The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.

Semantic labeling is becoming more and more popular among researchers in computer vision and machine learning. Many applications, such as autonomous driving, tracking, indoor navigation, augmented reality systems, semantic searching, medical imaging are on the rise, requiring more accurate and efficient segmentation mechanisms. In recent years, deep learning approaches based on Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have dramatically emerged as the dominant paradigm for solving many problems in computer vision and machine learning. The main focus of this thesis is to investigate robust approaches that can tackle the challenging semantic labeling tasks including semantic instance segmentation and scene understanding. In the first approach, we convert the classic variational Level Set method to a learnable deep framework by proposing a novel definition of contour evolution named Recurrent Level Set (RLS). The proposed RLS employs Gated Recurrent Units to solve the energy minimization of a variational Level Set functional. The curve deformation processes in RLS is formulated as a hidden state evolution procedure and is updated by minimizing an energy functional composed of fitting forces and contour length. We show that by sharing the convolutional features in a fully end-to-end trainable framework, RLS is able to be extended to Contextual Recurrent Level Set (CRLS) Networks to address semantic segmentation in the wild problem. The experimental results have shown that our proposed RLS improves both computational time and segmentation accuracy against the classic variational Level Set-based methods whereas the fully end-to-end system CRLS achieves competitive performance compared to the state-of-the-art semantic segmentation approaches on PAS CAL VOC 2012 and MS COCO 2014 databases. The second proposed approach, Contextual Recurrent Residual Networks (CRRN), inherits all the merits of sequence learning information and residual learning in order to simultaneously model long-range contextual infor- mation and learn powerful visual representation within a single deep network. Our proposed CRRN deep network consists of three parts corresponding to sequential input data, sequential output data and hidden state as in a recurrent network. Each unit in hidden state is designed as a combination of two components: a context-based component via sequence learning and a visualbased component via residual learning. That means, each hidden unit in our proposed CRRN simultaneously (1) learns long-range contextual dependencies via a context-based component. The relationship between the current unit and the previous units is performed as sequential information under an undirected cyclic graph (UCG) and (2) provides powerful encoded visual representation via residual component which contains blocks of convolution and/or batch normalization layers equipped with an identity skip connection. Furthermore, unlike previous scene labeling approaches [1, 2, 3], our method is not only able to exploit the long-range context and visual representation but also formed under a fully-end-to-end trainable system that effectively leads to the optimal model. In contrast to other existing deep learning networks which are based on pretrained models, our fully-end-to-end CRRN is completely trained from scratch. The experiments are conducted on four challenging scene labeling datasets, i.e. SiftFlow, CamVid, Stanford background, and SUN datasets, and compared against various state-of-the-art scene labeling methods.

[EN] The main topic of the present thesis is the improvement of fabrication processes simulation by means of the Level Set (LS) method. The LS is a mathematical approach used for evolving fronts according to a motion defined by certain laws. The main advantage of this method is that the front is embedded inside a higher dimensional function such that updating this function instead of directly the front itself enables a trivial handling of complex situations like the splitting or coalescing of multiple fronts. In particular, this document is focused on wet and dry etching processes, which are widely used in the micromachining process of Micro-Electro-Mechanical Systems (MEMS). A MEMS is a system formed by mechanical elements, sensors, actuators, and electronics. These devices have gained a lot of popularity in last decades and are employed in several industry fields such as automotive security, motion sensors, and smartphones. Wet etching process consists in removing selectively substrate material (e.g. silicon or quartz) with a liquid solution in order to form a certain structure. This is a complex process since the result of a particular experiment depends on many factors, such as crystallographic structure of the material, etchant solution or its temperature. Similarly, dry etching processes are used for removing substrate material, however, gaseous substances are employed in the etching stage. In both cases, the usage of a simulator capable of predicting accurately the result of a certain experiment would imply a significant reduction of design time and costs. There exist a few LS-based wet etching simulators but they have many limitations and they have never been validated with real experiments. On the other hand, atomistic models are currently considered the most advanced simulators. Nevertheless, atomistic simulators present some drawbacks like the requirement of a prior calibration process in order to use the experimental data. Additionally, a lot of effort must be invested to create an atomistic model for simulating the etching process of substrate materials with different atomistic structures. Furthermore, the final result is always formed by unconnected atoms, which makes difficult a proper visualization and understanding of complex structures, thus, usually an additional visualization technique must be employed. For its part, dry etching simulators usually employ an explicit representation technique to evolve the surface being etched according to etching models. This strategy can produce unrealistic results, specially in complex situations like the interaction of multiple surfaces. Despite some models that use implicit representation have been published, they have never been directly compared with real experiments and computational performance of the implementations have not been properly analysed. The commented limitations are addressed in the various chapters of the present thesis, producing the following contributions: - An efficient LS implementation in order to improve the visual representation of atomistic wet etching simulators. This implementation produces continuous surfaces from atomistic results. - Definition of a new LS-based model which can directly use experimental data of many etchant solutions (such as KOH, TMAH, NH4HF2, and IPA and Triton additives) to simulate wet etching processes of various substrate materials (e.g. silicon and quartz). - Validation of the developed wet etching simulator by comparing it to experimental and atomistic simulator results. - Implementation of a LS-based tool which evolves the surface being etched according to dry etching models in order to enable the simulation of complex processes. This implementation is also validated experimentally. - Acceleration of the developed wet and dry etching simulators by using Graphics Processing Units (GPUs). / [ES] El tema principal de la presente tesis consiste en mejorar la simulación de los procesos de fabricación utilizando el método Level Set (LS). El LS es una técnica matemática utilizada para la evolución de frentes según un movimiento definido por unas leyes. La principal ventaja de este método es que el frente está embebido dentro de una función definida en una dimensión superior. Actualizar dicha función en lugar del propio frente permite tratar de forma trivial situaciones complejas como la separación o la colisión de diversos frentes. En concreto, este documento se centra en los procesos de atacado húmedo y seco, los cuales son ampliamente utilizados en el proceso de fabricación de Sistemas Micro-Electro-Mecánicos (MEMS, de sus siglas en inglés). Un MEMS es un sistema formado por elementos mecánicos, sensores, actuadores y electrónica. Estos dispositivos hoy en día son utilizados en muchos campos de la industria como la seguridad automovilística, sensores de movimiento y teléfonos inteligentes. El proceso de atacado húmedo consiste en eliminar de forma selectiva el material del sustrato (por ejemplo, silicio o cuarzo) con una solución líquida con el fin de formar una estructura específica. Éste es un proceso complejo pues el resultado depende de muchos factores, tales como la estructura cristalográfica del material, la solución atacante o su temperatura. De forma similar, los procesos de atacado seco son utilizados para eliminar el material del sustrato, sin embargo, se utilizan sustancias gaseosas en la fase de atacado. En ambos casos, la utilización de un simulador capaz de predecir de forma precisa el resultado de un experimento concreto implicaría una reducción significativa del tiempo de diseño y de los costes. Existen unos pocos simuladores del proceso de atacado húmedo basados en el método LS, no obstante tienen muchas limitaciones y nunca han sido validados con experimentos reales. Por otro lado, los simuladores atomísticos son hoy en día considerados los simuladores más avanzados pero tienen algunos inconvenientes como la necesidad de un proceso de calibración previo para poder utilizar los datos experimentales. Además, debe invertirse mucho esfuerzo para crear un modelo atomístico para la simulación de materiales de sustrato con distintas estructuras atomísticas. Asimismo, el resultado final siempre está formado por átomos inconexos que dificultan una correcta visualización y un correcto entendimiento de aquellas estructuras complejas, por tanto, normalmente debe emplearse una técnica adicional para la visualización de dichos resultados. Por su parte, los simuladores del proceso de atacado seco normalmente utilizan técnicas de representación explícita para evolucionar, según los modelos de atacado, la superficie que está siendo atacada. Esta técnica puede producir resultados poco realistas, sobre todo en situaciones complejas como la interacción de múltiples superficies. A pesar de que unos pocos modelos son capaces de solventar estos problemas, nunca han sido comparados con experimentos reales ni el rendimiento computacional de las correspondientes implementaciones ha sido adecuadamente analizado. Las expuestas limitaciones son abordadas en la presente tesis y se han producido las siguientes contribuciones: - Implementación eficiente del método LS para mejorar la representación visual de los simuladores atomísticos del proceso de atacado húmedo. - Definición de un nuevo modelo basado en el LS que pueda usar directamente los datos experimentales de muchos atacantes para simular el proceso de atacado húmedo de diversos materiales de sustrato. - Validación del simulador comparándolo con resultados experimentales y con los de simuladores atomísticos. - Implementación de una herramienta basada en el método LS que evolucione la superficie que está siendo atacada según los modelos de atacado seco para habilitar la simulación de procesos comple / [CAT] El tema principal de la present tesi consisteix en millorar la simulació de processos de fabricació mitjançant el mètode Level Set (LS). El LS és una tècnica matemàtica utilitzada per a l'evolució de fronts segons un moviment definit per unes lleis en concret. El principal avantatge d'aquest mètode és que el front està embegut dins d'una funció definida en una dimensió superior. D'aquesta forma, actualitzar la dita funció en lloc del propi front, permet tractar de forma trivial situacions complexes com la separació o la col·lisió de diversos fronts. En concret, aquest document es centra en els processos d'atacat humit i sec, els quals són àmpliament utilitzats en el procés de fabricació de Sistemes Micro-Electro-Mecànics (MEMS, de les sigles en anglès). Un MEMS és un sistema format per elements mecànics, sensors, actuadors i electrònica. Aquests dispositius han guanyat molta popularitat en les últimes dècades i són utilitzats en molts camps de la indústria, com la seguretat automobilística, sensors de moviment i telèfons intel·ligents. El procés d'atacat humit consisteix en eliminar de forma selectiva el material del substrat (per exemple, silici o quars) amb una solució líquida, amb la finalitat de formar una estructura específica. Aquest és un procés complex ja que el resultat de un determinat experiment depèn de molts factors, com l'estructura cristal·logràfica del material, la solució atacant o la seva temperatura. De manera similar, els processos d'atacat sec son utilitzats per a eliminar el material del substrat, no obstant, s'utilitzen substàncies gasoses en la fase d'atacat. En ambdós casos, la utilització d'un simulador capaç de predir de forma precisa el resultat d'un experiment en concret implicaria una reducció significativa del temps de disseny i dels costos. Existeixen uns pocs simuladors del procés d'atacat humit basats en el mètode LS, no obstant tenen moltes limitacions i mai han sigut validats amb experiments reals. Per la seva part, els simuladors atomístics tenen alguns inconvenients com la necessitat d'un procés de calibratge previ per a poder utilitzar les dades experimentals. A més, deu invertir-se molt d'esforç per crear un model atomístic per a la simulació de materials de substrat amb diferents estructures atomístiques. Així mateix, el resultat final sempre està format per àtoms inconnexos que dificulten una correcta visualització i un correcte enteniment d'aquelles estructures complexes, per tant, normalment deu emprar-se una tècnica addicional per a la visualització d'aquests resultats. D'altra banda, els simuladors del procés d'atacat sec normalment utilitzen tècniques de representació explícita per evolucionar, segons els models d'atacat, la superfície que està sent atacada. Aquesta tècnica pot introduir resultats poc realistes, sobretot en situacions complexes com per exemple la interacció de múltiples superfícies. A pesar que uns pocs models son capaços de resoldre aquests problemes, mai han sigut comparats amb experiments reals ni tampoc el rendiment computacional de les corresponents implementacions ha sigut adequadament analitzat. Les exposades limitacions son abordades en els diferents capítols de la present tesi i s'han produït les següents contribucions: - Implementació eficient del mètode LS per millorar la representació visual dels simuladors atomístics del procés d'atacat humit. - Definició d'un nou model basat en el mètode LS que puga utilitzar directament les dades experimentals de molts atacants per a simular el procés d'atacat humit de diversos materials de substrat. - Validació del simulador d'atacat humit desenvolupat comparant-lo amb resultats experimentals i amb els de simuladors atomístics. - Implementació d'una ferramenta basada en el mètode LS que evolucione la superfície que està sent atacada segons els models d'atacat sec per, d'aquesta forma, habilitar la simulació de processo / Montoliu Álvaro, C. (2015). Study, Modelling and Implementation of the Level Set Method Used in Micromachining Processes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/58609 / TESIS

The aim of the thesis was familiarity of segmentation methods for automatic segmentation of MR images, using multiparametrical display. The theoretical part focuses on the description of methods of segmentation techniques. In the practical part are implemented K-means and level-set method. The methods are tested on the images of the brain obtained by different sequences (T1, T1c, T2, FLAIR). Segmentation methods are implemented in the program MATLAB. Implemented segmentation accuracy is demonstrated on data which there are reports reference results. Evaluation methods is performed using different classifiers decision. The K-means method is tested different metrics and different combinations of the input image. Finally, both methods are compared with one another and visually evaluated against the reference image.

Memoria para optar al título de Ingeniero Civil Matemático / El objetivo principal de este trabajo es estudiar un problema inverso geométrico con ruido estocástico, que consiste en una EDP lineal asociada a un funcional no lineal de mínimos. cuadrados. Posteriormente se quiere realizar un proceso de reconstrucción numérica con el objetivo de comparar la solución obtenida de forma determinista con la solución obtenida con ruido estocástico. Para la primera parte de este trabajo nos basamos en el estudio de Allaire y Dapogny [21]. Para la otra parte nos basamos en el método level set introducido por Osher y Sethian [18]. Dentro del enfoque estándar de resolución de problemas inversos geométricos está el parametrizar la forma geométrica y aplicar métodos de regularización a la parametrización. Este enfoque sufre de la limitación que para obtener aproximaciones convergentes se tiene que tener un conocimiento a priori de la estructura y topología de la forma geométrica buscada. Por la no linealidad del funcional, las derivadas de forma de segundo orden son complicadas de trabajar en su forma explícita, motivo por el cual es complicado aplicar un método de level set desde el punto de vista clásico, nos basaremos en la idea de level set para aplicar un método que solo use las derivadas de forma de primer orden. / PIA/Concurso de Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal AFB170001 CMM UMI 2807 CNRS y Fondecyt 1171854

In this thesis we introduce a new fluid-structure interaction model in the Eulerian description. This model is developed for blood flow in viscoelastic artery. For the fluid part a non-Newtonian model Oldroyd-B is used and for the structure part Kelvin-Voigt model is employed. Kelvin-Voigt model will be reached by a limiting process of the Oldroyd-B model. Interface between these two materials is guaranteed by conservative level-set method. Numerical tests of this model is performed by finite element method. This model is used for a simulation of two problems: a two dimensional channel with viscoelastic walls and pulsating inflow and Turek-Hron FSI benchmark. 1

Distributed modal filters based on piezoelectric polymer have especially become popular in the field of active vibration control to reduce the problem of spillover. While distributed modal filters for one-dimensional structures can be found analytically based on the orthogonality between the mode shapes, the design for two-dimensional structures is not straightforward. It requires a continuous gain variation in two dimensions, which is not realizable from the current manufacturing point of view. In this thesis, a structural optimization problem is considered to approximate distributed modal sensors for two-dimensional plate structures, where the thickness is constant but the polarization can switch between positive and negative. The problem is solved through an explicit parametric level set method. In this framework, the boundary of a domain is represented implicitly by the zero isoline of a level set function. This allows simultaneous shape and topology changes. The level set function is approximated by a linear combination of Gaussian radial basis functions. As a result, the structural optimization problem can be directly posed in terms of the parameters of the approximation. This allows to apply standard optimization methods and bypasses the numerical drawbacks, such as reinitialization, velocity extension and regularization, which are associated with the numerical solution of the Hamilton-Jacobi equation in conventional methods.Since the level set method based on the shape derivative formally only allows shape but not topology transformation, the optimization problem is firstly tackled with a derivative-free optimization algorithm. It is shown that the approach is able to find approximate modal sensor designs with only few design variables. However, this approach becomes unsuitable as soon as the number of optimization variables is growing. Therefore, a sensitivity-based optimization approach is being applied, based on the parametric shape derivative which is with respect to the parameters of the radial basis functions. Although the shape derivatives does not exist at points where the topology changes, it is demonstrated that an optimization routine based on a SQP solver is able to perform topological changes during the optimization and finds optimal designs even from poor initial designs. In order to include the sensors' distribution as design variable, the parametric level set approach is extended to multiple level sets. It turns out that, despite the increased design space, optimal solutions always converge to full-material polarization designs. Numerical examples are provided for a simply supported as well as a cantilever square plate. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Consider a mixture of two immiscible, incompressible fluids e.g. oil and water. Since the fluids do not mix, an interface between the two fluids will form and move in time. The motion of the two fluids can be modelled by the incompressible Navier-Stokes equations for two phase flow with surface tension together with a representation of the moving interface. The parameters in the Navier-Stokes equations will depend on the position and other properties of the interface. The interface should move with the velocity of the flow at the interface. Since the fluids are incompressible, the density of each fluid is constant. Mass conservation then implies that the volume occupied by each of the two fluids should not change with time. The object of this thesis has been to develop a new numerical method to simulate incompressible two phase flow accurately that conserves mass and volume of each fluid correctly. Numerical simulations of incompressible two phase flow with surface tension have been a challenge for many years. Several methods have been developed and used prior to the work presented in this thesis. The two most commonly used methods are volume of fluid methods and level set methods. There are advantages and disadvantages of both of the methods. In volume of fluid methods the interface is represented by a discontinuity of a globally defined function. Because of the discontinuity it is hard both to move the interface as well as to calculate properties of the interface such as curvature. Specially designed methods have to be used, and all these methods are low order accurate. Volume of fluid methods do however conserve the volumes of the two fluids correctly. In level set methods the interface is represented by the zero contour of the globally defined signed distance function. This function is smooth across the interface. Since the function is smooth, standard methods for partial differential equations can be used to advect the interface accurately. A reinitialization is however needed to make sure that the level set function remains a signed distance function. During this process the zero contour might move slightly. Because of this, the volume conservation of the method becomes poor. In this thesis we present a new level set method. The method is designed such that the volume of each fluid is conserved, at least approximately. The interface is represented by the 0.5 contour of a regularized characteristic function. As for standard level set methods, the interface is moved first by an advective step, and then reinitialized. Unlike traditional level set methods, we can formulate the reinitialization as a conservation law. Conservative methods can then be used to move and to reinitialize the level set function numerically. Since the level set function is a regularized characteristic function, we can expect good conservation of the volume bounded by the interface. The method is discretized using both finite differences and finite elements. Uniform and adaptive grids are used in both two and three space dimensions. Good convergence as well as volume conservation is observed. Theoretical studies are performed to investigate the conservation and the computational time needed for reinitialization. / QC 20101122

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18469号 / 工博第3905号 / 新制||工||1599(附属図書館) / 31347 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 椹木 哲夫, 教授 松原 厚 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(農学) / 甲第23527号 / 農博第2474号 / 新制||農||1087(附属図書館) / 学位論文||R3||N5358(農学部図書室) / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 中村 公人, 准教授 宇波 耕一 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DGAM