BACKGROUND: One of the central determinants of functional outcome in schizophrenia is social cognition (SC). With the wide array of SC domains, factor-analysis provides a powerful tool to identify commonalities amongst their underlying dysfunctions and its neural underpinnings. METHODS: The present study performed exploratory factor analysis (EFA) on 93 patients with early course schizophrenia using eight validated SC subtests. Factors derived from this analysis were then used to investigate their relationships with neurocognitive performance, clinical symptoms, and functional outcome. Moreover, subsequent shape analysis of the amygdala and hippocampus was performed using the MAGeT Brain pipeline to investigate their relationship to the composite scores of SC factors. RESULTS: EFA revealed a 3-factor solution, representing the domains of emotion management, emotion recognition, and theory of mind-social contextual appraisal, together accounting for 63.58% of the variance. Interestingly, only the theory of mind-social context appraisal factor correlated with measures of functional outcome. Addition analysis revealed that higher score on the theory of mind factor is significantly related with higher functional outcome measures and verbal learning performance, as well as with lower negative symptoms. Both emotion management and emotion perception factors indicated significant positive correlations with attention-vigilance while only emotion perception significantly correlated with visual learning and memory. Outward convexity of the right amygdala was identified to be positively correlated with the theory of mind-social context appraisal factor (p<0.05, FDR corrected), while the left and right hippocampus, specifically greater surface area of the dorsal-medial and ventral-lateral aspect of the hippocampus respectively, were positively correlated with higher composite score on theory of mind factor (p<0.05, FDR corrected). CONCLUSION: Our EFA indicates overlap amongst SC subtests which represent three different SC subdomains. Furthermore, shape analysis reveals that displacement and surface area of the amygdala and hippocampus respectively play a role in theory of mind. In the future, the SC factors that we identified, along with their neural correlates, could provide essential diagnostic tools to assess SC functioning in early schizophrenia patients, as well as identify strategies for potential improvement following cognitive remediation therapy.

Abstract This thesis presents a multiscale framework for the construction of affine invariant pattern recognition and registration methods. The idea in the introduced approach is to extend the given pattern to a set of affine covariant versions, each carrying slightly different information, and then to apply known affine invariants to each of them separately. The key part of the framework is the construction of the affine covariant set, and this is done by combining several scaled representations of the original pattern. The advantages compared to previous approaches include the possibility of many variations and the inclusion of spatial information on the patterns in the features. The application of the multiscale framework is demonstrated by constructing several new affine invariant methods using different preprocessing techniques, combination schemes, and final recognition and registration approaches. The techniques introduced are briefly described from the perspective of the multiscale framework, and further treatment and properties are presented in the corresponding original publications. The theoretical discussion is supported by several experiments where the new methods are compared to existing approaches. In this thesis the patterns are assumed to be gray scale images, since this is the main application where affine relations arise. Nevertheless, multiscale methods can also be applied to other kinds of patterns where an affine relation is present. An additional application of one multiscale based technique in convexity measurements is introduced. The method, called multiscale autoconvolution, can be used to build a convexity measure which is a descriptor of object shape. The proposed measure has two special features compared to existing approaches. It can be applied directly to gray scale images approximating binary objects, and it can be easily modified to produce a number of measures. The new measure is shown to be straightforward to evaluate for a given shape, and it performs well in the applications, as demonstrated by the experiments in the original paper.

Doctor of Philosophy / Department of Computing and Information Sciences / David A. Schmidt / We are interested in modular static analysis to analyze softwares automatically. We focus on programs with data structures, and in particular, programs with pointers. The final goal is to find errors in a program (problems of dereferencing, aliasing, etc) or to prove that a program is correct (regarding those problems) in an automatic way. Isthiaq, Pym, O'Hearn and Reynolds have recently developed separation logics, which are Hoare logics with assertions and predicates language that allow to prove the correctness of programs that manipulate pointers. The semantics of the logic's triples ({P}C{P'}) is defined by predicate transformers in the style of weakest preconditions. We expressed and proved the correctness of those weakest preconditions (wlp) and strongest postconditions (sp), in particular in the case of while-loops. The advance from the existing work is that wlp and sp are defined for any formula, while previously existing rules had syntactic restrictions. We added fixpoints to the logic as well as a postponed substitution which then allow to express recursive formula. We expressed wlp and sp in the extended logic and proved their correctness. The postponed substitution is directly useful to express recursive formula. For example, [equations removed, still appears in abstract] describes the set of memory where x points to a list of integers. Next, the goal was to use separation logic with fixpoints as an interface language for pointer analysis. That is, translating the domains of those analyses into formula of the logic (and conversely) and to prove their correctness. One might also use the translations to prove the correctness of the pointer analysis itself. We illustrate this approach with a simple pointers-partitioning analysis. We translate the logic formula into an abstract language we designed which allows us to describe the type of values registered in the memory (nil, integer, booleans, pointers to pairs of some types, etc.) as well as the aliasing and non-aliasing relations between variables and locations in the memory. The main contribution is the definition of the abstract language and its semantics in a concrete domain which is the same as the one for the semantics of formula. In particular, the semantics of the auxiliary variables, which is usually a question of implementation, is explicit in our language and its semantics. The abstract language is a partially reduced product of several subdomains and can be parametrised with existing numerical domains. We created a subdomain which is a tabular data structure to cope with the imprecision from not having sets of graphs. We expressed and proved the translations of formula into this abstract language.

Die Skelettextraktion ist besonders in der Formanalyse ein wichtiges Werkzeug. Im Rahmen des Forschungsprojektes ’Extraktion fertigungsrelevanter Merkmale aus 3D-Daten umformtechnischer Bauteile zur featurebasierten Fertigungsprozessgestaltung’ als Kooperationsprojekt zwischen der Professur Graphische Datenverarbeitung und Visualisierung an der Technischen Universität Chemnitz und des Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik Chemnitz wurde diese zur Featureerkennung umgesetzt. Dieses Dokument gibt zunächst Einblick in grundlegende Verfahren und Problemstellungen einer solchen Extraktion. Die Ergebnisse mehrerer Forschungsschwerpunkte, die sich aus den zu untersuchenden Massivumformteilen ergaben, werden vorgestellt. Hierbei besonders interessant ist die robuste Extraktion von Kurvenskeletten bei Bauteilen mit nicht-zylindrischer Hauptform, sowie bei Bauteilen mit Nebenformelementen. Desweiteren werden Nachverarbeitung und Auswertung des Kurvenskeletts, sowie verwandte Forschungsarbeiten und -ergebnisse diskutiert.

Changes occur to the mandible with dental loss and senescence. However, the influence that these changes have on sex and ancestry estimations remains unclear. The purpose of this study was to investigate the influence of dental loss and senescence on changes in mandibular morphology. The outcome has implications for both forensic anthropology and restorative dentistry. The study sample consisted of 717 mandibles consisting of both male and female South Africans of African (SAA) and European ancestry (SAE). To minimise the effects of variation in dentition amongst sex-ancestry groups, the sample included individuals with a spectrum of tooth loss patterns, namely efficient and inefficient occlusions as well as no occlusions. Dentition was considered efficient when the remaining teeth in occlusion were evenly distributed between the sides. Linear measurements as well as geometric morphometric shape analyses were performed. Shape analyses of the complete mandible were performed on models from digitised landmarks by using a MicroScribe G2. Detailed shape analyses of the ramus and chin area as well as measurements of the cortical thickness at specific sites were executed on images generated by cone beam computed tomography (CBCT). A comprehensive assessment of changes in shape, size and cortical thickness of the mandible with age and dental loss were made. Shape and size differences of the mandible were evaluated for discriminant abilities between sex and ancestry groups. Although most dimensions decreased with tooth loss, the greatest impact was noted in the loss of alveolar bone. The mandibular angle increased minimally in size when a few teeth were lost, but recovered to some extent with further tooth loss. The cortical thicknesses at the mental foramen lingually as well as in the midline in females, were relatively spared with tooth loss. Male individuals of SAA were often the most resilient to tooth loss. In general external linear dimensions were maintained with age despite tooth loss. Conversely, measurements of cortical bone thickness decreased slightly, but could have been influenced by dental loss. The shape of the chin and gonial area was more affected by aging in SAE. The sex and ancestry discriminant ability of the linear dimensions when considered collectively approximated 90%, in general improving further when tooth loss was taken into account. All linear measurements were smaller in females and in general tooth loss accentuated sex differences. SAA exhibited greater dimensions, apart from maximum ramus height, bigonial breadth and cortical thickness at the gonion. The mental tubercles were more prominent than the pogonion in SAE (square chin) and vice versa in individuals of SAA (pointed chin). The gonial area in individuals of African ancestry was broad and more convex and the gonial eversion more prominent with a more upright ramus. Discriminant qualities of the gonial shape for sex in individuals of African ancestry reached 90% within dentition groups. Ramus flexure and chin shape were not found to be useful in sex estimation. In conclusion, this research elucidated the effects of tooth loss and senescence on the morphology of the mandible for the forensic anthropological setting. / Thesis (PhD)--University of Pretoria, 2015. / tm2015 / Anatomy / PhD / Unrestricted

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.

Every year a higher life expectancy is reported for people living in industrial countries. With increasing age, the risk of getting Alzheimer's Disease increases as well. Alzheimer's Disease is a neurodegenerative disease that is characterised by progressive deterioration of brain tissue. One of the first regions in the brain to be affected is the hippocampus. A common method to quantify the deterioration of the hippocampus is to measure its volume. However, decreasing volume is no specific marker of Alzheimer's Disease, but can be caused by other diseases as well. Thus, the deformation has to be observed in more detail, which can be done using shape analysis. A powerful shape analysis technique is the approximation of the surface by means of spherical harmonics. A process chain computing such an approximation is explained in this thesis. Therefore, the data is triangulated, forming a closed manifold. Afterwards, a homogeneous mapping of the surface to the unit sphere is computed in two steps. First an initial spherical parametrisation is computed, which is optimised afterwards to resemble the properties of the initial surface. The optimisation is mandatory, to allow for inter-subject comparability. The optimised parametrisation defines a function on the sphere, that can be approximated by spherical harmonics, a set of basis functions on the unit sphere. This procedure results in a mathematical description of the surface that can be analysed statistically. The method is applied to data of Alzheimer's Disease patients.

Many applications for 3d object analysis and visualization need to deal with object features. The most common features on triangulated surfaces are ridges and valleys which are interesting for matching, segmentation, smoothing, non-photo-realistic rendering and many other tasks. In some cases these features are interrupted or corrupted otherwise. In this paper we present an approach to close such gaps in feature regions. For this purpose a vectorfield on the surface, based on the detected features, is computed. The analysis of this vector field yields to possible junction points. These junction points are connected (guided by the vector field) to close the interrupted feature regions.:1 INTRODUCTION 2 RELATED WORK 3 BASIC DEFINITIONS AND NOTATIONS 4 DETECTION OF FEATURE REGIONS 5 PRE-PROCESSING STEPS 6 CONNECTING FEATURE REGIONS 7 EVALUATION 8 FEATURE RESEARCH

In the field of image analysis in pattern recognition, shape is an important attribute to characterize graphical objects. It provides important information about an image. In the thesis, I proposed a new descriptor for image identification and classification, named Average Degree Descriptor. We did some experiments and compared its performance with Degree Descriptor. We also analyzed the Average Degree Descriptor theoretically, by comparing the data of distorted shapes and shapes of Kiki/Bouba. Since we also need to classify or identify some 3-dimension shapes in practical application, we proposed an approach to transform 3-dimension shapes to 2-dimension shapes. Moreover, we also studied the robustness of the proposed Average Degree Descriptor in random degradation. Results show that the proposed Average Degree Descriptor has good performance in image identification, even with random degradation.

Background: The presence of AD pathology can result in diverse behavioral phenotypes, including the typical amnestic variant characterized by memory deficits, and an atypical aphasic variant characterized by language deficits. Previous research has identified unique cortical atrophy patterns in each phenotype, though less focus has been drawn to subcortical involvement. The current study sought to dissociate these behavioral phenotypes by characterizing their thalamic volume and shape features using high-dimensional brain mapping procedures. Relationships between brain metrics and specific language and memory deficits were also investigated in aphasic AD and amnestic AD, respectively. Method: Thalamic integrity was examined in aphasic AD (n = 25), amnestic AD (n = 21), and healthy control participants (n = 44). Age and supratentorial volume (STV) were used as covariates in all analyses. MR scans were acquired using high-resolution T1-weighted MPRAGE volumes following the ADNI protocol. Thalamic shape features were estimated using Large Deformation Diffeomorphic Metric Mapping. General linear models compared differences in thalamic shape between groups. Pearson correlation coefficients characterized relationships between thalamic nuclei (pulvinar, anterior, and mediodorsal) and language and memory performance in aphasic AD and amnestic AD, respectively. Results: After controlling for age and STV, thalamic volume did not differ between groups [F (2,85) = 2.55, p = 08]. However, AD phenotypes exhibited bilateral inward shape deformation in dorsal and ventral regions extending in an anterior to posterior fashion [left: F(20, 154) = 2.61, p < .001; right: F(20,154)= 2.26, p < .01]. Amnestic AD demonstrated right ventrolateral localized volume loss relative to aphasic AD. Pearson models revealed lower confrontation naming was correlated with localized volume loss of bilateral pulvinar (left: r = .59, p < .01; right: r = .55, p < .01), and bilateral anterior (left: r = .50, p = .01; right: r = .49, p = .01) thalamic nuclei for aphasic AD; lower delayed recall was significantly correlated with localized volume loss in left anterior (r = .46, p = .04) thalamic nuclei in amnestic AD. Conclusions: In the absence of volumetric differences, shape measures captured distinct patterns of localized volume loss in aphasic AD and amnestic AD behavioral phenotypes relative to control participants. Comparisons of AD variants demonstrated inward deformation in amnestic AD, particularly in right ventrolateral regions. Thalamic changes appear to be implicated in AD pathology, with relationships to the expected cognitive impairments, although thalamic atrophy patterns are unable to fully dissociate behavioral phenotypes.