Mesh adaptation for high-order flow simulations

Mesh adaptation has only been considered for high-order flow simulations in recent years and many techniques are still to be made more robust and efficient with curvilinear meshes required by these high-order methods. This thesis covers the developments made to improve the mesh generation and adaptation capabilities of the open-source spectral/hp element framework Nektar++ and its dedicated mesh utility NekMesh. This thesis first covers the generation of quality initial meshes typically required before an iterative adaptation procedure can be used. For optimal performance of the spectral/hp element method, quadrilateral and hexahedral meshes are preferred and two methods are presented to achieve this, either entirely or partially. The first method, inspired from cross field methods, solves a Laplace problem to obtain a guiding field from which a valid two-dimensional quadrilateral block decomposition can be automatically obtained. In turn, naturally curved meshes are generated. The second method takes advantage of the medial axis to generate structured partitions in the boundary layer region of three-dimensional domains. The method proves to be robust in generating hybrid high-order meshes with boundary layer aligned prismatic elements near boundaries and tetrahedral elements elsewhere. The thesis goes on to explore the adaptation of high-order meshes for the simulation of flows using a spectral/hp element formulation. First a new approach to moving meshes, referred to here as r-adaptation, based on a variational framework, is described. This new r-adaptation module is then enhanced by p-adaptation for the simulation of compressible inviscid flows with shocks. Where the flow is smooth, p-adaptation is used to benefit from the spectral convergence of the spectral/hp element methods. Where the flow is discontinuous, e.g. at shock waves, r-adaptation clusters nodes together to better capture these field discontinuities. The benefits of this dual, rp-adaptation approach are demonstrated through two-dimensional benchmark test cases.Open Acces

Yüz anotomisine dayalı ifade tanıma

Literatürde sunulan geometriye dayalı yüz ifadesi tanıma algoritmaları çoğunlukla araştırmacılar tarafından seçilen nirengi noktalarının devinimlerine veya yüz ifadesi kodlama sistemi (FACS) tarafından tanımlanan eylem birimlerinin etkinlik derecelerine odaklanır. Her iki yaklaşımda da nirengi noktaları, ifadenin en yoğun gözlemlendiği dudak, burun kenarları ve alın üzerinde konumlandırılır. Farklı kas etkinlikleri, birden fazla kasın etki alanında bulunan bu nirengi noktaları üzerinde benzer devinimlere neden olurlar. Bu nedenle, karmaşık ifadelerin belli noktalara konulan, sınırlı sayıdaki nirengi ile analizi oldukça zordur. Bu projede, yüz üzerinde kas etkinlik alanlarına dağıtılmış çok sayıda nirengi nokta-sının yüz ifadesinin oluşturulması sürecinde izlenmesi ile kas etkinlik derecelerinin belirlenmesini önerdik. Önerdiğimiz yüz ifadesi tanıma algoritması altı aşama içerir; (1) yüz modelinin deneğin yüzüne uyarlanması, (2) herhangi bir kasın etki alanında bulunan tüm nirengi noktalarının imge dizisinin ardışık çerçevelerinde izlenmesi, (3) baş yöneliminin belirlenmesi ve yüz modelinin imge üzerinde gözlemlenen yüz ile hizalanması, (4) yüze ait nirengi noktalarının deviniminden yola çıkarak model düğümlerinin yeni koordinatlarının kestirimi, (5) düğüm devinimlerinin kas kuvvetleri için çözülmesi, ve (6) elde edilen kas kuvvetleri ile yüz ifadesi sınıflandırılmasının yapılması. Algoritmamız, modelin yüze uyarlanması aşamasında yüz imgesi üzerinde nirengi noktalarının seçilmesi haricinde tamamen otomatiktir. Kas etkinliğine dayalı bu öznitelikleri temel ve belirsiz ifadelerin sınıflandırılması problemlerinde sınadık. Yedi adet temel yüz ifadesi üzerinde SVM sınıflandırıcısı ile %76 oranında başarı elde ettik. Bu oran, insanların ifade tanımadaki yetkinliklerine yakındır. Yedi temel ifadenin belirsiz gözlemlendiği çerçevelerde en yüksek başarıyı yine SVM sınıflandırıcısı ile %55 olarak elde ettik. Bu başarım, kas kuvvetlerinin genellikle hafif ve ani görülen istemsiz ifadelerin seziminde de başarılı olabileceğini göstermektedir. Kas kuvvetleri, yüz ifadesinin oluşturulmasındaki temel fiziksel gerçekliği yansıtan özniteliklerdir. Kas etkinliklerinin hassasiyetle kestirimi, belirsiz ifade değişikliklerinin sezimini sağladığı gibi, karmaşık yüz ifadelerinin sınıflandırılmalarını kolaylaştıracaktır. Ek olarak, araştırmacılar veya uzmanlar tarafından seçilen nirengi devinimleri ile kısıtlı kal-mayan bu yaklaşım, duygular ve yüz ifadeleri arasında bilinmeyen bağıntıların ortaya çıkarılmasını sağlayabilecektir.The geometric approaches to facial expression recognition commonly focus on the displa-cement of feature points that are selected by the researchers or the action units that aredefined by the facial action coding system (FACS). In both approaches the feature pointsare carefully located on lips, nose and the forehead, where an expression is observed at itsfull strength. Since these regions are under the influence of multiple muscles, distinct mus-cular activities could result in similar displacements of the feature points. Hence, analysisof complex expressions through a set of specific feature points is quite difficult.In this project we propose to extract the facial muscle activity levels through multiplepoints distributed over the muscular regions of influence. The proposed algorithm consistsof; (1) semi–automatic customization of the face model to a subject, (2) identification andtracking of facial features that reside in the region of influence of a muscle, (3) estimationof head orientation and alignment of the face model with the observed face, (4) estima-tion of relative displacements of vertices that produce facial expressions, (5) solving vertexdisplacements to obtain muscle forces, and (6) classification of facial expression with themuscle force features. Our algorithm requires manual intervention only in the stage ofmodel customization.We demonstrate the representative power of the proposed muscle–based features onclassification problems of seven basic and subtle expressions. The best performance onthe classification problem of basic expressions was 76%, obtained by use of SVM. Thisresult is close to the performance of humans in facial expression recognition. Our bestperformance for classification of seven subtle expressions was %55, once again by use ofSVM. This figure implies that muscle–based features are good candidates for involuntaryexpressions, which are often subtle and instantaneous.Muscle forces can be considered as the ultimate base functions that anatomicallycompose all expressions. Increased reliability in extraction of muscle forces will enabledetection and classification of subtle and complex expressions with higher precision. Mo-reover, the proposed algorithm may be used to reveal unknown mechanisms of emotionsand expressions as it is not limited to a predefined set of heuristic features.TÜBİTA

Research on generic interactive deformable 3D models: focus on the human inguinal region

The goal of this project is to research for real-time approximate methods of physicallybased animation in conjunction with static polygonal meshes with the aim of deforming them and simulating an elastic behaviour for these meshes. Because of this, in this project it has been developed a software suite capable of doing a lot of tasks, each one from different computer graphics research fields, conforming a versatile capability project

3D object reconstruction using computer vision : reconstruction and characterization applications for external human anatomical structures

Tese de doutoramento. Engenharia Informática. Faculdade de Engenharia. Universidade do Porto. 201

Computer Aided Grid Interface: An Interactive CFD Pre-Processor

NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the Computer Aided Grid Interface system (CAGI). The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and / or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system

Computer-Aided Geometry Modeling

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design

Photogrammetry as a surveying thechnique apllied to heritage constructions recording - avantages and limitations

Dissertação de Mestrado Integrado em Arquitetura, com a especialização em Arquitetura apresentada na Faculdade de Arquitetura da Universidade de Lisboa para obtenção do grau de Mestre.A presente dissertação tem por objectivo investigar e evidenciar as vantagens da aplicação da fotogrametria, e possíveis integrações com outros métodos de levantamento, como seja o varrimento laser terrestre, posicionamento por GPS, entre outros, para realizar levantamentos de construções patrimoniais ou eruditas e a respectiva produção de documentação base para viabilizar intervenções de conservação, restauro ou reabilitação. A motivação para a investigação advém da aplicação flexível, versátil, simples, acessível, e baixo-custo da fotogrametria em projectos de levantamento pequenos ou extensos. Tenciona-se igualmente colmatar as desvantagens tradicionais da fotogrametria, nomeadamente a transição entre espaços interiores e exteriores, e registo de espaços estreitos, de difícil acesso, e de geometrias complexas, num único projecto de documentação. Pretende-se ultrapassar estas dificuldades através da utilização máxima das potencialidades da fotogrametria com o uso de imagens olho de peixe e apenas como último recurso utilizar instrumentos complementares. No caso de estudo principal, o Castelo do Convento de Cristo, demonstra-se a aplicação dos métodos investigados. Nos casos de estudo secundários abordam-se problemas parcelares, desde elementos decorativos até à totalidade do edificado: Convento dos Capuchos, em Sintra; Alcáçova e trecho de muralha do Castelo de Sesimbra; Igreja de Stº André, em Mafra; entre outros. Os casos auxiliaram na determinação de procedimentos a generalizar posteriormente. Por fim, propõem-se algoritmos que auxiliam na produção de documentação.ABSTRACT: The present dissertation aims to research and demonstrate the advantages of the application of photogrammetry, and its possible integrations with other methods, such as terrestrial laser scanning, GPS positioning, and among others, to perform surveys of heritage or erudite buildings and respective production of base documentation to enable interventions of conservation, restoration, or rehabilitation. The motivation for researching is due to the flexible, versatile, simple, affordable, and low-cost application of photogrammetry in small and extensive survey projects. It is also intended to overcome the traditional disadvantages of photogrammetry, such as the transition between interior and exterior spaces, and difficulty of recording narrow, hard-to-access, and complex geometric spaces, in a single project. It is intended to overcome such challenges by maximizing the potential uses of photogrammetry with the use of fisheye images and by using other survey instruments as a last resort. In the main case study, the Castle of the Convent of Christ, the application of the investigated methods is demonstrated. In the secondary case studies, partial problems are addressed, ranging from decorative elements to the entire building: Convento dos Capuchos, in Sintra; Citadel and section of a wall of the Castle of Sesimbra; Igreja de St André, in Mafra; among others; The case studies aided in determining general procedures. Finally, algorithms that accelerate the production of documentation are proposed.N/

Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method

The doctoral thesis "Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method" aims to contribute to the development of finite element methods for the analysis of stamping processes, a problematic area with a clear industrial application. To achieve the proposed objectives, the first part of this thesis covers the solid-shell elements. This type of element is attractive for the simulation of forming processes, since any type of three-dimensional constitutive law can be formulated without the need to consider any additional conjecture. Additionally, the contact of both sides can be easily treated. This work first presents the development of a triangular prismatic solid-sheet element, for the analysis of thick and thin sheets with capacity for large deformations. This element is in total Lagrangian formulation, and uses neighboring elements to compute a field of quadratic displacements. In the original formulation, a modified right Cauchy tensor was obtained; however, in this work, the formulation is extended obtaining a modified strain gradient, which allows the concepts of push-forward and pull-back to be used. These concepts provide a mathematically consistent method for the definition of temporary derivatives of tensors and, therefore, can be used, for example, to work with elasto-plasticity. This work continues with the development of the contact formulation used, a methodology found in the bibliography on computational contact mechanics for implicit simulations. This formulation consists of an exact integration of the contact interface using mortar methods, which allows obtaining the most consistent integration possible between the integration domains, as well as the most exact possible solution. The most notable contribution of this work is the consideration of dual augmented Lagrange multipliers as an optimization method. To solve the system of equations, a semi-smooth Newton method is considered, which consists of an active set strategy, also extensible in the case of friction problems. The formulation is functional for both frictionless and friction problems, which is essential for simulating stamping processes. This frictional formulation is framed in traditional friction models, such as Coulomb friction, but the development presented can be extended to any type of friction model. The remaining necessary component for the simulation of industrial processes are the constitutive models. In this work, this is materialized in the formulation of plasticity considered. These constitutive models will be considered plasticity models for large deformations, with an arbitrary combination of creep surfaces and plastic potentials: the so-called non-associative models. To calculate the tangent tensor corresponding to these general laws, numerical implementations based on perturbation methods have been considered. Another fundamental contribution of this work is the development of techniques for adaptive remeshing, of which different approaches will be presented. On the one hand, metric-based techniques, including the level-set and Hessian approaches. These techniques are general-purpose and can be considered in both structural problems and fluid mechanics problems. On the other hand, the SPR error estimation method, more conventional than the previous ones, is presented. In this area, the contribution of this work consists in the estimation of error using the Hessian and SPR techniques for the application to numerical contact problems.La tesis doctoral "Modelos matemáticos y numéricos innovadores para el estudio de la deformación de láminas durante los procesos de conformado industrial por el Método de los Elementos Finitos" pretende contribuir al desarrollo de métodos de elementos finitos para el análisis de procesos de estampado, un área problemática con una clara aplicación industrial. De hecho, este tipo de problemas multidisciplinares requieren el conocimiento de múltiples disciplinas, como la mecánica de medios continuos, la plasticidad, la termodinámica y los problemas de contacto, entre otros. Para alcanzar los objetivos propuestos, la primera parte de esta tesis abarca los elementos de sólido lámina. Este tipo de elemento resulta atractivo para la simulación de procesos de conformado, dado que cualquier tipo de ley constitutiva tridimensional puede ser formulada sin necesidad de considerar ninguna conjetura adicional. Además, este tipo de elementos permite realizar una descripción tridimensional del cuerpo deformable, por tanto, el contacto de ambas caras puede ser tratado fácilmente. Este trabajo presenta en primer lugar el desarrollo de un elemento de sólido-lámina prismático triangular, para el análisis de láminas gruesas y delgadas con capacidad para grandes deformaciones. Este elemento figura en formulación Lagrangiana total, y emplea los elementos vecinos para poder computar un campo de desplazamientos cuadráticos. En la formulación original, se obtenía un tensor de Cauchy derecho modificado (¯C); sin embargo, en este trabajo, la formulación se extiende obteniendo un gradiente de deformación modificado (¯F), que permite emplear los conceptos de push-forward y pull-back. Dichos conceptos proveen de un método matemáticamente consistente para la definición de derivadas temporales de tensores y, por tanto, puede ser usado, por ejemplo, para trabajar con elasto-plasticidad. El elemento se basa en tres modificaciones: (a) una aproximación clásica de deformaciones transversales de corte mixtas impuestas; (b) una aproximación de deformaciones impuestas para las Componentes en el plano tangente de la lámina; y (c) una aproximación de deformaciones impuestas mejoradas en la dirección normal a través del espesor, mediante la consideración de un grado de libertad adicional. Los objetivos son poder utilizar el elemento para la simulación de láminas sin bloquear por cortante, mejorar el comportamiento membranal del elemento en el plano tangente, eliminar el bloqueo por efecto Poisson y poder tratar materiales elasto-plásticos con un flujo plástico incompresible, así como materiales elásticos cuasi-incompresibles o materiales con flujo plástico isocórico. El elemento considera un único punto de Gauss en el plano, mientras que permite considerar un número cualquiera de puntos de integración en su eje, con el objetivo de poder considerar problemas con una significativa no linealidad en cuanto a plasticidad. Este trabajo continúa con el desarrollo de la formulación de contacto empleada, una metodología que se encuentra en la bibliografía sobre la mecánica de contacto computacional para simulaciones implícitas. Dicha formulación consiste en una integración exacta de la interfaz de contacto mediante métodos de mortero, lo que permite obtener la integración más consistente posible entre los dominios de integración, así como la solución más exacta posible. La implementación también considera varios algoritmos de optimización, como la optimización mediante penalización. La contribución más notable de este trabajo es la consideración de multiplicadores de Lagrange aumentados duales como método de optimización. Estos permiten condensar estáticamente el sistema de ecuaciones, lo que permite eliminar los multiplicadores de Lagrange de la resolución y, por lo tanto, permite la consideración de solvers iterativos. Además, la formulación ha sido adecuadamente linealizada, asegurando la convergencia cuadrática del problema. Para resolver el sistema de ecuaciones, se considera un método de Newton semi-smooth, que consiste en una estrategia de set activo, extensible también en el caso de problemas friccionales. La formulación es funcional tanto para problemas sin fricción como para problemas friccionales, lo que es esencial para la simulación de procesos de estampado. Esta formulación friccional se enmarca en los modelos de fricción tradicionales, como la fricción de Coulomb, pero el desarrollo presentado puede extenderse a cualquier tipo de modelo de fricción. Esta formulación de contacto es totalmente compatible con el elemento sólido-lámina introducido en este trabajo. El componente necesario restante para la simulación de procesos industriales son los modelos constitutivos. En este trabajo, esto se ve materializado en la formulación de plasticidad considerada. Estos modelos constitutivos se considerarán modelos de plasticidad para grandes deformaciones, con una combinación arbitraria de superficies de fluencia y potenciales plásticos: los llamados modelos no asociados. Para calcular el tensor tangente correspondiente a estas leyes generales, se han considerado implementaciones numéricas basadas en métodos de perturbación. Otra contribución fundamental de este trabajo es el desarrollo de técnicas para el remallado adaptativo, de las que se presentarán distintos enfoques. Por un lado, las técnicas basadas en métricas, incluyendo los enfoques level-set y Hessiano. Estas técnicas son de propósito general y pueden considerarse tanto en la aplicación de problemas estructurales como en problemas de mecánica de fluidos. Por otro lado, se presenta el método de estimación de errores SPR, más convencional que los anteriores. En este ámbito, la contribución de este trabajo consiste en la estimación de error mediante las técnicas de Hessiano y SPR para la aplicación a problemas de contacto numérico. Con los desarrollos previamente introducidos, estaremos en disposición de introducir los casos de aplicación centrados en el contexto de procesos de estampado. Es relevante destacar que estos ejemplos son comparados con las soluciones de referencia disponibles en la bibliografía como forma de validar los desarrollos presentados hasta este punto. El presente documento está organizado de la siguiente manera. El primer capítulo establece los objetivos y revisa la bibliografía acerca de los temas clave de este trabajo. El segundo capítulo hace una introducción de la mecánica de medios continuos y los conceptos relativos al Método de los Elementos Finitos (MEF), necesarios en los desarrollos que se presentarán en los capítulos siguientes. El tercer capítulo aborda la formulación del elemento sólido-lámina, así como del elemento de lámina sin grados de libertad de rotación que inspira el sólido-lámina desarrollado. Esta parte muestra varios ejemplos académicos que son comúnmente empleados en la bibliografía como problemas de referencia de láminas. El cuarto capítulo presenta la formulación desarrollada para la resolución de problemas de contacto numérico, consistente en una formulación implícita de integración exacta mediante métodos mortero y multiplicadores de Lagrange aumentados duales. Este capítulo incluye, asimismo, varios ejemplos comúnmente encontrados en la bibliografía, que generalmente son considerados para su validación. El quinto capítulo presenta la formulación de plasticidad empleada, incluyendo algunos detalles técnicos desde el punto de vista de la implementación, así como varios ejemplos de validación. El sexto capítulo muestra los algoritmos de remallado adaptativo desarrollados en el contexto de este trabajo, y presenta varios ejemplos, que incluyen no solo casos estructurales, sino también de mecánica de fluidos. El séptimo capítulo encapsula algunos casos de validación y aplicación para procesos de estampado. El capítulo final comprende las conclusiones, así como los trabajos que podrían continuar el presente estudio.Postprint (published version

Image motion estimation for 3D model based video conferencing.

Cheung Man-kin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 116-120).Abstracts in English and Chinese.Chapter 1) --- Introduction --- p.1Chapter 1.1) --- Building of the 3D Wireframe and Facial Model --- p.2Chapter 1.2) --- Description of 3D Model Based Video Conferencing --- p.3Chapter 1.3) --- Wireframe Model Fitting or Conformation --- p.6Chapter 1.4) --- Pose Estimation --- p.8Chapter 1.5) --- Facial Motion Estimation and Synthesis --- p.9Chapter 1.6) --- Thesis Outline --- p.10Chapter 2) --- Wireframe model Fitting --- p.11Chapter 2.1) --- Algorithm of WFM Fitting --- p.12Chapter 2.1.1) --- Global Deformation --- p.14Chapter a) --- Scaling --- p.14Chapter b) --- Shifting --- p.15Chapter 2.1.2) --- Local Deformation --- p.15Chapter a) --- Shifting --- p.16Chapter b) --- Scaling --- p.17Chapter 2.1.3) --- Fine Updating --- p.17Chapter 2.2) --- Steps of Fitting --- p.18Chapter 2.3) --- Functions of Different Deformation --- p.18Chapter 2.4) --- Experimental Results --- p.19Chapter 2.4.1) --- Output wireframe in each step --- p.19Chapter 2.4.2) --- Examples of Mis-fitted wireframe with incoming image --- p.22Chapter 2.4.3) --- Fitted 3D facial wireframe --- p.23Chapter 2.4.4) --- Effect of mis-fitted wireframe after compensation of motion --- p.24Chapter 2.5) --- Summary --- p.26Chapter 3) --- Epipolar Geometry --- p.27Chapter 3.1) --- Pinhole Camera Model and Perspective Projection --- p.28Chapter 3.2) --- Concepts in Epipolar Geometry --- p.31Chapter 3.2.1) --- Working with normalized image coordinates --- p.33Chapter 3.2.2) --- Working with pixel image coordinates --- p.35Chapter 3.2.3) --- Summary --- p.37Chapter 3.3) --- 8-point Algorithm (Essential and Fundamental Matrix) --- p.38Chapter 3.3.1) --- Outline of the 8-point algorithm --- p.38Chapter 3.3.2) --- Modification on obtained Fundamental Matrix --- p.39Chapter 3.3.3) --- Transformation of Image Coordinates --- p.40Chapter a) --- Translation to mean of points --- p.40Chapter b) --- Normalizing transformation --- p.41Chapter 3.3.4) --- Summary of 8-point algorithm --- p.41Chapter 3.4) --- Estimation of Object Position by Decomposition of Essential Matrix --- p.43Chapter 3.4.1) --- Algorithm Derivation --- p.43Chapter 3.4.2) --- Algorithm Outline --- p.46Chapter 3.5) --- Noise Sensitivity --- p.48Chapter 3.5.1) --- Rotation vector of model --- p.48Chapter 3.5.2) --- The projection of rotated model --- p.49Chapter 3.5.3) --- Noisy image --- p.51Chapter 3.5.4) --- Summary --- p.51Chapter 4) --- Pose Estimation --- p.54Chapter 4.1) --- Linear Method --- p.55Chapter 4.1.1) --- Theory --- p.55Chapter 4.1.2) --- Normalization --- p.57Chapter 4.1.3) --- Experimental Results --- p.58Chapter a) --- Synthesized image by linear method without normalization --- p.58Chapter b) --- Performance between linear method with and without normalization --- p.60Chapter c) --- Performance of linear method under quantization noise with different transformation components --- p.62Chapter d) --- Performance of normalized case without transformation in z- component --- p.63Chapter 4.1.4) --- Summary --- p.64Chapter 4.2) --- Two Stage Algorithm --- p.66Chapter 4.2.1) --- Introduction --- p.66Chapter 4.2.2) --- The Two Stage Algorithm --- p.67Chapter a) --- Stage 1 (Iterative Method) --- p.68Chapter b) --- Stage 2 ( Non-linear Optimization) --- p.71Chapter 4.2.3) --- Summary of the Two Stage Algorithm --- p.72Chapter 4.2.4) --- Experimental Results --- p.72Chapter 4.2.5) --- Summary --- p.80Chapter 5) --- Facial Motion Estimation and Synthesis --- p.81Chapter 5.1) --- Facial Expression based on face muscles --- p.83Chapter 5.1.1) --- Review of Action Unit Approach --- p.83Chapter 5.1.2) --- Distribution of Motion Unit --- p.85Chapter 5.1.3) --- Algorithm --- p.89Chapter a) --- For Unidirectional Motion Unit --- p.89Chapter b) --- For Circular Motion Unit (eyes) --- p.90Chapter c) --- For Another Circular Motion Unit (mouth) --- p.90Chapter 5.1.4) --- Experimental Results --- p.91Chapter 5.1.5) --- Summary --- p.95Chapter 5.2) --- Detection of Facial Expression by Muscle-based Approach --- p.96Chapter 5.2.1) --- Theory --- p.96Chapter 5.2.2) --- Algorithm --- p.97Chapter a) --- For Sheet Muscle --- p.97Chapter b) --- For Circular Muscle --- p.98Chapter c) --- For Mouth Muscle --- p.99Chapter 5.2.3) --- Steps of Algorithm --- p.100Chapter 5.2.4) --- Experimental Results --- p.101Chapter 5.2.5) --- Summary --- p.103Chapter 6) --- Conclusion --- p.104Chapter 6.1) --- WFM fitting --- p.104Chapter 6.2) --- Pose Estimation --- p.105Chapter 6.3) --- Facial Estimation and Synthesis --- p.106Chapter 6.4) --- Discussion on Future Improvements --- p.107Chapter 6.4.1) --- WFM Fitting --- p.107Chapter 6.4.2) --- Pose Estimation --- p.109Chapter 6.4.3) --- Facial Motion Estimation and Synthesis --- p.110Chapter 7) --- Appendix --- p.111Chapter 7.1) --- Newton's Method or Newton-Raphson Method --- p.111Chapter 7.2) --- H.261 --- p.113Chapter 7.3) --- 3D Measurement --- p.114Bibliography --- p.11