We construct and investigate random geometric structures that are based on a homogeneous Poisson point process. We investigate the random Vietoris-Rips complex constructed as the clique complex of the well known gilbert graph as an infinite random simplicial complex and prove that every realizable finite sub-complex will occur infinitely many times almost sure as isolated complex and also in the case of percolations connected to the unique giant component. Similar results are derived for the Cech complex. We derive limit theorems for the f-vector of the Vietoris-Rips complex on the unit cube centered at the origin and provide a central limit theorem and a Poisson limit theorem based on the model parameters. Finally we investigate random polytopes that are given as convex hulls of a Poisson point process in a smooth convex body. We establish a central limit theorem for certain linear combinations of intrinsic volumes. A multivariate limit theorem involving the sequence of intrinsic volumes and the number of i-dimensional faces is derived. We derive the asymptotic normality of the oracle estimator of minimal variance for estimation of the volume of a convex body.

En regardant de près les outils juridiques et autres leviers, pour la conservation de la biodiversité, il semblerait que les invertébrés, et notamment les insectes, soient minoritaires ou absents. Ce constat est d’autant plus paradoxal lorsque l’on sait que 2/3 de la diversité biologique est composée par des insectes. Comment cette diversité essentielle pour le fonctionnement des écosystèmes se retrouve-t-elle dans l’angle mort de la conservation ?La première réponse avancée est le manque d’outils techniques pour étudier ces organismes petits et relativement insaisissables. La rencontre avec les nouvelles méthodes techniques pour la détection et l’étude des insectes est plus que jamais nécessaire. En effet, ces leviers permettront de faciliter l’étude de ces organismes, d’augmenter les connaissances et ainsi de développer une conservation plus adéquate. Nous évoquerons deux approches en particulier : la détection avec des outils moléculaires et l’utilisation de modèles statistiques pour l’exploration de la distribution potentielle des espèces.Mais les connaissances sont également fondées sur la demande sociétale. Et les connaissances alimentent elles-mêmes les outils de protection et de conservation de la biodiversité. À l’échelle des invertébrés, des disparités existent, privilégiant les « grands papillons bleus » aux « petits diptères marrons ». De fait, l’enjeu le plus important pour déverrouiller la conservation des insectes réside dans l’humain et la perception qu’il a de cette biodiversité. À travers une approche de psychologie de la conservation, nous sonderons la perception du grand public sur les insectes. De même, avec une approche de recherche-action-participative, nous tenterons d’engager divers acteurs vers la conservation d’un groupe d’insectes ordinaires : les coléoptères coprophages. Notre volonté est de proposer des moyens pour sensibiliser, éduquer et engager la société dans cet enjeu majeur qu’est la conservation de l’entomofaune. / Looking closely at the legal tools and other levers for preserving biodiversity, it would seem that invertebrates, in particular insects, are in a minority, or absent. This observation is all the more paradoxical when we know that 2/3 of the biological diversity consists of insects. How does this diversity, essential for the functioning of the ecosystems, find itself in the dead angle of conservation?The first answer that is usually put forward is lack of technical tools to study these small and relatively elusive animals. Getting to know and use new technical methods for the detection and the study of insects is more than ever necessary. Indeed, these levers will facilitate the study of these animals, and will thus increase knowledge, which will lead to developing more adequate conservation strategies. We shall evoke two approaches in particular: detection with molecular tools and use of statistical models to explore the potential distribution of the species.But knowledge is also based on what society asks for. Public interest orients the tools of protection and preservation of biodiversity. Among invertebrates, disparities exist, favoring the “big blue butterflies” over the “small brown dipterans”. A simple coincidence? No. Actually, the decisive factor to unlock the preservation of insects rests in human beings and how they perceive this biodiversity. Using a conservation psychology approach, we will explore how the general public perceives insects. We will also draw on participatory action research to see how various conservation actors can be committed towards preserving a group of ordinary insects: coprophagous beetles. Our aim is to propose ways to raise awareness, educate and engage society to this major issue: preserving entomofauna.

Object detection has been a fundamental part of many emerging technologies, such as autonomous vehicles, robotics, and security. As deep learning is the main reason behind the leap of performance in object detection, it has mostly been associated with a post-processing step of non-maximum suppression (NMS) to reduce the number of resulting bounding boxes output from the network to, ideally, one box per object. As non-maximum suppression blindly suppress the overlap with a pre-defined threshold, it introduces the problem of suppressing false negatives in crowded scenes by choosing a high threshold, or vice versa. This problem is critical, especially in the autonomous vehicle industry, as this concerns the safety of passengers. The problem of the machine understanding whether these bounding boxes belong to the same object or two near-by objects is still not directly solvable. Although a lot of previous research tried to invent a new box-reduction method, every method has its own drawbacks while solving the problem. That is why, until now, many researchers are still using non‐maximum suppression. In this research, a literature review was carried out to determine the best NMS alternatives. Then, an approach for box reduction based on determinantal point process (DPP) was implemented. Furthermore, an evaluation pipeline was introduced for experimental analysis for the differences between NMS and DPP. Although NMS shows a better performance in terms of precision and recall, DPP chooses better fitting bounding boxes. / Objektdetektering har varit en grundläggande del av många nya tekniker, t.ex. autonoma fordon, robotik och säkerhet. Eftersom djupinlärning är den främsta orsaken till den stora prestandaskillnaden vid objektsdetektering har den oftast varit förknippad med ett efterbehandlingssteg med icke-maximal undertryckning (NMS) för att minska antalet resulterande avgränsande rutor som produceras av nätverket till, idealt sett, en ruta per objekt. Eftersom icke-maximal undertryckning blint undertrycker överlappningen med ett fördefinierat tröskelvärde, uppstår problemet med att undertrycka falskt negativa resultat i överfulla scener genom att välja ett högt tröskelvärde, eller tvärtom. Detta problem är kritiskt, särskilt inom industrin för autonoma fordon, eftersom det gäller passagerarnas säkerhet. Problemet med att maskinen ska förstå om dessa avgränsande rutor tillhör samma objekt eller två närliggande objekt är fortfarande inte direkt lösbart. Även om man i tidigare forskning har försökt hitta en ny metod för att reducera boxar, har varje metod sina egna nackdelar när den löser problemet. Det är därför som många forskare fram till nu fortfarande använder sig av icke-maximalt undertryckande. I denna forskning gjordes en litteraturstudie för att fastställa de bästa NMS-alternativen. Därefter implementerades en metod för boxförminskning baserad på determinant punktprocess (DPP). Dessutom infördes en utvärderingsledning för experimentell analys av skillnaderna mellan NMS och DPP. Även om NMS visar en bättre prestanda när det gäller precision och återkallande, väljer DPP bättre passande avgränsande lådor.

<p>This dissertation establishes a variety of limit theorems pertaining to rare events in stochastic topology, exploiting probabilistic methods to study simplicial complex models. We focus on the filtration of \vc ech complexes and examine the asymptotic behavior of two topological functionals: the Betti numbers and critical faces. The filtration involves a parameter rn>0 that determines the growth rate of underlying Cech complexes. If rn depends also on the time parameter t, the obtained limit theorems will be established in a functional sense.</p> <p>The first part of this dissertation is devoted to investigating the layered structure of topological complexity in the tail of a probability distribution. We establish the functional strong law of large numbers for Betti numbers, a basic quantifier of algebraic topology, of a geometric complex outside an open ball of radius Rn, such that Rn to infinity as the sample size n increases. The nature of the obtained law of large numbers is determined by the decay rate of a probability density. It especially depends on whether the tail of a density decays at a regularly varying rate or an exponentially decaying rate. The nature of the limit theorem depends also on how rapidly Rn diverges. In particular, if Rn diverges sufficiently slowly, the limiting function in the law of large numbers is crucially affected by the emergence of arbitrarily large connected components supporting topological cycles in the limit.</p> <p>The second part of this dissertation investigates convergence of point processes associated with critical faces for a Cech filtration built over a homogeneous Poisson point process in the d-dimensional flat torus. The convergence of our point process is established in terms of the  Mo-topology, when the connecting radius of a Cech complex decays to 0, so slowly that critical faces are even less likely to occur than those in the regime of threshold for homological connectivity. We also obtain a series of limit theorems for positive and negative critical faces, all of which are considerably analogous to those for critical faces.</p>

With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is experiencing an unprecedented paradigm shift. These aerial platforms are specifically appealing for a variety of applications due to their rapid and flexible deployment, cost-effectiveness, and high chance of forming line-of-sight (LoS) links to the ground nodes. As with any new technology, the benefits of incorporating UAVs in existing cellular networks cannot be characterized without completely exploring the underlying trade space. This requires a detailed system-level analysis of drone cellular networks by taking the unique features of UAVs into account, which is the main objective of this dissertation. We first focus on a static setup and characterize the performance of a three-dimensional (3D) two-hop cellular network in which terrestrial base stations (BSs) coexist with UAVs to serve a set of ground user equipment (UE). In particular, a UE connects either directly to its serving terrestrial BS by an access link or connects first to its serving UAV which is then wirelessly backhauled to a terrestrial BS (joint access and backhaul). We consider realistic antenna radiation patterns for both BSs and UAVs using practical models developed by the third generation partnership project (3GPP). We assume a probabilistic channel model for the air-to-ground transmission, which incorporates both LoS and non-LoS links. Assuming the max-power association policy, we study the performance of the network in both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Using tools from stochastic geometry, we analyze the joint distribution of distance and zenith angle of the closest (and serving) UAV to the origin in a 3D setting. Further, we identify and extensively study key mathematical constructs as the building blocks of characterizing the received signal-to-interference-plus-noise ratio (SINR) distribution. Using these results, we obtain exact mathematical expressions for the coverage probability in both AF and DF relaying protocols. Furthermore, considering the fact that backhaul links could be quite weak because of the downtilted antennas at the BSs, we propose and analyze the addition of a directional uptilted antenna at the BS that is solely used for backhaul purposes. The superiority of having directional antennas with wirelessly backhauled UAVs is further demonstrated via extensive simulations. Second, we turn our attention to a mobile setup and characterize the performance of several canonical mobility models in a drone cellular network in which UAV base stations serve UEs on the ground. In particular, we consider the following four mobility models: (i) straight line (SL), (ii) random stop (RS), (iii) random walk (RW), and (iv) random waypoint (RWP), among which the SL mobility model is inspired by the simulation models used by the 3GPP for the placement and trajectory of UAVs, while the other three are well-known canonical models (or their variants) that offer a useful balance between realism and tractability. Assuming the nearest-neighbor association policy, we consider two service models for the UEs: (i) UE independent model (UIM), and (ii) UE dependent model (UDM). While the serving UAV follows the same mobility model as the other UAVs in the UIM, it is assumed to fly towards the UE of interest in the UDM and hover above its location after reaching there. We then present a unified approach to characterize the point process of UAVs for all the mobility and service models. Using this, we provide exact mathematical expressions for the average received rate and the session rate as seen by the typical UE. Further, using tools from the calculus of variations, we concretely demonstrate that the simple SL mobility model provides a lower bound on the performance of other general mobility models (including the ones in which UAVs follow curved trajectories) as long as the movement of each UAV in these models is independent and identically distributed (i.i.d.). Continuing our analysis on mobile setups, we analyze the handover probability in a drone cellular network, where the initial positions of the UAVs serving the ground UEs are modeled by a homogeneous Poisson point process (PPP). Inspired by the mobility model considered in the 3GPP studies, we assume that all the UAVs follow the SL mobility model, i.e., move along straight lines in random directions. We further consider two different scenarios for the UAV speeds: (i) same speed model (SSM), and (ii) different speed model (DSM). Assuming nearest-neighbor association policy, we characterize the handover probability of this network for both mobility scenarios. For the SSM, we compute the exact handover probability by establishing equivalence with a single-tier terrestrial cellular network, in which the BSs are static while the UEs are mobile. We then derive a lower bound for the handover probability in the DSM by characterizing the evolution of the spatial distribution of the UAVs over time. After performing these system-level analyses on UAV networks, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we first study the impact of UAV wobbling on the coherence time of the wireless channel between UAVs and a ground UE, using a Rician multi-path channel model. We consider two different scenarios for the number of UAVs: (i) single UAV scenario (SUS), and (ii) multiple UAV scenario (MUS). For each scenario, we model UAV wobbling by two random processes, i.e., the Wiener and sinusoidal processes, and characterize the channel autocorrelation function (ACF) which is then used to derive the coherence time of the channel. For the MUS, we further show that the UAV-UE channels for different UAVs are uncorrelated from each other. One key observation that is revealed from our analysis is that even for small UAV wobbling, the coherence time of the channel may degrade quickly, which may make it difficult to track the channel and establish a reliable communication link. Finally, we develop an impairments-aware air-to-ground unified channel model that incorporates the effect of both wobbling and hardware impairments, where the former is caused by random physical fluctuations of UAVs, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver, such as phase noise, in-phase/quadrature (I/Q) imbalance, and power amplifier (PA) nonlinearity. The impact of UAV wobbling is modeled by two stochastic processes, i.e., the canonical Wiener process and the more realistic sinusoidal process. On the other hand, the aggregate impact of all hardware impairments is modeled as two multiplicative and additive distortion noise processes, which is a well-accepted model. For the sake of generality, we consider both wide-sense stationary (WSS) and nonstationary processes for the distortion noises. We then rigorously characterize the ACF of the wireless channel, using which we provide a comprehensive analysis of four key channel-related metrics: (i) power delay profile (PDP), (ii) coherence time, (iii) coherence bandwidth, and (iv) power spectral density (PSD) of the distortion-plus-noise process. Furthermore, we evaluate these metrics with reasonable UAV wobbling and hardware impairment models to obtain useful insights. Similar to our observation above, this work again demonstrates that the coherence time severely degrades at high frequencies even for small UAV wobbling, which renders air-to-ground channel estimation very difficult at these frequencies. / Doctor of Philosophy / With the increasing maturity of unmanned aerial vehicles (UAVs), also known as drones, wireless ecosystem is changing dramatically. Owing to their ease of deployment and high chance of forming direct line-of-sight (LoS) links with the other UAVs and ground users, they are very appealing for numerous wireless applications. As with any new technology, exploring the full extent of the benefits of UAVs requires careful exploration of the underlying trade space. Therefore, in this dissertation, our main focus is on the analysis of such aerial networks, their interplay with the current terrestrial networks, and the unique features of UAVs that make them different from conventional ground nodes. One important aspect of aerial communication systems is their integration into our current cellular networks. Clearly, the addition of these new aerial components has the potential of benefiting both the ground users (such as mobile users watching a concert who need cellular connectivity to share the moments) and the cellular base station (BS). Therefore, careful analysis of these ``aerial-terrestrial" networks is of utmost importance. In the first phase of this dissertation, we perform this analysis by interpreting the network as a combination of one-hop (from the BS to the user) and two-hop (from the BS to the UAV and then from the UAV to the UE) links. Since the locations of BSs, UAVs, and users are irregular in general, we use tools from stochastic geometry to carry out our analysis, which is a field of mathematics that studies random shapes and patterns. Also, because existing terrestrial BSs are primarily designed to serve the ``ground", we propose the addition of a separate set of antennas at the BS site that is solely used to serve the ``air", i.e., to communicate with the UAVs, and demonstrate the benefits of this additional infrastructure in detail. One of our assumptions in the first phase of this dissertation was that the considered network was static, i.e., the UAVs were hovering in the air and the BSs/users were also not moving. In the second phase, on the other hand, we explore the benefits and challenges of a mobile network of UAVs and characterize the performance of several canonical mobility models in a drone cellular network. In particular, one of the models that we studied extensively is the so-called straight line (SL) mobility model, which was inspired by the simulation models used by the third generation partnership project (3GPP) for the placement and trajectory of UAVs. Since the locations of UAVs could be assumed random in general, we use tools from stochastic geometry and present a unified approach to characterize the point process of UAVs, using which we obtained exact mathematical expressions for the average received rate (i.e., throughput) as seen by the users. Continuing our analysis on mobile setups and using the SL mobility model, we also analyze the handover probability in a drone cellular network, which is defined as the event when the serving UAV of a user changes. By establishing equivalence between our aerial setup with a terrestrial cellular network, we compute the exact handover probability in drone cellular networks. In the final phase of this dissertation, we focus our attention on the air-to-ground wireless channel and attempt to understand its unique features. For that, we propose an impairments-aware unified channel model for an air-to-ground wireless communication system and extensively analyze the link between a hovering UAV in the air and a static user on the ground. In particular, we consider two different types of impairments: (i) UAV wobbling, and (ii) hardware impairments, where the former is caused by random physical fluctuations, and the latter by intrinsic radio frequency (RF) nonidealities at both the transmitter and receiver. Using appropriate models for each type of impairment, we rigorously characterize the autocorrelation function (ACF) of the wireless channel, using which we provide a comprehensive analysis of key channel-related metrics, such as coherence time and coherence bandwidth. One key observation that is revealed from our analysis is that even for small UAV wobbling and low hardware impairment levels, the coherence time of the channel may degrade quickly at high frequencies, which could make it difficult to track the channel and establish a reliable communication link at these frequencies.

The success of the Internet-of-Things (IoT) paradigm relies on, among other things, developing energy-efficient communication techniques that can enable information exchange among billions of battery-operated IoT devices. With its technological capability of simultaneous information and energy transfer, ambient backscatter is quickly emerging as an appealing solution for this communication paradigm, especially for the links with low data rate requirements. However, many challenges and limitations of ambient backscatter have to be overcome for widespread adoption of the technology in future wireless networks. Motivated by this, we study the design and implementation of ambient backscatter systems, including non-coherent detection and encoding schemes, and investigate techniques such as multiple antenna interference cancellation and frequency-shift backscatter to improve the bit error rate performance of the designed ambient backscatter systems. First, the problem of coherent and semi-coherent ambient backscatter is investigated by evaluating the exact bit error rate (BER) of the system. The test statistic used for the signal detection is based on the averaging of energy of the received signal samples. It is important to highlight that the conditional distributions of this test statistic are derived using the central limit theorem (CLT) approximation in the literature. The characterization of the exact conditional distributions of the test statistic as non-central chi-squared random variable for the binary hypothesis testing problem is first handled in our study, which is a key contribution of this particular work. The evaluation of the maximum likelihood (ML) detection threshold is also explored which is found to be intractable. To overcome this, alternate strategies to approximate the ML threshold are proposed. In addition, several insights for system design and implementation are provided both from analytical and numerical standpoints. Second, the highly appealing non-coherent signal detection is explored in the context of ambient backscatter for a time-selective channel. Modeling the time-selective fading as a first-order autoregressive (AR) process, we implement a new detection architecture at the receiver based on the direct averaging of the received signal samples, which departs significantly from the energy averaging-based receivers considered in the literature. For the proposed setup, we characterize the exact asymptotic BER for both single-antenna (SA) and multi-antenna (MA) receivers, and demonstrate the robustness of the new architecture to timing errors. Our results demonstrate that the direct-link (DL) interference from the ambient power source leads to a BER floor in the SA receiver, which the MA receiver can avoid by estimating the angle of arrival (AoA) of the DL. The analysis further quantifies the effect of improved angular resolution on the BER as a function of the number of receive antennas. Third, the advantages of utilizing Manchester encoding for the data transmission in the context of non-coherent ambient backscatter have been explored. Specifically, encoding is shown to simplify the detection procedure at the receiver since the optimal decision rule is found to be independent of the system parameters. Through extensive numerical results, it is further shown that a backscatter system with Manchester encoding can achieve a signal-to-noise ratio (SNR) gain compared to the commonly used uncoded direct on-off keying (OOK) modulation, when used in conjunction with a multi-antenna receiver employing the direct-link cancellation. Fourth, the BER performance of frequency-shift ambient backscatter, which achieves the self-interference mitigation by spatially separating the reflected backscatter signal from the impending source signal, is investigated. The performance of the system is evaluated for a non-coherent receiver under slow fading in two different network setups: 1) a single interfering link coming from the ambient transmission occurring in the shifted frequency region, and 2) a large-scale network with multiple interfering signals coming from the backscatter nodes and ambient source devices transmitting in the band of interest. Modeling the interfering devices as a two dimensional Poisson point process (PPP), tools from stochastic geometry are utilized to evaluate the bit error rate for the large-scale network setup. / Doctor of Philosophy / The emerging paradigm of Internet-of-Things (IoT) has the capability of radically transforming the human experience. At the heart of this technology are the smart edge devices that will monitor everyday physical processes, communicate regularly with the other nodes in the network chain, and automatically take appropriate actions when necessary. Naturally, many challenges need to be tackled in order to realize the true potential of this technology. Most relevant to this dissertation are the problems of powering potentially billions of such devices and enabling low-power communication among them. Ambient backscatter has emerged as a useful technology to handle the aforementioned challenges of the IoT networks due to its capability to support the simultaneous transfer of information and energy. This technology allows devices to harvest energy from the ambient signals in the environment thereby making them self-sustainable, and in addition provide carrier signals for information exchange. Using these attributes of ambient backscatter, the devices can operate at very low power which is an important feature when considering the reliability requirements of the IoT networks. That said, the ambient backscatter technology needs to overcome many challenges before its widespread adoption in IoT networks. For example, the range of backscatter is limited in comparison to the conventional communication systems due to self-interference from the power source at a receiver. In addition, the probability of detecting the data in error at the receiver, characterized by the bit error rate (BER) metric, in the presence of wireless multipath is generally poor in ambient backscatter due to double path loss and fading effects observed for the backscatter link. Inspired by this, the aim of this dissertation is to come up with new architecture designs for the transmitter and receiver devices that can improve the BER performance. The key contributions of the dissertation include the analytical derivations of BER which provide insights on the system design and the main parameters impacting the system performance. The exact design of the optimal detection technique for a communication system is dependent on the channel behavior, mainly the time-varying nature in the case of a flat fading channel. Depending on the mobility of devices and scatterers present in the wireless channel, it can either be described as time-selective or time-nonselective. In the time-nonselective channels, coherent detection that requires channel state information (CSI) estimation using pilot signals can be implemented for ambient backscatter. On the other hand, non-coherent detection is preferred when the channel is time-selective since the CSI estimation is not feasible in such scenarios. In the first part of this dissertation, we analyze the performance of ambient backscatter in a point-to-point single-link system for both time-nonselective and time-selective channels. In particular, we determine the BER performance of coherent and non-coherent detection techniques for ambient backscatter systems in this line of work. In addition, we investigate the possibility of improving the BER performance using multi-antenna and coding techniques. Our analyses demonstrate that the use of multi-antenna and coding can result in tremendous improvement of the performance and simplification of the detection procedure, respectively. In the second part of the dissertation, we study the performance of ambient backscatter in a large-scale network and compare it to that of the point-to-point single-link system. By leveraging tools from stochastic geometry, we analytically characterize the BER performance of ambient backscatter in a field of interfering devices modeled as a Poisson point process.

Les travaux réalisés dans cette thèse s'inscrivent dans le cadre du développement de techniques de mesure optiques pour la mécanique des fluides visant la reconstruction de volumes de particules 3D pour ensuite en déduire leurs déplacements. Cette technique de mesure volumique appelée encore Tomo-PIV est apparue en 2006 et a fait l'objet d'une multitude de travaux ayant pour objectif l'amélioration de la reconstruction qui représente l'une des principales étapes de cette technique de mesure. Les méthodes proposées en littérature ne prennent pas forcément en compte la forme particulière des objets à reconstruire et ne sont pas suffisamment robustes pour faire face au bruit présent dans les images. Pour pallier à ce déficit, nous avons proposé une méthode de reconstruction tomographique, appelée (IOD-PVRMPP), qui se base sur les processus ponctuels marqués. Notre méthode permet de résoudre le problème de manière parcimonieuse. Elle facilite l'introduction de l'information à priori et résout les problèmes de mémoire liés aux approches dites "basées voxels". La reconstruction d'un ensemble de particules 3D est obtenue en minimisant une fonction d'énergie ce qui définit le processus ponctuel marqué. A cet effet, nous utilisons un algorithme de recuit simulé basé sur les méthodes de Monte-Carlo par Chaines de Markov à Saut Réversible (RJMCMC). Afin d'accélérer la convergence du recuit simulé, nous avons développé une méthode d'initialisation permettant de fournir une distribution initiale de particules 3D base sur la détection des particules 2D localisées dans les images de projections. Enfin cette méthode est appliquée à des écoulements fluides soit simulé, soit issu d'une expérience dans un canal turbulent à surface libre. L'analyse des résultats et la comparaison de cette méthode avec les méthodes classiques montrent tout l'intérêt de ces approches parcimonieuses. / The research work fulfilled in this thesis fit within the development of optical measurement techniques for fluid mechanics. They are particularly related to 3D particle volume reconstruction in order to infer their movement. This volumetric measurement technic, called Tomo-PIV has appeared on 2006 and has been the subject of several works to enhance the reconstruction, which represents one of the most important steps of this measurement technique. The proposed methods in Literature don't necessarily take into account the particular form of objects to reconstruct and they are not sufficiently robust to deal with noisy images. To deal with these challenges, we propose a tomographic reconstruction method, called (IOD-PVRMPP), and based on marked point processes. Our method allows solving the problem in a parsimonious way. It facilitates the introduction of prior knowledge and solves memory problem, which is inherent to voxel-based approaches. The reconstruction of a 3D particle set is obtained by minimizing an energy function, which defines the marked point process. To this aim, we use a simulated annealing algorithm based on Reversible Jump Markov Chain Monte Carlo (RJMCMC) method. To speed up the convergence of the simulated annealing, we develop an initialization method, which provides the initial distribution of 3D particles based on the detection of 2D particles located in projection images. Finally, this method is applied to simulated fluid flow or real one produced in an open channel flow behind a turbulent grid. The results and the comparisons of this method with classical ones show the great interest of this parsimonious approach.

Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.

Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.

L’objectif principal de cette thèse est de développer des méthodologies statistiques adaptées au traitement de données issues de processus stochastiques et plus précisément de processus de Cox.Les problématiques étudiées dans cette thèse sont issues des trois domaines statistiques suivants : les tests non paramétriques, l’estimation non paramétrique à noyaux et l’estimation minimax.Dans un premier temps, nous proposons, dans un cadre fonctionnel, des statistiques de test pour détecter la nature Poissonienne d’un processus de Cox.Nous étudions ensuite le problème de l’estimation minimax de la régression sur un processus de Poisson ponctuel. En se basant sur la décomposition en chaos d’Itô, nous obtenons des vitesses comparables à celles atteintes pour le cas de la régression Lipschitz en dimension finie.Enfin, dans le dernier chapitre de cette thèse, nous présentons un estimateur non-paramétrique de l’intensité d’un processus de Cox lorsque celle-ci est une fonction déterministe d’un co-processus. / The main purpose of this thesis is to develop statistical methodologies for stochastic processes data and more precisely Cox process data.The problems considered arise from three different contexts: nonparametric tests, nonparametric kernel estimation and minimax estimation.We first study the statistical test problem of detecting wether a Cox process is Poisson or not.Then, we introduce a semiparametric estimate of the regression over a Poisson point process. Using Itô’s famous chaos expansion for Poisson functionals, we derive asymptotic minimax properties of our estimator.Finally, we introduce a nonparametric estimate of the intensity of a Cox process whenever it is a deterministic function of a known coprocess.