Modern clinical diagnoses and treatments have been increasingly reliant on medical imaging techniques. In return, medical images are required to provide more accurate and detailed information than ever. Aside from the evolution of hardware and software, multimodal imaging techniques offer a promising solution to produce higher quality images by fusing medical images from different modalities. This strategy utilizes more structural and/or functional image information, thereby allowing clinical results to be more comprehensive and better interpreted. Since their inception, multimodal imaging techniques have received a great deal of attention for achieving enhanced imaging performance. In this work, a novel joint reconstruction framework using sparse computed tomography (CT) and magnetic resonance imaging (MRI) data is developed and evaluated. The method proposed in this study is part of the planned joint CT-MRI system which assembles CT and MRI subsystems into a single entity. The CT and MRI images are synchronously acquired and registered from the hybrid CT-MRI platform. However, since their image data are highly undersampled, analytical methods, such as filtered backprojection, are unable to generate images of sufficient quality. To overcome this drawback, we resort to compressed sensing techniques, which employ sparse priors that result from an application of L₁-norm minimization. To utilize multimodal information, a projection distance is introduced and is tuned to tailor the texture and pattern of final images. Specifically CT and MRI images are alternately reconstructed using the updated multimodal results that are calculated at the latest step of the iterative optimization algorithm. This method exploits the structural similarities shared by the CT and MRI images to achieve better reconstruction quality. The improved performance of the proposed approach is demonstrated using a pair of undersampled CT-MRI body images and a pair of undersampled CT-MRI head images. These images are tested using joint reconstruction, analytical reconstruction, and independent reconstruction without using multimodal imaging information. Results show that the proposed method improves about 5dB in signal-to-noise ratio (SNR) and nearly 10% in structural similarity measurements compared to independent reconstruction methods. It offers a similar quality as fully sampled analytical reconstruction, yet requires as few as 25 projections for CT and a 30% sampling rate for MRI. It is concluded that structural similarities and correlations residing in images from different modalities are useful to mutually promote the quality of image reconstruction. / Ph. D. / Medical imaging techniques play a central role in modern clinical diagnoses and treatments. Consequently, there is a constant demand to increase the overall quality of medical images. Since their inception, multimodal imaging techniques have received a great deal of attention for achieving enhanced imaging performance. Multimodal imaging techniques can provide more detailed diagnostic information by fusing medical images from different imaging modalities, thereby allowing clinical results to be more comprehensive to improve clinical interpretation. A new form of multimodal imaging technique, which combines the imaging procedures of computed tomography (CT) and magnetic resonance imaging (MRI), is known as the “omnitomography.” Both computed tomography and magnetic resonance imaging are the most commonly used medical imaging techniques today and their intrinsic properties are complementary. For example, computed tomography performs well for bones whereas the magnetic resonance imaging excels at contrasting soft tissues. Therefore, a multimodal imaging system built upon the fusion of these two modalities can potentially bring much more information to improve clinical diagnoses. However, the planned omni-tomography systems face enormous challenges, such as the limited ability to perform image reconstruction due to mechanical and hardware restrictions that result in significant undersampling of the raw data. Image reconstruction is a procedure required by both computed tomography and magnetic resonance imaging to convert raw data into final images. A general condition required to produce a decent quality of an image is that the number of samples of raw data must be sufficient and abundant. Therefore, undersampling on the omni-tomography system can cause significant degradation of the image quality or artifacts after image reconstruction. To overcome this drawback, we resort to compressed sensing techniques, which exploit the sparsity of the medical images, to perform iterative based image reconstruction for both computed tomography and magnetic resonance imaging. The sparsity of the images is found by applying sparse transform such as discrete gradient transform or wavelet transform in the image domain. With the sparsity and undersampled raw data, an iterative algorithm can largely compensate for the data inadequacy problem and it can reconstruct the final images from the undersampled raw data with minimal loss of quality. In addition, a novel “projection distance” is created to perform a joint reconstruction which further promotes the quality of the reconstructed images. Specifically, the projection distance exploits the structural similarities shared between the image of computed tomography and magnetic resonance imaging such that the insufficiency of raw data caused by undersampling is further accounted for. The improved performance of the proposed approach is demonstrated using a pair of undersampled body images and a pair of undersampled head images, each of which consists of an image of computed tomography and its magnetic resonance imaging counterpart. These images are tested using the proposed joint reconstruction method in this work, the conventional reconstructions such as filtered backprojection and Fourier transform, and reconstruction strategy without using multimodal imaging information (independent reconstruction). The results from this work show that the proposed method addressed these challenges by significantly improving the image quality from highly undersampled raw data. In particular, it improves about 5dB in signal-to-noise ratio and nearly 10% in structural similarity measurements compared to other methods. It achieves similar image quality by using less than 5% of the X-ray dose for computed tomography and 30% sampling rate for magnetic resonance imaging. It is concluded that, by using compressed sensing techniques and exploiting structural similarities, the planned joint computed tomography and magnetic resonance imaging system can perform imaging outstanding tasks with highly undersampled raw data.

Visual perception has been a significant subject matter of robotics research for decades but has accelerated in recent years as both technology and community are more prepared to take on new challenges with autonomous systems. In this thesis, a framework for 3D reconstruction using a stereo camera for the purpose of obstacle detection and mapping is presented. In this application, a UAV works collaboratively with a UGV to provide high level information of the environment by using a downward facing stereo camera. The approach uses frame to frame SURF feature matching to detect candidate points within the camera image. These feature points are projected into a sparse cloud of 3D points using stereophotogrammetry for ICP registration to estimate the rigid transformation between frames. The RTK-GPS constrained pose estimate from the UAV is fused with the feature matched estimate to align the reconstruction and eliminate drift. The reconstruction was tested on both simulated and real data. The results indicate that this approach improves frame to frame registration and produces a well aligned reconstruction for a single pass compared to using the raw UAV position estimate alone. However, multi-pass registration errors occur on the order of about 0.6 meters between parallel passes, and approximately 2 degrees of local rotation error when compared to a reconstruction produced with Agisoft Metashape. However, the proposed system performed at an average frame rate of about 1.3 Hz compared to Agisoft at 0.03 Hz. Overall, the system improved obstacle registration and can perform online within existing ROS frameworks. / Master of Science / Visual perception has been a significant subject matter of robotics research for decades but has accelerated in recent years as both technology and community are more prepared to take on new challenges with autonomous systems. In this thesis, a framework for 3D reconstruction using cameras for the purpose of obstacle detection and mapping is presented. In this application, a UAV works collaboratively with a UGV to provide high level information of the environment by using a downward facing stereo camera. The approach uses features extracted from camera images to detect candidate points to be aligned. These feature points are projected into a sparse cloud of 3D points using stereo triangulation techniques. The 3D points are aligned using an iterative solver to estimate the translation and rotation between frames. The RTK (Real Time Kinematic) GPS constrained position and orientation estimate from the UAV is combined with the feature matched estimate to align the reconstruction and eliminate accumulated errors. The reconstruction was tested on both simulated and real data. The results indicate that this approach improves frame to frame registration and produces a well aligned reconstruction for a single pass compared to using the raw UAV position estimate alone. However, multi-pass registration errors occur on the order of about 0.6 meters between parallel passes that overlap, and approximately 2 degrees of local rotation error when compared to a reconstruction produced with the commercial product, Agisoft. However, the proposed system performed at an average frame rate of about 1.3 Hz compared to Agisoft at 0.03 Hz. Overall, the system improved obstacle registration and can perform online within existing Robot Operating System frameworks.

No / Elemental ratio data from archaeological and paleontological bone have often been used for paleoecological reconstruction, but recent studies have shown that, even when solubility profiling techniques are employed in an attempt to recover biogenic signals, bone is an unreliable material. As a result, there has been renewed interest in using enamel for such studies, as it is known to be less susceptible to diagenesis. Nevertheless, enamel is not immune from diagenetic processes, and several studies have suggested that paleoecologically relevant elements may be altered in fossil enamel. Here, we investigate Sr, Ba, Zn, and Pb compositions of enamel from South African karstic cave sites in an effort to ascertain whether or not this material provides reliable paleoecological information. We compared enamel data for mammals from three fossil sites aged 1.8¿3.0 Ma, all of which are on dolomites, with data from modern mammals living on dolomitic and granitic substrates. Sr/Ca and Ba/Ca are about three times higher in enamel from modern mammals on granites than those living on dolomites, stressing the need for geologically appropriate modern/fossil comparisons. After pretreatment with dilute acid, we found no evidence of increased Sr/Ca, Ba/Ca, or Pb/Ca in fossil enamel. In contrast, Zn/Ca increased by over five times at one site (Makapansgat), but much more subtly elsewhere. Ecological patterning in Sr/Ca, Ba/Ca, and Sr/Ba ratios was also retained in fossil enamel. This study suggests that Sr/Ca, Ba/Ca, and Pb/Ca data likely preserve paleoecological information from these sites, but also demonstrates that geologically similar sites can differ in the degree to which they impart certain elements (Zn in this case) to fossils. Thus, screening is probably necessary on a site-by-site basis. Lastly, further investigation of elemental distributions in modern foodwebs is necessary before elemental ratio analysis can become a common tool for paleoecological reconstruction.

Yes / The influence of the dyeing industry in Pompeii on the local economy has been under discussion since the publication by Moeller in 1976. Since no absolute answer has emerged, the question was re-examined using two additional methods, experimental archaeology and the principles of thermodynamics. A full-scale replica of a dyeing apparatus from Pompeii was constructed and used to simulate repeated dye runs, and so determine operating parameters such as the times involved to heat and cool a vat and the consumables needed. This first replica also allowed a better understanding of how the apparatus was actually used. Thermodynamic principles, which were applied to understand the successes and failures within the experimental work, suggested that the vat operated in a predictable way and enabled the operational mechanics of the vat to be established. It is now possible to use both the experimental results and the thermodynamic modelling to determine not just the consumables used, but also the working environment needed for the vat to operate, allowing an understanding of the limitations to dyeing and to workers. Issues of practicality such as storage of consumables and disposal of exhaust gases may now be thoroughly examined. 2 Eventually it will be possible to determine the operating parameters of each of the dye vats, the quantities of consumables involved and the amount that could be produced. This should help answer the question as to the significance of the dye industry in Pompeii to the local economy.

Usually, image compression techniques that use only one transform exhibit some poor properties. For instance, the Discrete Cosine Transform (DCT) cannot efficiently represent high frequency components, resulting in blurred images. The Multiple Bases Representation (MBR) compression technique, which uses two or more transforms, is found to be superior to the single transform techniques in terms of representation efficiency. However, some bits in the MBR representation are needed to track the basis information. The MBR image quality is deteriorated by discontinuities at block boundaries, as is the standard DCT transform. In this thesis, test images are distorted by MBR compression using a Recursive Residual Projection algorithm. This algorithm is a sub-optimal method to find the best basis vector subset for representing images based on multiple orthogonal bases. The MBR distorted images are reconstructed by the iterative method of Projection onto Convex Sets (POCS). Many constraints that form convex sets are reviewed and examined. Due to the high distortion at the block boundaries, some constraints are introduced particularly to reduce artifacts at the boundaries. Some constraints add energy to the reconstructed images while others remove energy. Thus, the initial vectors play a key role in the performance of the POCS method for better MBR reconstruction. This thesis also determines the most appropriate initial vector for each constraint. Finally, the composite projections associated with the sign, minimum decreasing and norm-of-slope constraints are used to improve the reconstruction of the MBR distorted images and the effect of ordering of the projections is investigated. / Master of Science

Yes / While Minimally Invasive Surgery (MIS) offers considerable benefits to patients, it also imposes big challenges on a surgeon's performance due to well-known issues and restrictions associated with the field of view (FOV), hand-eye misalignment and disorientation, as well as the lack of stereoscopic depth perception in monocular endoscopy. Augmented Reality (AR) technology can help to overcome these limitations by augmenting the real scene with annotations, labels, tumour measurements or even a 3D reconstruction of anatomy structures at the target surgical locations. However, previous research attempts of using AR technology in monocular MIS surgical scenes have been mainly focused on the information overlay without addressing correct spatial calibrations, which could lead to incorrect localization of annotations and labels, and inaccurate depth cues and tumour measurements. In this paper, we present a novel intra-operative dense surface reconstruction framework that is capable of providing geometry information from only monocular MIS videos for geometry-aware AR applications such as site measurements and depth cues. We address a number of compelling issues in augmenting a scene for a monocular MIS environment, such as drifting and inaccurate planar mapping. Methods A state-of-the-art Simultaneous Localization And Mapping (SLAM) algorithm used in robotics has been extended to deal with monocular MIS surgical scenes for reliable endoscopic camera tracking and salient point mapping. A robust global 3D surface reconstruction framework has been developed for building a dense surface using only unorganized sparse point clouds extracted from the SLAM. The 3D surface reconstruction framework employs the Moving Least Squares (MLS) smoothing algorithm and the Poisson surface reconstruction framework for real time processing of the point clouds data set. Finally, the 3D geometric information of the surgical scene allows better understanding and accurate placement AR augmentations based on a robust 3D calibration. Results We demonstrate the clinical relevance of our proposed system through two examples: a) measurement of the surface; b) depth cues in monocular endoscopy. The performance and accuracy evaluations of the proposed framework consist of two steps. First, we have created a computer-generated endoscopy simulation video to quantify the accuracy of the camera tracking by comparing the results of the video camera tracking with the recorded ground-truth camera trajectories. The accuracy of the surface reconstruction is assessed by evaluating the Root Mean Square Distance (RMSD) of surface vertices of the reconstructed mesh with that of the ground truth 3D models. An error of 1.24mm for the camera trajectories has been obtained and the RMSD for surface reconstruction is 2.54mm, which compare favourably with previous approaches. Second, \textit{in vivo} laparoscopic videos are used to examine the quality of accurate AR based annotation and measurement, and the creation of depth cues. These results show the potential promise of our geometry-aware AR technology to be used in MIS surgical scenes. Conclusions The results show that the new framework is robust and accurate in dealing with challenging situations such as the rapid endoscopy camera movements in monocular MIS scenes. Both camera tracking and surface reconstruction based on a sparse point cloud are effective and operated in real-time. This demonstrates the potential of our algorithm for accurate AR localization and depth augmentation with geometric cues and correct surface measurements in MIS with monocular endoscopes.

La science des réseaux est notamment à la recherche de modèles mathématiques capables de reproduire le comportement de systèmes complexes empiriques. Cependant, la représentation usuelle, le graphe, est parfois inadéquate étant donné sa limitation à encoder uniquement les relations par paires. De nombreux travaux récents suggèrent que l'utilisation de l'hypergraphe, une généralisation décrivant les interactions d'ordre supérieur (plus de deux composantes), permet d'expliquer des phénomènes auparavant incompris avec le graphe. Or, la structure de ces réseaux complexes est rarement ou difficilement observée directement. De fait, on mesure plutôt une quantité intermédiaire, comme la fréquence de chaque interaction, pour ensuite reconstruire la structure originale. Bien que de nombreuses méthodes de reconstruction de graphes aient été développées, peu d'approches permettent de retrouver les interactions d'ordre supérieur d'un système complexe. Dans ce mémoire, on développe une nouvelle approche de reconstruction pouvant déceler les interactions connectant trois noeuds parmi des observations dyadiques bruitées. Basée sur l'inférence bayésienne, cette méthode génère la distribution des hypergraphes les plus plausibles pour un jeu de données grâce à un algorithme de type Metropolis-Hastings-within-Gibbs, une méthode de Monte-Carlo par chaînes de Markov. En vue d'évaluer la pertinence d'un modèle d'interactions d'ordre supérieur pour des observations dyadiques, le modèle d'hypergraphe développé est comparé à un second modèle bayésien supposant que la structure sous-jacente est un graphe admettant deux types d'interactions par paires. Les résultats obtenus pour des hypergraphes synthétiques et empiriques indiquent que la corrélation intrinsèque à la projection d'interactions d'ordre supérieur améliore le processus de reconstruction lorsque les observations associées aux interactions dyadiques et triadiques sont semblables. / Network science is looking for mathematical models capable of reproducing the behavior of empirical complex systems. However, the usual representation, the graph, is sometimes inadequate given its limitation to encode only pairwise relationships. Many recent works suggest that the use of the hypergraph, a generalization describing higher-order interactions (more than two components), allows to explain phenomena previously not understood with graphs. However, the structure of these complex networks is seldom or hardly observed directly. Instead, we measure an intermediate quantity, such as the frequency of each interaction, and then reconstruct the original structure. Although many graph reconstruction methods have been developed, few approaches recover the higher-order interactions of a complex system. In this thesis, we develop a new reconstruction approach which detects interactions connecting three vertices among noisy dyadic observations. Based on Bayesian inference, this method generates the distribution of the most plausible hypergraphs for a dataset using a Metropolis-Hastings-within-Gibbs algorithm, a Markov chain Monte Carlo method. In order to evaluate the relevance of a higher-order interaction model for dyadic observations, the developed hypergraph model is compared to a second Bayesian model assuming that the underlying structure is a graph admitting two types of pairwise interactions. Results for synthetic and empirical hypergraphs indicate that the intrinsic correlation to the projection of higher-order interactions improves the reconstruction process when observations associated with dyadic and triadic interactions are similar.

La tomodensitométrie (TDM) permet d'obtenir, et ce de façon non invasive, une image tridimensionnelle de l'anatomie interne d'un sujet. Elle constitue l'évolution logique de la radiographie et permet l'observation d'un volume sous différents plans (sagittal, coronal, axial ou n'importe quel autre plan). La TDM peut avantageusement compléter la tomographie d'émission par positrons (TEP), un outil de prédilection utilisé en recherche biomédicale et pour le diagnostic du cancer. La TEP fournit une information fonctionnelle, physiologique et métabolique, permettant la localisation et la quantification de radiotraceurs à l'intérieur du corps humain. Cette dernière possède une sensibilité inégalée, mais peut néanmoins souffrir d'une faible résolution spatiale et d'un manque de repère anatomique selon le radiotraceur utilisé. La combinaison, ou fusion, des images TEP et TDM permet d'obtenir cette localisation anatomique de la distribution du radiotraceur. L'image TDM représente une carte de l'atténuation subie par les rayons-X lors de leur passage à travers les tissus. Elle permet donc aussi d'améliorer la quantification de l'image TEP en offrant la possibilité de corriger pour l'atténuation. L'image TDM s'obtient par la transformation de profils d'atténuation en une image cartésienne pouvant être interprétée par l'humain. Si la qualité de cette image est fortement influencée par les performances de l'appareil, elle dépend aussi grandement de la capacité de l'algorithme de reconstruction à obtenir une représentation fidèle du milieu imagé. Les techniques de reconstruction standards, basées sur la rétroprojection filtrée (FBP, filtered back-projection), reposent sur un modèle mathématiquement parfait de la géométrie d'acquisition. Une alternative à cette méthode étalon est appelée reconstruction statistique, ou itérative. Elle permet d'obtenir de meilleurs résultats en présence de bruit ou d'une quantité limitée d'information et peut virtuellement s'adapter à toutes formes de géométrie d'acquisition. Le présent mémoire se consacre à l'étude de ces algorithmes statistiques en imagerie TDM et à leur implantation logicielle. Le prototype d'imageur TEP/TDM basé sur la technologie LabPET[indice supérieur TM] de l'Université de Sherbrooke possède tous les pré-requis pour bénéficier de ces nombreux avantages.

Le sujet de cette thèse porte sur la reconstruction de formes à partir de coupes planaires. Dans de nombreux domaines d'application, il est nécessaire de reconstruire des formes à partir de sections. L'importance du sujet en imagerie médicale a conduit, depuis les années 1990, à des résultats importants qui sont cependant pour la plupart limités au cas de sections parallèles. Pourtant en échographie, les données obtenues au moyen d'une sonde guidée manuellement, forment une série d'images représentant des coupes de l'organe par des plans non parallèles. Cette application directe motivait le sujet de ma thèse. Dans cette thèse nous considérons le problème de la reconstruction d'une 3-variété à bord plongée dans R^3, à partir de ses intersections avec un ensemble de plans en positions arbitraires, appelées coupes. C'est pour la première fois que ce problème est étudié en toute généralité, dans le but de fournir des garanties théoriques satisfaisantes sur le résultat de la reconstruction. Aucune garantie théorique n'a été obtenue même pour le cas de coupes parallèles avant cette thèse. Dans le premier chapitre de ce manuscrit, nous étudions la méthode de reconstruction proposée par Liu et al. en 2008. Nous prouvons que si certaines conditions d'échantillonnage sont vérifiées, cette méthode permet de reconstruire la topologie de l'objet à partir des coupes données. Nous prouvons également que l'objet reconstruit est homéomorphe (et isotope) à l'objet. Le deuxième chapitre présente une nouvelle méthode de reconstruction en utilisant le diagramme de Voronoi des sections. Cette méthode permet d'établir plus de connections entre les sections par rapport à la première méthode. Favoriser les connections entre les sections est motivé par la reconstruction d'objets fins à partir de sections peu denses. Nous présentons des conditions d'échantillonnage qui sont adaptées aux objets fins et qui permettent de prouver l'équivalence homotopique entre l'objet reconstruit et l'objet de départ. En effet, nous prouvons que si les plans de coupe sont suffisamment transversales à l'objet, notre méthode de reconstruction est topologiquement valide et peut traiter des topologies complexes des sections avec plusieurs branchements. Dans le dernier chapitre de ce manuscrit, nous présentons une autre méthode de reconstruction qui permet d'établir encore plus de connections entre les sections en comparant avec les deux premières méthodes. Notre méthode est basée sur la triangulation de Delaunay et suit une approche duale en considérant le diagramme de Voronoi des sections. L'algorithme correspondant a été implémenté en C++, en utilisant la bibliothèque CGAL. Les résultats de la reconstruction obtenus par cet algorithme sont très satisfaisants pour les topologies complexes des sections. En se basant sur les études que nous avons développées durant cette thèse, nous espérons pouvoir fournir un fondement solide pour le processus d'acquisition et de reconstruction des données échographiques afin d'avoir un logiciel fiable pour les diagnostics.

L'analyse du visage est un sujet très étudié dans de nombreux domaines : Interaction Homme Machine, sécurité, post-production cinématographique, jeux video. . . Cela comprend la détection, la reconnaissance, la reconstruction 3D, l'animation et l'analyse d'émotions. L'animation du visage a été la motivation principale durant toute la thèse. Nous nous intéressons à la plupart des domaines liés au visage : tout d'abord la reconstruction 3D et la modélisation de visage, avec un nouveau modèle de visage. Ensuite, nous introduisons des contraintes anthropométriques par champs de Markov pour la détection globale de points d'intérêts. Partant de contraintes anthropométriques, nous sommes capables d'estimer la pose 3D du visage à partir d'une seule image, et de l'étendre au suivi du visage. L'analyse d'émotion conclut notre travail : nous présentons une technique de modélisation d'expression définie comme une série temporelle et proposons de l'utiliser pour la prédiction d'émotions.