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Esta tese de doutorado aborda os tópicos de modelagem e de reconhecimento de objetos estruturados, ou sistemas estruturados de objetos, em imagens. Um objeto ou sistema estruturado é aquele que pode ser descrito através de elementos primitivos que o compõem e pelas relações existentes entre esses elementos. Por exemplo, uma aeronave pode ser descrita pelos seguintes elementos primitivos: asas direita e esquerda, fuselagem e cockpit. O aspecto relacional de um objeto estruturado direciona sua representação computacional e seu reconhecimento em imagens ao paradigma estrutural de reconhecimento de padrões. Contudo, a variabilidade das características dos seus elementos primitivos é melhor representada através do paradigma estatístico de reconhecimento de padrões. Devido à complementaridade dos paradigmas, a conjunção dessas abordagens é um tema de pesquisa de interesse atual. Para conjugar esses dois aspectos, esta tese propôs uma metodologia que combina o conhecimento a priori das relações que caracterizam um objeto estruturado com dados estatísticos coletados de amostras desse objeto, num modelo híbrido denominado grafo estatístico-relacional (GER). Segundo essa representação, foi estudada uma abordagem probabilística para reconhecer um objeto estruturado em imagens. Nesse cenário, o GER modelo é considerado uma variável aleatória, enquanto uma rotulação de uma imagem de entrada é interpretada como uma potencial observação do modelo. A tarefa de reconhecimento foi então formulada como um problema de otimização, que busca maximizar a probabilidade da observação de acordo com o modelo. O método foi aplicado à modelagem de órgãos abdominais em imagens de ressonância magnética não-contrastadas. Esses órgãos apresentam um arranjo espacial consistente em imagens distintas, além de propriedades de aparência e anatômicas variáveis, o que vem ao encontro da proposta da representação por GER e da abordagem probabilística para o reconhecimento dos órgãos em novas imagens. / The purpose of this thesis was to propose a formalism for the problems of modeling and recognition of a structured object, or a system of structured objects, in images. A structured object is one that may be described in terms of its compound primitive elements and their inherent relations. For instance, an aircraft may be described in terms of the following primitives: right and left wings, fuselage, and cockpit. The relational aspect of structured objects leads these problems to solutions in structural pattern recognition, which describes patterns as primitives and relations. Nevertheless, the variability of primitive elements and of their relations is better modeled by traditional statistical pattern recognition methods. Because of the complementary capabilities of these approaches, the fusion of both has recently been pointed out as a trend in computer vision. To consider these sources of information, the methodology presented herein combines relational cues inherent to a structured object with statistical information learned from a set of object samples. A hybrid model of a structured object is represented by means of a statistical relational graph (SRG). The SRG is a prototype attributed relational graph (ARG) in which nodes represent primitive elements and arcs link nodes representing related primitives. Each node or arc is associated with attributes which are parameters of probability distributions that describe random variables representing primitive or relational attributes. Based on this representation, a probabilistic approach was proposed to tackle the problem of recognizing a structured object in an input image. The model SRG is interpreted as a random variable, whereas a labeling of the input image is considered a potential observation of the model. The recognition task was formulated as the optimization of an objective-function that is actually a probability measure to be maximized. The proposed approach was applied to the modeling of abdominal organs in non-contrasted magnetic resonance images. These organs present consistent spatial arrangement in distinct images, as well as varying appearance and anatomical properties, which meet the principle of the SRG representation and the associated probabilistic recognition scenario.

This thesis describes a set of image analysis tools developed for the purpose of quantifying the distribution of chromatin in (light) microscope images of cell nuclei. The distribution or pattern of chromatin is influenced by both external and internal variations of the cell environment, including variations associated with the cell cycle, neoplasia, apoptosis, and malignancy associated changes (MACs). The quantitative characterisation of this pattern makes possible the prediction of the biological state of a cell, or the detection of subtle changes in a population of cells. This has important application to automated cancer screening. The majority of existing methods for quantifying chromatin distribution (texture) are based on the stochastic approach to defining texture. However, it is the premise of this thesis that the structural approach is more appropriate because pathologists use terms such as clumping, margination, granulation, condensation, and clearing to describe chromatin texture, and refer to the regions of condensed chromatin as granules, particles, and blobs. The key to the structural approach is the segmentation of the chromatin into its texture primitives. Unfortunately all of the chromatin segmentation algorithms published in the literature suffer from one or both of the following drawbacks: (i) a segmentation that is not consistent with a human's perception of blobs, particles, or granules; and (ii) the need to specify, a priori, one or more subjective operating parameters. The latter drawback limits the robustness of the algorithm to variations in illumination and staining quality. The structural model developed in this thesis is based on several novel low-, med-ium-, and high-level image analysis tools. These tools include: a class of non-linear self-dual filters, called folding induced self-dual filters, for filtering impulse noise; an algorithm, based on seeded region growing, for robustly segmenting chromatin; an improved seeded region growing algorithm that is independent of the order of pixel processing; a fast priority queue implementation suitable for implementing the watershed transform (special case of seeded region growing); the adjacency graph attribute co-occurrence matrix (AGACM) method for quantifying blob and mosaic patterns in the plane; a simple and fast algorithm for computing the exact Euclidean distance transform for the purpose of deriving contextual features (measurements) and constructing geometric adjacency graphs for disjoint connected components; a theoretical result establishing an equivalence between the distance transform of a binary image and the grey-scale erosion of its characteristic function by an elliptic poweroid structuring element; and a host of chromatin features that can be related to qualitative descriptions of chromatin distribution used by pathologists. In addition, this thesis demonstrates the application of this new structural model to automated cervical cancer screening. The results provide empirical evidence that it is possible to detect differences in the pattern of nuclear chromatin between samples of cells from a normal Papanicolaou-stained cervical smear and those from an abnormal smear. These differences are supportive of the existence of the MACs phenomenon. Moreover the results compare favourably with those reported in the literature for other stains developed specifically for automated cytometry. To the author's knowledge this is the first time, based on a sizable and uncontaminated data set, that MACs have been demonstrated in Papanicolaou stain. This is an important finding because the primary screening test for cervical cancer, the Papanicolaou test, is based on this stain.

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 future. / Tiivistelmä 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.

Esta tese de doutorado aborda os tópicos de modelagem e de reconhecimento de objetos estruturados, ou sistemas estruturados de objetos, em imagens. Um objeto ou sistema estruturado é aquele que pode ser descrito através de elementos primitivos que o compõem e pelas relações existentes entre esses elementos. Por exemplo, uma aeronave pode ser descrita pelos seguintes elementos primitivos: asas direita e esquerda, fuselagem e cockpit. O aspecto relacional de um objeto estruturado direciona sua representação computacional e seu reconhecimento em imagens ao paradigma estrutural de reconhecimento de padrões. Contudo, a variabilidade das características dos seus elementos primitivos é melhor representada através do paradigma estatístico de reconhecimento de padrões. Devido à complementaridade dos paradigmas, a conjunção dessas abordagens é um tema de pesquisa de interesse atual. Para conjugar esses dois aspectos, esta tese propôs uma metodologia que combina o conhecimento a priori das relações que caracterizam um objeto estruturado com dados estatísticos coletados de amostras desse objeto, num modelo híbrido denominado grafo estatístico-relacional (GER). Segundo essa representação, foi estudada uma abordagem probabilística para reconhecer um objeto estruturado em imagens. Nesse cenário, o GER modelo é considerado uma variável aleatória, enquanto uma rotulação de uma imagem de entrada é interpretada como uma potencial observação do modelo. A tarefa de reconhecimento foi então formulada como um problema de otimização, que busca maximizar a probabilidade da observação de acordo com o modelo. O método foi aplicado à modelagem de órgãos abdominais em imagens de ressonância magnética não-contrastadas. Esses órgãos apresentam um arranjo espacial consistente em imagens distintas, além de propriedades de aparência e anatômicas variáveis, o que vem ao encontro da proposta da representação por GER e da abordagem probabilística para o reconhecimento dos órgãos em novas imagens. / The purpose of this thesis was to propose a formalism for the problems of modeling and recognition of a structured object, or a system of structured objects, in images. A structured object is one that may be described in terms of its compound primitive elements and their inherent relations. For instance, an aircraft may be described in terms of the following primitives: right and left wings, fuselage, and cockpit. The relational aspect of structured objects leads these problems to solutions in structural pattern recognition, which describes patterns as primitives and relations. Nevertheless, the variability of primitive elements and of their relations is better modeled by traditional statistical pattern recognition methods. Because of the complementary capabilities of these approaches, the fusion of both has recently been pointed out as a trend in computer vision. To consider these sources of information, the methodology presented herein combines relational cues inherent to a structured object with statistical information learned from a set of object samples. A hybrid model of a structured object is represented by means of a statistical relational graph (SRG). The SRG is a prototype attributed relational graph (ARG) in which nodes represent primitive elements and arcs link nodes representing related primitives. Each node or arc is associated with attributes which are parameters of probability distributions that describe random variables representing primitive or relational attributes. Based on this representation, a probabilistic approach was proposed to tackle the problem of recognizing a structured object in an input image. The model SRG is interpreted as a random variable, whereas a labeling of the input image is considered a potential observation of the model. The recognition task was formulated as the optimization of an objective-function that is actually a probability measure to be maximized. The proposed approach was applied to the modeling of abdominal organs in non-contrasted magnetic resonance images. These organs present consistent spatial arrangement in distinct images, as well as varying appearance and anatomical properties, which meet the principle of the SRG representation and the associated probabilistic recognition scenario.

Esta tesis reune algunas contribuciones al reconocimiento de formas estadístico y, más especícamente, a varias tareas del procesamiento del lenguaje natural. Varias técnicas estadísticas bien conocidas se revisan en esta tesis, a saber: estimación paramétrica, diseño de la función de pérdida y modelado estadístico. Estas técnicas se aplican a varias tareas del procesamiento del lenguajes natural tales como clasicación de documentos, modelado del lenguaje natural y traducción automática estadística. En relación con la estimación paramétrica, abordamos el problema del suavizado proponiendo una nueva técnica de estimación por máxima verosimilitud con dominio restringido (CDMLEa ). La técnica CDMLE evita la necesidad de la etapa de suavizado que propicia la pérdida de las propiedades del estimador máximo verosímil. Esta técnica se aplica a clasicación de documentos mediante el clasificador Naive Bayes. Más tarde, la técnica CDMLE se extiende a la estimación por máxima verosimilitud por leaving-one-out aplicandola al suavizado de modelos de lenguaje. Los resultados obtenidos en varias tareas de modelado del lenguaje natural, muestran una mejora en términos de perplejidad. En a la función de pérdida, se estudia cuidadosamente el diseño de funciones de pérdida diferentes a la 0-1. El estudio se centra en aquellas funciones de pérdida que reteniendo una complejidad de decodificación similar a la función 0-1, proporcionan una mayor flexibilidad. Analizamos y presentamos varias funciones de pérdida en varias tareas de traducción automática y con varios modelos de traducción. También, analizamos algunas reglas de traducción que destacan por causas prácticas tales como la regla de traducción directa; y, así mismo, profundizamos en la comprensión de los modelos log-lineares, que son de hecho, casos particulares de funciones de pérdida. Finalmente, se proponen varios modelos de traducción monótonos basados en técnicas de modelado estadístico . / Andrés Ferrer, J. (2010). Statistical approaches for natural language modelling and monotone statistical machine translation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/7109 / Palancia