogical equation given by their solution parts. Second, when the problem and solution spaces are the same (P = S), a single case adaptation can be performed by solving an equation x s :y s ::x tgt :? (see [START_REF] Lepage | The French Correction: When Retrieval is Harder to Specify than Adaptation[END_REF]). In the following, analogical proportions are used according to this second way.

General approach

This section presents the general approach to propose an alternative to OV 2 ASSION based on CBR. This approach outputs a partial segmentation, that is, a segmentation with some "undecided" pixels, as described in Section 3.1. Then, the problem setting is formulated in CBR terms ( §3.2) and a CBR approach is proposed with a straightforward retrieval step ( §3.3) and an adaptation step based on analogical proportions ( §3.4). Finally, the approach is evaluated wrt OV 2 ASSION, from accuracy and computation time viewpoints ( §3.5).

Partial Segmentations

A partial segmentation is a mapping PS : Dom → {0, u, 1} where PS ij = 0 and PS ij = 1 have the same meaning as for segmentations and PS ij = u means that PS is undecided about the status of the pixel. For some computations in this paper, u is replaced by the value 0.5. A partial segmentation PS extends a partial segmentation PS means that, for every

(i, j) ∈ Dom, if PS ij = u then PS ij = PS ij .
Now, in order to evaluate a partial segmentation PS 1 proposed by the system in comparison to a reference segmentation S 2 , the idea is to consider the values DICE(S 1 , S 2 ) for S 1 in the set of segmentations that extend PS 1 . Following this idea, the definition of pessimistic, optimistic and average Dice coefficients (the latter being the average of the two formers) can be defined:

DICE pessim (PS 1 , S 2 ) = min DICE(S 1 , S 2 ) | S 1 extends PS 1
(2)

DICE optim (PS 1 , S 2 ) = max DICE(S 1 , S 2 ) | S 1 extends PS 1 (3) DICE avg (PS 1 , S 2 ) = DICE pessim (PS 1 , S 2 ) + DICE optim (PS 1 , S 2 ) /2 (4)
Pessimistic and optimistic Dice coefficients can be computed as follows. Let S 1,pessim and S 1,optim be the segmentations extending PS 1 such that, for (i, j) ∈ Dom:

S 1,pessim ij = 1 -S 2 ij if PS 1 ij = u PS 1 ij otherwise S 1,optim ij = S 2 ij if PS 1 ij = u PS 1 ij otherwise
It can be shown that the pessimistic and optimistic Dice coefficients can be computed according to the following equalities:

DICE pessim (PS 1 , S 2 ) = DICE(S 1,pessim , S 2 ) DICE optim (PS 1 , S 2 ) = DICE(S 1,optim , S 2 )

Problem setting in CBR terms

It is assumed that a CNN has been trained on the images of a set of patients and that it can be used on a new patient to propose segmentations. This CNN is used in this approach as a black box: CNN : scanner image of a slice → proposed segmentation of this image Now, let {image 1 , image2, . . . , image N } be the set of scanner images of slices for the new patient, at the level of the kidneys. The image indexes are ordered from the top to the bottom: image i is above image i+1 (i ∈ {1, 2, . . . , N -1}). In this application, for the new patient, N = 136 (there is a variation of the value of N depending on the size of the kidney which depends in particular on the age of the patient). Only a sample {image s | s ∈ IIMS} of images are manually segmented, to lower the required expert time (IIMS is the set of indexes of the images that are manually segmented). In this application, IIMS = {1 + 11k | k ∈ {0, 1, . . . , 12}}, so the required manual segmentation is about 30 to 45 minutes of expert time. For s ∈ IIMS, two segmentations are available:

-The segmentation computed by the CNN and denoted in the following x s :

x s = CNN(image s ); -The manual segmentation of image s given by the expert and denoted in the following y s .

The pair (x s , y s ) is considered as a source case that encodes the experience of correcting the CNN segmentation. So, the case base is CB = {(x s , y s ) | s ∈ IIMS}. Now, let IINMS = {1, 2, . . . , N } \ IIMS, the set of indexes of images for which no manual segmentation is available. Let tgt ∈ IINMS and x tgt = CNN(image tgt ). The objective is to find a segmentation y tgt of image tgt by reusing CB, the available experience on CNN to expert corrections in the context of the new patient. For this purpose, a classical CBR approach with the retrieval of a single source case and an adaptation of this case is considered.

Retrieval

In this application, the implemented case retrieval is straightforward: for a given target problem x tgt with tgt ∈ IINMS, the source case (x s , y s ) which minimizes |s-tgt| is chosen. This choice is justified by the fact that the CNN segmentation of the tumor varies rather smoothly according to the slice vertical position.

Adaptation using an analogical proportion

Given the target problem x tgt and the retrieved case (x s , y s ), the adaptation consists in considering that the proposed solution y tgt to x tgt is such that x s is to y s as x tgt is to y tgt . In other words, the expert "correction" from x s to y s is applied on x tgt . The implemented approach works at the pixel level, meaning that it is based on the analogical equations x s ij :y s ij ::x tgt ij :? for each (i, j) ∈ Dom. The minimal analogical equation is chosen, thus such an equation may have no solution. Therefore, the result of this adaptation is only a partial segmentation. Formally, adaptation is computed this way:

-For each (i, j) ∈ Dom,

• Solve the analogical equation x s ij :y s ij ::x tgt ij :?. • If it has no solution, then y tgt ij ← u. • Otherwise, let d be the solution of this equation. 2 Then y tgt ij ← d. -The partial segmentation y tgt is proposed as a (partial) solution to x tgt . Figure 2 presents an example of the outcome of such a process.

Evaluation

The data for this evaluation are constituted by the scanner images of 14 patients with about 100 images per patient and an expert segmentation for each image. A CNN was trained on the images and segmentations of 13 patients. For the 14 th patient, the expert segmentations of 1/11 images where kept, with a constant gap between them, which has constituted the case base. The approach was tested on the 10/11 images remaining.

Figure 3 and Table 1 present the results with pessimistic, average and optimistic 3D Dice coefficients, compared to the 3D Dice coefficients for the segmentations provided by the CNN and by OV 2 ASSION. The figure presents these results slice by slice, for slices number 40 to 100 (for the other slices, the number of pixels for the predicted and expert segmentations that belong to the tumor is very low, making the Dice coefficient of little relevance). The table presents these results with 3D Dice coefficients, comparing predicted and expert segmentations on the tumor as a whole. The initial CNN training (with 200 epochs, and with 16 as batch size) took 2 hours and 42 minutes and the segmentation 5 minutes (this time is common to the three approaches). As indicated in Table 1, the computation on the images of the new patient take 299 seconds with the trained CNN, 772 seconds with our proposed approach (written in Python), and 971 with OV2 ASSION. 3This shows that the simple case-based approach presented in this section actually improves the output of the CNN thanks to a sample of additional segmentations, but that it is still overcome by the OV 2 ASSION approach using the same sample (and using a little bit more time). It also shows that the choice of values for undecided pixels could improve the approach, which is studied in the next section.

Improvements of the approach based on post-processing techniques

This section presents some ways to improve the approach of Section 3 and ends with an evaluation. Second, considering that the patterns for minimal analogical proportions are (u, u, v, v) and (u, v, u, v) (u, v ∈ {0, 1}), the solution requiring the least modifications to these patterns are d = 1 for (a, b, c) = (0, 1, 1) and d = 0 for (a, b, c) = (1, 0, 0), i.e., d = c for both cases (where the considered modifications are flips of Boolean values). This strategy is called conservative approach in the following.

Therefore, these two strategies give the opposite proposition for changing a value y tgt ij = u to y tgt ij ∈ {0, 1}. These two strategies have been compared, following the same evaluation protocol as in Section 3.5, and gives a significant preference for the second one (cf. the evaluation, at the end of this section).

Use of convolution masks

The approaches presented and compared in Section 4.1 are limited by the fact that they do not take into account the context, i.e., the segmentations of the pixels that are around an undecided pixel. For example, it seems natural to consider that an undecided pixel surrounded by pixels that are all 0s or all 1s is likely to be associated with the same common value. More generally, the strategy consists in choosing the "main tendancy" of these pixels. For this purpose, a convolution mask is used. By contrast to the CNN approach, the weights of such a mask are not learned but are chosen parameters.

For the sake of simplicity of the presentation, in this section, for a partial segmentation PS, if (i, j) is an "out of bound index" pair (i.e., (i, j) ∈ Dom), then PS ij = u (the undecided value u is assimilated to u = 0.5). 3 types of convolution masks were tested, with different values of their weights, knowing that the results (described in §4.4) are poorly sensitive to the choice of the weights.

Use of a 3 × 3 convolution. A 3 × 3 convolution mask is a 3 × 3 matrix M of real numbers, assumed to be indexed on {-1, 0, 1} (i.e., M kl is defined for -1 ≤ k, ≤ 1). Following a symmetry principle, the masks considered here are of the form

  w C w B w C w B w M w B w C w B w C   ,
thus are parametrized by w M (the weight at the middle), w B (the weight at a border) and w C (the weight at a corner). Moreover, the mask is assumed to be normalized: the sum of its elements is

w M + 4w B + 4w C = 1.
Given a partial segmentation PS and a mask M, a new partial segmentation PS is defined as follows, for (i, j) ∈ Dom:

with σ = (k, )∈{-1,0,1} 2 M k × PS i+k,j+ , PS ij =      0 if σ < 0.5 u if σ = 0.5 1 otherwise
This partial segmentation PS is then proposed as a result. Different values of the parameter triple (w M , w B , w C ) were considered. In order to have PS extending PS, the choice w M > 0.5 was made: when PS ij = u, this weight is of no consequence on the decision made and when PS ij = u then PS ij = PS ij . As a consequence, w M > 4w B + 4w C : the weight of the middle is greater than the weight of all the other pixels (borders and corners). Moreover, the relation w B > w C was made, since the non-corner borders of the mask being closest to the middle that the corners, they have more importance. With these constraints, various values of the parameter triple were chosen, given similar result. The evaluation was made with the triple (0.6, 0.075, 0.025).

Use of a 5 × 5 convolution. A 5 × 5 convolution mask was used in a similar way. The convolution mask is based on 6-tuple of weights (because of the symmetry, there are only 6 different values and they are ordered in the tuple by decreasing distance to the center). The evaluation was carried out with the weight tuple (0.6, 0.05, 0.025, 0.025, 0, 0).

Use of a 3 × 3 × 3 convolution. A 3 × 3 × 3 mask is the fusion of three 3 × 3 masks obtained on the target slice and the slices preceding and following this target slice. This construction supposes beforehand to have obtained the partial segmentations of all the target slices. The 3D convolution mask is based on a 4-tuple of weights (because of the symmetry, there are only 4 different values and they are ordered in the tuple by decreasing distance to the center). In the experiment, the chosen tuple was (0.6, 0.0333, 0.0083, 0.0125).

Use of closures

The idea has emerged to use convex closures for improving the result and then, more generally, to use other closure functions.

Convex closure and other closures. Given a set X of points of the plane, the convex closure (also called convex hull) of X, is the minimal set of points CC(X) such that for every pair (P, Q) ∈ X 2 , the segment [P, Q] is included in X. Formally: Another example of closures on sets of points of the Euclidian plane is C ∆ , where ∆ is a line of the plan: for a set of points X of the plane, C ∆ (X) is defined in a similar way as CC(X), except that the segment [P, Q] has to be parallel to ∆. In particular, given an affine coordinate system Oxy, horizontal closures (resp. vertical closure, rising diagonal closure, and downward diagonal closure) is the closure C ∆ where ∆ is defined by the equation y = 0 (resp. x = 0, y = x and y = -x). A final example of closure is the rectangular closure, i.e., the smallest rectangle whose edges are parallel to the axis that contains all the values of a set of points X.

CC(X) = [P, Q] | (P, Q) ∈ X 2
How to use closures for the post-treatment. The notions of closures are defined on sets of points of the plane, but are applied on images, making the approximation that a pixel corresponds to a point. Moreover, a segmentation S is assimilated to the set of pixels (or points) (i, j) ∈ Dom such that S ij = 1: S = (i, j) ∈ Dom | S ij = 1 , hence the notion of closure C(S) of a segmentation S (given a closure function). Now, given three segmentations x s , y s and x tgt (corresponding to a source case (x s , y s ) and a target problem x tgt ), the approach of section 3 (possibly with some post-treatments of the current section) provides a partial segmentation y tgt . For each of these three segmentations, a closure can be computed with a closure function C, hence the three segmentations C(x s ), C(y s ) and C(x tgt ). Then, a partial segmentation PS can be found by applying the section 3 approach on these three segmentations: PS ij is obtained by solving the analogical equations C(x s ) ij :C(y s ) ij ::C(x tgt ) ij :? (for any (i, j) ∈ Dom). This partial segmentation PS is used as a prediction of the closure of the desired segmentation. Thus, for (i, j) ∈ Dom, it is expected that y tgt ij ≤ PS ij . Therefore, the situation y tgt ij > PS ij is considered to be abnormal and, when it occurs, y tgt is changed into PS ij . Figure 4 shows that a closure can remove distant noisy pixels. This approach has been tested for horizontal, vertical, rising diagonal, downward diagonal, and rectangular closures.

Evaluation

Table 2 presents an evaluation of the different segmentation approaches: CNN, OV 2 ASSION, the case-based approach of Section 3, and the improvements of this approach proposed in the current section.

The lines are ordered by decreasing 3D DICE avg . For these data, the best result, according to DICE avg is obtained by applying the general approach of Section 3 followed by the conservative choice of pixels described in Section 4.1. It is noteworthy that (1) for other segmentation problems (e.g. kidneys) this order may be different and (2) some of the other approaches may be improved.

For this first version of our approach, the results are just over the middle between CNN and OV 2 ASSION ones, but there is room for improvement, as is detailed in the conclusion of the paper. Every approach considered here uses the CNN computation (that requires 2 hours and 42 minutes of computing time).

The required computing times of our best approach and OV 2 ASSION are similar (1243 s for the former and 971 s for the latter, knowing that the former has been programmed in Python and the second uses a highly optimized library). Now, if the expert just want an improvement of the CNN segmentation of one slice (at at time), as a starting point for manual segmentation, our approach needs only about 1243/100 12 s.

Conclusion

This article has presented a first case-based approach to improve CNN-based image segmentations given a new sample of expert segmentations from the current context, i.e., in the application, in the context of a new patient suffering from nephroblastoma. This approach improves the result of the CNN but gives still less accurate results than the OV 2 ASSION approach that consists in re-running the CNN with the additional segmentation sample.

This work gives encouraging results, but has to be improved. Other directions of work follow this study.

First, it can be noticed that the approach presented in this paper relies only on segmentations (given by the CNN and the experts). By contrast, the CNN and the OV 2 ASSION system use also the images taken from the scanner, with gray levels. A future work aims at using these images for improving the approach. This can be done as an additional post-processing technique for the choice of undecided values for segmentation. This can be done also by using analogical proportions directly on gray levels. More precisely, the idea is as follows. With the current approach, the adaptation consists in solving the analogical equation x s :y s ::x tgt :? pixel by pixel. Now, if the mapping of image, an image described by gray levels, into a segmentation S is denoted by (image → S) then, the adaptation would consist in solving the analogical equation (image s → x s ):(image s → y s )::(image tgt → x tgt ):?

and obtaining a mapping (image tgt → y tgt ) from which a segmentation would be obtained. How to actually realize this idea is still a challenging question.

A second work consists in studying the use of geometrical moments of a segmentation, i.e. the area of the set of tumor pixels, its centroid and its orientation. The principle is that the geometrical moments can be predicted by analogy (e.g. by solving in R the analogical equation area(x s ):area(y s )::area(x tgt ):?) and to use these predictions to modify y tgt (e.g. by making choices for undecided pixels based on the difference between the predicted area and area(y tgt )).

Third, it is planned to use the interpolation approach presented in [START_REF] Lieber | Making the best of cases by approximation, interpolation and extrapolation[END_REF] to improve the results. This approach is based on the retrieval of two source cases (x r , y r ) and (x s , y s ) such that x tgt is between x r and x s . Then, it is plausibly inferred that the expected segmentation y tgt has to be between y r and y s (at a pixel by pixel level or globally).

Fourth, the search for a smart combination of these approaches remains to be studied.

Finally, these approaches will be tested for other anatomical structures which still challenge the segmentation using CNN and OV 2 ASSION: kidneys, veins, arteries, and cavities.

Following [ 13 ]

 13 , an analogical proportion on a set U is a quaternary relation on U denoted, for (a, b, c, d) ∈ U 4 , by a:b::c:d and read "a is to b as c is to d", that satisfies the following postulates: a:b::a:b (reflexivity); if a:b::c:d then c:d::a:b (symmetry); if a:b::c:d then a:c::b:d (central permutation).

Fig. 2 :

 2 Fig. 2: Example of adaptation based on the proposed approach, with segmentations x s , y s and x tgt , and partial segmentation y tgt . In a (partial) segmentation S, S ij = 1 (resp. S ij = 0) is represented by a white (resp. black) pixel. For the partial segmentation PS = y tgt , PS ij = u is represented by a green pixel. x s and y s correspond to slice number s = 90, x tgt , y tgt and expert tgt correspond to slice number tgt = 85, respectively corresponding to what the CNN proposes, how the CBR approach corrects it and what the expert gives.

Fig. 3 :

 3 Fig. 3: Evaluation of the approach, slice by slice.

4. 1

 1 Two local strategies for choosing a value for undecided pixels An analogical equation a:b::c:? on Booleans with minimal analogical proportion has no solution d for (a, b, c) ∈ {(0, 1, 1), (1, 0, 0)}. Two ways of proposing a solution are considered. First, considering the Sheldon Klein proportion gives the solution d = 1 -c.

Fig. 4 :

 4 Fig. 4: Example of post-treatment using the rectangular closure. Left: y tgt provided by the approach of §3. Center: correction of y tgt using rectangular closure. Right: expert segmentation.

Table 1 :

 1

	Approach	DICE pessim	DICE avg	DICE optim	Calculation time (s)
	OV 2 ASSION	-	0.9489	-	762 + 209 = 971
	proposed approach	0.8806	0.8974	0.9143	299 + 473 = 772
	CNN	-	0.8648	-	299

Dice evaluation and calculation time of the general approach. For approaches without undecided pixels (CNN and OV 2 ASSION), the values DICE avg and DICE are equal. The computation time does not include the CNN training.

  Method DICE pessim DICE avg DICE optim Computation time (s) OV

	2 ASSION	-	0.9489	-	762 + 209
	(b) conservative approach	-	0.9129	-	299 + 473 + 471
	(c) 5 × 5 convolution	0.9078 0.9078 0.9078	299 + 473 + 643
	(c) 3 × 3 convolution	0.8984 0.9056 0.9128	299 + 473 + 496
	(c) 3 × 3 × 3 convolution	0.9010 0.9028 0.9045	299 + 473 + 711
	(a) general approach	0.8806 0.8974 0.9143	299 + 473
	(d) rectangular closure	0.8713 0.8904 0.9095	299 + 473 + 1644
	(d) horizontal closure	0.8635 0.8829		299 + 473 + 1626
	(d) vertical closure	0.8630 0.8828 0.9026	299 + 473 + 1632
	(b) Sheldon Klein	-	0.8820	-	299 + 473 + 487
	(d) rising diagonal closure	0.8621 0.8815 0.9010	299 + 473 + 1573
	(d) downward diagonal closure 0.8612 0.8808 0.9005	299 + 473 + 1385
	CNN	-	0.8648	-	299
	(a) General approach, providing a partial segmentation (cf. §3).
	(b) Using two local strategies for choosing a value for undecided pixels (cf. §4.1).
	(c) Using convolution masks (cf. §4.2).
	(d) Using horizontal, vertical, diagonal and rectangular closures (cf. §4.3).

Table 2 :

 2 Evaluation of various improvement strategies.

(i, j) ∈ Dom is substituted by ((i, j), k) ∈ Dom × {1,

2, . . . , N }, S 1 and S 2 are substituted by S1(k) and S2(k) in the numerator and #S 1 + #S 2 is substituted with #S1 + #S2, where #S is the number of ((i, j), k) such that Sij(k).

With the chosen analogical proportion, the solution, when it exists is unique.

All these computations have been made on the Mesocenter of computation of Franche-Comté, equiped of processor Intel(R) Xeon(R) Gold 6126 CPU @ 2.60GHz and Nvidia Volta V100 GPU.

Acknowledgement

The authors would like to thank the European Union for financing this project as part of the SAIAD and SAIAD 2 INTERREG V programs and the SAIAD and SAIAD 2 consortiums partners. Computations have been performed on the supercomputer facilities of the Franche-Comté Computation Mesocenter.


Nico Valentini
email: n.valentini@brgm.fr

Eric Palvadeau

Perrine Fleury

Yann Balouin

Clara Rondeau

Marianne Gabirot

Vulnerability of reed beds to climate change in the Occitanie region

Keywords: Coastal management, Reed beds, Coastal ecosystems, Vegetation resilience

Reed beds communities play important structural and functional roles in wetland ecosystems, as they work as efficient filters for pollutants and provide habitat for fauna species and avifauna in particular. In the Mediterranean (GIGANTE et al., 2014), a decline of these ecosystems has been observed during the last decades, resulting mainly from eutrophication together with anoxic conditions. Intrusions of seawater by coastal flooding during storms can radically transform the balance of the environments making them, for a certain period, unsuitable for the development of the reed beds and the species they shelter. The reed beds are so vulnerable to climate change in the near future (ADENA, 2022). This study aims at assessing the vulnerability to climate change of reed beds ecosystems along the Mediterranean coast of Occitanie by comparing the topography of 29 reed beds, approximated as accurately as possible by recent topographic datasets, with marine flooding scenarios calculated for two periods: 2030-2050, 2100 and 2100+ (pessimistic scenario). A simplified static approach is used without considering duration of flooding nor the speed of water propagation. Three different scenarios are proposed at each time scale: permanent flooding, recurrent (flooding once a year without storm event) and exceptional (100y return period storm event). Water levels are defined using hypotheses of the 4 th IPCC report together with the previous studies of extreme water levels and regional storm characteristics. The first finding from the analysis is that 50% (16) of the regional reed beds will be already impacted by 2030-2050 permanently (most of the year) and seven recurrently, corresponding to a sea level rise of between +40 cm and +70 cm NGF. Most of the regional reed beds areas are impacted by the less severe scenarios, pointing out the important vulnerability of these coastal ecosystems.

Introduction

Reed beds develop in wetlands and, particularly in coastal areas, they are located at altitudes very close to the level of lagoons and the sea or close to them. In this context, the groundwater is strongly influenced by the salty environments. The root system of reed beds is generally shallow (less than 1 m), and the development of these plants is possible thanks to the presence of a low salinity surface water table. The reed bed is in fact tolerant of salinity as long as the water remains at a brackish stage (salinity below 10 g/l). A direct supply of seawater is thus directly harmful to the plant. When the salinity of the surface water becomes high, the plant will eventually die. The number of reed beds in the Occitan region, censed in the context of the study from PALVADEAU et al., (2021) is 29, and each one of them is unique with its own way of functioning. This is linked to its history and developments (e.g. former saline activity, wastewater plant, dyke, irrigation canals, anti-salt dam), its current management (irrigation or low input, input of fresh or salty water, input from a lagoon station) and its relationship with the surrounding environment (connection lagoon environment, etc.) throughout the overall year or only during specific periods (floods, storms). Almost all of the reed beds are sensitive to salinization, due to their proximity to lagoons or the sea. In the context of climate change, salinization phenomena will increase under the effect of two main interconnecting phenomena: (1) the sea level rise, (2) the potential increase in flooding during storm events, as a direct consequence of the sea level rise and (3) a decrease in available water resources for irrigation due to increased periods of drought. The intrusion of seawater during storms can radically transform the equilibrium of the environment by greatly increasing its salinity, making it unsuitable for the development of reed beds and the species they shelter for a certain time. It is therefore likely that an increase in the frequency and intensity of these episodes and the associated flooding could eventually have a greater or even lasting impact. The vulnerability of reed beds to climate change is assessed in this study by comparing their topography, approximated as accurately as possible by recent topographic datasets, with marine flooding scenarios calculated for two main timeframes: 2030-2050 and 2100.

Method

The method used here for flooding areas is based on that of the MISEEVA project conducted by BRGM in 2010 (SERRAND et al., 2013). It uses a simplified approach of static projection of sea level on land characterized by: -No notion on the duration of the submersion nor on the speed of water propagation; -The same sea level is considered for the entire coastline despite the differences from one site to another. The chosen scenarios, based on MISEEVA project consider two main timeframes, 2030-2050 and 2100. The chosen sea levels here are those used in the CEREMA-BRGM study carried out in 2020 for the EPF i Occitanie to characterise the impact of sea level rise on the property values of the Occitanie coastline (CEREMA-BRGM, 2020). These levels (see Table1) are those closest to knowledge and recommendations (at year 2020) for carrying out this type of analysis: DGEC ii -ONERC iii (2010) synthesis -considering sea level rise in order to estimate the impacts of climate change and possible adaptation measures ; DGPR iv , 2014 Methodological guide -Coastal risk prevention plan. For each scenario, the submerged areas are estimated as: -Permanent: represents land that will be under water for a large part of the year. The corresponding sea level currently considered is the average level at Sète (0.17 m); -Recurrent: level reached once a year under calm weather conditions and average waves (without storms); -Exceptional: corresponds to a storm of 100-year occurrence (probability of 1/100 of occurring each year). For marine flooding propagation, on land, several methods exist, from the simple projection on land of a water surface, which fill the basins to the more complicated nonhydrostatic numerical modelling (NICOLAE LERMA et al., 2017). At the regional scale of this work, methods that are more refined would be too much expensive. The processing of the digital terrain model (DTM) in a homogeneous and exhaustive way (enriching the DTM precisely with all the obstacles present on the physical path of the flooding) and the calculation of the volumes of water overtopping the natural and human infrastructures or entering from the lagoons' sides would have high computational demand and time.

In this study, for the scenario used, the water level is propagated on land using a homogeneous way, so over the entire coastal zone concerned, according to two methods implemented by the CEREMA-BRGM (2020) study. The first method, the so-called 'Low Zone' method, consists of filling in all low zones below sea level in each scenario (Figure 1). This method is realistic in the case of a rise in mean sea level. The level of the lagoons connected to the sea will follow the evolution of the mean sea level. It is very likely that the water basins in the littoral area will fill up even if they are not directly connected to the sea or to a lagoon; because the water table will also rise and the low areas will not be able to drain by gravity.

The second method, the 'Connected Zone' method, is to fill in low-lying areas below sea level but stop at the first obstacles (Figure 1), as there is no known or proven connection with the areas behind. Incoming volumes cannot fill large areas. These methods are based on altimetry analysis and flow directions and not on numerical modelling of the phenomena.

Figure 1. Methods for filling in the flooded areas for a given sea level according to the "Low Zone" on the left and the "Connected Zone" method on the right.

In this study, the Connected Zone method is applied to all the reed beds except for two, Grande Palude and Grau du Roi (Espiguette). For these two cases, the study of their hydrogeological context (PALVADEAU et al., 2021) showed that their flooding will most probably be controlled by the rise in the water table, even though the reed beds are not directly connected to the sea by channels or lagoons. For these two reeds beds the Low Zone method is therefore applied.

For the application of the Connected Zone method, the existing connections between the reed beds and the coastline (maritime or lagoon) were therefore sought in order, if necessary, to propagate the flooding further inland. The coastline used is the HISTOLITT® coastline of SHOM.

Data used

The topographic data available on the regional territory where the reed beds are distributed are:

-IGN data, digital terrain model (DTM) representing a regular grid 25 metres-spaced; -LiDAR Litto3D® points cloud data (SHOM-IGN, 2009) and DTM with a regular grid of one point every meter.

An initial analysis carried out by ADENA in 2019 showed that the IGN topographic data (5-metre step) and Litto3D® 2009 (1-metre DTM) are unsatisfactory for reliably describing the topography of reed beds. There is still a significant difference (until around 1 metre, locally) between the field data (reed bed bottom) and Litto3D® data. As the bathymetry of reed beds is not available now of the study, it is therefore proposed to work on the point clouds from the 2009 LiDAR Litto3D survey. A preliminary analysis shows that these points are closer to real topography of reed beds then the DTM, which is a modelled approximation. With the help of Cloud Compare© software, these original points were filtered using the Cloth Simulation Filter (CSF) plugin (ZHANG et al., 2016) to exclude the tallest portion corresponding to the vegetation, particularly. Principle of the CSF under Cloud Compare© is in Figure 2.

A preliminary test was carried out on the La Matte reed bed shows that the DTM surface created from the points filtered is indeed locally below the Litto3D® DTM and closer to observations. The spatial distribution of the differences, in metres, between the altitudes given by the Litto3D® DTM 2009 and those from of the DTM created with the point clouds of the same Litto3D® survey, filtered with the Cloth Simulation Filter (CSF) is presented for the reed bed "La Matte" (reaching several decimetres) in Figure 3. The measurement points from the 2009 Litto3D survey were therefore extracted and processed at each polygon, representing a reed bed. A regional new DTM has been built. The method therefore makes it possible to determine which scenarios will impact the reed beds permanently, recurrently or during an exceptional event, for each of the selected timeframes, and to estimate the level of impact in terms of the percentage of surface area potentially covered.

Figure 2. Cloth Simulation Filter (CSF) principle (ZHANG et al., 2016) in Cloud Compare©.

Results

The mapping results of the flooding scenarios applied to each reed bed studied in this project have been post-processed.

Examination of this mapping and the statistical values associated to the different layers produced for each scenario provides the elements for analysing the vulnerability of the reed beds according to three (3) main criteria, which are summarised in the columns of Figure 4:

-The first scenario of flooding reaching each reed bed; -The first scenario of permanent flooding, where the reed bed will be partially or totally under seawater for a large part of the year; -The first scenario where the reed bed will be totally covered, with a distinction made between permanent, recurrent and exceptional scenarios.

For each criterion, the percentage of the total surface area of each reed bed affected is specified. The main result from the analysis is that 50% (16) of the reed beds in the study will already be impacted by 2030-2050: nine (9) in permanent way (most of the year) and seven (7) recurrently, corresponding to a rise in sea level between +40 cm and +70 cm NGF. Unsurprisingly, Figure 4 shows that the reed beds most affected are mostly located close to the coastline or lagoons. From the reed beds already permanently concerned by 2030-2050, four (4) are particularly affected with a concerned area in the range of 50% to 100%: Bagnas (50%), Grande Palude (100%), Bentenac (52%) and Pierre Fiche (100%). Some of them are no permanently impacted: La Matte, l'Estagnol and La Tour Carbonnière. Only one reed bed, that of Capestang, is not affected by any of the scenarios analysed, due to its huge distance to the sea and the absence of communication with lagoons.

Conclusions

In this context, due to their proximity to the sea or lagoons, almost all of the reed beds surveyed are highly vulnerable to climate change in the near future. Indeed, a direct supply of seawater salinizes the surface water table, which is linked to the root system of the plants, which ultimately leads to their death. However, by 2030-2050, almost half of them will already be impacted, permanently or recurrently. The approach proposed here concerning flooding is static and therefore tends to maximize the impacts, although the "connected zone" is applied. However, it should be noted that the sea levels currently reached during certain storms already exceed the levels of the first two scenarios, and natural protection (clay barriers) may be damaged during these episodes, leading to impacts (case of the Méjean reed bed). Finally, the analysis carried out on the current behaviour of the reed beds shows that these environments could be maintained by adapting the management of water resources, in particular by maintaining a low mineralized water lens in the water body throughout the year. Indeed, maintaining a column of low mineralized water makes it possible to maintain a hydraulic load gradient in the reed bed and thus to guarantee the salt water

Figure 3 .

 3 Figure 3. Difference, in meters, between the altitude given by the Litto3D® 2009 DTM and that of the DTM created with the measurement points (point cloud) of the same Litto3D® survey filtered with the Cloth Simulation Filter (CSF) plugin of the Cloud.

Figure 1 .

 1 Figure 1. Table of criteria for analyzing the vulnerability of reed beds inOccitanie to marine flooding. The type of flooding is associated with the scenario number: "P" for Permanent, "R" for Recurrent and "E" for Exceptional.

  Tableau 1. Flooding scenarios selected for the study (rounded up to the nearest ten centimeters).

	Scenario	2030-2050	2100	2100 +
	Permanent	+0.4 NGF	+0.8 NGF	+1.2 NGF
	Recurrent	+0.7 NGF	+1.1 NGF	+1.5 NGF
	Exceptional	+2.0 NGF	+2.4 NGF	+2.8 NGF
	2.1 Water propagation on land

  table at greater depth (PALVADEAU et al., 2021, ADENA, 2022). Water resource management, where possible (sufficient resource) could thus reduce the vulnerability of the reed bed to climate change. Comptes Rendus Biologies, 337(7-8), 487-498. NICOLAE-LERMA A., PEDREROS R., BALOUIN Y., BULTEAU T. (2017). de la submersion marine: Comparaison des méthodes de détermination de la submersion marine par modélisation numérique. Rapport final. BRGM/RP-67361-FR, 74 p., 1 ann. PALVADEAU E., FLEURY P., VALENTINI N. (2021). Vers une stratégie de conservation à long terme des roselières littorales d'Occitanie -Rapport Axe 3 -Volet hydrogéologique et volet Submersion. Rapport final. BRGM/RP-70715 -FR, 127 p., 66 ill., 2 ann. SERRAND M. (2013). MISEEVA. Méthodologie d'évaluation de la vulnérabilité de la zone côtière du Languedoc-Roussillon face à la submersion marine: élaboration d'indicateurs de vulnérabilité socio-économiques et environnementaux Rapport final. BRGM/RP-60980-FR. 160 p., 32 fig., 5 tabl., 11 ann.ZHANG W., QI J., WAN P., WANG H., XIE D., WANG X., YAN G. (2016). An easyto-use airborne LiDAR data filtering method based on cloth simulation. Remote Sensing; 8(6):501.

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