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Dissertations / Theses on the topic 'Shape statistics'
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Tola, Omer Onder. "Generalized Beam Angle Statistics For Shape Description." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/2/12605412/index.pdf.
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In this thesis, we introduce a new shape descriptor and a graph based matching algorithm to detect a template shape in an image that contains a single object. The shape descriptor, Generalized Beam Angle Statistics, GBAS is obtained with the generalization of the boundary based shape descriptor, Beam Angle Statistics, BAS cite{BAS}. GBAS improves BAS so that it can compute the feature vector of a boundary point without the requirement of the parametric boundary representation. This way, it can be used in matching an individual edge pixel with a boundary point of template shape, even if it is not possible to extract the shape boundary in the image with the available techniques.
Given a template shape, the matching algorithm solves the correspondence problem between the sampled boundary points of the template and the edges of the query image, using the GBAS feature vectors and the spatial information of edges. The match graph represents the correspondence problem and the optimum path on this graph gives the solution of it. Optimum path is found using a polynomial time algorithm that is based on the dynamic programming approach.
In the experiments, we show that the proposed shape descriptor is very powerful and the matching algorithm is capable of detecting a template shape in edge detected images under a variety of transformations and noise.
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Chen, Yining. "Aspects of shape-constrained estimation in statistics." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648300.
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Gao, Zhikun. "Automatic Shape-Constrained Non-Parametric Regression." Thesis, The George Washington University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13813788.
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We propose an automatic shape-constrained non-parametric estimation methodology in least squares and quantile regression, where the regression function and its shape are simultaneously estimated and identified.
We build the estimation based on the quadratic B-spline expansion with penalization about its first and second derivatives on spline knots in a group manner. By penalizing the positive and negative parts of the introduced group derivatives, the shape of the estimated regression curve is determined according to the sparsity of the parameters considered. In the quadratic B-spline expansion, the parameters referring to the shape can be written through some simple linear combinations of the basis coefficients, which makes it convenient to impose penalization for shape identification is efficient in computation and is flexible in various shape identification. In both least squares and quantile regression scenarios, under some regularity conditions, we show that the proposed method can identify the correct shape of the regression function with probability approaching one, and the resulting non-parametric estimator can achieve the optimal convergence rate. Simulation study shows that the proposed method gives more stable curve estimation and more accurate curve shape classification than the conventional unconstrained B-spline estimator in both mean and quantile regressions, and it is competitive in terms of the estimation accuracy to the artificial shape-constrained estimator built by knowing prior information of the curve shape. In addition, across multiple quantile levels, the proposed estimator shows less crossing between the estimated quantile curves than the unpenalized counterpart.
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Er, Fikret. "Robust methods in statistical shape analysis." Thesis, University of Leeds, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.342394.
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Butt, R. "Optimal shape design for differential inequalities." Thesis, University of Leeds, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233771.
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Strait, Justin. "Elastic Statistical Shape Analysis with Landmark Constraints." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1530966023478484.
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Walder, Alistair Neil. "Statistics of shape and size for landmark data." Thesis, University of Leeds, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303425.
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Prieto, Bernal Juan Carlos. "Multiparametric organ modeling for shape statistics and simulation procedures." Thesis, Lyon, INSA, 2014. http://www.theses.fr/2014ISAL0010/document.
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La modélisation géométrique a été l'un des sujets les plus étudiés pour la représentation des structures anatomiques dans le domaine médical. Aujourd'hui, il n'y a toujours pas de méthode bien établie pour modéliser la forme d'un organe. Cependant, il y a plusieurs types d'approches disponibles et chaque approche a ses forces et ses faiblesses. La plupart des méthodes de pointe utilisent uniquement l'information surfacique mais un besoin croissant de modéliser l'information volumique des objets apparaît. En plus de la description géométrique, il faut pouvoir différencier les objets d'une population selon leur forme. Cela nécessite de disposer des statistiques sur la forme dans organe dans une population donné. Dans ce travail de thèse, on utilise une représentation capable de modéliser les caractéristiques surfaciques et internes d'un objet. La représentation choisie (s-rep) a en plus l'avantage de permettre de déterminer les statistiques de forme pour une population d'objets. En s'appuyant sur cette représentation, une procédure pour modéliser le cortex cérébral humain est proposée. Cette nouvelle modélisation offre de nouvelles possibilités pour analyser les lésions corticales et calculer des statistiques de forme sur le cortex. La deuxième partie de ce travail propose une méthodologie pour décrire de manière paramétrique l'intérieur d'un objet. La méthode est flexible et peut améliorer l'aspect visuel ou la description des propriétés physiques d'un objet. La modélisation géométrique enrichie avec des paramètres physiques volumiques est utilisée pour la simulation d'image par résonance magnétique pour produire des simulations plus réalistes. Cette approche de simulation d'images est validée en analysant le comportement et les performances des méthodes de segmentations classiquement utilisées pour traiter des images réelles du cerveauGeometric modeling has been one of the most researched areas in the medical domain. Today, there is not a well established methodology to model the shape of an organ. There are many approaches available and each one of them have different strengths and weaknesses. Most state of the art methods to model shape use surface information only. There is an increasing need for techniques to support volumetric information. Besides shape characterization, a technique to differentiate objects by shape is needed. This requires computing statistics on shape. The current challenge of research in life sciences is to create models to represent the surface, the interior of an object, and give statistical differences based on shape. In this work, we use a technique for shape modeling that is able to model surface and internal features, and is suited to compute shape statistics. Using this technique (s-rep), a procedure to model the human cerebral cortex is proposed. This novel representation offers new possibilities to analyze cortical lesions and compute shape statistics on the cortex. The second part of this work proposes a methodology to parameterize the interior of an object. The method is flexible and can enhance the visual aspect or the description of physical properties of an object. The geometric modeling enhanced with physical parameters is used to produce simulated magnetic resonance images. This image simulation approach is validated by analyzing the behavior and performance of classic segmentation algorithms for real images
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Terriberry, Timothy B. Gerig Guido. "Continuous medial models in two-sample statistics of shape." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,579.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Computer Science." Discipline: Computer Science; Department/School: Computer Science.
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Bhattacharya, Abhishek. "Nonparametric Statistics on Manifolds With Applications to Shape Spaces." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/194508.
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This thesis presents certain recent methodologies and some new results for the statistical analysis of probability distributions on non-Euclidean manifolds. The notions of Frechet mean and variation as measures of center and spread are introduced and their properties are discussed. The sample estimates from a random sample are shown to be consistent under fairly broad conditions. Depending on the choice of distance on the manifold, intrinsic and extrinsic statistical analyses are carried out. In both cases, sufficient conditions are derived for the uniqueness of the population means and for the asymptotic normality of the sample estimates. Analytic expressions for the parameters in the asymptotic distributions are derived. The manifolds of particular interest in this thesis are the shape spaces of k-ads. The statistical analysis tools developed on general manifolds are applied to the spaces of direct similarity shapes, planar shapes, reflection similarity shapes, affine shapes and projective shapes. Two-sample nonparametric tests are constructed to compare the mean shapes and variation in shapes for two random samples. The samples in consideration can be either independent of each other or be the outcome of a matched pair experiment. The testing procedures are based on the asymptotic distribution of the test statistics, or on nonparametric bootstrap methods suitably constructed. Real life examples are included to illustrate the theory.
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Dai, Xiaotian. "Novel Statistical Models for Quantitative Shape-Gene Association Selection." DigitalCommons@USU, 2017. https://digitalcommons.usu.edu/etd/6856.
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Other research reported that genetic mechanism plays a major role in the development process of biological shapes. The primary goal of this dissertation is to develop novel statistical models to investigate the quantitative relationships between biological shapes and genetic variants. However, these problems can be extremely challenging to traditional statistical models for a number of reasons: 1) the biological phenotypes cannot be effectively represented by single-valued traits, while traditional regression only handles one dependent variable; 2) in real-life genetic data, the number of candidate genes to be investigated is extremely large, and the signal-to-noise ratio of candidate genes is expected to be very high. In order to address these challenges, we propose three statistical models to handle multivariate, functional, and multilevel functional phenotypes, with applications to biological shape data using different shape descriptors. To the best of our knowledge, there is no statistical model developed for multilevel functional phenotypes. Even though multivariate regressions have been well-explored and these approaches can be applied to genetic studies, we show that the model proposed in this dissertation can outperform other alternatives regarding variable selection and prediction through simulation examples and real data examples. Although motivated ultimately by genetic research, the proposed models can be used as general-purpose machine learning algorithms with far-reaching applications.
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Hyde, Andrew. "Statistical shape analysis of wheat root systems." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/52255/.
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The roots of a plant play a vital role in its growth and development, but due to practical difficulties of observing underground roots, the study of their shape has long been neglected. Recent advances in CT imaging technology have allowed for accurate non-destructive imaging of root systems in soil. This technique has formed the basis of the FutureRoots project. The main challenge with analysing the shape of a plant root system is that they have varying topological structure, so traditional shape analysis methods cannot be applied. In this thesis, we develop three approaches for analysing wheat root systems. The first approach involves measuring a set of pre-chosen root traits, and analysing this set using conventional statistical methods. This approach is effective but may miss potentially important shape information and the large number of measurable traits reduces the potential power of statistical tests. The second approach is to perform pairwise comparisons based on the Hausdorff Metric and use Multidimensional scaling to reduce a large set of pairwise comparisons to a dataset which can be analysed with conventional statistical methods. This approach can detect and test for overall shape differences but can fail to detect subtle differences. The third approach is to apply the Persistent Homology technique from Topological Data Analysis, which is designed to find underlying topological differences between two shapes. This method successfully finds differences but it is difficult to interpret the results. We will apply these three techniques to simulated data and a real life dataset. In addition, because of experimental considerations, the wheat roots had to be unnaturally constrained to a small area so we have developed a method to estimate how they would have grown unconstrained.
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Zhao, Zhiye. "Shape design sensitivity analysis and optimization using the boundary element method." Thesis, University of South Wales, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.254866.
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Sajib, Anamul. "A Bayesian model for the unlabelled size-and-shape analysis." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/55511/.
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This thesis considers the development of efficient MCMC sampling methods for Bayesian models used for the pairwise alignment of two unlabelled configurations. We introduce ideas from differential geometry along with other recent developments in unlabelled shape analysis as a means of creating novel and more efficient MCMC sampling methods for such models. For example, we have improved the performance of the sampler for the model of Green and Mardia (2006) by sampling rotation, A ∈ SO(3), and matching matrix using geodesic Monte Carlo (MCMC defined on manifold) and Forbes and Lauritzen (2014) matching sampler, developed for finger print matching problem, respectively. We also propose a new Bayesian model, together with implementation methods, motivated by the desire for further improvement. The model and its implementation methods proposed exploit the continuous nature of the parameter space of our Bayesian model and thus move around easily in this continuous space, providing highly efficient convergence and exploration of the target posterior distribution. The proposed Bayesian model and its implementation methods provide generalizations of the existing two models, Bayesian Hierarchical and regression models, introduced by Green and Mardia (2006) and Taylor, Mardia and Kent (2003) respectively, and resolve many shortcomings of existing implementation methods; slow convergence, traps in local mode and dependence on initial starting values when sampling from high dimensional and multi-modal posterior distributions. We illustrate our model and its implementation methods on the alignment of two proteins and two gels, and we find that the performance of proposed implementation methods under proposed model is better than current implementation techniques of existing models in both real and simulated data sets.
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Zaetz, Jiaqi L. "A Riemannian Framework for Shape Analysis of Annotated 3D Objects." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1440368778.
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Amaral, Getulio J. A. "Bootstrap and empirical likelihood methods in statistical shape analysis." Thesis, University of Nottingham, 2004. http://eprints.nottingham.ac.uk/11399/.
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The aim of this thesis is to propose bootstrap and empirical likelihood confidence regions and hypothesis tests for use in statistical shape analysis. Bootstrap and empirical likelihood methods have some advantages when compared to conventional methods. In particular, they are nonparametric methods and so it is not necessary to choose a family of distribution for building confidence regions or testing hypotheses. There has been very little work on bootstrap and empirical likelihood methods in statistical shape analysis. Only one paper (Bhattacharya and Patrangenaru, 2003) has considered bootstrap methods in statistical shape analysis, but just for constructing confidence regions. There are no published papers on the use of empirical likelihood methods in statistical shape analysis. Existing methods for building confidence regions and testing hypotheses in shape analysis have some limitations. The Hotelling and Goodall confidence regions and hypothesis tests are not appropriate for data sets with low concentration. The main reason is that these methods are designed for data with high concentration, and if this hypothesis is violated, the methods do not perform well. On the other hand, simulation results have showed that bootstrap and empirical likelihood methods developed in this thesis are appropriate to the statistical shape analysis of low concentrated data sets. For highly concentrated data sets all the methods show similar performance. Theoretical aspects of bootstrap and empirical likelihood methods are also considered. Both methods are based on asymptotic results and those results are explained in this thesis. It is proved that the bootstrap methods proposed in this thesis are asymptotically pivotal. Computational aspects are discussed. All the bootstrap algorithms are implemented in “R”. An algorithm for computing empirical likelihood tests for several populations is also implemented in “R”.
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Gkolias, Theodoros. "Shape analysis in protein structure alignment." Thesis, University of Kent, 2018. https://kar.kent.ac.uk/66682/.
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In this Thesis we explore the problem of structural alignment of protein molecules using statistical shape analysis techniques. The structural alignment problem can be divided into three smaller ones: the representation of protein structures, the sampling of possible alignments between the molecules and the evaluation of a given alignment. Previous work done in this field, can be divided in two approaches: an adhoc algorithmic approach from the Bioinformatics literature and an approach using statistical methods either in a likelihood or Bayesian framework. Both approaches address the problem from a different scope. For example, the algorithmic approach is easy to implement but lacks an overall modelling framework, and the Bayesian address this issue but sometimes the implementation is not straightforward. We develop a method which is easy to implement and is based on statistical assumptions. In order to asses the quality of a given alignment we use a size and shape likelihood density which is based in the structure information of the molecules. This likelihood density is also extended to include sequence infor- mation and gap penalty parameters so that biologically meaningful solution can be produced. Furthermore, we develop a search algorithm to explore possible alignments from a given starting point. The results suggest that our approach produces better or equal alignments when it is compared to the most recent struc- tural alignment methods. In most of the cases we managed to achieve a higher number of matched atoms combined with a high TMscore. Moreover, we extended our method using Bayesian techniques to perform alignments based on posterior modes. In our approach, we estimate directly the mode of the posterior distribution which provides the final alignment between two molecules. We also, choose a different approach for treating the mean parameter. In previous methods the mean was either integrated out of the likelihood density or considered as fixed. We choose to assign a prior over it and obtain its posterior mode. Finally, we consider an extension of the likelihood model assuming a Normal density for both the matched and unmatched parts of a molecule and diagonal covariance structure. We explore two different variants. In the first we consider a fixed zero mean for the unmatched parts of the molecules and in the second we consider a common mean for both the matched and unmatched parts. Based on simulated and real results, both models seems to perform well in obtaining high number of matched atoms and high TMscore.
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Chiang, Lisa Gee. "Passive coincidence technique to determine the shape of plutonium objects using second order statistics." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/17893.
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Easton, Valerie J. "Describing size and shape changes in the human mandible from 9 to 15 years : comparison of elliptical Fourier function and Procrustes methods." Thesis, University of Glasgow, 2000. http://theses.gla.ac.uk/8392/.
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In the past, there have been many attempts to capture the size and shape information inherent in complex irregular objects by numerical representation. There is much to be gained in a biological sense by numerical description of complex forms, like the craniofacial complex, in the field of dentistry. This thesis aims to review, utilise and build on past research methods in an attempt to describe the size and shape changes of a sample of human mandibles from the age of 9 through to 15 years. Specifically, two methods are considered and contrasted, the elliptical Fourier function and Procrustes analysis (including Bookstein co-ordinates). In chapter 1 the background and motivation for such an investigation is introduced, describing the need for a mathematical description of complex irregular forms with an emphasis on the importance of such models in dentistry with particular reference to the way in which the human mandible grows over time. The methodological and clinical issues of the problem are outlined, including a summary of up to date methods that have been used to capture size and shape information of a growing complex morphological form and an overview of the way in which the mandible grows. Both the so-called landmark dependent and landmark independent (boundary outline) methods are summarised. Whilst all the methods considered are not without constraint in describing the size and shape of complex forms, all have been seen in the past to be beneficial in some way in that they all model 'form' in one way or another at the very least. Chapter 2 then considers in more depth, what is fast becoming a much-promoted method of describing irregular forms, the elliptical Fourier function (EFF). The use of conventional Fourier methods, as well as the newer EFF method in describing size and shape changes is reviewed. A suite of programs that have been specially written to apply the EFF method in the description of complex irregular forms is introduced and an overview of the specific routines available in the package is given. The data sample available for investigation, which consists of a series of lateral head cephalograms (x-rays) from the BC Leighton Growth Study, is described in Chapter 3. The way in which a subset is selected following certain inclusion and exclusion criteria from the available x-rays is outlined. The way in which the mandibular data is then prepared for subsequent use in the EFF suite of programs, as well as with the method of Procrustes (and Bookstein co-ordinates) is also described in some detail. In Chapter 4, an error study is undertaken to investigate the reproducibility of the tracings of the sample of mandibular outlines prepared in the previous chapter. Both 11 within- and between-rater studies are looked at. The EFF method is then applied to the sample of tracings collected by one observer to explore any changes in size and shape that may occur as the mandible grows, concentrating on ages 9, 11, 13 and 15 years. As well as producing some very informative plots of the observed and predicted mandibular outlines, and centroid to boundary outline distances, the usefulness of the harmonic information available from the EFF procedure for numerically describing size and shape changes of a complex irregular form is investigated. Whether or not there are differences between males and females in the data sample, in terms of the size and / or shape of the mandible is also explored. Finally, the method of Procrustes analysis (and Bookstein co-ordinates) is described in more depth in Chapter 5. This particular method is also applied to the same sample of mandibular outlines in order to investigate its usefulness in describing size and shape changes of the human mandible from age 9 to 15 years. Shape variability within samples is also explored by way of principal components analysis. In addition, the method of thin plate splines (TPS) is applied in order to examine shape change between males and females. Similar observations were made about mandibular growth in the sample investigated using both the EFF and Procrustes (along with Bookstein co-ordinates) procedures. Overall, the mandible was observed to be 'growing' between ages 9 and 15 i.e. changing in both size and shape over a period of time. There was no difference in terms of the size and shape of the bone between males and females in the sample, for each age. Further, using Procrustes analysis (and Bookstein co-ordinates) there did not appear to be any association between the size and shape of the mandibular outlines in either the male or female samples, for all ages. In addition, investigating shape variability using Procrustes methods by way of principal components analysis, resulted in broadly similar patterns for males and females, as well as combined samples, and different age groups. It is concluded in Chapter 6 that the methods of elliptical Fourier function and Procrustes (and Bookstein co-ordinates) both provide a very useful framework in which to describe the size and shape of complex irregular forms like the mandible. Although both methods have their advantages and disadvantages, Procrustes (including the very useful method using Bookstein co-ordinates) is preferred for statistical purposes.
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Brandao, Renata. "Study shows : how statistics are used to articulate and shape discourses of science in the newsroom." Thesis, University of Sheffield, 2016. http://etheses.whiterose.ac.uk/16438/.
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This thesis examines the use of peer-reviewed data and statistics in news communication of science through a content analysis and close reading analysis of statistical data in the United Kingdom science news and in-depth interviews with science journalists. The content analysis yields three key insights into the use of science data in the United Kingdom and Brazilian press: (1) statistics are used overwhelmingly to treat science as hard news, (2) there is an immense lack of fundamental background information about how the reported data are produced and (3) science journalists tend to use peer-reviewed data in a unique fashion: their stories include either too few or too many statistics from original sources. The in-depth interviews attempt to explain this content pattern, examining how journalists access and interpret quantitative data when producing stories about science, the nature of statistical news sources that they regularly use, and how they evaluate and treat such sources in articulating science news stories. Overall, this research finds that journalists tend to see and use statistics mainly to maintain the strategic ritual of objectivity in their social construction of science. The findings will be discussed in relation to a comprehensive body of literature on the use and abuse of statistical information as a key tool in the construction of journalistic objectivity.
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Slezak, Thomas Joseph. "Quantitative Morphological Classification of Planetary Craterforms Using Multivariate Methods of Outline-Based Shape Analysis." BYU ScholarsArchive, 2017. https://scholarsarchive.byu.edu/etd/6639.
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Craters formed by impact and volcanic processes are among the most fundamental planetary landforms. This study examines the morphology of diverse craterforms on Io, the Moon, Mars, and Earth using quantitative, outline-based shape analysis and multivariate statistical methods to evaluate the differences between different types of. Ultimately, this should help establish relationships between the form and origin of craterforms. Developed in the field of geometric morphometrics by paleontological and biological sciences communities, these methods were used for the analysis of the shapes of crater outlines. The shapes of terrestrial ash-flow calderas, terrestrial basaltic shield calderas, martian calderas, Ionian paterae, and lunar impact craters were quantified and compared. Specifically, we used circularity, ellipticity, elliptic Fourier analysis (EFA), Zahn and Roskies (Z-R) shape function, and diameter. Quantitative shape descriptors obtained from EFA yield coefficients from decomposition of the Fourier series that separates the vertical and horizontal components among the outline points for each shape. The shape descriptors extracted from Z-R analysis represent the angular deviation of the shapes from a circle. These quantities were subjected to multivariate statistical analysis including principal component analysis (PCA) and discriminant analysis, to examine maximum differences between each a priori established group. Univariate analyses of morphological quantities including diameter, circularity, and ellipticity, as well as multivariate analyses of elliptic Fourier coefficients and Z-R shape function angular quantities show that ash-flow calderas and paterae on Io, as well as basaltic shield calderas and martian calderas, are most similar in shape. Other classes of craters are also shown to be statistically distinct from one another. Multivariate statistical models provide successful classification of different types of craters. Three classification models were built with overall successful classification rates ranging from 90% to 75%, each conveying different shape information. The EFA model including coefficients from the 2nd to 10th harmonic was the most successful supervised model with the highest overall classification rate and most successful predictive group membership assignments for the population of examined craterforms. Multivariate statistical methods and classification models can be effective tools for analyzing landforms on planetary surfaces and geologic morphology. With larger data sets used to enhance supervision of the model, more successful classification by the supervised model could likely reveal clues to the formation and variables involved in the genesis of landforms.
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Hamsici, Onur C. "Bayes Optimality in Classification, Feature Extraction and Shape Analysis." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218513562.
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Paranjape, Harshad Madhukar. "Modeling of Shape Memory Alloys: Phase Transformation/Plasticity Interaction at the Nano Scale and the Statistics of Variation in Pseudoelastic Performance." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1417605178.
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Bartels, Brandon L. "Heterogeneity in Supreme Court decision making how situational factors shape preference-based behavior /." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1148557321.
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Van, Bever Germain. "Contributions to nonparametric and semiparametric inference based on statistical depth." Doctoral thesis, Universite Libre de Bruxelles, 2013. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209438.
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L'objectif général de cette thèse est d'introduire de nouveaux concepts ou d'étendre certaines procédures statistiques déjà existantes touchant à la notion de profondeur statistique. Celle-ci, originellement introduite afin de généraliser la notion de médiane et de fournir naturellement un ordre (depuis un centre, vers l'extérieur) dans un contexte multivarié, a, depuis son développement, démontré ses nombreuses qualités, tant en termes de robustesse, que d'utilité dans de nombreuses procédures inférentielles.
Les résultats proposés dans ce travail se développent le long de trois axes.
Pour commencer, la thèse s'intéresse à la classification supervisée. La profondeur a, en effet, déjà été utilisée avec succès dans ce contexte. Cependant, jusqu'ici, les outils développés restaient limités aux distributions elliptiques, constituant ainsi une sévère restriction des méthodes utilisant les fonctions de profondeur, qui, pour la plupart, sont par essence nonparamétrique. La première partie de cette thèse propose donc une nouvelle méthode de classification, fondée sur la profondeur, dont on montrera qu'elle est essentiellement universellement convergente. En particulier, la règle de discrimination proposée se fonde sur les idées utilisées dans la classification par plus proches voisins, en introduisant cependant des voisinages fondés sur la profondeur, mieux à même de cerner le comportement des populations sous-jacentes.
Ces voisinages d'un point quelconque, et surtout l'information sur le comportement local de la distribution en ce point qu'ils apportent, ont été réutilisés dans la seconde partie de ce travail. Plusieurs auteurs ont en effet reconnu certaines limitations aux fonctions de profondeur, de par leur caractère global et la difficulté d'étudier par leur biais des distributions multimodales ou à support convexe. Une nouvelle définition de profondeur locale est donc développée et étudiée. Son utilité dans différents problèmes d'inférence est également explorée.
Enfin, la thèse s'intéresse au paramètre de forme pour les distributions elliptiques. Ce paramètre d'importance est utilisé dans de nombreuses procédures statistiques (analyse en composantes principales, analyse en corrélations canoniques, entre autres) et aucune fonction de profondeur pour celui-ci n'existait à ce jour. La profondeur de forme est donc définie et ses propriétés sont étudiées. En particulier, on montrera que le cadre général de la profondeur paramétrique n'est pas suffisant en raison de la présence du paramètre de nuisance (d'influence non nulle) qu'est l'échelle. Une application inférentielle est présentée dans le cadre des tests d'hypothèses.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Vuollo, V. (Ville). "3D imaging and nonparametric function estimation methods for analysis of infant cranial shape and detection of twin zygosity." Doctoral thesis, Oulun yliopisto, 2018. http://urn.fi/urn:isbn:9789526218557.
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Abstract The use of 3D imaging of craniofacial soft tissue has increased in medical science, and imaging technology has been developed greatly in recent years. 3D models are quite accurate and with imaging devices based on stereophotogrammetry, capturing the data is a quick and easy operation for the subject. However, analyzing 3D models of the face or head can be challenging and there is a growing need for efficient quantitative methods. In this thesis, new mathematical methods and tools for measuring craniofacial structures are developed. The thesis is divided into three parts. In the first part, facial 3D data of Lithuanian twins are used for the determination of zygosity. Statistical pattern recognition methodology is used for classification and the results are compared with DNA testing. In the second part of the thesis, the distribution of surface normal vector directions of a 3D infant head model is used to analyze skull deformation. The level of flatness and asymmetry are quantified by functionals of the kernel density estimate of the normal vector directions. Using 3D models from infants at the age of three months and clinical ratings made by experts, this novel method is compared with some previously suggested approaches. The method is also applied to clinical longitudinal research in which 3D images from three different time points are analyzed to find the course of positional cranial deformation and associated risk factors. The final part of the thesis introduces a novel statistical scale space method, SphereSiZer, for exploring the structures of a probability density function defined on the unit sphere. The tools developed in the second part are used for the implementation of SphereSiZer. In SphereSiZer, the scale-dependent features of the density are visualized by projecting the statistically significant gradients onto a planar contour plot of the density function. The method is tested by analyzing samples of surface unit normal vector data of an infant head as well as data from generated simulated spherical densities. The results and examples of the study show that the proposed novel methods perform well. The methods can be extended and developed in further studies. Cranial and facial 3D models will offer many opportunities for the development of new and sophisticated analytical methods in the futureTiivistelmä Pään ja kasvojen pehmytkudoksen 3D-kuvantaminen on yleistynyt lääketieteessä, ja siihen tarvittava teknologia on kehittynyt huomattavasti viime vuosina. 3D-mallit ovat melko tarkkoja, ja kuvaus stereofotogrammetriaan perustuvalla laitteella on nopea ja helppo tilanne kuvattavalle. Kasvojen ja pään 3D-mallien analysointi voi kuitenkin olla haastavaa, ja tarve tehokkaille kvantitatiivisille menetelmille on kasvanut. Tässä väitöskirjassa kehitetään uusia matemaattisia kraniofakiaalisten rakenteiden mittausmenetelmiä ja -työkaluja. Työ on jaettu kolmeen osaan. Ensimmäisessä osassa pyritään määrittämään liettualaisten kaksosten tsygositeetti kasvojen 3D-datan perusteella. Luokituksessa hyödynnetään tilastollista hahmontunnistusta, ja tuloksia verrataan DNA-testituloksiin. Toisessa osassa analysoidaan pään epämuodostumia imeväisikäisten päiden 3D-kuvista laskettujen pintanormaalivektorien suuntiin perustuvan jakauman avulla. Tasaisuuden ja epäsymmetrian määrää mitataan normaalivektorien suuntakulmien ydinestimaatin funktionaalien avulla. Kehitettyä menetelmää verrataan joihinkin aiemmin ehdotettuihin lähestymistapoihin mittaamalla kolmen kuukauden ikäisten imeväisten 3D-malleja ja tarkastelemalla asiantuntijoiden tekemiä kliinisiä pisteytyksiä. Menetelmää sovelletaan myös kliiniseen pitkittäistutkimukseen, jossa tutkitaan pään epämuodostumien ja niihin liittyvien riskitekijöiden kehitystä kolmena eri ajankohtana otettujen 3D-kuvien perusteella. Viimeisessä osassa esitellään uusi tilastollinen skaala-avaruusmenetelmä SphereSiZer, jolla tutkitaan yksikköpallon tiheysfunktion rakenteita. Toisessa osassa kehitettyjä työkaluja sovelletaan SphereSiZerin toteutukseen. SphereSiZer-menetelmässä tiheysfunktion eri skaalojen piirteet visualisoidaan projisoimalla tilastollisesti merkitsevät gradientit tiheysfunktiota kuvaavalle isoviivakartalle. Menetelmää sovelletaan imeväisikäisen pään pintanormaalivektoridataan ja simuloituihin, pallotiheysfunktioihin perustuviin otoksiin. Tulosten ja esimerkkien perusteella väitöskirjassa esitetyt uudet menetelmät toimivat hyvin. Menetelmiä voidaan myös kehittää edelleen ja laajentaa jatkotutkimuksissa. Pään ja kasvojen 3D-mallit tarjoavat paljon mahdollisuuksia uusien ja laadukkaiden analyysityökalujen kehitykseen myöhemmissä tutkimuksissa
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Ozbahceci, Oztunali Berguzar. "Effect Of Wave Grouping,spectral Shape And Exreme Waves In A Wave Train On The Stability Of Rubble Mound Breakwaters." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605170/index.pdf.
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There are some empirical formulas used in the design of rubble mound breakwaters to find the weight of armour layer stone. The effect of wave grouping and spectral shape could not put into these design formulas since their effects are still under question. The influences of wave groups and spectral shape on the stability of rubble mound breakwaters have been investigated by several researchers up to now. However, results were not conclusive in these researches, where different wave grouping and spectral shape parameters were used.
This study aims to investigate the influences of wave groups and spectral shape on the stability of rubble mound breakwaters by means of hydraulic model experiments. According to the result of the experiments, the damage
to breakwater armour layer is almost same for different spectrum shapes and pronounced wave grouping, under the condition of similar wave statistics. Experiments also indicated that the wave trains with same significant wave height, H1/3, but with different distribution of the heights of extreme waves which were defined as wave heights higher than H1/3 in this
study, cause different damage levels. Based on these results, extended experiments were conducted to observe the effect of heights of extreme waves in a wave train on the stability of rubble mound breakwaters. Results of the experiments showed that the higher the extreme waves are, the more
destructive the wave train is. By carrying experimental results into design conditions, it was shown that a wave train with high extreme waves may affect the design weight of armour stone.
Finally, in order to achieve more practical tools for engineering applications, occurrence probabilities of extreme waves under different spectral shapes were obtained by a numerical simulation. As a result, for different occurrence probabilities of extreme waves under the most widely used spectrums of PM and JONSWAP, necessary weight of armour stone was given in a range comparing with the formula of Meer. Moreover, it was noted that the spectral shape indirectly affects the stability not due to the wave grouping but due to the extreme waves in a wave train since the occurrence probability of the high extreme waves becomes higher as the spectral shape
becomes narrower under same significant wave height condition.
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Su, Z. "Statistical shape modelling : automatic shape model building." Thesis, University College London (University of London), 2011. http://discovery.ucl.ac.uk/1213097/.
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Statistical Shape Models (SSM) have wide applications in image segmentation, surface registration and morphometry. This thesis deals with an important issue in SSM, which is establishing correspondence between a set of shape surfaces on either 2D or 3D. Current methods involve either manual annotation of the data (current ‘gold standard’); or establishing correspondences by using segmentation or registration algorithms; or using an information technique, Minimum Description Length (MDL), as an objective function that measures the utility of a model (the state-of-the-art). This thesis presents in principle another framework for establishing correspondences completely automatically by treating it as a learning process. Shannon theory is used extensively to develop an objective function, which measures the performance of a model along each eigenvector direction, and a proper weighting is automatically calculated for each energy component. Correspondence finding can then be treated as optimizing the objective function. An efficient optimization method is also incorporated by deriving the gradient of the cost function. Experimental results on various data are presented on both 2D and 3D. In the end, a quantitative evaluation between the proposed algorithm and MDL shows that the proposed model has better Generalization Ability, Specificity and similar Compactness. It also shows a good potential ability to solve the so-called “Pile Up” problem that exists in MDL. In terms of application, I used the proposed algorithm to help build a facial contour classifier. First, correspondence points across facial contours are found automatically and classifiers are trained by using the correspondence points found by the MDL, proposed method and direct human observer. These classification schemes are then used to perform gender prediction on facial contours. The final conclusion for the experiments is that MEM found correspondence points built classification scheme conveys a relatively more accurate gender prediction result. Although, we have explored the potential of our proposed method to some extent, this is not the end of the research for this topic. The future work is also clearly stated which includes more validations on various 3D datasets; discrimination analysis between normal and abnormal subjects could be the direct application for the proposed algorithm, extension to model-building using appearance information, etc.
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Alfahad, Mai F. A. M. "Statistical shape analysis of helices." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/21675/.
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Consider a sequence of equally spaced points along a helix in three-dimensional space, which are observed subject to statistical noise. In this thesis, maximum likelihood (ML) method is developed to estimate the parameters of the helix. Statistical properties of the estimator are studied and comparisons are made to other estimators found in the literature. Methods are established here for the fitting of unkinked and kinked helices. For an unkinked helix an initial estimate of a helix axis is estimated by a modified eigen-decomposition or a method from the literature. Mardia-Holmes model can be used to estimate the initial helix axis but it is often not very successful one since it requires initial parameters. A better method for initial axis estimation is the Rotfit method. If the the axis is known, we minimize the residual sum of squares (RSS) to estimate the helix parameters and then optimize the axis estimate. For a kinked helix, we specify a test statistic by simulating the null distribution of unkinked helices. If the kink position is known, then the test statistic approximately follows an F-distribution. If the null hypothesis is rejected i.e. the helix has a change point, and then cut the helix into two sub-helices between the change point where the helix has the maximum statistic. Statistics test are studied to test how differ these two sub-helices from each other. Parametric bootstrap procedure is used to study these statistics. The shapes of protein alpha-helices are used to illustrate the procedure.
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Mei, Lin. "Statistical analysis of shape and deformation." Thesis, Imperial College London, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.542932.
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Ruwanthi, Kolamunnage Dona Rasanga. "Statistical shape analysis for bilateral symmetry." Thesis, University of Leeds, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.418233.
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Dryden, Ian Leslie. "The statistical analysis of shape data." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392774.
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Golland, Poilna 1971. "Statistical shape analysis of anatomical structures." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/86776.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 123-130).
In this thesis, we develop a computational framework for image-based statistical analysis of anatomical shape in different populations. Applications of such analysis include understanding developmental and anatomical aspects of disorders when comparing patients vs. normal controls, studying morphological changes caused by aging, or even differences in normal anatomy, for example, differences between genders. Once a quantitative description of organ shape is extracted from input images, the problem of identifying differences between the two groups can be reduced to one of the classical questions in machine learning, namely constructing a classifier function for assigning new examples to one of the two groups while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data that are captured by the discriminative model. In contrast, interpretation of the statistical model in the original image domain is an important component of morphological analysis. We propose a novel approach to such interpretation that allows medical researchers to argue about the identified shape differences in anatomically meaningful terms of organ development and deformation. For each example in the input space, we derive a discriminative direction that corresponds to the differences between the classes implicitly represented by the classifier function.
(cont.) For morphological studies, the discriminative direction can be conveniently represented by a deformation of the original shape, yielding an intuitive description of shape differences for visualization and further analysis. Based on this approach, we present a system for statistical shape analysis using distance transforms for shape representation and the Support Vector Machines learning algorithm for the optimal classifier estimation. We demonstrate it on artificially generated data sets, as well as real medical studies.
by Polina Golland.
Ph.D.
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Valdés, Amaro Daniel Alejandro. "Statistical shape analysis for bio-structures : local shape modelling, techniques and applications." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/3810/.
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A Statistical Shape Model (SSM) is a statistical representation of a shape obtained from data to study variation in shapes. Work on shape modelling is constrained by many unsolved problems, for instance, difficulties in modelling local versus global variation. SSM have been successfully applied in medical image applications such as the analysis of brain anatomy. Since brain structure is so complex and varies across subjects, methods to identify morphological variability can be useful for diagnosis and treatment. The main objective of this research is to generate and develop a statistical shape model to analyse local variation in shapes. Within this particular context, this work addresses the question of what are the local elements that need to be identified for effective shape analysis. Here, the proposed method is based on a Point Distribution Model and uses a combination of other well known techniques: Fractal analysis; Markov Chain Monte Carlo methods; and the Curvature Scale Space representation for the problem of contour localisation. Similarly, Diffusion Maps are employed as a spectral shape clustering tool to identify sets of local partitions useful in the shape analysis. Additionally, a novel Hierarchical Shape Analysis method based on the Gaussian and Laplacian pyramids is explained and used to compare the featured Local Shape Model. Experimental results on a number of real contours such as animal, leaf and brain white matter outlines have been shown to demonstrate the effectiveness of the proposed model. These results show that local shape models are efficient in modelling the statistical variation of shape of biological structures. Particularly, the development of this model provides an approach to the analysis of brain images and brain morphometrics. Likewise, the model can be adapted to the problem of content based image retrieval, where global and local shape similarity needs to be measured.
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Golalizadeh, Lehi Mousa. "Statistical modelling and inference for shape diffusions." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435446.
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Lima, Verônica Maria Cadena. "Resistant fitting methods for statistical shape comparison." Thesis, University of Leeds, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275749.
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Cremers, Daniel. "Statistical shape knowledge in variational image segmentation." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10605028.
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Xu, Yuan. "Statistical shape analysis for deep brain structures." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1581917061&sid=11&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Rayner, Glen. "Statistical methodologies for quantile-based distributional families." Thesis, Queensland University of Technology, 1999.
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Bell, Paul W. "Statistical inference for multidimensional scaling." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327197.
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Besbes, Ahmed. "Image segmentation using MRFs and statistical shape modeling." Phd thesis, Ecole Centrale Paris, 2010. http://tel.archives-ouvertes.fr/tel-00594246.
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Nous présentons dans cette thèse un nouveau modèle statistique de forme et l'utilisons pour la segmentation d'images avec a priori. Ce modèle est représenté par un champ de Markov. Les noeuds du graphe correspondent aux points de contrôle situés sur le contour de la forme géométrique, et les arêtes du graphe représentent les dépendances entre les points de contrôle. La structure du champ de Markov est déterminée à partir d'un ensemble de formes, en utilisant des techniques d'apprentissage de variétés et de groupement non-supervisé. Les contraintes entre les points sont assurées par l'estimation des fonctions de densité de probabilité des longueurs de cordes normalisées. Dans une deuxième étape, nous construisons un algorithme de segmentation qui intègre le modèle statistique de forme, et qui le relie à l'image grâce à un terme région, à travers l'utilisation de diagrammes de Voronoi. Dans cette approche, un contour de forme déformable évolue vers l'objet à segmenter. Nous formulons aussi un algorithme de segmentation basé sur des détecteurs de points d'intérêt, où le terme de régularisation est lié à l'apriori de forme. Dans ce cas, on cherche à faire correspondre le modèle aux meilleurs points candidats extraits de l'image par le détecteur. L'optimisation pour les deux algorithmes est faite en utilisant des méthodes récentes et efficaces. Nous validons notre approche à travers plusieurs jeux de données en 2D et en 3D, pour des applications de vision par ordinateur ainsi que l'analyse d'images médicales.
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Brignell, Christopher. "Shape analysis and statistical modelling in brain imaging." Thesis, University of Nottingham, 2007. http://eprints.nottingham.ac.uk/12106/.
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This thesis considers the registration of shapes, estimation of shape variability and the statistical modelling of human brain magnetic resonance images (MRI). Current shape registration techniques, such as Procrustes analysis, superimpose shapes in order to make inferences regarding the mean shape and shape variability. We apply Procrustes analysis to a subset of the landmarks and give distributional results for the Euclidean distance of a shape from a template. Procrustes analysis is then generalised to minimise a Mahalanobis norm, with respect to a symmetric, positive denite matrix, and the weighted Procrustes estimators for scaling, rotation and translation obtained. This weighted registration criterion is shown, through a simulation study, to reduce the bias and error in maximum likelihood estimates of the mean shape and covariance matrix compared to isotropic Procrustes. A Bayesian Markov chain Monte Carlo algorithm is also presented and shown to be less sensitive to prior information. We consider two MRI data sets in detail. We examine the first data set for large-scale shape dierences between two volunteer groups, healthy controls and schizophrenia patients. The images are registered to a template through modelling the voxel values and we maximise the likelihood over the transformation parameters. Using a suitable labelling and principal components analysis we show schizophrenia patients have less brain asymmetry than healthy controls. The second data set is a sequence of functional MRI scans of an individual's motor cortex taken while they repeatedly press a button. We construct a model with temporal correlations to estimate the trial-to-trial variability in the haemodynamic response using the Expectation-Maximisation algorithm. The response is shown to change with task and through time. For both data sets we compare our techniques with existing software packages and improvements to data pre-processing are suggested. We conclude by discussing potential areas for future research.
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Robinson, David L. "Statistical methods for the analysis of tooth shape." Thesis, University of Sheffield, 2005. http://etheses.whiterose.ac.uk/6077/.
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The study of tooth shape has traditionally involved analysing distances or angles between established points of correspondence, known as landmarks. Digital imaging has aided this process, yet improved statistical techniques, which offer advantages by retaining information on the geometry of objects throughout the analysis, have so far received little attention. Since methods must be suitable for use on un-extracted teeth, a key difficulty is that unwanted variation in recorded shape results from differences in the position of patients' gingival (gum) tissue. Here we present new methodology for addressing this problem and for use in more general applications, where objects are analysed as configurations of landmarks and one would wish to account for lack of precise correspondence between certain points, in a better way than is possible using existing techniques. After introducing the ideas of Procrustes analysis to this field, we use newly proposed methods of reliability assessment to show how, in addition to failing to allow for gum variation, implementation of this technique in its standard form is problematic, due to the poor reproducibility of particular landmarks. Use of Bookstein's (1996a, d, e) semi- landmark method, which aims to overcome lack of precise correspondence along certain directions by allowing landmarks to move iteratively along chords during Procrustes registration, is investigated but found to produce unrealistic results in certain situations. Novel modifications of this method are then proposed and evaluated in terms of addressing the issues noted above. Alternatives to minimising the `bending energy' of a pair of splines mapping from the mean shape, in order to determine new semi- landmark positions are explored and two new methods, using a `nearest point' or `full Procrustes' criterion, identified as most promising. Further investigation, by application to tooth shape problems (including a simulation study of gingival tissue variation) and use on distorted configurations generated from simple geometric shapes, show that these methods offer improvements over existing techniques in terms of filtering out unwanted variation.
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Evans, Kim. "Statistical analysis of shape curves and surface matching." Thesis, Nottingham Trent University, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444660.
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Alemneh, Tewodros. "Articulated Statistical Shape Modelling of the Shoulder Joint." Master's thesis, Faculty of Health Sciences, 2020. http://hdl.handle.net/11427/32190.
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The shoulder joint is the most mobile and unstable joint in the human body. This makes it vulnerable to soft tissue pathologies and dislocation. Insight into the kinematics of the joint may enable improved diagnosis and treatment of different shoulder pathologies. Shoulder joint kinematics can be influenced by the articular geometry of the joint. The aim of this project was to develop an analysis framework for shoulder joint kinematics via the use of articulated statistical shape models (ASSMs). Articulated statistical shape models extend conventional statistical shape models by combining the shape variability of anatomical objects collected from different subjects (statistical shape models), with the physical variation of pose between the same objects (articulation). The developed pipeline involved manual annotation of anatomical landmarks selected on 3D surface meshes of scapulae and humeri and establishing dense surface correspondence across these data through a registration process. The registration was performed using a Gaussian process morphable model fitting approach. In order to register two objects separately, while keeping their shape and kinematics relationship intact, one of the objects (scapula) was fixed leaving the other (humerus) to be mobile. All the pairs of registered humeri and scapulae were brought back to their native imaged position using the inverse of the associated registration transformation. The glenohumeral rotational center and local anatomic coordinate system of the humeri and scapulae were determined using the definitions suggested by the International Society of Biomechanics. Three motions (flexion, abduction, and internal rotation) were generated using Euler angle sequences. The ASSM of the model was built using principal component analysis and validated. The validation results show that the model adequately estimated the shape and pose encoded in the training data. Developing ASSM of the shoulder joint helps to define the statistical shape and pose parameters of the gleno humeral articulating surfaces. An ASSM of the shoulder joint has potential applications in the analysis and investigation of population-wide joint posture variation and kinematics. Such analyses may include determining and quantifying abnormal articulation of the joint based on the range of motion; understanding of detailed glenohumeral joint function and internal joint measurement; and diagnosis of shoulder pathologies. Future work will involve developing a protocol for encoding the shoulder ASSM with real, rather than handcrafted, pose variation.
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Tardugno, Angelo. "Novel approaches to statistical shape modelling of bone." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/5881.
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The femur is the longest bone in the human body and serves the important purposes of load-bearing and allowing bipedal locomotion. Accurate modelling of the variation in shape within the healthy adult population can be useful for a variety of applications: from the mere anatomical description of its features, in order to better understand its function, to more complex tasks such as pathology detection or surgical planning. Statistical Shape Modelling (SSM) is a well-established technique that enables to capture the variability within a set of training shapes and describes it with a reduced set of variables. The aim of this thesis is to evaluate the performance of a SSM based on a point cloud representation of shape, and introduce and test subsequent improvements to the modelling process that can increase its clinical relevance and scope of application. The standard approach to SSM employs a dimension-reducing technique, generally by means of Principal Component Analysis (PCA). However, this approach favours the compactness of the model, thus not focusing on other aspects that may be more relevant to clinical practice. Although rotation of the principal components is commonly performed as a post-processing step in statistical analysis involving PCA, it is not routinely applied in SSM. By applying this class of rotation, the components' effects are more localised, allowing a better interpretation, understanding and classification of pathological deformities. Among other possible representations, the Medial Axis Transform (MAT) could offer a further insight into shape modelling, since it allows the information about thickness to be decoupled from the rest of the shape. SSMs based on this representation can lead to a di erent perspective on the understanding of femoral anatomy and function,and can also enable the reconstruction of the complete anatomy starting from a reduced set of features, with diverse applications in the elds of surgical planning, forensic science and paleontology.
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Hennessey, Anthony. "Statistical shape analysis of large molecular data sets." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/52088/.
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Protein classification databases are widely used in the prediction of protein structure and function, and amongst these databases the manually-curated Structural Classification of Proteins database (SCOP) is considered to be a gold standard. In SCOP, functional relationships are described by hyperfamily and superfamily categories and structural relationships are described by family, species and protein categories. We present a method to calculate a difference measure between pairs of proteins that can be used to reproduce SCOP2 structural relationship classifications, and that can also be used to reproduce a subset of functional relationship classifications at the superfamily level. Calculating the difference measure requires first finding the best correspondence between atoms in two protein configurations. The problem of finding the best correspondence is known as the unlabelled, partial matching problem. We consider the unlabelled, partial matching problem through a detailed analysis of the approach presented in Green and Mardia (2006). Using this analysis, and applying domain-specific constraints, we develop a new algorithm called GProtA for protein structure alignment. The proposed difference measure is constructed from the root mean squared deviation of the aligned protein structures and a binary similarity measure, where the binary similarity measure takes into account the proportions of atoms matching from each configuration. The GProtA algorithm and difference measure are applied to protein structure data taken from the Protein Data Bank. The difference measure is shown to correctly classify 62 of a set of 72 proteins into the correct SCOP family categories when clustered. Of the remaining 9 proteins, 2 are assigned incorrectly and 7 are considered indeterminate. In addition, a method for deriving characteristic signatures for categories is proposed. The signatures offer a mechanism by which a single comparison can be made to judge similarity to a particular category. Comparison using characteristic signatures is shown to correctly delineate proteins at the family level, including the identification of both families for a subset of proteins described by two family level categories.
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Brombin, Chiara. "A nonparametric permutation approach to statistical shape analysis." Doctoral thesis, Università degli studi di Padova, 2009. http://hdl.handle.net/11577/3426066.
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The statistical community has shown an increased interest in shape analysis in the last decade, in particular with reference to the development of robust inferential statistical methods.
In this Ph.D. thesis we present an extension of NonParametric Combination (NPC) methodology (Pesarin, 2001) to shape analysis. At first we review inferential methods known in the shape analysis literature, highlighting some drawbacks of using Hotelling's T^2 test statistic. Then, focussing on the two independent sample case, through an exhaustive comparative simulation study, we evaluate the behaviour of traditional tests along with nonparametric permutation tests using also Multiple Aspect (MA) procedures and domain combinations.
The case of heterogeneous and dependent variation at each landmark is also investigated, along with the effects of superimposition on the power of NPC tests.
Permutation tests have been evaluated also in the particular case in which the number of variables is larger than the cardinality of permutation sample space. We have performed a simulation study to evaluate the power of multivariate NPC tests, showing that the power for the proposed tests increases when increasing the number of the processed variables provided that the noncentrality parameter increases, even when the number of covariates is larger than the permutation sample space.
These preliminary results allowed us to extend the notion of finite-sample consistency for permutation tests combination-based to the shape analysis field.
Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable alpha-value, when the number of variables diverges, provided that the noncentrality induced by test statistics also diverges.
On the basis of these findings, we emphasize that the proposed tests provide efficient solutions to multivariate small sample problems, like those encountered in the shape analysis field.
Along with simulation studies, we present two applications to real data sets concerning Mediterranean monk seal skulls and aortic valve morphology.Nell'ultimo decennio la comunità statistica ha mostrato un crescente interesse per i problemi di shape analysis, con particolare riferimento allo sviluppo di tecniche inferenziali robuste. In questa tesi di dottorato presentiamo un'estensione della metodologia NPC per la combinazione non parametrica di test di permutazione dipendenti (Pesarin, 2001) nell'ambito della shape analysis. Inizialmente si introduce una revisione dei metodi inferenziali noti in letteratura, evidenziando alcune problematiche legate all'uso della statistica test T^2 di Hotelling. Focalizzandoci poi sul caso di due campioni indipendenti, tramite un esauriente studio di simulazione, abbiamo confrontato il comportamento, in termini di potenza, dei test parametrici tradizionali con quello dei test non parametrici proposti. Sono state utilizzate anche procedure di tipo multi aspetto (MA) e combinazioni per domini. E’ stato anche esaminato il caso in cui i landmark sono correlati tra loro. Inoltre è stato valutato l'impatto della superimposizione sulla potenza dei test NPC. I test di permutazione sono stati valutati in potenza e sotto H_0 nel caso in cui il numero di variabili processate è superiore alla cardinalità dello spazio di permutazione. Abbiamo inoltre effettuato uno studio di simulazione per valutare la potenza dei test multivariati NPC, evidenziando che la potenza di questi test cresce al crescere del numero di variabili processate, qualora apportino un aumento della non centralità, anche quando il numero di variabili è superiore alla cardinalità dello spazio di permutazione. Questi risultati preliminari ci hanno consentito di estendere la nozione di finite-sample consistency per i test NPC nell'ambito della shape analysis. Vengono fornite condizioni sufficienti tali per cui la potenza del test converge a uno, per ampiezze campionarie fissate ad ogni livello raggiungibile alpha, quando il numero di variabili diverge, posto che diverga anche la non centralità indotta dall'aumento del numero di variabili. Sulla base dei risultati ottenuti, possiamo affermare che i test NPC forniscono soluzioni efficienti per i problemi multivariati di shape analysis in presenza di bassa numerosità campionarie, problemi del resto frequenti nell'ambito della shape analysis. Oltre agli studi di simulazione, vengono presentati due casi studio, uno relativo allo studio della forma del cranio della foca monaca del Mediterraneo e l'altro relativo alla morfologia della valvola aortica.
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Czogiel, Irina. "Statistical inference for molecular shapes." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/12217/.
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This thesis is concerned with developing statistical methods for evaluating and comparing molecular shapes. Techniques from statistical shape analysis serve as a basis for our methods. However, as molecules are fuzzy objects of electron clouds which constantly undergo vibrational motions and conformational changes, these techniques should be modified to be more suitable for the distinctive features of molecular shape. The first part of this thesis is concerned with the continuous nature of molecules. Based on molecular properties which have been measured at the atom positions, a continuous field--based representation of a molecule is obtained using methods from spatial statistics. Within the framework of reproducing kernel Hilbert spaces, a similarity index for two molecular shapes is proposed which can then be used for the pairwise alignment of molecules. The alignment is carried out using Markov chain Monte Carlo methods and posterior inference. In the Bayesian setting, it is also possible to introduce additional parameters (mask vectors) which allow for the fact that only part of the molecules may be similar. We apply our methods to a dataset of 31 steroid molecules which fall into three activity classes with respect to the binding activity to a common receptor protein. To investigate which molecular features distinguish the activity classes, we also propose a generalisation of the pairwise method to the simultaneous alignment of several molecules. The second part of this thesis is concerned with the dynamic aspect of molecular shapes. Here, we consider a dataset containing time series of DNA configurations which have been obtained using molecular dynamic simulations. For each considered DNA duplex, both a damaged and an undamaged version are available, and the objective is to investigate whether or not the damage induces a significant difference to the the mean shape of the molecule. To do so, we consider bootstrap hypothesis tests for the equality of mean shapes. In particular, we investigate the use of a computationally inexpensive algorithm which is based on the Procrustes tangent space. Two versions of this algorithm are proposed. The first version is designed for independent configuration matrices while the second version is specifically designed to accommodate temporal dependence of the configurations within each group and is hence more suitable for the DNA data.
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Quan, Wei. "3-D facial expression representation using statistical shape models." Thesis, University of Central Lancashire, 2009. http://clok.uclan.ac.uk/21147/.
Full textAbstract:
Facial expressions are visible signs of person's affective state, cognitive activity and personality. Automatic recognition of facial expressions is an important component for a wide spectrum of applications including human-computer interfaces, video conferencing, augmented reality and human activity monitoring to mention a few. Facial expression representation is an essential part in the automatic recognition of facial expressions. It is concerned with finding distinguishable features that can be utilised for representing different facial expressions without constraints of age, ethnicity or gender. This thesis reports on research and development in the facial expression representation. The author has proposed two novel methods for representing facial expressions. One is based on the shape space vector (SSV) of the statistical shape model (SSM); the other is based on the SSV of the B-spline statistical shape model (BSSM). The first proposed method uses the SSV of the SSM as a significant feature for representing facial expressions embedded in 3-D facial surfaces. In order to obtain the SSV, a novel model-based surface registration method is proposed that iteratively deforms and matches the model to an unseen new facial surface. Two major stages are included in this method, namely, model building and model fitting. In the model building stage, a SSM is built by using a training data set with estimated correspondences. In the model fitting stage, the built model is adapted to represent the shape of the new facial surface, which has not been included in the training data set. To build the model, the thin plate spline warping has been used so that all of the facial surfaces in the training data set are aligned into a common reference facial surface and the dense correspondences of points between these facial surfaces can be calculated. To fit the model to the new facial surface a modified iterative closest point (ICP) algorithm and least-squares projection on to the estimated shape space, constructed using the training data set, are applied. The second proposed method uses the SSV of the BSSM for facial expression representation. The mddel is built using B-spline control points instead of the surface points as in the SSM based method. In order to obtain the control points of B-spline, a novel method for the B-spline surface fitting has been proposed. The robustness and efficiency of both model-based facial expression representation methods are improved by introducing a multi-resolution scheme in the model fitting stage. The experimental results on simulated and real 3-D facial surfaces show that the proposed methods can effectively provide distinguishable features for facial expression analysis and recognition.