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On a certain class of cyclically presented groupsSpanu, Bruno January 2009 (has links)
Abstract. The present thesis is devoted to the study of a class of cyclically presented groups, an important theme in combinatorial group theory. 1. Introduction We introduce the cyclic presentations which will be the object of our study. We explain why these are important and we state some known results. In view of this we propose a conjecture (Conjecture 1.2.7) to which we give a partial answer in the following chapters. We finally give a definition of irreducibility, p-irreducibility and f-irreducibility for a presentation in the class which we are studying. 2. Method of proof Here we give a short report on split extensions and (van Kampen) diagrams, which are the two basic ingredients involved in our proofs. We then outline the method of proof, which is a generalization of the method used in [11] and makes use of an analysis of modified diagrams. 3. The p-irreducible case We start giving a geometric constraint on diagrams and we show, as described in Chapter 2, that a presentation whose diagram respects this constraint gives rise to an infinite group. After studying four particular cases we give conditions on the integer parameters of a presentation in the class considered in order to have a diagram which satisfies the given geometric constraint. Finally, we prove Theorem 2 which partially answers Conjecture 1.2.7 in the p-irreducible case. 4. The f-irreducible case Given certain constraints the problem is reduced to a particular case. We then study this case as outlined in Chapter 2. We also show that these constraints can be weakened if the number of generators is odd. 5. Conclusions We show how the results achieved can be used to prove a theorem in a more general setting; we explain what one should prove in order to confirm Conjecture 1.2.7 and why our method fails in these cases.
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Extending procrustes analysis : building multi-view 2-D models from 3-D human shape samplesPérez Sala, Xavier 29 April 2015 (has links)
This dissertation formalizes the construction of multi-view 2D shape models from 3D data. We propose several extensions of the well-known Procrustes Analysis (PA) algorithm that allow modeling rigid and non-rigid transformations in an efficient manner. The proposed strategies are successfully tested on faces and human bodies datasets.
In human perception applications one can set physical restrictions, such as defining faces and human skeletons as sets of anatomical landmarks or articulated bodies. However, the high variation of facial expressions and human postures from different viewpoints makes problems like face tracking or human pose estimation extremely challenging. The common approach to handle large viewpoint variations is training the models with several labeled images from different viewpoints. However, this approach has several important drawbacks: (1) it is not clear how much it is necessary to enhance the dataset with images from different viewpoints in order to build unbiased 2D models; (2) extending the training set without this evaluation would unnecessarily increase memory and computation requirements to train the models; and (3) obtaining new labeled images from different viewpoints can be a difficult task because of the expensive labeling cost; finally, (4) a non-uniform coverage of the different viewpoints of a person leads to biased 2D models. In this dissertation we propose successive extensions of PA to address these issues.
First of all, we introduce Projected Procrustes Analysis (PPA) as a formalization for building multi-view 2D rigid models from 3D datasets. PPA rotates and projects every 3D training shape and builds a multi-view 2D model from this enhanced training set. We also introduce common parameterizations of rotations, as well as mechanisms to uniformly sample the rotation space. We show that uniformly distributed rotations generate unbiased 2D models, while non-uniform rotations lead to models representing some viewpoints better than others.
Although PPA has been successful in building multi-view 2D models, it requires an enhanced dataset that increases the computational requirements in space and time. In order to address these PA and PPA drawbacks, we propose Continuous Procrustes Analysis (CPA). CPA extends PPA within a functional analysis framework and constructs multi-view 2D rigid models in an efficient way through integrating all possible rotations in a given domain. We show that CPA models are inherently unbiased because of their integral formulation. However, CPA is not able to capture non-rigid deformations from the dataset.
Next, in order to efficiently compute multi-view 2D deformable models from 3D data, we introduce Subspace Procrustes Analysis (SPA). By adding a subspace in the PA formulation, SPA is able to model non-rigid deformations, as well as rigid 3D transformations of the training set. We developed a discrete (DSPA) and continuous (CSPA) formulation to provide a better understanding of the problem, where DSPA samples and CSPA integrates the 3D rotation space.
Finally, we illustrate the benefits of our multi-view 2D deformable models in the task of human pose estimation. We first reformulate the problem as feature selection by subspace matching, and propose an efficient approach for this task. Our method is much more efficient than the state-of-the-art feature selection by subspace matching approaches, and it is able to handle larger number of outliers. Next, we show that our multi-view 2D deformable models, combined with the subspace matching method, outperform state-of-the-art methods of human pose estimation. Our approach is more accurate in the joint positions and limb lengths because we use unbiased 2D models trained on 3D Motion Capture datasets. Our models are not biased to any particular point of view and they can successfully reconstruct different non-rigid deformations and viewpoints. Moreover, they are efficient in both learning and test times. / En esta tesis se formaliza la construcción de modelos multivista 2D a partir de datos 3D, a través de varias extensiones del conocido método Procrustes Analysis (PA). Las extensiones propuestas permiten modelar transformaciones rígidas y no rígidas eficientemente, y se han puesto a prueba en bases de datos de caras y cuerpos humanos. Las aplicaciones donde se perciben humanos permiten establecer restricciones físicas, tales como definir caras y esqueletos como conjuntos de puntos anatómicos. Sin embargo, la gran variación que sufren las expresiones faciales y las posturas humanas desde distintos puntos de vista convierten problemas como el seguimiento de caras o la estimación de la postura humana en retos extremadamente complejos. El planteamiento habitual para gestionar grandes variaciones de punto de vista consiste en entrenar los modelos con imágenes etiquetadas tomadas con distintas orientaciones. Sin embargo, este enfoque sufre importantes inconvenientes: (1) no queda claro cuántas imágenes adicionales con distintas orientaciones son necesarias con tal de construir modelos 2D no sesgados por ningún punto de vista; (2) extender el conjunto de datos de entrenamiento sin esta evaluación incrementaría innecesariamente el coste computacional en tiempo y en memoria; (3) obtener nuevas imágenes etiquetadas con distintas orientaciones puede tratarse de una tarea compleja debido al elevado coste del etiquetado manual; finalmente, (4) no cubrir uniformemente los distintos puntos de vista de una persona conduce a modelos sesgados. En esta tesis se proponen sucesivas extensiones de PA para hacer frente a estos problemas. Primero, proponemos Projected Procrustes Analysis (PPA) para formalizar la construcción de modelos rígidos multivista 2D a partir de conjuntos de datos 3D. PPA rota y proyecta cada objeto 3D y construye un modelo 2D a partir de este conjunto de datos enriquecido. También mostramos como rotaciones uniformemente distribuidas generan modelos 2D no sesgados, mientras rotaciones no uniformes conducen a modelos que representan algunos puntos de vista mejor que otros. Aunque PPA construye modelos multivista 2D, necesita un conjunto de entrenamiento enriquecido que incrementa los requisitos computacionales. Para solventar este problema de PA y PPA, proponemos Continuous Procrustes Analysis (CPA). CPA extiende PPA en un marco de análisis funcional y construye modelos rígidos multivista 2D de un modo eficiente, integrando todas las posibles rotaciones en un dominio dado. Mostramos como los modelos generados con CPA son inherentemente no sesgados debido a la formulación integral. Sin embargo, CPA no captura las deformaciones no rígidas de los datos. En consecuencia, proponemos Subspace Procrustes Analysis (SPA) con el objetivo de construir modelos deformables multivista 2D de un modo eficiente a partir de datos 3D. Añadiendo un subespacio a la formulación de PA, SPA es capaz de modelar deformaciones no rígidas, así como transformaciones 3D de los datos. Desarrollamos una formulación discreta (DSPA) y otra continua (CSPA), donde DSPA muestrea y CSPA integra el espacio de rotaciones 3D. Finalmente, ilustramos las ventajas de nuestros modelos deformables multivista 2D en la tarea de estimar la postura humana. Primero reformulamos el problema como una selección de características por subespacio coincidente y proponemos un método para resolver esta tarea eficientemente. Después, mostramos como nuestros modelos multivista 2D, combinados con la selección de características por subespacio coincidente, mejoran el estado del arte de estimación de la pose humana. Nuestro método es más preciso en la posición de las articulaciones y la longitud de las extremidades por el uso de modelos multivista 2D entrenados en bases de datos de captura de movimiento 3D. Nuestros modelos no están sesgados por punto de vista y pueden reconstruir deformaciones rígidas y no rígidas. Además, estos modelos son eficientes tanto en su construcción como en su uso
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Fixed point free elements of prime order in permutation groupsGiudici, Michael Robert January 2002 (has links)
No description available.
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Permutation group algebras and parking functionsGilbey, Julian David January 2002 (has links)
No description available.
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Explicitly restarted Lanczos methods for the computation of partial solutions for large eigenvalue problemsCooper, Amanda January 2003 (has links)
No description available.
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Repetitive structures : Eigenanalysis continuum beam modelling and pre-twisted formZhang, Yong January 2003 (has links)
No description available.
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On Herstein's conjecture and primary decompositionCovington, Ashley January 2001 (has links)
No description available.
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The growth of student conceptions of 'eqivalence relations & partitions'Erh-Tsung, Chin January 2002 (has links)
No description available.
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On the perfect closure of a commutative Noetherian ring of positive prime characteristicNossem, Nicole January 2002 (has links)
No description available.
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The submodule structure of Specht modulesReuter, Alain January 2002 (has links)
No description available.
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