Call number: LD2668 .T4 1950 D35 / Master of Science

Nous proposons dans le cadre de cette thèse une nouvelle approche permettant de s'affranchir de l'atténuation mammaire en tomographie par émission monophotonique (TEMP) de perfusion myocardique. Elle est constituée de deux parties : - la première consiste à rendre les projections acquises consistantes. - la deuxième consiste à pondérer ces même les projections corrigées durant la reconstruction. Nous avons effectué l'étude de validité de nos méthodes sur quelques exemples de simulation TEMP de perfusion myocardique simulant l'atténuation mammaire et sur quelques exemples d'études patients réelles notamment : des cas d'atténuation mammaire, d'infarctus inférieure, d'infarctus apical, d'infarctus antérieur, d'ischémie antérieure et inférieure. Les résultats semblent encourageants. Il s'agit dans le proche avenir de mener une étude de validation chez les patients versus un gold standard (coronarographie, coroscanner) / We propose in this thesis a new approach to correct the breast attenuation in SPECT myocardial perfusion imaging. It consists of two parts: -The first is to make the acquired projections consistent with each other. - The second is to weight the corrected attenuated projection during the reconstruction. We conducted a validation of our methods on some examples of myocardial perfusion SPECT imaging simulating the breast attenuation and some examples of real patient studies including: breast attenuation, anterior myocardial infarction, inferior myocardial infarction, anterior myocardial ischemia and inferior myocardial ischemia. The obtained results are encouraging. At this step, it is interesting in the near future to conduct a validation study in patients versus a gold standard (angiography, coroscan).Key words: SPECT, tomographic reconstruction, breast attenuation, Iterative reconstruction, attenuation correction, myocardial perfusion imaging, nuclear medicine

The Kaapvaal Craton was the scene of two major magmatic events around 2.0 Ga, namely the Bushveld Complex and the Phalaborwa Complex. Both complexes have been the subject of numerous palaeomagnetic studies during and prior to the 1980s. Despite these studies, systematic inconstancies for emplacement ages, in particular for the Bushveld Complex, have been found between the palaeomagnetic findings and well constrained ages. The greatest concern with the Bushveld Complex results are the large spread in pole positions previously determined for the different zones. This has been interpreted in prior studies to indicate that the Bushveld Complex was emplaced and cooled below the Curie temperature of magnetite over a time span of 50 my. The results obtained previously for the Phalaborwa Complex appear to be out of position (~16°) with respect to those for the Bushveld Complex. This is of concern because new geochronological data show that the Rustenburg Layered Suite of the Bushveld Complex was emplaced approximately 1 my after the Phalaborwa Complex. These inconsistencies have prompted the current re-investigation of the palaeomagnetic results for both the Bushveld Complex and the Phalaborwa Complex. New palaeomagnetic data collected from all zones of the Rustenburg Layered Suite from the Eastern, Northern and Western Lobes of the Bushveld Complex, yielded palaeomagnetic poles that eliminated the spread in the apparent polar wander path. This observation is in agreement with precise age data, constraining the time period of emplacement of the complex to ~ 6 my. Resulting beddingcorrected high blocking components from all zones produced better groupings, thereby supporting a primary magnetic signature and indicating that the complex was intruded in a near-horizontal position. Dual polarities identified within each zone of the complex and positive reversal tests have identified one of the oldest known reversals of the Earth’s magnetic field. iii Palaeomagnetic data from the Phalaborwa Complex have produced a pole position that is in close proximity to those obtained from the coeval Bushveld Complex. In an attempt to achieve a better understanding of tectonic events occurring in the Kaapvaal Craton a number of dual polarity dykes within the Bushvled and Phalaborwa Complexes were palaeomagnetic analysed. Results revealed that the acquired pole positions are in agreement with ~1.9 Ga dykes, indicating the possibility that the dykes occurring in both complexes are part of the same magmatic event. Palaeopoles generated during this study were used in refining the Kaapvaal Craton apparent polar wander path around 2.0 Ga, and in conjunction with other welldefined 2.0 Ga poles for the Kaapvaal Craton, a robust cratonic pole was produced that was used in Precambrian palaeographic reconstructions with emphasis on the postulated Vaalbara continent and the Columbia supercontinent. Palaeomagnetic reconstruction derived in this study has cast doubt on the existence of the Vaalbara continent at 2.0 Ga. Although, some support is given to the existence of the Columbia supercontinent at the same period.

Le raffinement de nuage de points et la reconstruction de surface sont deux problèmes fondamentaux dans le traitement de la géométrie. La plupart des méthodes existantes ont été ciblées sur les données de capteur de distance et se sont avérées être mal adaptées aux données multi-vues. Dans cette thèse, deux nouvelles méthodes sont proposées respectivement pour les deux problèmes avec une attention particulière aux données multi-vues. La première méthode permet de lisser les nuages de points provenant de la reconstruction multi-vue sans endommager les données. Le problème est formulé comme une optimisation non-linéaire sous contrainte et ensuite résolu par une série de problèmes d’optimisation sans contrainte au moyen d’une méthode de barrière. La seconde méthode effectue une triangulation du nuage de points d’entrée pour générer un maillage en utilisant une stratégie de l’avancement du front pilotée par un critère de l’empilement compact de sphères. L’algorithme est simple et permet de produire efficacement des maillages de haute qualité. Les expérimentations sur des données synthétiques et du monde réel démontrent la robustesse et l’efficacité des méthodes proposées. Notre méthodes sont adaptées aux applications qui nécessitent des informations de position précises et cohérentes telles que la photogrammétrie et le suivi des objets en vision par ordinateur / Point cloud refinement and surface reconstruction are two fundamental problems in geometry processing. Most of the existing methods have been targeted at range sensor data and turned out be ill-adapted to multi-view data. In this thesis, two novel methods are proposed respectively for the two problems with special attention to multi-view data. The first method smooths point clouds originating from multi-view reconstruction without impairing the data. The problem is formulated as a nonlinear constrained optimization and addressed as a series of unconstrained optimization problems by means of a barrier method. The second method triangulates point clouds into meshes using an advancing front strategy directed by a sphere packing criterion. The method is algorithmically simple and can produce high-quality meshes efficiently. The experiments on synthetic and real-world data have been conducted as well, which demonstrates the robustness and the efficiency of the methods. The developed methods are suitable for applications which require accurate and consistent position information such photogrammetry and tracking in computer vision

Total hip replacement (THR) is one of the most successful and most frequently performed operations. For most implants the published rate of revision at 10 years is less than 10%. However the revision rates are higher for younger and more active patients who are likely to outlive their implants. The most frequent cause of THR failure is aseptic loosening, commonly accompanied by bone loss at the implant site. THR revisions give worse functional results and fail sooner than primary THR and are complicated by this loss of bone stock. A resurfacing hip prosthesis replaces the diseased surface layer of bone and cartilage and retains the majority of the femoral head. The stress distribution in the proximal femur is closer to that in an intact hip. A conservative resurfacing prosthesis will present the surgeon with no greater problems at revision than encountered at primary conventional 11-JR. Early designs of resurfacing prosthesis conserved femoral bone stock at the expense of acetabular bone. Revision rates were high and while some failures were caused by avascular necrosis and femoral neck fracture the predominant cause was acetabular loosening. The design of a bone conserving prosthesis requires knowledge of the shape of the bony surfaces of the hip joint. A survey of the morphology of the acetabulum showed a wide variation in shape. While early resurfacing designs had hemispherical acetabular cups the bony surface is less than hemispherical. The morphology and desired range of hip motion constrain prosthesis thickness and shape. A novel resurfacing design using a polyacetal femoral component and an UHMWPE acetabular component is proposed. This bearing combination has a lower volumetric wear rate than an equivalent Co-Cr on UHWMPE bearing. Computer modelling of the resurfacing concept showed that lower moduli materials reduced stress shielding and distributed implant-bone interface stresses more evenly. Mechanical testing of polyacetal following immersion in Ringer's solution showed substantial decreases in Young's modulus while strength was unaffected.

This research addresses the problem of efficiently and robustly reconstructing semantically-rich 3D architectural models from laser-scanned point-clouds. It first covers the pre-existing literature and industrial developments in active-sensing, 3D reconstruction of the built-environment and procedural modelling. It then documents a number of novel contributions to the classical problems of change-detection between temporally varying multi-modal geometric representations and automatic 3D asset creation from airborne and ground point-clouds of buildings. Finally this thesis outlines on-going research and avenues for continued investigation - most notably fully automatic temporal update and revision management for city-scale CAD models via data-driven procedural modelling from point-clouds. In short this thesis documents the outcomes of a research project whose primary aim was to engineer fast, accurate and sparse building reconstruction algorithms. Formally: this thesis puts forward the hypothesis (and advocates) that architectural reconstruction from actively-sensed point-clouds can be addressed more efficiently and affording greater control (over the geometric results) - via deterministic procedurally-driven analysis and optimisation than via stochastic sampling.

EEG has been used to explore the electrical activity of the brain for manydecades. During that time, different components of the EEG signal have been iso-lated, characterized, and associated with a variety of brain activities. However, nowidely accepted model characterizing the spatio-temporal structure of the full-brainEEG signal exists to date.Modeling the spatio-temporal nature of the EEG signal is a daunting task. Thespatial component of EEG is defined by the locations of recording electrodes (rang-ing between 2 to 256 in number) placed on the scalp, while its temporal componentis defined by the electrical potentials the electrodes detect. The EEG signal is gen-erated by the composite electrical activity of large neuron assemblies in the brain.These neuronal units often perform independent tasks, giving the EEG signal ahighly dynamic and non-linear character. These characteristics make the raw EEGsignal challenging to work with. Thus, most research focuses on extracting andisolating targeted spatial and temporal components of interest. While componentisolation strategies like independent component analysis are useful, their effective-ness is limited by noise contamination and poor reproducibility. These drawbacks tofeature extraction could be improved significantly if they were informed by a globalspatio-temporal model of EEG data.The aim of this thesis is to introduce a novel data-surface reconstruction (DSR)technique for EEG which can model the integrated spatio-temporal structure of EEGdata. To produce physically intuitive results, we utilize a hyper-coordinate transfor-mation which integrates both spatial and temporal information of the EEG signalinto a unified coordinate system. We then apply a non-uniform rational B spline(NURBS) fitting technique which minimizes the point distance from the computedsurface to each element of the transformed data. To validate the effectiveness of thisproposed method, we conduct an evaluation using a 5-state classification problem;with 1 baseline and 4 meditation states comparing the classification accuracy usingthe raw EEG data versus the surface reconstructed data in the broadband rangeand the alpha, beta, delta, gamma and higher gamma frequencies. Results demon-strate that the fitted data consistently outperforms the raw data in the broadbandspectrum and all frequency spectrums.

Thesis (M.Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Bibliography: p. 259-263. / Architectural preservation in America has led to an increase in imitative architecture in many sectors of the profession and, as one architectural historian has pointed out, there is no historical precedent for imitative architecture. Fortunately, buildings can only rarely be preserved in a static form: they grow, evolve, and change in response to many circumstances. Too often the form of an addition or extension is determined by aligning cornice lines, using the same building materials, the same window and doors, and a similar roof structure. Essential formal issues are often not addressed. Four case studies are made, each being either an addition, an extension, or a transformation. Differing sizes and scales are explored. Accesses and circulation options are studied, as well as room sizes design decisions. Mostly drawings comprise the work, and they are additive form studies. / by Robert Peabody Brown, Jr. / M.Arch.

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稀疏性在最近的圖像恢復技術發展中起到了重要作用。在這個碩士研究中，我們專注於兩種通過信號稀疏性假設相聯繫的圖像恢復問題。具體來講，在第一個圖像恢復問題中，信號本身在某些變換域是稀疏的，例如小波變換。在本研究的第二部分，信號並非傳統意義上的稀疏，但它可以用很少的幾個參數來表示--亦即信號具有稀疏的表示。我們希望通過講述一個「雙城記」，聯繫起這兩個稀疏圖像重建問題。 / 在第二章中，我們提出了一種創新的算法框架，用於解決信號稀疏假設下的圖像恢復問題。重建圖像的目標函數，由一個數據保真項和`1正則項組成。然而，我們不是直接估計重建的圖像，而是專注於如何獲得重建的這個過程。我們的策略是將這個重建過程表示成基本閾值函數的線性組合（LET）：這些線性係數可以通過最小化目標函數解得。然後，可以更新閾值函數并迭代這個過程（i-LET）。這種線性參數化的主要優點是可以大幅降低問題的規模-每次我們只需解決一個線性係數維度大小的優化問題（通常小於十），而不是整個圖像大小的問題。如果閾值函滿足一定的條件，迭代LET算法可以保證全局的收斂性。多個測試圖像在不同噪音水平和不同卷積核類型的測試清楚地表明，我們提出的框架在所需運算時間和迭代循環次數方面，通常超越當今最好水平。 / 在第三章中，我們擴展了有限創新率採樣框架至某一種特定二維曲線。我們用掩模函數的解來間接定義這個二維曲線。這裡，掩模函數可以表示為有限數目的正弦信號加權求和。因此，從這個角度講，我們定義的二維曲線具有「有限創新率」（FRI）。由於與定義曲線相關聯的指示器圖像沒有帶寬限制，因而根據經典香農採樣定理，不能在有限數量的採樣基礎上獲得完全重建。然而，我們證明，仍然可以設計一個針對指示器圖像採樣的框架，實現完美重構。此外，對於這一方法的空間域解釋，使我們能夠拓展嚴格的FRI曲線模型用於描述自然圖像的邊緣，可以在各種圖像處理的問題中保持圖像的邊緣。我們用一個潛在的在圖像上採樣中的應用作為示例。 / Sparsity has played an important role in recent developments of various image restoration techniques. In this MPhil study, we focus on two different types of image restoration problems, which are related by the sparsity assumptions. Specifically, in the first image restoration problem, the signal (i.e. the restored image) itself is sparse in some transformation domain, e.g. wavelet. While in the second part of this study, the signal is not sparse in the traditional sense but that it can be parametrized with a few parameters hence having a sparse representation. Our goal is to tell a "tale of two cities" and to show the connections between the two sparse image restoration problems in this thesis. / In Chapter 2, we proposed a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an ℓ₁ regularization. However, instead of estimating the reconstructed image that minimizes the objective functional directly, we focus on the restoration process that maps the degraded measurements to the reconstruction. Our idea amounts to parameterizing the process as a linear combination of few elementary thresholding functions (LET) and solve for the linear weighting coefficients by minimizing the objective functional. It is then possible to update the thresholding functions and to iterate this process (i-LET). The key advantage of such a linear parametrization is that the problem size reduces dramatically--each time we only need to solve an optimization problem over the dimension of the linear coefficients (typically less than 10) instead of the whole image dimensio . With the elementary thresholding functions satisfying certain constraints, global convergence of the iterated LET algorithm is guaranteed. Experiments on several test images over a wide range of noise levels and different types of convolution kernels clearly indicate that the proposed framework usually outperform state-of-theart algorithms in terms of both CPU time and number of iterations. / In Chapter 3, we extended the sampling framework for signals with finite rate of innovation to a specific class of two-dimensional curves, which are defined implicitly as the roots of a mask function. Here the mask function has a parametric representation as weighted summation of a finite number of sinusoids, and therefore, has finite rate of innovation [1]. The associated indicator image of the defined curve is not bandlimited and cannot be perfectly reconstructed based on the classical Shannon's sampling theorem. Yet, we show that it is possible to devise a sampling scheme and have a perfect reconstruction from finite number of (noiseless) samples of the indicator image with the annihilating filter method (also known as Prony's method). Robust reconstruction algorithms with noisy samples are also developed. Furthermore, the new spatial domain interpretation of the annihilating filter enables us to generalize the exact FRI curve model to characterize edges of a natural image. We can impose the annihilation constraint to preserve edges in various image processing problems. We exemplified the effectiveness of the annihilation constraint with a potential application in image up-sampling. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Pan, Hanjie. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 69-74). / Abstracts also in Chinese. / Acknowledgments --- p.iii / Abstract --- p.vii / Contents --- p.xii / List of Figures --- p.xv / List of Tables --- p.xvii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Sampling Sparse Signals --- p.1 / Chapter 1.2 --- Thesis Organizations and Contributions --- p.3 / Chapter 2 --- An Iterated Linear Expansion of Thresholds for ℓ₁-based Image Restoration --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.1.1 --- Problem Description --- p.5 / Chapter 2.1.2 --- Approaches to Solve the Problem --- p.6 / Chapter 2.1.3 --- Proposed Approach --- p.8 / Chapter 2.1.4 --- Organization of the Chapter --- p.9 / Chapter 2.2 --- Basic Ingredients --- p.9 / Chapter 2.2.1 --- Iterative Reweighted Least Square Methods --- p.9 / Chapter 2.2.2 --- Linear Expansion of Thresholds (LET) --- p.11 / Chapter 2.3 --- Iterative LET Restoration --- p.15 / Chapter 2.3.1 --- Selection of i-LET Bases --- p.15 / Chapter 2.3.2 --- Convergence of the i-LET Scheme --- p.16 / Chapter 2.3.3 --- Examples of i-LET Bases --- p.18 / Chapter 2.4 --- Experimental Results --- p.23 / Chapter 2.4.1 --- Deconvolution with Decimated Wavelet Transform --- p.24 / Chapter 2.4.2 --- Deconvolution with Redundant Wavelet Transform --- p.28 / Chapter 2.4.3 --- Algorithm Complexity Analysis --- p.29 / Chapter 2.4.4 --- Choice of Regularization Weight λ --- p.30 / Chapter 2.4.5 --- Deconvolution with Cycle Spinnings --- p.30 / Chapter 2.5 --- Summary --- p.31 / Chapter 3 --- Sampling Curves with Finite Rate of Innovation --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.2 --- Two-dimensional Curves with Finite Rate of Innovation --- p.34 / Chapter 3.2.1 --- FRI Curves --- p.34 / Chapter 3.2.2 --- Interior Indicator Image --- p.35 / Chapter 3.2.3 --- Acquisition of Indicator Image Samples --- p.36 / Chapter 3.3 --- Reconstruction of the Annihilable Curves --- p.37 / Chapter 3.3.1 --- Annihilating Filter Method --- p.37 / Chapter 3.3.2 --- Relate Fourier Transform with Spatial Domain Samples --- p.39 / Chapter 3.3.3 --- Reconstruction of Annihilation Coe cients --- p.39 / Chapter 3.3.4 --- Reconstruction with Model Mismatch --- p.42 / Chapter 3.3.5 --- Retrieval of the Annihilable Curve Amplitudes --- p.46 / Chapter 3.4 --- Dealing with Non-ideal Low-pass Filtered Samples --- p.48 / Chapter 3.5 --- Generalization of the FRI Framework for Natural Images --- p.49 / Chapter 3.5.1 --- Spatial Domain Interpretation of the Annihilation Equation --- p.50 / Chapter 3.5.2 --- Annihilable Curve Approximation of Image Edges --- p.51 / Chapter 3.5.3 --- Up-sampling with Annihilation Constraint --- p.53 / Chapter 3.6 --- Conclusion --- p.57 / Chapter 4 --- Conclusions --- p.59 / Chapter 4.1 --- Thesis Summary --- p.59 / Chapter 4.2 --- Perspectives --- p.60 / Chapter A --- Proofs and Derivations --- p.61 / Chapter A.1 --- Proof of Lemma 3 --- p.61 / Chapter A.2 --- Proof of Theorem 2 --- p.62 / Chapter A.3 --- Efficient Implementation of IRLS Inner Loop with Matlab --- p.63 / Chapter A.4 --- Derivations of the Sampling Formula (3.7) --- p.64 / Chapter A.5 --- Correspondence between the Spatial and Fourier Domain Samples --- p.65 / Chapter A.6 --- Optimal Post-filter Applied to Non-ideal Samples --- p.66 / Bibliography --- p.69