Gravitational lensing, initially a phenomenon used as a solid confirmation of General Relativity, has defined itself in the past decade as a standard astrophysical tool. The ability of a lensing system to produce multiple images of a luminous source is one of the aspects of gravitational lensing that is exploited both theoretically and observationally to improve our understanding of the Universe. In this thesis, within the field of multiple imaging we explore the case of maximal lensing, that is, the configurations and conditions under which a set of deflecting masses can produce the maximum number of images of a distant luminous source, as well as a study of the value for this maximum number itself. We study the case of a symmetric distribution of n-1 point-mass lenses at the vertices of a regular polygon of n-1 sides. By the addition of a perturbation in the form of an n-th mass at the center of the polygon it is proven that, as long as the mass is small enough, the system is a maximal lensing configuration that produces 5(n-1) images. Using the explicit value for the upper bound on the central mass that leads to maximal lensing, we illustrate how this result can be used to find and constrain the mass of planets or brown dwarfs in multiple star systems. For the case of more realistic mass distributions, we prove that when a point-mass is replaced with a distributed lens that does not overlap with existing images or lensing objects, an additional image is formed within the distributed mass while positions and numbers of existing images are left unchanged. This is then used to conclude that the maximum number of images that n isolated distributed lenses can produce is 6(n-1)+1. In order to explore the likelihood of observational verification, we analyze the stability properties of the symmetric maximal lensing configurations. Finally, for the cases of n=4, 5, and 6 point-mass lenses, we study asymmetric maximal lensing configurations and compare their stability properties against the symmetric case.

Gravitational lensing, initially a phenomenon used as a solid confirmation of General Relativity, has defined itself in the past decade as a standard astrophysical tool. The ability of a lensing system to produce multiple images of a luminous source is one of the aspects of gravitational lensing that is exploited both theoretically and observationally to improve our understanding of the Universe. In this thesis, within the field of multiple imaging we explore the case of maximal lensing, that is, the configurations and conditions under which a set of deflecting masses can produce the maximum number of images of a distant luminous source, as well as a study of the value for this maximum number itself. We study the case of a symmetric distribution of n-1 point-mass lenses at the vertices of a regular polygon of n-1 sides. By the addition of a perturbation in the form of an n-th mass at the center of the polygon it is proven that, as long as the mass is small enough, the system is a maximal lensing configuration that produces 5(n-1) images. Using the explicit value for the upper bound on the central mass that leads to maximal lensing, we illustrate how this result can be used to find and constrain the mass of planets or brown dwarfs in multiple star systems. For the case of more realistic mass distributions, we prove that when a point-mass is replaced with a distributed lens that does not overlap with existing images or lensing objects, an additional image is formed within the distributed mass while positions and numbers of existing images are left unchanged. This is then used to conclude that the maximum number of images that n isolated distributed lenses can produce is 6(n-1)+1. In order to explore the likelihood of observational verification, we analyze the stability properties of the symmetric maximal lensing configurations. Finally, for the cases of n=4, 5, and 6 point-mass lenses, we study asymmetric maximal lensing configurations and compare their stability properties against the symmetric case.

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近年來，隨著數位科技快速的發展，影像資料量迅速的增加，因此影像檢索成為重要的多媒體技術之一。在傳統的影像內容檢索技術中，使用影像低階特徵值，例如顏色(Color)、紋理(Texture)、形狀(Shape)等來描述影像的內容並進行圖片相似度的比對。然而，傳統的影像內容檢索僅提供單張影像查詢，很少研究多張影像的查詢。因此，本研究提出一個可針對多張影像查詢的方法以提供多張影像查詢的影像內容檢索。本研究將影像內容檢索結合社群網絡演算法，使用MPEG-7中相關特徵描述子和SIFT做為主要特徵向量，擷取影像的低階影像特徵，透過特徵相似度計算建立影像之間的網絡，並利用社群網絡演算法找出與多張查詢影像相似的影像。實驗結果顯示所提出的方法可精確的擷取到相似的影像。 / In recent years, with the faster and faster development of computer technology, the number of digital images is grown rapidly so that the Content-Based Image Retrieval has become one of important multimedia technologies. Much research has been done on Content-Based Image Retrieval. However, little research has been done on query by multiple images. This thesis investigates the mechanism for query by multiple images. First, MPEG-7 image features and SIFT are extracted from images. Then, we calculate the similarity of images to construct the proximity graph which represents the similarity structure between images. Last, processing of query by multiple images is achieved based on the social network algorithms. Experimental results indicate the proposed method provides high accuracy and precision.

RERUME: Les modèles personnalisés 3D sont de plus en plus demandés pour la planification chirurgicale et les recherches en biomécanique. L’objectif principal de cette thèse cotutelle était d’améliorer la méthode de reconstruction 3D à partir des images radiographies biplanes proposée par Lagacé, Ohl et al., afin que celle-ci puisse être plus facilement utilisée en clinique et qu’elle puisse permettre d’aider à la planification chirurgicale et/ou l’évaluation post-chirurgicale. Le système de radiographie biplane EOS à faible dose d’irradiation est le résultat d’une collaboration entre la société EOS imaging, l’institut biomécanique humaine Georges Charpak d’Arts et Métiers ParisTech, le laboratoire de recherche en imagerie et orthopédie (LIO) de l’école de technologie supérieure de Montréal, Georges Charpak, Jean Dubousset et Gabriel Kalifa (Dubousset et al. 2010). Le principe du détecteur de rayon X est basé sur les travaux développés par le Prof. Charpak, qui réduit significativement la dose de rayonnement comparé à la radiographie standard (Dubousset et al. 2010) Quatorze indices cliniques utilisés plus ou moins couramment en clinique pour le diagnostic et le suivi des pathologies de l’épaule et pour la planification chirurgicale et son évaluation post-opératoire ont été calculé. La justesse est acceptable (biais <1 mm sauf la distance sous acrominale) et une reproductibilité (2 fois écart-type inférieur à 5 mm ou 5° sauf 2 paramètres) qui est similaire à ce qui est présenté dans la littérature. L’approche proposée apporte sur une amélioration de la reconstruction dans un contexte où il serait intéressant qu’elle devienne utilisable en routine clinique. Bien que les améliorations soient encore nécessaires, cette contribution apporte une pierre à l’analyse de l’articulation intacte et pathologique et est prometteuse quant à la possibilité de son implantation dans la routine clinique pour évaluer les interventions chirurgicales en pré- et post-opératoire. / Three-dimensional subject-specific models are increasingly requested for surgical planning and research in biomechanics. The main objective of this cotutelle thesis was to improve the 3D reconstruction method using biplane radiography images proposed by Lagacé, Ohl et al., in order to facilitate its application in clinic, especially to assist surgical planning and/or post-surgical evaluation. The low-dose biplane radiography EOS was used and an improvement to the reconstruction method was proposed. Fourteen clinical indices used more or less routinely in clinical diagnosis for monitoring of shoulder disorders and for surgical planning and postoperative evaluation were calculated and evaluated. The accuracy is acceptable and reproducibility is similar to what is presented in the literature. The proposed approach brings an improvement of reconstruction in a context where it would be interesting for clinical routine use. Although improvements are required, this contribution brings a stone to the analysis of intact and pathological joint and is promising as to the possibility of its presence in the clinical routine for evaluating pre- and post-operative surgery.

As of June 2020, the first all-sky X-ray survey with the eROSITA instrument aboard the spacecraft Spektr-RG has been completed. A high percentage of the 1.1 million objects included in the survey are expected to be active galactic nuclei (AGN). Such an extensive catalogue of X-ray sources offers a unique opportunity for large scale observations of distinct classes of X-ray emitters. This report explores methods of refining the catalogue to include only candidates for lensed AGN. Of the differing types of AGN known, quasi-stellar objects, or QSOs, are some of the most luminous, meaning they are well-suited for observation over large distances. This is particularly befitting for observation of gravitationally lensed objects as, for lensing effects to take place, large distances are required over which more faint objects would not be able to be viewed. An indication of strong gravitational lensing is several images of the same object seen in close proximity on the sky. In order to reduce the data to more likely candidates, counterparts within a given radius are found in the second data release from Gaia; a survey in the optical with higher resolution than eROSITA. An algorithm is produced which removes most likely stellar Gaia sources using their X-ray to optical flux ratios and astrometry parameters. The Gaia sources which have no neighbours within another given radius are then also removed, leaving a catalogue of potential multiply lensed QSOs. This automated script was then applied to an eROSITA catalogue and the results compared with known lenses. The remaining sources were also checked visually using Pan-STARRS optical survey data. The results seem to be promising, although a great deal further refinement is needed through visual inspection to find the most promising candidates for lensed QSOs. / <p>Written under the joint supervision of Georg Lamer at the Leibniz Institute for Astrophysics in Potsdam. The presentation was held online at the Institute due to the COVID-19 pandemic.</p>

Dengue and Zika are two arboviral viruses that affect a significant portion of the world population. The principal vector species of both viruses are Aedes aegypti and Aedes albopictus mosquitoes. They breed in very slow flowing or standing pools of water. It is important to reduce and control such potential breeding grounds to contain the spread of these diseases. This thesis investigates a model for the detection of water bodies using high-resolution images collected by Unmanned Aerial Vehicles (UAVs) in tropical countries, exemplified by Sri Lanka, and their multispectral information to help detect water bodies where larvae are most likely to breed quickly and accurately. Although machine learning has been studied in previous work to process multispectral image information to obtain the location of water bodies, different machine learning methods have not been compared, only random forest algorithms have been used. Because Convolutional Neural Networks (CNNs) are known to provide advanced classification performance for visual recognition tasks, in this thesis, faster region-based CNNs are introduced to perform fast and accurate identification of water body locations. In order to better evaluate the experimental results, this thesis introduces Intersection over Union (IoU) as a criterion for evaluating the results. On the one hand, IoU can judge the success rate of the model for water region recognition, and on the other hand, analysis of the model recall rate under different IoU values can also evaluate the model’s ability to detect the range of water regions. Meanwhile, the basic CNN network and random forest algorithm in the previous work are also implemented to compare the results of faster region-based CNNs. In conclusion, the faster region-based CNN model achieves the best results with a 98.33% recognition success rate for water bodies in multispectral images, compared to 95.80% for the CNN model and 95.74% for the random forest model. In addition, the faster region-based CNN model significantly outperformed the CNN model and the random forest model for training speed. / Dengue och zika är två arbovirala virus som drabbar en stor del av världens befolkning. De viktigaste vektorerna för båda virusen är myggorna Aedes aegypti och Aedes albopictus. De förökar sig i mycket långsamt rinnande eller stående vattensamlingar. Det är viktigt att minska och kontrollera sådana potentiella grogrunder för att begränsa spridningen av dessa sjukdomar. I denna avhandling undersöks en modell för att upptäcka vattenområden med hjälp av högupplösta bilder som samlas in av Unmanned Aerial Vehicles (UAV) i tropiska länder, exemplifierat av Sri Lanka, och deras multispektrala information för att hjälpa till att upptäcka vattenområden där larverna sannolikt förökar sig snabbt och noggrant. Även om maskininlärning har studerats i tidigare arbeten för att bearbeta multispektral information från bilder för att få fram platsen för vattenförekomster, har olika metoder för maskininlärning inte jämförts, utan endast random forest-algoritmer har använts. Eftersom Convolutional Neural Networks (CNN) är kända för att erbjuda avancerade klassificeringsprestanda för visuella igenkänningsuppgifter i denna avhandling introduceras snabbare regionbaserade CNN för att utföra snabb och exakt identifiering av vattenkropparnas läge. För att bättre kunna utvärdera de experimentella resultaten införs i denna avhandling Intersection over Union (IoU) som ett kriterium för utvärdering av resultaten. Å ena sidan kan IoU bedöma modellens framgång för igenkänning av vattenområden, och å andra sidan kan analysen av modellens återkallningsfrekvens under olika IoU-värden också utvärdera modellens förmåga att upptäcka olika vattenområden. Samtidigt genomförs även det grundläggande CNN-nätverket och algoritmen för slumpmässig skog i det tidigare arbetet för att jämföra resultaten av Faster regionbaserad CNN. Sammanfattningsvis ger den snabbare regionbaserade CNN-modellen de bästa resultaten med 98,33% av alla igenkänningsresultat för vattenkroppar i multispektrala bilder, jämfört med 95,80% för CNN-modellen och 95,74% för modellen med slumpmässig skog. Dessutom överträffade den snabbare regionbaserade CNN-modellen CNN-modellen och random forest-modellen avsevärt när det gäller träningshastighet.