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Conditional Random Fields (CRFs) is a discriminative and supervised approach for simultaneous sequence segmentation and frame labeling. Latent-Dynamic Conditional Random Fields (LDCRFs) incorporates hidden state variables within CRFs which model sub-structure motion patterns and dynamics between labels. Motivated by the success of LDCRFs in gesture recognition, we propose a framework for automatic facial expression recognition from continuous video sequence by modeling temporal variations within shapes using LDCRFs. We show that the proposed approach outperforms CRFs for recognizing facial expressions. Using Principal Component Analysis (PCA) we study the separability of various expression classes in lower dimension projected spaces. By comparing the performance of CRFs and LDCRFs against that of Support Vector Machines (SVMs) and a template based approach, we demonstrate that temporal variations within shapes are crucial in classifying expressions especially for those with small facial motion like anger and sadness. We also show empirically that only using changes in facial appearance over time without using the shape variations fails to obtain high performance for facial expression recognition. This reflects the importance of geometric deformations on face for recognizing expressions. / text

Session ID: TH-A4-3 / Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, September 17-21, 2008, Nagoya University, Nagoya, Japan

Canonical variate analysis (CVA) is a widely used method for analyzing group structure in multivariate data. It is mathematically equivalent to a one-way multivariate analysis of variance and often goes by the name of canonical discriminant analysis. Change over time is a central feature of many phenomena of interest to researchers. This dissertation extends CVA to longitudinal data. It develops models whose purpose is to determine what is changing and what is not changing in the group structure. Three approaches are taken: a maximum likelihood approach, a least squares approach, and a covariance structure analysis approach. All methods have in common that they hypothesize canonical variates which are stable over time. The maximum likelihood approach models the positions of the group means in the subspace of the canonical variates. It also requires modeling the structure of the within-groups covariance matrix, which is assumed to be constant or proportional over time. In addition to hypothesizing stable variates over time, one can also hypothesize canonical variates that change over time. Hypothesis tests and confidence intervals are developed. The least squares methods are exploratory. They are based on three-mode PCA methods such as the Tucker2 and parallel factor analysis. Graphical methods are developed to display the relationships between the variables over time. Stable variates over time imply a particular structure for the between-groups covariance matrix. This structure is modeled using covariance structure analysis, which is available in the SAS package Proc Calis. Methods related to CVA are also discussed. First, the least squares methods are extended to canonical correlation analysis, redundancy analysis, Procrustes rotation and correspondence analysis with longitudinal data. These least squares methods lend themselves equally well to data from multiple datasets. Lastly, a least squares method for the common principal components model is developed. / Ph. D.

The morphologic variability of a fossil assemblage is of interest in many paleontological studies. However, many fossil assemblages are time-averaged; that is, many generations of non-contemporaneous organisms are mixed into the same fossil bed. Assemblages of robust mollusk shells deposited in nearshore marine environments are often time-averaged over 100's to 1000's of years. Mixing many generations of a taxon can increase measured morphologic variability over that of a single generation if morphology is changing during the interval of time-averaging. If morphology is changing, time-averaging can also alter observed correlations between morphologic variables, as well as allometric growth patterns. If morphology is static, then time-averaging will not increase variability or otherwise obscure patterns of morphologic variability. Testing the effects of time-averaging on morphology will help determine the reliability of information derived from the fossil record. In this study, morphologic variability was compared between 6 standing crop, living populations of Mercenaria campechiensis (Bivalvia) and two fossil assemblages of M. campechiensis and M. permagna. One fossil sample was collected as a series of superposed units that could be analyzed individually or in aggregate. The x,y coordinates of 13 landmarks and pseudolandmarks were recorded on over 600 valves, and variability was calculated using Least Squares Procrustes Analysis. Once corrections were made for allometry, the variabilities of the samples drawn from single time-averaged fossil beds were indistinguishable from the variabilities of the recent samples. For this data set, the variabilities of the fossil samples could be used without reservation to estimate the variability of the standing crop populations from which they formed. Morphology was quite stable over the 100's to 1000's of years that likely passed as the assemblages accumulated. A small amount of analytical time-averaging of the samples increases variability slightly, but additional analytical time-averaging causes no further increase. Very slight morphologic fluctuations are evident at time spans exceeding 100's to 1000's of years. Lumping geographically separated samples and samples of different species also increases variability. Morphologic stasis is evident in Mercenaria over 100's to 1000's of years, but previous studies have indicated that evolutionary rates over this time frame are typically high. These studies are based on colonization events, however, and are biased towards high rates. Data gathered here and in previous studies suggest that local populations may evolve rapidly at their founding, but that stasis follows this initial burst of change. This model describes a pattern similar to Punctuated Equilibrium at a lower level of the genealogical hierarchy, and is here termed "Punctuated Equilibrium, Jr." This model can be further tested in empirical studies and should aid in determining the causes of species-level evolutionary patterns. / Master of Science

As cobras são um grupo de vertebrados extremamente bem sucedido. Apesar da aparente simplicidade, elas conseguiram ocupar uma grande diversidade de habitats. O esqueleto axial das serpentes apresenta relação com vários aspectos da vida que puderam ter tido influência direta em seu sucesso evolutivo. Além disso, a forma dos elementos vertebrais possui valor taxonômico, fato que desperta particular interesse, visto que a maior parte do registro fóssil deste grupo é constituído por elementos vertebrais desarticulados. A morfometria geométrica utiliza informações sobre a posição de pontos em duas ou três dimensões, localizados sobre estruturas anatômicas para análise estatística da variação da forma. Esse conjunto de técnicas tem se mostrado eficaz em avaliar variações da forma que não seriam diagnosticadas por métodos tradicionais. O presente trabalho buscou avaliar as vértebras do esqueleto pré-cloacal de Serpentes no contexto da morfometria geométrica, considerando as influências ecológicas e filogenéticas sob estas estruturas, e investigando ainda a utilidade taxonômica da forma vertebral. Os resultados apresentados aqui sugerem a existência de uma padronização do esqueleto axial de serpentes que é conservada ao longo da história evolutiva desse grupo. Análises ecomorfológicas demonstram que a forma vertebral é fortemente influenciada por hábitos de vida como fossorialidade e constrição. A despeito da ausência de sinal filogenético, as análises de classificação de elementos vertebrais dissociados demonstram que a forma vertebral pode ser utilizada para a diagnose de vértebras isoladas. Esses resultados reforçam a necessidade de realização de análises de variação longitudinal para a identificação correta de material fóssil referente a este grupo. / Snakes are an extremely successful group of vertebrates. Despite their apparent morphological simplicity, they managed to occupy a great diversity of habitats. The axial skeleton of snakes has relationships with various aspects of their life history that could have had direct influence in the evolutionary success of these animals. Furthermore, the shape of the vertebrae is recognized as being of taxonomic value, a fact that elicits a special interest, since the majority of the fossil record of this group is composed of disarticulated vertebral elements. Geometric morphometrics methods use information about the position of landmarks in two or three dimensions, placed over anatomical structures for statistical analyses of shape variation. This group of techniques has been shown to identify shape variations that would not be diagnosed through traditional methods. The present work sought to evaluate the vertebrae of the pre-cloacal skeleton of Serpentes in the context of geometric morphometrics, evaluating the influences of ecology and phylogeny over the shape of these structures, and also investigating the taxonomic usefulness of vertebral shape. Results presented here suggest the existence of a patterning of the axial skeleton that is conserved throughout the evolutionary history of the group. An ecomorphological analysis demonstrates that the vertebral shape is highly influenced by life-history traits such as fossoriality and constriction. Despite the absence of phylogenetic signal, analyzes of classification of dissociated vertebral elements show that the vertebral shape can be used to diagnose isolated vertebrae. These results reiterate the necessity of performing studies of longitudinal variation in order to correctly identify fossil material associated with this group.

As cobras são um grupo de vertebrados extremamente bem sucedido. Apesar da aparente simplicidade, elas conseguiram ocupar uma grande diversidade de habitats. O esqueleto axial das serpentes apresenta relação com vários aspectos da vida que puderam ter tido influência direta em seu sucesso evolutivo. Além disso, a forma dos elementos vertebrais possui valor taxonômico, fato que desperta particular interesse, visto que a maior parte do registro fóssil deste grupo é constituído por elementos vertebrais desarticulados. A morfometria geométrica utiliza informações sobre a posição de pontos em duas ou três dimensões, localizados sobre estruturas anatômicas para análise estatística da variação da forma. Esse conjunto de técnicas tem se mostrado eficaz em avaliar variações da forma que não seriam diagnosticadas por métodos tradicionais. O presente trabalho buscou avaliar as vértebras do esqueleto pré-cloacal de Serpentes no contexto da morfometria geométrica, considerando as influências ecológicas e filogenéticas sob estas estruturas, e investigando ainda a utilidade taxonômica da forma vertebral. Os resultados apresentados aqui sugerem a existência de uma padronização do esqueleto axial de serpentes que é conservada ao longo da história evolutiva desse grupo. Análises ecomorfológicas demonstram que a forma vertebral é fortemente influenciada por hábitos de vida como fossorialidade e constrição. A despeito da ausência de sinal filogenético, as análises de classificação de elementos vertebrais dissociados demonstram que a forma vertebral pode ser utilizada para a diagnose de vértebras isoladas. Esses resultados reforçam a necessidade de realização de análises de variação longitudinal para a identificação correta de material fóssil referente a este grupo. / Snakes are an extremely successful group of vertebrates. Despite their apparent morphological simplicity, they managed to occupy a great diversity of habitats. The axial skeleton of snakes has relationships with various aspects of their life history that could have had direct influence in the evolutionary success of these animals. Furthermore, the shape of the vertebrae is recognized as being of taxonomic value, a fact that elicits a special interest, since the majority of the fossil record of this group is composed of disarticulated vertebral elements. Geometric morphometrics methods use information about the position of landmarks in two or three dimensions, placed over anatomical structures for statistical analyses of shape variation. This group of techniques has been shown to identify shape variations that would not be diagnosed through traditional methods. The present work sought to evaluate the vertebrae of the pre-cloacal skeleton of Serpentes in the context of geometric morphometrics, evaluating the influences of ecology and phylogeny over the shape of these structures, and also investigating the taxonomic usefulness of vertebral shape. Results presented here suggest the existence of a patterning of the axial skeleton that is conserved throughout the evolutionary history of the group. An ecomorphological analysis demonstrates that the vertebral shape is highly influenced by life-history traits such as fossoriality and constriction. Despite the absence of phylogenetic signal, analyzes of classification of dissociated vertebral elements show that the vertebral shape can be used to diagnose isolated vertebrae. These results reiterate the necessity of performing studies of longitudinal variation in order to correctly identify fossil material associated with this group.

<p>In this thesis, we present algorithms for local and global minimization of some <i>Procrustes</i> type problems. Typically, these problems are about rotating and scaling a known set of data to fit another set with applications related to determination of rigid body movements, factor analysis and multidimensional scaling. The known sets of data are usually represented as matrices, and the rotation to be determined is commonly a matrix <i>Q</i> with orthonormal columns.</p><p>The algorithms presented use Newton and Gauss-Newton search directions with optimal step lengths, which in most cases result in a fast computation of a solution.</p><p>Some of these problems are known to have several minima, e.g., the weighted orthogonal Procrustes problem (WOPP). A study on the maximal amount of minima has been done for this problem. Theoretical results and empirical observations gives strong indications that there are not more than 2ⁿ minimizers, where <i>n</i> is the number of columns in <i>Q</i>. A global optimization method to compute all 2ⁿ minima is presented.</p><p>Also considered in this thesis is a cubically convergent iteration method for solving nonlinear equations. The iteration method presented uses second order information (derivatives) when computing a search direction. Normally this is a computational heavy task, but if the second order derivatives are constant, which is the case for quadratic equations, a performance gain can be obtained. This is confirmed by a small numerical study.</p><p>Finally, regularization of ill-posed nonlinear least squares problems is considered. The quite well known L-curve for linear least squares problems is put in context for nonlinear problems.</p>

In this thesis, we present algorithms for local and global minimization of some Procrustes type problems. Typically, these problems are about rotating and scaling a known set of data to fit another set with applications related to determination of rigid body movements, factor analysis and multidimensional scaling. The known sets of data are usually represented as matrices, and the rotation to be determined is commonly a matrix Q with orthonormal columns. The algorithms presented use Newton and Gauss-Newton search directions with optimal step lengths, which in most cases result in a fast computation of a solution. Some of these problems are known to have several minima, e.g., the weighted orthogonal Procrustes problem (WOPP). A study on the maximal amount of minima has been done for this problem. Theoretical results and empirical observations gives strong indications that there are not more than 2n minimizers, where n is the number of columns in Q. A global optimization method to compute all 2n minima is presented. Also considered in this thesis is a cubically convergent iteration method for solving nonlinear equations. The iteration method presented uses second order information (derivatives) when computing a search direction. Normally this is a computational heavy task, but if the second order derivatives are constant, which is the case for quadratic equations, a performance gain can be obtained. This is confirmed by a small numerical study. Finally, regularization of ill-posed nonlinear least squares problems is considered. The quite well known L-curve for linear least squares problems is put in context for nonlinear problems.