Jean-Luc Moriceau

DEATH LINES

Keywords: Deadline, research as practice, performative writing, autoethnography

Approaching research as a lived experience, one quickly understands that deadlines grant research with a specific and peculiar temporality and meaning. Thanks to an autoethnographic narrative and a performative writing, the author realizes that the closer he gets to the end and the higher become his vitality, ideas, engagement, relatedness, and reflexivity. Approaching the end quickens deconstruction and reconstructions of his text, the multiplicity of ends and mournings, of traces and ghosts. A figure of research thus appears, diverging from those in epistemology, as well as a tragic parallel with existence.

Indeed research is not linear but syncopated by a series of deadlines that brings in a strange and specific temporality. Especially writing, that is supposed to come at the end, is yet one of its most lively moments, however always threatened by petrification, by the end of research as process. Then, is not this intimate proximity with its end not only displaying a different temporality, but also relating research to life and to other researches, relating the researcher with the research? And would not we earn another understanding of what research is by contemplating it as a dialogue and a fight with and against its own end, its own death? This text's writing, as a lived experience narrative in first person, will gradually be justified in the text. Description and reflexivity on experience will intertwine to present research in constant dialogue with its own ends, from which it draws creativity, situated intersubjectivity and meaning.

PROSPECT OF DEATH

I've never felt so much alive. I like those moments more than many others. My body and brain are just but one. All tensed towards this search for ideas, for expression, for comprehension. So tensed, looking for what I don't know yet, but that I feel so close to discover. For something that needs to be created, but that seems to already exist somewhere. That I am going to touch thanks to my keyboard. Time seems so short, but things go so fast, joyfully; smooth and easy. Time has the very taste of life.

What makes me so lively? The prospect of death! Or more exactly, of a line of death. A line which is both of nascence and of death: a dead-line. A bell will ring soon, and will declare the end of the game. Beyond that bell, beyond that line, there will be no more possibility. The creation will need to be finished. Or even unfinished, always seeming unfinished, the creation will not be able to change, to move or to step back. It will be born and dead at the same moment. This line, this specific line, this dead-line, is what makes me so alive nowseizing life before ceasing life; because it is going to sentence a kind of death very soon.

What is this strange line, why so strange a time pattern? What does it mean about research? Research is given rhythm by deadlines. The time of research is a time stressed and syncopated by deadlines. And this odd temporality commands much of my research activity.

I had so much time. I had three weeks to write my research article. But I have to confess that I found so many reasons to postpone. I haven't written any line before this morning. And the lines were scarce at the beginning. Now that the deadline is approaching, the time has become denser, so creative, even burning. I regret all the lost hours before I started to write. But no, this was no lost time. Unknowingly, something started to take shape in a part of my thought. Thought is constructing over time, but the time of research is very specific. Slow, incomprehensibly slow in the beginning, and then accelerating, accelerating, towards nearly thought speed. And suddenly, thought has to stop, to freeze, to restrain itselfand the very closeness to the end is rightly what makes it so powerful and lively.

Please, give me one more day, one more hour, ten more minutes! I haven't finished yet. I still want possibilities. And I want that the moment of creation, when I feel so right, would never cease. I am afraid of the other side, of death, of the nonreversible, of the non-amendable. I am afraid I will regret what I did not write. I am afraid of the ideas that will come afterwards, afraid that these too late ideas would be good enough, that they would have improved the text, that they would have unveiled what I really meant, to which I was so close. I am afraid of discovering I did not give all my living and loving before the deadline.

Where have all those ideas gone, that used to be so clear, and that I don't have enough time left now to recall? And I look at all those books that scream to be open and read, and of which I don't have enough time now to make friends, allies, mine... And if we had to better understand this time of research in order to really be able to read a research text? Research is made under the constraint, the pressure of time, and a time that has so strange a pattern. [START_REF] Bergson | Creative Evolution[END_REF]

ALREADY DEAD?

But maybe my research died a long time ago. I am trying to get the right representation of what I saw and heard on my research empirical field. But by building a model, didn't I cross another death line? Am I not freezing a multifaceted process into a single representation? Again, in this model, in this neatly arranged set of concepts, there is no more change, move or step back. No more becoming. In a model, and its wired connections, all is given [START_REF] Bergson | The Creative Mind: An Introduction to Metaphysics[END_REF] from the outset on. Organization and research are nothing but the unfolding of a process. There is no creation.

Is it the right time to think about such considerations? I've nearly run out of time. But it is as if all that was written on my pages appeared meaningless. Irrelevant and untrue. Vain and pathetic. As if I had consumed all my time, and that the last glimmers of the candle were making me see, in a sudden and cruel clarity, what was so obviously in front of my eyes. It is a research about researching, research as practice, as lived experience, that entails passion, engagement, creativity, desires and betrayals. An activity full of affects, morale ups and downs, demands on the body. How could I have been so dully rational? How could I pretend to make sense if my five senses were deactivated by my sensibility? Of course rationality is required but it turns in a void if it loses sight of sensitivity. Is it possible that I bracketed and forgot all the sensuous impressions, all the emotional sensitivity, all this erotic and implicit understanding that were offered by being there, participating and being acquainted not only to facts and words, but rather to an experience? And am I doing justice to this experience with my neurotic representation?

How pretentious was I to try to perfect a work of meaning instead of casting and sending bits of senses, trying to induce movementsmovements testifying that what I am studying and myself are still alive?

By wanting to reliably stick to the facts, I happened to burry all intuition and imagination. But when am I going to start thinking? When am I going to start bringing something of my own? By wanting to connect to existing theory, by wanting to ground my sayings on previous works in my research community, I may have missed the singularities and uniqueness of what I was present to. But why did I study this specific world if I am to end up with the same shapes, insights and vocabulary? If I don't change the words, the script, the plot, the masks, the focus, the connection between things and words? By wanting to triangulate, to ensure I got persistent and generalizable relations, to explain by causes and antecedents, I may have overlooked any starting of creativity and innovation, all the hesitations and trials, what is still waiting to take shape. And I've neglected to unquiet my ideas by the demands of taste, of beauty, of the sublime, of pleasure, of tragedy, of the fear of boredom.

No, I am not going to send this. It seems like a parody of research. No risk, no attempts, and nothing meaningful to aim at. I feel wretched and dispirited. And these bloody ticks of the clock as so many laughters and warnings.

But I can't afford not sending anything! Research is made of deadlines, but of pressure for publications too. I need this one more line on my assessment if I want to survive in this competitive research jungle. The deadline is definitively well named. Not only it means the death of any possibility for my work, but it can also mean the death of my research career. Publish or perish, as they say. The lines on the resume are so many blows to repel the death line a little bit farther. I will send something anyway. I felt so alive some minutes ago, and now it is as if the shadow of the Ripper was making all my moves and thoughts heavy. Again, I need to make the perspective of the death line rendering me light, meaningful, fast and concentrated. I have to play with that line of death, to gain energy and a supplement of life.

But an idea slaps my face with the brutality of evidence. And if my research even never started; would not have gone dead, but would never be born? LIVING I realize I sit here in my little studio, fourteen floors up, on a grey Paris night, staring at my computer screen as imploring for a quick answer. Even my notes around, my books around, are addressing a sorry smile, for not being able to help me.

Is it possible, I think, that I have not seen, known, or said anything real and important.2 Is it possible that I have had dozens of months to look, meditate, and record, and that I have let these dozens of months slip away like a recess at school, when there is just enough time to eat your sandwich and an apple? -Yes, it is possible. Is it possible that, in spite of the method books, in spite of culture, religion, and wisdom I tried to get from reading, I had remained at the surface of life? Is it possible that even this surface, which would at least have been something, has been covered with an incredibly dull material till it looks like salon furniture during the summer vacation? -Yes, it is possible! And if reading books and article have distanced myself from life? I feel the need to live experiences, to be transformed, in order to start thinking. Of course I was on the field, I observed, took notes, interviewed, but I was so weary at getting the right data for my construct that I did not live those moments. It's not that I overlooked or remained blind to some aspects, it is that I feel that I have no experience. Or more exactly, that I don't let my experiences enter the research, and above all that I don't live this research as a life experience. If I am not affected, if I am not transformed, if all these experiences would not resonate with previous experiences in life, if I haven't learn to think from experience, if I haven't experienced this dance between life and thought, then what could I write?

To write a single line about researching, I need to have spent many hours of reading, doubting, not knowing what to tell, to have received many sorry smiles of colleagues and reviewers that find it premature, to have felt the anger, disgust or admiration that triggers projects, and my unreadiness and unworthiness in front of other brilliant minds. I need to have experienced the infinite energy given by love, and the pangs of separation, the betrayal of friends and the death of people that used to be so close. And as Rilke wrote, I still have to wait that these experiences transform themselves into blood inside of me, in gazes and gestures, that they lose their names and become no longer distinct from me, then I may become ready to start research, and start to write this bloody article.

Of course living, experiencing, growing transports us closer to death, put the death lines inside of us, but if it was the precondition to start writing?

NO RETURN

How could I have done that? What was I thinking about? At the bottom of the screen, the clock shows '00.08'. It can't be true. No. It is too late. The deadline has passed! And I know from experience that now with the computerized submission systems, I will no longer be able to upload my article. It can't be true: so many hours of figuring out what to write, of so difficultly writing already eight pages and half, of neglecting the invitation to go out or of being with my partner, after so many excitements, readings, hopes and dreams, all is over now.

After ten minutes of incredulity, comes the time of remorse.

Having crossed the deadline, starts not only the end of possibilities, the end of creation and liveliness, but also the end of meaning. It's not enough to say that I feel disillusion, it's really an experience of a kind of death. My body, already used by the fatigue from sorrows and bad sleeps, is hardly able to move. I can just sit on my bed, a void in the gaze, with an overwhelming sadness that impedes any thought. I felt so lively one hour before, I feel so lifeless, desireless now. I hardly feel any use in breathing. Then angriness starts to work my belly, and spreads all over the body and beyond.

It's too late. I have to realize it. I need to learn from it. I need to swear I won't let such thoughts, about experience, meaning, life and death pollute my work anymore. I need to become realistic, to grow and understand that time is given by the clock, and that no thought or imagination can do something against it. There is no return.

I don't know how I manage to get asleep, but I do. And I certainly won't let any thought about the relation between sleep and death to interfere. I dreamt about a line being removed from my resume…

GHOSTLY SURVIVAL

The next morning I learn that the deadline was extended to two more days. First I felt panic. The mourning night has been very uneasy, and I did not want to go through so many emotions again. And what kind of life after am I in? Is it Hell or Paradise?

I feel inside my body and my thoughts that I am experiencing the fabrication of the academic subject. From these uneven times, these ups and downs, this flirt with death, this addiction to deadlines, theses excitements, this pride for performance, this masochistic behavior, this split from the outside world… I feel I am getting scholarized, academic-ized, transformed into a university-man. What if I, and my addictions, were nothing but a toy of the system? And how have I come to accept, even want that violence? Is it by pride, by laziness to rebel or by a kind of instinct for survival? Is this the kind of life I wanted?

But why do I take it that personally? After all, I just need to write a text. And should not the researcher keep at an objective distance, a safe distance, and write himself out of his texts? Then should not I take an eraser and delete myself of my research (Solé, 2004)? Should not I start at last to speak from a universal 'we', and squeeze myself into the standard academic text format? Here is the rub: research materializes in the text, the text grants it a body. This very text, that again is supposed to come at the end, is where and when research is granted a material presence, where and when it comes to existence. Research is text all the way through. Even in the natural sciences, as [START_REF] Latour | Laboratory Life: The Social Construction of Scientific Facts[END_REF] as pointed out, research is triggered by texts, it is discussion and writing of texts. Even in the disciplines so careful to maintain the otherness of their objects of study, such as ethnography, it has long been recognized that research is the production of texts by an author, and that representation is before all an invention (e.g. [START_REF] Clifford | Introduction: Partial Truths[END_REF], where theory is inextricably intertwined with writing style [START_REF] Geertz | Works and Lives: The Anthropologist as Author[END_REF][START_REF] Van Maanen | Style as Theory[END_REF]. Text is the body of research. And all bodies have a finitude. They get born, grow, mature, and die, possibly survive after death as ghosts, as traces in other texts or other lives.

I am starting to realize why I was finding so hard to write this bloody text. I was trying to cut my text off from any personal input, from any affect, from anything I might have learnt from life, from all the traces I could leave across the lineshow then could it have born some meaning [START_REF] Bochner | Narrative's Virtues[END_REF]? And probably, at some other times, I was wanting to invent a fully original text, sanitizing it from all the traces let by other texts and encounters. Those traces are what relate the text, and then the research, to life and to the whole world of texts. Those traces come from my experiences, my readings, my thoughts, but they are not purely subjective. They run through me. Others run through similar experiences, of course with difference and repetitions. Those traces are intersubjectives, and that is why they are understandable. They connect research to the life world, and to the research world. Such relatedness is what keeps our texts' meaningfulness.

Oups, again I feel swept by a swirl of doubts and hesitations. I feel the urge to pour in my experience, to draw on my affects, to explain how this research has transformed my thinking; and at the same time to recognize that these experiences happened to me, those affects occurred to me, these ideas of mine come from reading others. And at the minute I try to write, I need to acknowledge that my language is inherited, that my phrases were already used by other writers. I cannot do as if I had not read Barthes (1977), Foucault (1969) and [START_REF] Derrida | Like the Sound of a Sea Deep within a Shell: Paul de Man's war[END_REF], and their compelling arguments towards the death of the author, the end of me as the creator of my lines. Another end, another death, another becoming-specter. All the more killing that this is me that has to hit the keyboard and put one character after the other to get a text ready to be sent.

Maybe it is far easiest in this way. If I could manage to mourn this navelgazing will to be an author, a pure creator, the very beginning of something; if I could simply try and attend to, describe and reflect on those experiences, affects, ideas that have come to me; if I could gratefully make use of linguistic arts passed on by predecessors; if I could keep my ego on the back seat, then writing would probably come less painfully, and more truthfully. Using criteria against myself [START_REF] Bochner | Criteria Against Ourselves[END_REF], I could just write from such a situated subjectivity [START_REF] Burke | The Death and return of the Author[END_REF].

Yes, if I could try to write just before all these ends: end of time, end of onlyrationality-and-objectivity-are-allowed, end of pure authorship claim, end of stick-inthe-format-or-die, end of publish and perish, etc… I would write a text as a performance rather than a representation, to make the reader feel what it is to research with deadlines, with multiple death lines. I would write a text giving to think that the repetition of an imposed and overused format grants the text with a structure far more superficial than other more profound and decisive structures that need to be understoodbecause the latter, and not the former, confer academic interest. I would argue that we need more than one language. I would admit that sometimes I am just repeating what others have said. I would unashamedly leave traces of the many external influences in the text, some explicit others not. And if I dared, I would use Jacques Derrida's work (e.g. 1967aDerrida's work (e.g. , 1967bDerrida's work (e.g. , 1994) ) as theoretical frame, including his concepts of writing, traces, ghost, etc. And I would use my own experience as a method to inquire about research as practice. I would use this vulnerable experience of mine, yet trying to fight against the ego, and knowing that getting it right is always differed. But as much of the things that matter, and to make it possible, this realization would always come at the end, just before ending.

EVER CLOSER TO THE END

I realize that the closer I get to the end, the higher I feel a kind of desire. A desire for meaning, for experience, for being and becoming. A desire for a better life, a truer life, a more authentic one. And I wish something could move inside my certitudes. I want to start to lose ground from the sure thoughts that were passed on to me by reference books and common knowledge, to shake the overused theoretical frameworks populating our reviews. It is as if I was trying to become a man, a thinker. I have certainly not started to think. I feel I am just giving the first trials and I will be exhausted before any exhaustion of meaning. I am still intimidated by the great books all over the bookshelves and now all over my carpet, and by the daring propositions of thoughts by some colleagues. But I need to stop that and start to dare some bits: the deadline is approaching again; and soon it will be too late.

But I have time. Something like 36 hours before the deadline will whistle the end of the game. I don't feel any urge for hurrying. No, I know that I am back to my good terrestrial life. And it's good to feel my body, to breathe, to jump up in the air, to sing. Good to hear even the too loud music of the neighbors and see the piles of plate in need of washing.

At some time, I see my face in the mirror. I notice all those grey hair on the sides of my head, and the lines on the sides of my eyes and mouth. I say to myself: "some people accuse me of wrongly bringing my subjectivity into my research. It's worse! In fact, it's a part of my existence that I am investing in my research." Let it be, before I cross the line of death.

  is certainly right when he says that we are wrong in considering time as if it was space-like. A space that we would have to fill with many activities. Research time is a time of creation. Time creates research, time creates thoughts. It guides towards the complexification of thought. And when time is over, thought freezes. But I should chase these ideas out of my mind. Time is not over yet. I am just before, very close, nearly at the deadline, however still not yet, still not beyond. There is still a little amount of life, of possibilities. Surpassing, getting beyond where I reached, is still possible. I still strive to be surprised by what is going to come, what is still to come. I am calling what has not arrived yet, what needs to arrive very quickly. I

	still am desire. I am still open. I have always been astonished by how the prospect of
	death makes me so more alive -I dare say so more clever and lucid.
	I feel far more aware, far more authentic as I feel death coming closer. Is this
	a kind of Heideggerian awareness?

The following passage intentionally paraphrases[START_REF] Rilke | The Notebooks of Malte Laurids Brigge[END_REF]. In this semi-autobiographial novel, Rilke, sitting in a small flat in Paris, reflects on death, creation, his ability to write, the meaning of writing for his life. Explanation of paraphrasing is proposed closer to the end.


Saad El Jaouhari
email: saad.eljaouhari@telecom-bretagne.eu

Ahmed Bouabdallah
email: ahmed.bouabdallah@telecom-bretagne.eu

Jean-Marie Bonnin
email: jm.bonnin@telecom-bretagne.eu

Tayeb Lemlouma
email: tayeb.lemlouma@irisa.fr

Toward a Smart Health-care Architecture Using WebRTC and WoT

By coupling the real-time communication capabilities of We-bRTC and the advantages brought by the Web of Things (WoT), we introduce the design of a new flexible healthcare architecture, in order to propose divers e-health services. In this ongoing work, we mainly focus on the services related to the remote healthcare of patients and elderly persons. We illustrate the interest of our architecture through the analysis of three main use cases: a remote and continuous monitoring of elderly peoples and a remote medical examination of patients and emergency intervention in case of an accident.

Introduction

In the last few decades, with the advances in the networking technologies and database systems, Ambient Assisted Living (AAL) researches have been applied in several domains in order to ensure end-users safety and quality of life (QoL) at home. As a result, several new concepts have been introduced such as personal health management and monitoring, health prevention, healthcare and welfare, in order to provide better medical services, in particular to the persons with special needs such as elderly and disabled persons.

The notion of e-health had emerged, where an enormous amount of health data and valuable medical knowledge have been electronically available and remotely accessible by different entities, specially through the Web. Hence it becomes easier to get, store, disseminate and exploit health information, especially with the improvement in the medical embedded sensors. Currently, the use of those medical Things is significantly increasing since they can continuously and rapidly provide medical information about the patient. Thus, we need an efficient way to manage all of those Things through a WoT/IoT architecture. Moreover, we need to define a way to transmit health data to the dedicated entity (Doctor, Hospital, etc.) in real-time.

In our vision of the e-health, we want to gain better relation between the doctor and the patient, where the doctor can access the medical Things of the patient in order to get a better understanding of the state of the patient. Hence we propose a new concept where we benefit both from the advantages of the real-time communication, and the WoT/IoT. For instance, we propose the case of the remote continuous monitoring of disabled or elderly persons, especially in the context of an aging population.

To better understand the problems of this ongoing work, first we need to explain the main technologies that we will use all along this paper in section 2. Then, we will discuss the related works in section 3. Then, we present our new architecture in the section 4, and next we will show how we can use this architecture in a relevant use case of the smart health, in section 5. In section 6, we will demonstrate the implemented part of our ongoing work. Finally, we will discuss the future perspectives of our work.

Technologies

In this section, we will first introduce the technology used to establish the communication between the different users of this framework. Then we will introduce the notion of the Web of Things which, will enable us to control and interact with the different smart objects in our system.

WebRTC

As described in many RFCs, WebRTC overcame the challenge of converging into a single technology two traditionally opposite side of the Web represented by the asynchronous client-server paradigm on one hand, and the domain of the peer-topeer multimedia and real-time communications on the other hand.Technically, it allows Web-based application (running in a browser) to exploit dedicate native APIs implemented in the browser. They allow the secure exchange of media and data in real time and in a peer-to-peer fashion [START_REF] Sergiienko | WebRTC Blueprints[END_REF][START_REF] Jennings | Real-time communications for the web[END_REF]. This technology is still under standardization by IETF and W3C. Currently, many browsers such as Google Chrome or Mozilla Firefox natively support WebRTC technology. It appears to be a very promising technology since it was estimated that it can have more than one billion endpoint in 2013 3 . In addition to the powerful communication capabilities provided by WebRTC, security was considered from the beginning in order to guarantee authentication, confidentiality and integrity in the system.

WebRTC uses mainly three APIs. MediaStream is responsible of the access to the Input/Output devices and the creation of the media stream. RTCPeerConnection is responsible of the creation of a secure media channel via SRTP (Secure Real-time Transport Protocol); it also encompasses signaling, NAT traversal and other important tasks. Finally RTCDataChannel allows the creation of a secure data channel via SCTP (Stream Control Transmission Protocol) encapsulated in DTLS (Datagram Transport Layer Security). One of the advantages of We-bRTC compared to the other real-time communication technologies, is that the security have been taken into account from the beginning, by providing a strong security architecture [START_REF] Sergiienko | WebRTC Blueprints[END_REF][START_REF] Jennings | Real-time communications for the web[END_REF].

In addition to the basic functionalities of WebRTC, sending media and data in real-time, we think that we can extend it to a whole new level of innovation. This innovation can be achieved by opening for WebRTC applications a door to the Web of Things.

Web of Things

The Web of Things (WoT) is a specialization of the Internet of Things (IoT). In one hand, all the complexity of the connectivity part of the smart objects (or Things) is abstracted. In the other hand, the WoT provides a standard application layer based on Web standards to simplify the creation of IoT applications. In the IoT, the one-application one-communication protocol overwhelms, which creates silos of users and which does not present the full potential of the IoT. One of the main interest of using the WoT instead of the IoT is the different advantages it offers. Just to mention, the simplicity of development, the loose coupling, since HTTP is loosely coupled by design, and the openness of the standards. The idea is that all the Things can communicate using a Web language by exposing a REST API. This API can be either present in the Thing itself or in an intermediary that can act on behalf of the Thing to expose the Web API [START_REF] Guinard | Building the Web of Things[END_REF]. This has become possible with the improvement of the embedded systems fortunately. Nowadays, we can run tiny servers inside the constrained devices such as lighttpd[4] and Nginx[5].

Related works

The literature provides several examples of Web-based infrastructures aiming at improving the management of patients diseases. Some of them are based on old communication technologies such as in [START_REF] Magrabi | Home telecare: system architecture to support chronic disease management[END_REF] [START_REF] Lau | Asynchronous web-based patient-centered home telemedicine system[END_REF] [8] [START_REF] Chiang | An efficient component-based framework for intelligent home-care system design with video and physiological monitoring machineries[END_REF]. We present below a summary of the main solutions that uses WebRTC.

We will focus on recent solutions some of which use WebRTC. We provide below a comparative analysis of some representative works.

A recent work [START_REF] Pierleoni | An innovative webrtc solution for e-health services[END_REF] uses in addition to the audio/video communication part of WebRTC, the DataChannels to exchange medical data between different medical entities. Moreover the patients have access to medical sensors. In [START_REF] Al-Taee | Web-of-things inspired e-health platform for integrated diabetes care management[END_REF], the authors propose an e-health platform, providing specific services to the diabetic persons (Type 1 diabetes mellitus (T1DM)). The proposed solution uses medical sensors and a humanoid robot. The robot interacts/dialogs with the patient in order to get better information on his state. All of the data (sensors and dialog) are collected by the robot, and then sent to the health carers. The work of [START_REF] Azevedo | An api proposal for integrating sensor data into web apps and webrtc[END_REF] presents an extension to WebRTC to enable peer-to-peer exchange of sensor data, and a proposal to enable Web applications to access sensor data and to bring nearby sensor streams to Web applications and multimedia communication over the Web. They mainly propose to extend the MediaStream API of WebRTC in order to manipulate also the sensor streams and to provide them to the customers. The approach is only theoretical without any implementation. In [START_REF] Jang-Jaccard | Webrtc-based video conferencing service for telehealth[END_REF],

the authors present a video conferencing system allowing online meetings between remotely located care coordinators and patients at their homes. They use a special device (TeleMedCare) to monitor the vital sign of the patients. In this work, there is no interaction with medical sensors apart from the TeleMedCare.

General architecture

To develop the full potential of WebRTC, we propose innovative usages, which helps to extend its limits. It consists in adding new functionalities to control, manage and send data from/into the Things available in the WebRTC endpoint surroundings. We want indeed during a WebRTC multimedia session to be able to access the Things and to send data to the other side of the communication in real-time. This enables us to create new opportunities, since in this case, we consider that each WebRTC endpoint is a gateway to his own Things. Moreover, we can delegate the access to other persons for instance the remote person with whom we are talking. We think also that the security and the privacy aspects are very important, so we will dedicate particular interests in the problems that can occur inside our architecture. A simplified view of the architecture of our platform is shown in Figure 1. Using a WebRTC compatible browser, a user can, in one hand, communicate in real-time, and in the other hand, access his Things. Accordingly to our WoT approach, the client application should both take care of the communication and the access to the Things. We suppose that each Thing is identified using a URI and offers a Web API which allows us to access the Things resources. The Things are located in the private network of user (his home, office, . . . ).

We can use this architecture in e-health, as shown in figure2, where the users can be the patient/elderly/injured person in one endpoint of the We-bRTC session, and the remote medical support, such as doctor/medical relief center/hospital, in the other endpoint. The Things represent the different medical embedded devices. Finally, we have the different stakeholders that can interact directly with the patient/elderly such as nurses, paramedics, . . . They also have the authorization to access the personal medical devices of the person.

e-Health Scenarios

To gain a better understanding of the idea behind this proposed architecture, we will illustrate it with a set of scenarios applicable in the field of the smart health (or e-health).

Continuous monitoring

The first use case is for continuous monitoring of a patient or an older person. In this case, wearable devices (such as a falling sensor, pressure sensor, peacemaker, . . . ) are continually monitoring the state of the patient. In case of abnormal behavior (falling, heart problem, . . . ), an alert is sent to the emergency relief center or to a doctor using WebRTC. In this case, we suppose that the WebRTC session is either always set on or established urgently, as shown in Figure 3. We can also imagine the mobility use case, where we continuously monitor the health status of a mobile patient. The patient is wearing embedded devices that continuously send health information to the medical center. This can be very useful to be able to detect abnormality in the comportment of the patient and to quickly provide medical help in the extreme case. We can also try to detect early syndromes of the most known diseases such as early detection of diabetes, AIDS, Alzheimer . . .

Remote medical consultation

The case of a remote consultation with a doctor can be applied to disabled persons or old persons that cannot visit a doctor. We suppose in this case that, the patient has access to a set of medical devices. So, the patient starts a multimedia conversation with his remote personal doctor. At a certain stage, the doctor wants to know some health information about the patient. The patient puts on the wearable devices, accessible through the platform, and then sends the information received from those devices to the doctor. With this information, the doctor with his monitoring window showing all the information in real-time, can give advices or prescription, as shown in Figure 4. We can also have an emergency relief center (ERC), instead of a doctor. In this case, the self quantifying sensors of the patient, and the medical sensors prescribed by a doctor, do not have to transmit their data permanently to a medical center. This alleviates the deployment constraints regarding availability of the network and legal constraints regarding the storage of private data. The patient remains master of his data produced by the different sensors and decides when and with whom they can be shared.

Emergency intervention in case of an accident

The last use case is the one of an accident, as shown in Figure 5. Once a paramedic arrives to the place of the accident, to help the injured person. First she/he will attach all the available wearable medical devices to the body of the person. We suppose that the paramedic had already an equipment that speaks WebRTC with a doctor or with an ERC that implements our architecture (capable of accessing smart objects in this case we consider the case of medical wearable smart objects). Then, the paramedic starts a communication with the remote ERC/ doctor, and at the same time the wearable objects will start sending vital information in real-time to the ERC, using WebRTC Datachannel.The paramedic will at the same time apply first aides to the person in the simple case, and in case of serious injuries the ERC/doctor can give real-time instructions, while transporting the patient. Moreover, the ERC can also contact the different hospitals to see availability for receiving the injured person and to start preparing a room for surgery, if the person needs emergency intervention. Currently, we implemented a platform using Node. js. This platform can in one hand, establish a multimedia communication between two users just using their browsers. On the other hand, it enables users to access a set of predefined Things in his possession. Each user can then retrieve data from the different Things and send them to the remote user in real-time using WebRTC Datachannel. The figure 6 shows that a user can access an accelerometer and an ultrasound sensor. Such an approach can be nearly extended to all kinds of Things.

The first part of the architecture is WebRTC, it is composed of two clients, a signaling server and an Identity Provider (IdP). First the client gets the WebRTC JavaScript application from the server, and execute it inside the sandbox of the browser. Then, the signaling process where the user reaches/contacts the remote part of the communication. Finally, with all the exchanged parameters, a WebRTC media/data channel can be set. As for the IdP part, it provides the users with an identity (after a valid authentication on the IdP side), so that they can authenticate themselves to the other side of the communication.

The second part is the WoT part. Each endpoint is considered as a gateway to his set of Things. Also, each user has a control on those Things and only his can access the respective Things. In our case, the user communicate with the less constrained Things using HTTP, and using HTTP with an intermediary in case of constrained Things. The intermediary can then communicate with the constrained Things using one of the well known communication protocols (Zigbee, Bluetooth, WIFI . . . ). In our current platform, we have an accelerometer (ADXL335) attached to a Raspberry Pi 2, and an ultrasound (HC-SR04) attached to an Arduino UNO, which send data to another Raspberry using WIFI adapted to the Arduino. The Raspberry used in our architecture is a Model B with ARMv6 single core, 700 MHz and 512 MB SDRAM. In this case, the Web API is implemented in the Raspberry and each Thing is identified by using a URI. Each user has access to an accelerometer and to an ultrasound sensor.

In the case of the e-health scenarios, all we need to have are wearable medical Things. They can communicate with any protocol, since the WoT abstracts all the complexity of the connectivity of the Things. Using the current state of the architecture, an implementation of the remote consultation use case is possible, where a doctor is communicating with a patient using WebRTC. The patient has access to a set of Things. Then, the patient can send these information to the doctor in real-time using WebRTC's Datachannel. Finally, the doctor can monitor the received data and provide a prescription to the patient (this prescription can also be sent to the patient using WebRTC).

Conclusion and perspectives

The following paper present an ongoing work for the creation of an e-health framework specially conceived for remote examination of patients and injured persons in case of accidents. Though the different use cases, we demonstrated the advantages that can be brought by such framework, such as better and more efficient interaction with the medical entities, the continuous monitoring of the patients, the remote healthcare services and so on and so fourth. Finally we presented our current implementation of this framework. We also analyzed other use cases mainly related to the emergency intervention in case of an accident, and in the case of the mobility of the patient outside his habitual system (home, hospital, . . . ). However, due to the lack of space, we couldn't include them in this paper.

The next step of our work is to investigate of all the security and privacy aspects of this platform. Currently, the communication between the WebRTC clients and the different Things is not secured yet. We need first to evaluate the main WoT security mechanisms existing today. CoAP/DTLS [START_REF] Shelby | The Constrained Application Protocol (CoAP)[END_REF] seems an interesting candidate to secure the communication with the different Things. The second aspect is the access control. Only the authorized persons should access the Things. We identified several possible solutions to control the access such as RBAC [START_REF] Sandhu | Role-based access control models[END_REF] and ACL [START_REF] Medaglia | An Overview of Privacy and Security Issues in the Internet of Things[END_REF]. The delegation of the access which opens interesting use cases, can be tackled with OAuth 2.0 [START_REF] Hardt | The OAuth 2.0 Authorization Framework[END_REF]. However, in term of performance, OAuth is not very lightweight, so we consider this solution in the case of the use of a gateway. We are also interested to analyze the introduction of the notion of the profile of the patient [START_REF] Mshali | Analysis of Dependency Evaluation Models for e-Health Services[END_REF] (the persons profile can include medical record, chronicle diseases, . . . ). Depending on this profile, the framework will use a defined set of medical devices to monitor the physiological status of the patient. This can be interesting in case where the patient is in a hospital, the nurse can install the wearable medical devices on the body of the patient, and according his profile, the corresponding Things will transmit the medical data to the framework. This includes also, managing the transmission frequency of the different medical devices in a given environment (smart-house, smart-hospital, smart-city . . . ), depending on its importance/priority [START_REF]Context-aware adaptive framework for e-health monitoring[END_REF], in order to optimize our system and to have better and secure management of the data. This priority can be accorded depending on the profile of the patient. We think that this approach can open the door to the development of new healthcare ecosystems that combine the communication technologies, the WoT/IoT and the medical expertises of the different medical entities, in order to provide quicker, better and more efficient medical intervention to the persons in needs.

Fig. 1 :

 1 Fig. 1: Proposed architecture

Fig. 2 :

 2 Fig. 2: Adapted architecture for e-health scenarios

Fig. 3 :

 3 Fig. 3: Continuous monitoring of a falling

Fig. 4 :

 4 Fig. 4: General case

Fig. 5 :

 5 Fig. 5: Emergency intervention in case of an accident

Fig. 6 :

 6 Fig. 6: Current Implementation of the platform

http://io13webrtc.appspot.com/#10

Acknowledgment

For the first two authors, this work has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 645342, project reTHINK.


Mathieu Hatt

Frédéric Lamare

Nicolas Boussion

Christian Roux

Alexandre Turzo

Catherine Cheze-Lerest

P Jarritt

K Carson

Fabien Salzenstein

Christophe Collet

C Cheze-Le Rest

D Visvikis

Fuzzy hidden Markov chains segmentation for volume determination and quantitation in PET

Introduction

Positron Emission Tomography (PET) has been long established as a powerful tool in oncology, particularly in the area of diagnosis. However, alternative applications such as the use of PET in radiotherapy planning [START_REF] Jarritt | The role of PET/CT scanning in radiotherapy planning[END_REF] and response to therapy studies [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF] are rapidly gaining ground. Whereas accurate activity concentration recovery is crucial for correct diagnosis and monitoring response to therapy, applications such as the use of PET in Intensity-Modulated Radiation Therapy (IMRT) treatment planning renders equally vital the accurate shape and volume determination of lesions. Different volume of interest (VOI) determination methodologies have been proposed that can be classified as manual or automatic. On the one hand, manual segmentation methods to delineate boundaries are laborious and highly subjective [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF].

On the other hand, automatic segmentation of objects of interest in PET [START_REF] Reutter | Automated 3D Segmentation of Respiratory-Gated PET Transmission Images[END_REF][START_REF] Zhu | Automation Segmentation of PET Image for Brain Tumors[END_REF], Kim et al 2003[START_REF] Riddell | The Watershed Algorithm: A Method to Segment Noisy PET Transmission Images[END_REF] is not a trivial task because of low spatial resolution and resulting partial volume effects (PVE), low contrast ratios, as well as noise resulting from the statistical nature of radioactive decay or the choice of the reconstruction process.

The most widely used method to semi-automatically determine VOIs in PET is thresholding, either adaptive, using a priori Computed Tomography (CT) knowledge [START_REF] Erdi | Segmentation of Lung Lesion Volume by Adaptative Positron Emission[END_REF], or fixed threshold [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF] using values derived from phantom studies (from 30 to 75% of maximum local activity concentration value) [START_REF] Jarritt | The role of PET/CT scanning in radiotherapy planning[END_REF][START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF][START_REF] Erdi | Segmentation of Lung Lesion Volume by Adaptative Positron Emission[END_REF]. Such thresholding techniques however lead to variable VOIs determination as shown in recent clinical studies [START_REF] Nestle | Comparison of Different Methods for Delineation of 18F-FDG PET-Positive Tissue for Target Volume Definition in Radiotherapy of Patients with Non-Small Cell Lung Cancer[END_REF]. On the other hand, numerous works have addressed automatic lesion detection from PET datasets, including different methodologies such as edge detection [START_REF] Reutter | Automated 3D Segmentation of Respiratory-Gated PET Transmission Images[END_REF], fuzzy C-Means [START_REF] Zhu | Automation Segmentation of PET Image for Brain Tumors[END_REF], clustering (Kim et al 2003) or watersheds [START_REF] Riddell | The Watershed Algorithm: A Method to Segment Noisy PET Transmission Images[END_REF].

The performance of these algorithms is sensitive to variations of noise intensity and/or lesion contrast.

In addition, past work has in its majority considered the ability of such automatic methodologies for the detection of lesions but not the accuracy with which the methods are capable for VOI and/or activity concentration determination. Furthermore, all of the afore-mentioned algorithms often involve user-dependent initializations, pre-and post-processing, or additional information like CT or expert knowledge; rendering their employment more complicated and the outcome dependent on choices made by the user in relation to the pre-and/or post-processing steps necessary. For example in the case of the watershed algorithm a filtering pass as pre-processing step to smooth the image, and a postprocessing step to fuse the different regions resulting from the algorithm are necessary.

Hidden Markov Models are automatic segmentation algorithms allowing noise modelling and have proven to be less sensitive to variation of the values in the regions of the images than other segmentation approaches thanks to their statistical modelling. They have only been previously used in PET in the form of Hidden Markov Fields (HMF) [START_REF] Chen | Markov Random Field Model for segmentation of PET images[END_REF]. Hidden Markov Chains (HMC) [START_REF] Benmiloud | Estimation des paramètres dans les chaînes de Markov cachées et segmentation d'images[END_REF] is a faster model and can offer competitive results [START_REF] Salzenstein | Sur le choix de méthode de segmentation statistique d'images[END_REF].

Furthermore, HMC leads to shorter computational times, as quantities of interest can be computed directly on the chain, whereas the HMF algorithm needs iterative Monte-Carlo like estimation procedures [START_REF] Salzenstein | Sur le choix de méthode de segmentation statistique d'images[END_REF] that are time consuming. These algorithms offer an unsupervised estimation of the parameters needed for the image segmentation and limit the user's input to the number of classes to be searched for in the image. Reconstructed images require no further pre-or post-processing treatment (such as for example filtering) prior to the segmentation process. Instead, image noise is considered as additional information (a parameter in the classification decision process) to be taken into account, not to be suppressed or avoided.

The objectives of our study were to (a). develop a new fuzzy HMC (FHMC) model in an attempt to account for the limited spatial resolution in PET and (b) compare the performance of FHMC with these of the thresholding methodologies currently used in clinical practice. Different imaging conditions in terms of statistical quality, as well as lesion size and source-to-background (S/B) ratio were considered in this study. The analysis was carried out on both simulated and acquired images reconstructed using iterative algorithms which form today's state of the art in whole body PET imaging in routine clinical oncology practice [START_REF] Visvikis | Influence of OSEM and segmented attenuation correction in the calculation of standardised uptake values for FDG PET[END_REF][START_REF] Visvikis | Characterisation of SUV accuracy in FDG PET using 3D RAMLA and the Philips Allegro PET scanner[END_REF].

Materials and methods

Hard and Fuzzy Hidden Markov Chain models

The HMC model is an unsupervised methodology that takes place in the Bayesian framework.

Although we place ourselves in the application of image segmentation this methodology can be used in other applications such as for example speech recognition [START_REF] Dai | Hybrid approach to speech recognition using hidden Markov models and Markov chains[END_REF]). Let T be a finite set corresponding to the voxels of an image. We consider two random processes Y ( )

t t T y ∈ = and X ( ) t t T x ∈ =
. Y represents the observed image, and X represents the "hidden" segmentation map. X takes its values in

{ } 1,..., K Ω =
with K being the number of classes c , and Y takes its values in » .

We assume that a Markov process can model the prior distribution of X . The segmentation problem consists in estimating the hidden X from the available noisy observation Y . The relationship between X and Y can be modelled by the joint distribution (X,Y) P . This distribution can be obtained thanks to the Bayes formula:

(X,Y) (Y | X) (X) (X | Y) (Y) (Y) P P P P P P = = (1).
(Y|X) P is the likelihood of the observation Y conditionally with respect to the hidden ground-truth X , and (X) P is the prior knowledge concerning X . The Bayes rule allows us to know the posterior distribution of X with respect to the observation Y . In the Markov Chain framework we have to assume the random variables Y ( )

t t T y ∈ =
are conditionally independent with respect to X and that the distribution of each t y conditional on X is equal to its distribution conditional on t

x . Many applications of Hidden Markov Models with unsupervised estimation have been successful

considering different types of images (radar, sonar, Magnetic Resonance Images (MRI), CT, satellite or astronomical) [START_REF] Pieczynski | Modèles de Markov en traitement d'images[END_REF][START_REF] Salzenstein | Champs de Markov flous pour images multispectrales[END_REF][START_REF] Delignon | Estimation of Generalized Mixtures and Its Application in Image Segmentation[END_REF], but this kind of approach was almost never applied on PET data.

Markov Chain definition

X is a Markov chain if:

1 1 1 ( | , ..., ) ( | ) for 1 t t t t P x x x P x x t T - - = < ≤ (2)
The distribution of X is then defined by the distribution of 1 = . As X and Y are one-dimensional elements in the HMC context, a spatial transformation is necessary to process threedimensional VOIs. For the best preservation of the spatial correlation between voxels we use the Hilbert-Peano space-filling curve. This fractal path can be extended to explore 3D VOIs [START_REF] Kamata | A New Algorithm for N-dimensional Hilbert Scanning[END_REF]. A visual illustration of the Hilbert-Peano path for a 4× 4× 4 voxels 3D VOI is given in figure 1.

Once the chain has been segmented, the inverse path is used to reconstruct the 3D segmentation map. on [ ] 0,1 . Note that, for example, using two hard classes and two fuzzy levels in the FHMC model is not equivalent to using four hard classes in the HMC model where 1 2

... K ν δ δ δ = + + + . This has been previously stated using Markov Fields based segmentation [START_REF] Salzenstein | Parameter Estimation in hidden fuzzy Markov random fields and image segmentation[END_REF].

The distribution of X can then be defined using a conjoint density g for 1 ( , )

t t x x + on [ ] [ ] 0,1 0,1 × : let [ ] [ ] ( , ) 0,1 0,1 a b ∈ × 1 2 1 2 ( 0, 0) and ( 1, 1) ( 0, 1) and ( 1, 0) g a b g a b g a b g a b α α γ γ = = = = = = = = = = = = { } ( , ) (
, ) if ( , ) (0,0),(0,1),(1,0),(1,1)

g g a b f a b a b β = ≠ (3) With [ ] [ ] 0,1 0,1 ( , ) ( )( , ) 1 g a b d a b ν ν ⊗ = ∫ ∫
} ( ) ( ) 1 1 1 1 0 1 1 1 1 0 0 0,1 ( , ) ( ) ( ) 1 1 ( , ) ( )( , ) ( , ) ( )( ) ( ) i N i i i i N P x g x b d b h x P x F g a b d a b g b d b h N N ν ν ν ε ν ε - ∈ = = ∈ = ⊗ = ∫ ∫ ∫ ∫ (6)
( , ) trans c d using the conditional density f deduced from (1) :

1 1 ( , ) ( | ) ( ) t t t t t g x x f x x h x + + = ( ) { } ( ) { } ( ) { } { } ( ) 1 1 1 1 1 1 ( , ) ( )( , ) | ( ) ( ) ( , ) ( ) | 0,1 ( ) ( , ) ( ) 0,1 | ( ) ( ) ( , ) 0,1 | 0,1 ( ) j i i j i i j i j i F F t j t i i i F j t j F t j t t t i i F t t i i i F t t t t t g d P x F x F h d g x d P x F x h x g x d P x x F h d g x x P x x h x ε ε ν ν ε ε ε ν ε ε ν ε ε ν ε ε ν ε + + + + + + ⊗ ∈ ∈ = ∈ ∈ = ∈ ∈ = ∈ ∈ = ∫ ∫ ∫ ∫ ∫ ∫ (7)
where 1 N -is the number of fuzzy levels and i i N ε =

is the value associated to a fuzzy level i F .

The fuzzy model is a generalization of the hard model. The use of the Dirac measures allows one to retrieve the standard hard model when the fuzzy component is null. As the theoretical framework described above has not been developed for a specific kind of image, but as a general segmentation algorithm, the a priori and the noise (also called observation) models are not directly derived from PET image characteristics. However this segmentation approach may be appropriate in segmenting PET images since they are both noisy and of low resolution. The "noise" aspect when considering Hidden Markov Models in general is the way the values of each class to be found in the image are distributed around a mean value. The noise model used, whose respective mean and variance are to be determined by the estimation steps, can therefore be adapted to image specific characteristics. On the other hand, the fuzzy measure allows a more realistic modelling of the objects' borders transitions between foreground and background, allowing in such a way to indirectly account for the effects of blurring (partial volume effects) associated with low resolution images, such as those in PET.

Segmentation and parameters estimation

In order to perform segmentation on the chain level, we need to use a criterion to classify each element as background or functional VOI. For this purpose we use the Marginal Posterior Mode (MPM) [START_REF] Marroquin | Probabilistic solution of ill-posed problems in computational vision[END_REF]. This approach aims to minimize the expectation { }

( , ) | t t E L x x Y
where L is a loss (or cost) function:

ˆ( , )

t t t t L x x x x = - (8) With t
x the real class and ˆˆ( )

t t
x s y = the one affected by the segmentation process ŝ . This criterion is adequate for the segmentation problem as it penalizes a configuration with respect to the number of misclassified elements. In order to compute a solution, the MPM segmentation needs the parameters defining the a priori model (initial and transition probabilities of the chain) as well as the noisy observation data model (mean and variance of each class). The assumption that the noise for each class of the observed data can fit a Gaussian distribution was made as a first step. The mean and variance of each fuzzy level i F is derived from the ones estimated in the two hard classes as follows:

0 1 2 2 2 2 2 0 1
(1 )

(1 )

i i F i i F i i µ µ ε ε µ σ σ ε ε σ = -+ = - + (9)
Both a priori and noise models parameters are unknown in the real case and therefore they must be estimated. In order to achieve such estimation, we use the stochastic iterative procedure called Stochastic Expectation Maximization (SEM) [START_REF] Celeux | L'algorithme SEM : un algorithme d'apprentissage probabiliste pour la reconnaissance de mélanges de densités Revue de statistique appliquée[END_REF], a stochastic version of the EM algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF]. This is achieved in a similar fashion to that used in the classical HMC context by simulating posterior realizations of X (see Appendix for detailed posterior realization of X and the SEM procedure) and computing empirical values of the parameters of interest using the simulated chain. The stochastic nature of this procedure makes it less sensitive to the initial guess of the parameters using the K-Means (McQueen 1967) than deterministic procedures like the EM algorithm. Both the MPM segmentation and SEM parameters estimation use a practical recursive computation of the values of interest called Forward-Backward procedure that is performed directly on the chain [START_REF] Benmiloud | Estimation des paramètres dans les chaînes de Markov cachées et segmentation d'images[END_REF]. The implementation of the FHMC segmentation algorithm in a step by step fashion can be found in the Appendix. Note that the overall algorithm is entirely unsupervised (except for the number of classes and fuzzy levels to use) and it is able to adjust to a large spectrum of image structures, noise or contrast. For example, no a priori is made on the shape of the objects to extract or the source-to-background ratio in the image.

Thresholding

Various thresholding methodologies have been proposed in the past for both functional volume segmentation and/or activity concentration recovery [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF][START_REF] Erdi | Segmentation of Lung Lesion Volume by Adaptative Positron Emission[END_REF][START_REF] Nestle | Comparison of Different Methods for Delineation of 18F-FDG PET-Positive Tissue for Target Volume Definition in Radiotherapy of Patients with Non-Small Cell Lung Cancer[END_REF]. Thresholding using 42% and 50% of the maximum value in the lesion was chosen for VOI determination and quantitation purposes respectively, based on previous publications [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF][START_REF] Erdi | Segmentation of Lung Lesion Volume by Adaptative Positron Emission[END_REF]. The methodology was implemented through region growing using the voxel of maximum intensity in the object of interest as a seed. Using a 3-D neighbourhood (26 neighbours) the region is iteratively increased by adding neighbouring voxels if their intensity is superior or equal to the selected threshold value. The results derived using these methods will be denoted from here onwards as T42 and T50 for the thresholds of 42% and 50% respectively.

Validation studies 2.3.1 Simulated and acquired datasets

Simulated datasets using the IEC image quality phantom (Jordan 1990), containing six different spherical lesions of 10, 13, 17, 22, 28 and 37 mm in diameter (figure 2), were generated using Geant4 Application for Tomographic Emission (GATE) and a validated model of the Philips Allegro PET scanner [START_REF] Lamare | Validation of a Monte Carlo simulation of the Philips Allegro/GEMINI PET systems using[END_REF]. Images, considering only the detected true coincidences, were subsequently reconstructed using the OPL-EM iterative algorithm [START_REF] Reader | One-pass list-mode EM algorithm for high-resolution 3D PET image reconstruction into large array[END_REF] with 7

iterations [START_REF] Lamare | Validation of a Monte Carlo simulation of the Philips Allegro/GEMINI PET systems using[END_REF]. Two different voxel sizes were considered in the reconstructed images; In addition to the simulated datasets, acquisitions of the IEC phantom were carried out in list mode format using a Philips GEMINI PET/CT scanner. The only difference with the simulated datasets was the exclusion of the 28 mm diameter sphere in the study because in the phantom used it was replaced by a plastic sphere of unknown diameter. The same S/B ratios of 4:1 and 8:1 used in the simulations were also employed in this part of the study, by introducing 7.4kBq/cm 3 in the background and 29.6 or 59.2kBq/cm 3 respectively in the spheres. Different count statistical qualities were obtained by reconstructing 1 min, 2min or 5min list-mode time frames using the 3D RAMLA algorithm, with specific parameters previously optimised [START_REF] Visvikis | Characterisation of SUV accuracy in FDG PET using 3D RAMLA and the Philips Allegro PET scanner[END_REF]. The same voxel sizes as for the simulated datasets (8 mm 3 and 64 mm 3 ) were used in the reconstruction of each of the different statistical quality datasets considered. Visual illustration of the acquired images is given in figure 3(e)-(h). Each sphere in both simulated and acquired images was isolated in a box of the same size (16× 16× 10 for the 4mm case, and 32× 32× 20 for the 2mm case) prior to the segmentation process.

Computed volume versus classification error measurement

The majority of previous works dealing with VOI determination in PET measure the performance of a given methodology by computing the VOI obtained on the segmentation map and comparing it with the true known volume of the object of interest. This type of approach has the potential of leading to biased performance measurements since a segmentation result may contain two different types of error. On the one hand, one may have voxels of the background that are classified as belonging to the object of interest, denoted from here on as positive classification errors (PCE), while on the other hand, one may end up with voxels of the object that are classified as belonging to the background, denoted from here on as negative classification errors (NCE). These classification errors essentially occur on the boundaries of the objects of interest because of "spill in" (increasing probabilities of a NCE) and "spill out" (increasing probabilities of a PCE). If the segmentation results in PCEs and NCEs of equal amounts, the computed VOI would be very close to the true known volume whereas the shape and position of the object would be incorrect. The shape and position information is as important as the total volume of the object in order to accurately derive a radiotherapy treatment planning or the activity concentration of interest in a response to therapy study based on the derived functional volume. For example, let us assume that the segmentation process results in 20% NCEs and 15% PCEs. This leads to a classification error of 35% whereas the error in the overall computed volume is only -5%. Hence, the use of classification error is a more pertinent measurement of the accuracy with which a given algorithm performs the task of functional volume delineation since it takes into account not only the segmented volume in comparison to the actual volume of interest but also its position and shape.

In the simulation study the total number of PCEs and NCEs is considered with respect to the number of voxels defining the sphere (VoS) in the digital phantom (the ground truth) in order to obtain a percentage classification error (CE):

( ) 100 PCE NCE CE VoS + = × (10)
The size of classification errors can be bigger than 100% in the case where a large number of background voxels in the selected area of interest are misclassified as belonging to the sphere. In practical terms, maximum classification errors calculated during this work where limited to 200%, since any such values represent complete failure of the segmentation process. In addition, the interest of classification errors is when they occur at the borders of the objects and not in other regions of the background. One should also keep in mind that a combined representation of PCE and NCE into CE leads to a loss of information as far as the direction of the bias is concerned. It does however still represent more pertinent information than overall volume estimation errors, which reflect neither accurate magnitude nor direction of the bias for a segmented volume.

On the other hand in the case of the images reconstructed from the acquired datasets only overall computed volumes were considered in order to avoid any biases as a result of misalignment and rescaling inaccuracies, as well as reconstruction artefacts in the higher and lower slices of the associated CT datasets. As the goal is not to detect the lesion in the whole image but to estimate its volume, shape and position with the best accuracy possible, we assume that the lesion has been previously identified by the clinician and automatically or manually placed in a 3-D "box" well encompassing the object. Subsequently, the images of the selected area were segmented in two classes (functional VOI and background) using each of the three methods under evaluation (thresholding, FHMC and HMC). In the FHMC case, different numbers of fuzzy levels were considered in the segmentation process (namely 2 and 3). Following the segmentation by FHMC, volumes of interest can be defined using the hard classes and any number of the fuzzy levels considered.

Quantitation Accuracy

In terms of quantitation the objective of our study was to determine the accuracy of the average activity concentration recovered from a volume derived using a given segmentation algorithm.

The "ground truth" for comparison purposes was established using the exact size, shape and location of each lesion (using the known digital phantom employed in the generation of the simulated datasets).

As a result, these recovered activity concentration values represented an under-estimation of the true activity due to PVE. A comparison on a lesion by lesion basis was subsequently carried out with the measured activity concentration from the segmented volumes obtained by the three algorithms considered. T50 should lead to some improvements in the lesion activity recovery with respect to T42 as a result of including less voxels in the volume used to compute the activity and therefore less voxels associated with PVE. Similarly FHMC 0/2 (see section 3. Results for the definition of FHMC x/y) should lead to concentration recovery improvements with respect to FHMC 1/2, since voxels belonging to the fuzzy levels are found at the edges of the lesions and their intensity is most significantly reduced by PVE. Therefore the inclusion of these voxels should only result in even stronger under-evaluation of the true lesion activity concentrations.

Results

Different segmentation maps obtained using each of the methods under evaluation are presented in figure 4 for a slice centred on the 28 mm sphere of the simulated images to visually illustrate the variations of the segmentation maps obtained. Considering the simulated datasets, the introduction of FHMC led to superior results in comparison to the current "gold standard" in functional volume delineation of T42. FHMC segmentations led to <25% classification errors in computed volumes for lesions sizes >13mm irrespective of contrast ratio, level of noise or lesion size. Errors of more than 200% for FHMC were only observed for the 10mm sphere. Results for the T42 were more dependent on the lesion size, relative to FHMC results, varying from 10% to more than 200% (even for spheres up to 22mm in diameter for a contrast of 4:1 and 64mm 3 voxel size). However, the use of T42 was found to work well for lesion sizes of >17mm and a lesion to background ratio of 8:1 with % classification errors of 20-30%. On the other hand, for a lesion to background ratio of 4:1, the T42 threshold led to over 100% overestimation in the functional volume for lesions <28mm in diameter. As the errors bars in the different figures reveal, there was a larger dependence on the statistical quality of the reconstructed images observed with T42 in comparison to FHMC for the majority of the lesion sizes and contrast configurations considered. In particular this was true for all of the lesions for a contrast ratio of 4:1 and for lesions <22mm for a contrast ratio of 8:1. For example, for the 17mm sphere and a contrast ratio of 8:1, T42 resulted in classification errors of 20 to 35% whereas FHMC classification errors from 15 to 17% were observed (fig. 6). On the other hand in the case of the 28mm sphere and a contrast ratio of 4:1, T42 errors were ranging from 85 to 110% whereas FHMC resulted in errors of 17-18%. The reduction in the reconstruction voxel size (from 64 mm 3 to 8 mm 3 ) led to small differences in the functional volumes determined using the FHMC segmentation algorithm, and although it led to improvements in the T42 based segmented volumes, the % classification errors remained at 80-200%. The trend observed with the standard voxel sizes on the variation of the segmentation results as a function of statistical quality was similar for the reduced voxel size images.

For example in the case of the 22m sphere and a contrast ratio of 4:1 errors of 77-100% and 26-27%

were observed for T42 and FHMC respectively. In general, the largest errors were observed for the smaller lesions of 10 and 13mm, where none of the segmentation algorithms considered performed well under any of the configurations tested, with errors largely >200%. As shown in figure 7 FHMC results on errors of up to 10% and between 10% and 20% for contrast ratio of 8:1 and 4:1 respectively, for lesions >13mm. T42 led to volume determination errors of <10% for lesions >17mm in diameter and a lesion to background ratio of 8:1, while errors of over 100% where observed for lesions <28mm with a lesion to background ratio of 4:1. However, while the lowest overall volume error of T42 was around 10%, the corresponding classification error was >20%. In the case of an 8 mm 3 reconstructed voxel size (figure 8(b)) small improvements were seen using the T42 for lesions ≥ 13mm and >22mm for a lesion to background ratio of 8:1 and 4:1 respectively. Finally, no noticeable differences were seen in the FHMC based segmentation results, apart from an improvement to <15% in the volume estimation error for the 13mm lesion with a contrast size of 8:1.

Figures 9(a)-(b) show the results in terms of % error in the recovered activity as a function of lesion size and contrast ratio considering the segmented volumes using 64 mm 3 and 8 mm 3 reconstructed voxel sizes. As it can be seen from this figure, FHMC and T50 led to the best results in comparison to the "ground truth" throughout the different lesions sizes and contrasts evaluated, although T50 introduces larger errors in comparison to the "ground truth" for lesion sizes of <22mm and a contrast of 4:1. The use of the 8 mm 3 voxels does not alter the conclusions as far as the relationship between the results for the two methods evaluated is concerned, although in absolute terms all algorithms perform worse in comparison to the results obtained for 64 mm 3 voxels.

Considering the acquired datasets, figures 10(a)-(b) contains the results for the % overall lesion volume estimation for the 64 mm 3 and 8 mm 3 voxels, while figures 11(a)-(b) show the corresponding results for the activity quantitation errors. In terms of the volume estimation the general trends were similar to those observed for the simulated datasets, with the FHMC performing better than the T42 throughout the range of lesion sizes and contrasts evaluated. In absolute terms, the FHMC results were better particularly in the case of 8 mm 3 voxels where errors of <20% and 10%

were seen for lesions >10mm and >22mm respectively. T42 errors were similar to FHMC for the 8:1 ratio and spheres >13mm but ranged from 20 to >100% for the 4:1 ratio configuration. A larger dependence to the statistical quality of the reconstructed images can be observed with the acquired datasets, demonstrating the more robust performance of the FHMC algorithm in comparison to the T42 methodology which was seen to be more affected by the images' statistical quality. Using again the example of the 22mm sphere (figure 10(a)), T42 errors were from 30 to 95% while FHMC errors were less than 5%. Although the variation of the FHMC results was higher for smaller spheres (10 and 13 mm), it was still smaller than in the case of the T42 results. For example, FHMC applied to the 13mm sphere with a 4:1 contrast ratio (figure 10(b)) resulted in errors between 5 and 30% whereas T42 errors ranged from 50 to 150%. Similar results between the FHMC and the T50 algorithms were globally seen in terms of the % accuracy of the recovered activity concentration, confirming the trends observed with the simulated datasets. Finally, similarly with the volume estimation, better results were seen with the 8 mm 3 reconstructed voxel's size for both the T50 and the FHMC leading to activity concentration estimation errors of between +10% and -10% for lesions >17mm in diameter.

Discussion

Although PET imaging applications are currently, in their majority, diagnostic and largely based on visual interpretation, there is increasing interest in applications such as the use of PET for radiotherapy treatment planning, as well as response to therapy and outcome prediction studies where accurate functional volume and concentration of activity estimation respectively are indispensable.

Current state of the art methodologies for functional volume determination involve the use of adaptive thresholding based on anatomical information or phantom studies. The performance of these techniques is greatly dependent on lesion contrast and image noise characteristics and as this work has demonstrated can lead to variable performance. On the other hand, already proposed automatic segmentation methodologies have been mostly evaluated for use in lesion detection rather than lesion volume determination. In addition, their performance is highly dependent, similarly to the thresholding algorithms, on image contrast and noise characteristics.

Hidden Markov Chains is an automatic segmentation algorithm that allows noise modelling in the images but has also previously been evaluated for lesion detection rather than functional volume estimation. In the presented work a new algorithm (Fuzzy HMC) has been introduced and evaluated allowing the incorporation within Hidden Markov Chains of a finite number of fuzzy levels in combination with the "hard" classes considered in HMC, adding this way an estimation of imprecision that can account for the effects of limited spatial resolution in emission tomography images. During the evaluation of the FHMC, the inclusion of more than 2 fuzzy levels was found to not substantially alter the segmentation results, while only the inclusion of the voxels belonging to the first fuzzy level led to the most accurate results in terms of functional volume calculations throughout the range of configurations considered. Although it would be possible to consider the use of HMC with four hard classes and an additional rule to cluster the resulting segmentation map, the fuzzy nature of the borders leads to computation issues in transition probabilities that HMC is not able to deal with. Note that the significant addition of the fuzzy measure and mathematical changes in the model allows FHMC to take into account such a configuration, mainly due to the fact that one given voxel can contain both classes.

Finally, in this paper we have introduced the concept of classification errors rather than volume estimation errors in the evaluation of segmentation algorithms for volume determination tasks.

An evaluation based on classification errors is more robust since it does not simply consider the segmented volume but also its location with respect to the "ground truth" known in simulated datasets.

Therefore, while the absolute segmented volume may be correct its location may be wrong, a fact that is as significant as the correct estimation of the overall functional volume particularly for applications such as the use of PET volumes in radiotherapy treatment planning.

In comparison to the recommended T42 for the accurate functional volume determination in PET [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF], the FHMC algorithm gave clearly superior results for lesions <28mm, in particular considering a lesion contrast of 4:1, where the T42 methodology completely failed to recover the functional volume. In addition, FHMC was more robust considering the different image statistical quality levels evaluated, while the results of T42 were greatly influenced by the level of noise present in the images. Differences between classification and volume estimation errors across the different configurations evaluated were smaller for the segmented volumes provided by the FHMC algorithm. In addition, the classification error results allows us to establish that the accuracy obtained on the estimated volumes using the FHMC algorithm is not by chance due to a similar levels of negative and positive classification errors. A smaller reconstructed voxel size at the same statistical quality level led to worse overall segmentation results, without altering the conclusions as far as the relative performance of the different algorithms evaluated is concerned.

The performance of the segmentation algorithms under evaluation in the reconstructed images of the acquired datasets was similar to that obtained with the simulated datasets in terms of volume estimation errors. The only difference observed in comparison with the simulated dataset results was an improvement in the overall segmentation results for 8 mm 3 reconstructed images in comparison to the 64 mm 3 , which can be attributed to an associated adjustment of the optimised reconstruction parameters as a function of the voxel size in the 3D RAMLA algorithm used to reconstruct the acquired datasets.

As far as concentration recovery results are concerned, the performance of the different segmentation algorithms was compared in the simulated datasets to the recovered activity concentration considering the exact size and location of the simulated lesions. These results were influenced by the effects of partial volume leading to increasing underestimation of the activity concentration with decreasing lesion size. Segmentation algorithms concentrate on accurate edge modelling in the object of interest and do not as such account for changes in the values of the voxels as a result of PVE. FHMC and the current "state of the art" threshold of 50% of the maximum lesion value [START_REF] Krak | Effects of ROI definition and reconstruction method on quantitative outcome and applicability in a response monitoring trial[END_REF] led to similar results independently of the configurations evaluated, with absolute differences of 10-15% (due to an extra underestimation for the T50 results). Similar trends to those observed with the simulated datasets were obtained from the segmentation of the acquired images.

The presented results demonstrate the interest of FHMC over thresholding algorithms as the flexibility of the fuzzy levels choice may allow the use of the same segmentation map for different tasks, across a large range of lesion contrasts and sizes. FHMC through the addition of the fuzzy levels associated with each hard class is able to more accurately model the object of interest edges in reconstructed PET images. In addition, FHMC is clearly less susceptible to alterations in statistical image quality and lesion contrasts than other methodologies. This was observed on both images of simulated and acquired datasets. Having said that, none of the evaluated algorithms was successful in accurate volume estimation for lesion sizes of <17mm, considering typical PET image statistical qualities and reconstructed voxels of either 8mm 3 or 64mm 3 . The main reason behind the failure of FHMC concerning the segmentation of such small lesions is the small number of voxels associated with the object of interest in combination to image noise levels, and the Hilbert-Peano path used to transform the image into a chain. The spatial correlation of such small objects may be lost once the image is transformed into a chain. A local model may be able to overcome such an issue [START_REF] Hatt | 3D Fuzzy Adaptive Unsupervised Bayesian Segmentation for[END_REF].

The results for FHMC may be further improved. Firstly, the direct estimation of the noise in the reconstructed images may lead to better results in comparison to the assumed Gaussian model used in this work to fit the distribution for each of the classes. Secondly, other a priori models may be used for Markovian modelling, like couple [START_REF] Pieczynski | Signal and Image Segmentation Using Pairwise Markov Chains[END_REF] or triplet [START_REF] Lanchantin | Unsupervised non stationary image segmentation using triplet Markov chains Advanced Concepts for Intelligent Vision Systems[END_REF] Markov

Chains or Fields. These may be of interest considering a better modelling of the transitions between boundaries classes, as well as the non stationary nature of the hidden a priori model. In addition, the 20 fuzzy model may be extended to more than two hard classes to better model inhomogeneous or non spherical objects of interest.

Conclusion

A modified version of Hard Markov Chains segmentation algorithm has been developed by introducing a fuzzy measure (FHMC). Our results with both simulated and acquired datasets have shown that FHMC is more effective than these of the reference thresholding methodologies for both VOI determination and quantification in PET imaging. As part of the evaluation process, we have also introduced and assessed the interest of classification errors as a robust measurement of the performance of segmentation algorithms for VOI determination in contrast to a simple volume estimation which may introduce biases in terms of the segmented lesion location. Future developments will concentrate on the use of more than two "hard" classes in FHMC, which may more accurately account for the presence of inhomogeneous or non-spherical functional volumes, as well as an investigation into more adequate noise and a priori models.

APPENDIX. The FHMC algorithm step by step

For the calculation of the expressions a quantization of the interval [ ] 0,1 into intervals 1. Transformation of the 2D or 3D image in a 1D chain using the Hilbert-Peano path [START_REF] Kamata | A New Algorithm for N-dimensional Hilbert Scanning[END_REF] (save the path to be used in step 5 of the procedure).

From this point on, every step is performed on the image transformed into a chain.

Parameters initialization:

A priori model parameters: 4) and the following:

1 1 1 1 2 1 1 1 1 2 1 1 1 | 1| 1 | | N N N N i i i j i i i j N N N N N N λ - - - - = = = =         = - + - - + - -                 ∑ ∑ ∑∑ 1 2 1 2 1 ( ) α α γ γ β λ - + + + =
Initial and transition probabilities initializations can then be computed as follows:

( ) ( ) 1 1 1 1 1 2 2 1 1 1 (0) (1 )
(1)

(1 |1 |) 1 ( ) 1 1 | 1| 1 | | N i N i N i i i i j i init N N i init N N j init N N N β α γ β α γ β ε ε ε ε - = - = - = = + + - = + + --     = -+ --+ --         ∑ ∑ ∑ { } ] [ 1 if 0,1 ( , ) ( , ) with 1 ( ) if 0,1 C d g c d trans c d C h d C d N = ∈   =  = ∈   Noise model parameters: { } { } 0 1 0 1 ( , , , ) ( , 2) KMeans Y µ µ σ σ =
with Y the image and 2 for the two hard classes to look for.

Then we determine parameters of each fuzzy level with (9).

SEM procedure for parameters estimation

At each iteration q until no significant modification of the estimated parameters (convergence):

a. fwd and bwd densities computation for each class c ,

{ } 0,1, , 1,..., 1 i c i N ε ∈ = -is performed
recursively as follows:

For 1 t = : 1 1 ( ) ( ) ( ) c fwd c h c G y = For 1 t > : 1 1 1 1 1 1 ( ) ( ) (0) ( , 0) (1) ( ,1) ( ) ( , ) N c t i i t t t t i fwd c G y fwd trans c fwd trans c fwd trans c N ε ε - - - - =   = + +     ∑ For t T = : ( ) 1 T bwd c = For t T < : 1 0 1 ( ) ( ) (0) (0, ) t t t bwd c G y bwd trans c + + = 1 1 1 1 1 1 1 1 ( ) (1) (1, ) ( ) ( , ) ( ) i N t t t t i i i G y bwd trans c G y trans c bwd N ε ε ε - + + + + = + + ∑ These computations must be normalized. c G is given by: 2 2 ( ) 1 ( ) exp 2 2 c c c c y G y µ σ σ π   - = -     b.

Stochastic re-estimation of parameters:

To obtain one a posteriori realization of X , simulate a fuzzy Markov chain using the following : Posterior distributions of X are defined by: 1

( ) ( ) init c fwdbwd c = and 1 1 1 1 1 1 0 ( | ) ( ) ( ) ( , ) ( | ) ( ) ( ) ( ) t t d t t d t f d c G y bwd d trans c d f d c G y bwd d dv d + + + + + = ∫ { } ] [ (c) if 0,1 ( ) 1 (c) if 0,1 init c init c init c N  ∈  =  ∈   and { } ] [ t (c,d) if 0,1 ( , ) 1 (c,d) if 0,1 t trans d trans c d trans d N  ∈  =  ∈  
It has to be noted that ( , ) t trans c d depends on t since a different transition matrix is computed for each element of the posterior realization, as we are dealing with a non stationary Markov chain.

The estimated values of the parameters at the iteration q are computed on the simulated a posteriori chain { } | 1...

t x t T = as follows:

For the a priori model: (1) (1, ( )) 5. Reverse transformation of the 1D segmented chain into the 2D or 3D segmentation map using the path saved at step 1.

[ ] [ ] [ ] [ ] [ ] [ ] 1 1 2 1 2 ( ) ( , ) ( , ) ( , ) ( , ) ( , ) q q T q q t t q t T q t t init c x c x c x d trans c d x c δ δ δ δ - = - = = = ∑ ∑ For the noise model: [ ] [ ] [ ] 1 1 ( , ) ( , ) T q t t q t c T q t t y x c x c δ µ δ = = = ∑ ∑ [ ] [ ] [ ] [ ] 2 2 1 1 ( , )( ) ( , ) T q q t t c q t c T q t t x c

2. 1 . 2 F

 12 Adding a fuzzy measure to the modelThe general idea behind the implementation of a fuzzy model within the Bayesian framework was previously introduced by Salzenstein[START_REF] Salzenstein | Parameter Estimation in hidden fuzzy Markov random fields and image segmentation[END_REF]. Its implementation in association with HMC developed as part of this work is based on the incorporation of a finite number of fuzzy levels i in combination with two homogeneous (or "hard") classes, in comparison to HMC where only a finite number of hard classes are considered. This model allows the coexistence of voxels belonging to one of two hard classes and voxels belonging to a "fuzzy level" depending on its membership to the two hard classes. Therefore, FHMC adds an estimation of imprecision of the hidden data (X, see section 2.1) in contrast to HMC which only models uncertainty of the observed data (Y, see section 2.1). The statistical part of the algorithm models the uncertainty of the classification, with the assumption being that the voxel is clearly identified but the observed data is noisy. On the other hand, the fuzzy part models the imprecision of the voxel's membership, with the assumption being that the voxel may contain both classes. One way to achieve this extension is to simultaneously use Dirac and Lesbegue measures at the class chain level. Hence we consider that X in the fuzzy model takes its values in [ ]

  for integration with respect to the (a,b) variables, each one being with respect to the measure ν on the interval [0,1]. λ is a constant depending on the form of ) using the conjoint density g and an utility density h on [ ] c using densities g and h :

{

namely 2 ×

 2 2× 2 mm 3 and 4× 4× 4 mm 3 . The 8 mm 3 voxel size configuration leads to better sampled objects of interest but with higher noise due to the number of counts being divided by eight in each voxel in comparison to the 64 mm 3 voxel sizes. A uniform activity was simulated throughout the phantom cylinder and the lesions. Different parameters were however considered to cover a large spectrum of configurations allowing assessment of the influence of different parameters susceptible to affect the functional VOI determination or quantitation accuracy. The statistical quality of the images was varied by considering 20, 40 and 60 millions of true coincidences. Two different signal to background (S/B) ratios were also considered; 4:1 and 8:1 (with around 6kBq/cm 3 in the background, and 24 or 48kBq/cm 3 in the spheres respectively). Visual illustration of the reconstructed images corresponding to different simulated configurations is given in figure3(a)-(d).

  Figure 5(a) shows the impact of the number of fuzzy levels included in the FHMC segmentation. The various FHMC maps are denoted as FHMC x/y with x being the number of fuzzy levels included in the segmentation map, and y being the total number of fuzzy levels used in the segmentation process. The error bars in these figures represent different results obtained for each of the 3 different levels of statistical quality considered (the top of the error bar is the result concerning the worst statistical quality, the medium one concerns the medium quality, and the lowest one corresponds to the best quality considered). As Figure5(a) shows, for the range of simulated spheres considered, no improvement was obtained in the % classification errors by having more than 2 fuzzy levels in the FHMC segmentation process and keeping in the overall segmented volume more than the voxels identified in the first fuzzy level. It should be emphasized at this point, that this conclusion was reached considering the results on the whole of the range of simulated sphere diameters and keeping in mind that our objective is determining a single best configuration of the algorithm parameters across a wide range of imaging conditions and not different parameters for individual lesion sizes, image statistics or contrast ratios. In addition, it is clearly showed in figure5that HMC leads to worse segmentation results in comparison to FHMC for all different configurations considered. Therefore for all subsequent volume determination analyses, the results associated with the FHMC 1/2 versus T42 are presented. As shown in figure5(b), no benefits are observed through the inclusion in the segmentation map of any voxels belonging to the fuzzy domain. This confirms what was anticipated in section 2.3.3. Therefore from here onwards all the quantitation results presented for FHMC have been calculated using only the hard class voxels resulting from the segmentation process (FHMC 0/2).The % classification errors for reconstructed images of the simulated datasets as a function of lesion size and contrast are presented in figure6(a) for 64 mm 3 and (b) for 8 mm 3 , for the FHMC and the threshold based method (T42). A breakdown, in terms of PCEs and NCEs, of the % classification errors in figure 6(a) is given in figures 7(a)-(c) for the FHMC, HMC and T42 segmentation methods respectively. Finally, in order to facilitate a comparison of the segmentation results between the simulated and the acquired datasets, the % computed volume error is given in figures 8(a)-(b) for the same configurations as in figures 6(a)-(b).

  (a) FHMC classification errors are essentially NCEs for the two biggest spheres and PCEs for the small ones. In contrast, as shown in figures 7(b)-(c), T42 and HMC methods result essentially in PCEs, apart from T42 in association with lesions >28mm in diameter and a lesion to background ratio of 8:1. In terms of overall volume estimation errors on simulated datasets (see figures 8(a)-(b))

F

  Note : the symbol .... denotes a density instead of a probability.

  segmentation of the chain using estimated parameters: For each t x , determine the class (hard class or fuzzy level) minimizing the error classification probability by minimizing the following expression:

Figure 1 :

 1 Figure 1: The 3D Hilbert-Peano space filling curve for a 4 × 4 × 4 voxels VOI.

Figure 2 :

 2 Figure 2: (a) A graphical representation of the IEC phantom, and the central slice of the digital IEC phantom used in the generation of the simulated datasets (b) with 2 × 2 × 2 mm 3 and (c) 4 × 4 × 4 mm 3 .

Figure 3 :

 3 Figure 3: Different images used in the segmentation study; (a)-(d) simulated : (a) ratio 4:1, 20 millions of coincidences, 64 mm 3 , (b) ratio 8:1, 40 millions, 64 mm 3 , (c) ratio 4:1, 20 millions of coincidences, 8 mm 3 , (d) ratio 8:1, 40 millions, 8 mm 3 (e)-(h) acquired : (e) ratio 4:1, 2min acquisition time, 64 mm 3 , (f) ratio 8:1, 5min, 64 mm 3 , (g) ratio 4:1, 5min, 8 mm 3 , (h), ratio 8:1, 5min, 8 mm 3 .

Figure 4 :

 4 Figure 4: Examples of segmentation maps for the 28mm sphere (one slice) (a) PET ROI, (b) Digital "ground truth", (c) HMC map, (d) T42 map, (e) FHMC with 2 fuzzy levels (light and dark grey voxels) segmentation map, (f) Map used for VOI (hard class + 1 st fuzzy level, FHMC 1/2), (g) Map for quantitation (only hard class voxels, FHMC 0/2), (h) T50 map. Note that in this particular case, FHMC 1/2 for VOI and T50 result in the same map but this is of course not always the case (especially having considered the complete 3D volume).

Figure 5 :

 5 Figure 5: (a) Classification errors for the lesion VOI determination and (b) lesion activity recovery errors in the simulated images for the FHMC vs HMC segmentation. Different number of fuzzy levels (2 or 3) were used in the segmentation process and different number of these were subsequently selected to (a) form the segmented volumes or (b) determine lesion average activity concentrations for the different imaging conditions considered.

Figure 6 :

 6 Figure 6: Classification errors in lesion VOI determination from the simulated images: (a) 64 mm 3 voxels and (b) 8 mm 3 voxels for the FHMC 1/2 vs T42 segmentation under variable imaging conditions.

Figure 7 :

 7 Figure 7: Repartition of PCEs and NCEs from the (a) FHMC 1/2, (b) HMC and (c) T42 segmentation results for the different simulated imaging configurations considered.

Figure 8 :

 8 Figure 8: Lesion VOI estimation errors from the simulated images: (a) 64 mm 3 voxels and (b) 8 mm 3 voxels for the FHMC 1/2 vs T42 segmentation under variable imaging conditions.

Figure 9 :

 9 Figure 9: Lesion average activity concentration estimation errors from the simulated images: (a) 64 mm 3 voxels and (b) 8 mm 3 voxels for FHMC 0/2 vs T50 segmentation under variable imaging conditions.

Figure 10 :

 10 Figure 10: Lesion VOI estimation errors from the acquired images: (a) 64 mm 3 voxels and (b) 8 mm 3 voxels for the FHMC 1/2 vs T42 segmentation under variable imaging conditions.

Figure 11 :

 11 Figure 11: Lesion average activity concentration estimation errors from the acquired images: (a) 64 mm 3 voxels and (b) 8 mm 3 voxels for the FHMC 0/2 vs T50 segmentation under variable imaging conditions.

  , and where fwdbwd denotes the product of the forward and backward densities. The cost function L is given by (8).

	fwdbwd	t	t L s y	+	t fwdbwd L s y t	1 + ∫	fwdbwd	t	( ) ( , ( )) i t L s y d ε ε i ε	i
						0
	for every ( )

t s y

Acknowledgments

This work is financially supported by a Region of Brittany research grant under the "Renouvelement des competences" program 1202-2004.

PCEs and NCEs of FHMC (1 / 2) segmentation method

Classification errors (%) (b) Figure 9