Multi-frame image super-resolution focuses on reconstructing a high-resolution image from a set of low-resolution images with high similarity. Since super-resolution is an ill-posted problem, regularization techniques are widely used to constrain the minimization function. Combining image prior knowledge with fidelity model, Bayesian-based methods can effectively solve this ill-posed problem, which makes this kind of methods more popular than other methods. Our proposed model is based on maximum a posteriori probability (MAP) estimation. In this thesis, we propose a novel initialization method based on median operator to initialize our estimated high-resolution image. For the fidelity term in our proposed algorithm, the half-quadratic estimation is used to choose error norm adaptively instead of using fixed L1 or L2 norm. Furthermore, for our regularization term, we propose a novel regularization method based on Difference Curvature (DC) and Bilateral Total Variation (BTV) to suppress mixed noises and preserve image edges simultaneously. In our experimental results, synthetic data and real data are both tested to demonstrate the superiority of our proposed method in terms of clearer texture and less noise over other state-of-the-art methods.

In this paper we have developed a general theory of characteristic classes of modules. To a given invariant map defined on a Lie algebra, we associate a cohomology class by using the curvature form of a certain kind of connections. Here we present a very simple proof of the invariance theorem (Theorem 12), which states that equivalent connections give rise to the same characteristic class. We have used those invariant maps of {9} to define Chern classes of projective modules and we have derived their basic properties. It might be interesting to observe that this theory could be applied to define characteristic classes of bilinear maps. In particular, the Euler classes of {6} can be obtained in this way.

Orientador: Rene Brenzikofer / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação Fisica / Made available in DSpace on 2018-07-19T06:10:52Z (GMT). No. of bitstreams: 1 Ortale_RenataLanducci_M.pdf: 1976071 bytes, checksum: 279fd16f5e25de85f875d6b90acfe76d (MD5) Previous issue date: 1993 / Resumo: O propósito deste trabalho é apresentar um método para análise quantitativa e tridimensional da coluna vertebral em posição estática. O método apresentado utiliza registros fotográficos estereoscópicos, medição das imagens em mesa digitalizadora e análise dos dados através de programas computacionais, os quais foram desenvolvidos para agilizar os procedimentos da reconstrução e fornecer resultados quantitativos, sob a forma de gráficos, das curvaturas e das torções geométricas 3D da espinha. A reconstrução 3D dos pontos antõmicos, marcados na pele sobre os processos espinhosos da coluna vertebral, foi desenvolvido por BRENZIKOFER (1991, 1993). A análise matemática em termos de curvatura e torção geométrica 3D dos pontos anatômicos é obtida a partir de um ajuste polinomial por quadrados mínimos. Aplicamos este método em três voluntários, os quais foram submetidos a uma avaliação postural clinica, antes da realização dos experimentos fotográficos. Os pontos anatômicos foram marcados com adesivos autocolantes e contrastantes nos indivíduos na posição ereta e estática, prontos para serem fotografados. Os pontos de interesse, estenderam-se da base do occipital até o processo espinhoso da quarta vértebra lombar, somando um total de vinte pontos. Os resultados obtidos são apresentados sob a forma de seis gráficos, para cada sujeito: dois correspondem ao ajuste polinomial das projeções das curvas da coluna vertebral nos planos sagital e frontal, outros dois às curvaturas bidimensionais nos mesmos planos, um à curvatura 3D e finalmente à torção geométrica 3D. Em todos os gráficos estas variáveis estão representadas em função da coordenada vertical. Através do método ora proposto, detectamos as regiões da coluna onde aparecem as curvaturas e torções geométricas 3D. Também mostramos que o método desenvolvido permite quantificar, com boa sensibilidade, as deformidades da coluna vertebral, como por exemplo: lordoses, cifoses e escolioses. Os resultados obtidos mostraram uma boa correlação com os do diagnóstico clínico / Abstract: This paper aims at presenting a method for quantitative and tridimensional analysis of the spinal column in a static position. The method utilizes stereoscopic photographic registers, image measurement in digitalized table and data analysis using software developed in order to accelerate the reconstruction procedures and supply quantitative results in the format of graphs representing the 3D curvatures and geometrical torsions of the spinal column. The 3D reconstruction of the anatomic points, marked on the skin over the spinous processes, was developed by Brenzikofer (1991, 1993). The mathematical analysis of 3D curvature and torsion of the anatomic points is obtained through an adjustment of the parametric polynomial least square fit. This method was applied to three voluntary subjects who, before having their photographic registers taken, were submitted to a clinical posture evaluation. A total of twenty anatomic points were marked with contrasting adhesive disks. The subjects were in a static and upright position. The points of reference went from the occipital basis until the spinous process of the fourth lumbar vertebra. The results are presented in six graphs for each subject. Two graphs represent the polynomial fit of the projection of the spinal column curves in the sagittaland frontal plane. Two other graphs represent the bidimensional curvatures in the same planes. One graph represents the 3D curvature and the last one represents the geometric 3D torsion. In alI these graphs the variables are represented in function of the vertical coordinate. This method successfully detected in which areas of the spinal column 3D curvatures and geometrical torsions occur. It also enables the user to quantify, with accuracy, spinal column deformities such as, lordosis, kyphosis, and scoliosis. There is a positive correlation between the results of the proposed method and the clinical diagnosis / Mestrado / Mestre em Educação Física

Orientador: Olivâine Santana de Queiroz / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T03:06:43Z (GMT). No. of bitstreams: 1 Hitomi_EduardoEizoAramaki_M.pdf: 5800906 bytes, checksum: 04b93921a20d8ab0f71d4977b9e93e73 (MD5) Previous issue date: 2015 / Resumo: Nesta dissertação realizamos um estudo sobre o fluxo de curvatura média em espaços Euclidianos sob as perspectivas analítica e geométrica. Tratamos inicialmente da existência e regularidade de soluções em tempos pequenos de equações parabólicas quase lineares de segunda ordem em variedades Riemannianas, o que é essencial para garantirmos a existência de uma solução suave em tempo pequeno do fluxo de curvatura média. Em uma segunda parte, passamos a alguns resultados sobre o comportamento no intervalo maximal de existência de uma solução suave da hipersuperfície em evolução, por meio de equações das componentes geométricas associadas e de Princípios de Máximo. Próximo desse tempo maximal, analisamos a formação de singularidades do Tipo I por meio da Fórmula de Monotonicidade de Huisken e de rescalings, e do Tipo II por meio de uma técnica de blow-up devida a Hamilton. Em especial, reservamos o caso de curvas a um capítulo a parte e apresentamos resultados clássicos da teoria de curve-shortening flows / Abstract: In this dissertation we study the mean curvature flow in Euclidean spaces from the analytic and geometric point of view. We deal initially with short-time existence and regularity of a solution for second order quasilinear parabolic equations on Riemannian manifolds, which is essential to guarantee the short-time existence of a smooth solution to the mean curvature flow. In a second part, we present some results concerning the behavior of the evolving hypersurface close to the maximal time of existence of a smooth solution, by means of Maximum Principles and evolution equations of the associated geometric components. Close to this maximal time, we analyse the formation of singularities of Type I by means of rescalings and Huisken's Monotonicity Formula, and of Type II by means of a blow-up technique due to Hamilton. In particular, we reserve the case of curves to a separate chapter, where we present some classical results in curve-shortening flow theory / Mestrado / Matematica / Mestre em Matemática

We numerically investigate crystalline order on negative Gaussian curvature capillary bridges. In agreement with the experimental results in [W. Irvine et al., Nature, Pleats in crystals on curved surfaces, 2010, 468, 947] we observe for decreasing integrated Gaussian curvature, a sequence of transitions, from no defects to isolated dislocations, pleats, scars and isolated sevenfold disclinations. We especially focus on the dependency of topological charge on the integrated Gaussian curvature, for which we observe, again in agreement with the experimental results, no net disclination for an integrated curvature down to −10, and an approximately linear behavior from there on until the disclinations match the integrated curvature of −12. In contrast to previous studies in which ground states for each geometry are searched for, we here show that the experimental results, which are likely to be in a metastable state, can be best resembled by mimicking the experimental settings and continuously changing the geometry. The obtained configurations are only low energy local minima. The results are computed using a phase field crystal approach on catenoid-like surfaces and are highly sensitive to the initialization.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22975号 / 理博第4652号 / 新制||理||1668(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 山口 孝男, 教授 藤原 耕二, 教授 入谷 寛 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this thesis, research starts by questioning Berry curvature dipole's role in electronic properties in solids. Strongly inspired by the recent studies, we discover a more profound interpretation of the Berry curvature dipole. It is demonstrated that the anomalous correction to the electron acceleration is proportional to the Berry curvature dipole and is responsible for the Non-linear Hall effect recently discovered in materials with broken inversion symmetry. This allows uncovering a deeper meaning of the Berry curvature dipole as a non-linear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. Later, we introduce the Quantum Rectification Sum Rule in time-reversal invariant materials is derived by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies or relaxation rates. In the final part of the thesis, we use the Keldysch-Floquet formalism to obtain non-perturbative predictions of the optical responses in solids, mainly focusing on the clean limit response of systems with broken time-reversal symmetry.

This diploma thesis deals with simulation of cross-roll straightening using computational modeling with finite element method in software ANSYS. The main goal of this thesis is to quantify the influence of inaccurate knowledge of mechanical properties on the straightening process and correct setting of machine. It also aims for comparison of hardening models and their influence on the final curvature and residual stresses in the cross section of the bar.

<div>In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.</div>

Thin films have become very important in the past years as there is a tremendous increase in the need for small-scale devices. Thin films are preferred because of their electrical, mechanical, chemical, and other unique properties. They are often used for coatings, and in the fabrication of Microelectronic devices and Micro-electro Mechanical Systems (MEMS). Internal (residual) stress always exists when a thin film is employed in the device design. Residual and thermal stresses cause membrane bow, altering the anticipated dynamic response of a membrane-based MEMS design. The device may even become inoperable under the high stresses conditions. As a result, the stresses that act upon the membrane should be minimized for optimum operation of a MEMS device. In this research, the fabrication process parameters leading to low stress silicon nitride films were investigated. Silicon nitride was deposited using Plasma Enhanced Chemical Vapor Deposition (PECVD) and the residual stresses on these films were determined using a wafer curvature technique. By adjusting the silane (SiH4) and nitrogen (N2) gas flow rates, and the radiofrequency (RF) power; high quality silicon nitride films with residual stress as low as 11 MPa were obtained. Furthermore, an analytical study was also conducted to explore the effect of thermal stresses between layers of thin films on the MEMS device operation. In this thesis, we concentrated our efforts on three layers of thin films, as that is the most commonly encountered in a membrane based MEMS device. The results obtained from a parametric study of the membrane center deflection indicate that the deflection can be minimized by the appropriate choice of materials used. In addition, our results indicate that thin films with similar coefficient of thermal expansion should be employed in the design to minimize the deflection of the membrane, leading to anticipated device operation and increased yield. A complete understanding of the thermal and residual stress in MEMS structures can improve survival rate during fabrication, thereby increasing yield and ultimately reducing the device cost. In addition, reliability, durability, and overall performance of membrane-based structures are improved when substrate curvature and membrane deflection caused by stresses are kept at a minimum.