Segmentación robusta de imágenes mediante campos aleatorios de Markov y estimación de la entropía

In a first part of this work, a novel model of Markov random field (MRF) is introduced. Such a model is based on a proposed semi-Huber potential function and it is applied successfully to image segmentation in presence of noise. The main difference with respect to other half-quadratic models, which have been taken here as a reference for comparison purposes, is that the number of parameters to be tuned in the proposed model is smaller. It also makes the tunning simpler. The idea is then, to choose adequate parameter values heuristically for a good segmentation of the image. Some experiments were carried out where the results showed that the proposed model allows an easier tuning of the parameters, with reasonable computation times. In a second part, we introduce a new approach for robust image segmentation. The idea is to combine two strategies within a Bayesian framework. The first one is to use an MRF to allows the introduction of prior information to preserve the edges in the image. The second strategy comes from the fact that the probability density function (pdf) of the likelihood function is non Gaussian or unknown, so it should be approximated by an estimated version. For this, the classical non parametric or kernel density estimation is used. This two strategies lead us to the definition of a new maximum a posteriori (MAP) estimator based on the minimization of the entropy of the estimated pdf of the likelihood function and the MRF simultaneously, named MAP entropy estimator (MAPEE). Some experiments were done for different kind of images degraded with impulsive noise. The segmentation results are very satisfactory and promising.En una primera parte de este trabajo, se introduce un nuevo modelo de campo aleatorio de Markov (CAM), el cual se basa en una función de potencial propuesta denominada semi-Huber. Este nuevo modelo de CAM se utiliza para desarrollar un nuevo algoritmo para segmentación, mismo que fue aplicado a imágenes en presencia de ruido, obteniendo resultados satisfactorios. La principal diferencia con respecto a otros modelos semi-cuadráticos que fueron tomados como referencia con fines de comparación, es que el número de parámetros que deben ser ajustados en el modelo propuesto es menor, y en ese sentido, el ajuste es más sencillo. La idea es pues, elegir valores adecuados de los parámetros de manera heurística para obtener un buen resultado de segmentación de la imagen. Se realizaron algunos experimentos y los resultados mostraron que el modelo propuesto permite efectivamente, un ajuste de los parámetros más sencillo con tiempos de cálculo razonables. En una segunda etapa, se introduce un nuevo enfoque para segmentación robusta de imágenes. La idea es combinar dos estrategias dentro de un marco Bayesiano. La primera consiste en usar un CAM, el cual permite introducir información a priori, es decir, conocimiento previo acerca de los datos, con el fin de preservar los bordes presentes en la imagen. La segunda estrategia proviene del hecho de que la función de densidad de probabilidad (fdp) de la función de verosimilitud es no Gaussiana o desconocida, por lo que debe ser aproximada por medio de una versión estimada, y para realizar esta estimación, se utiliza un procedimiento clásico de estimación no paramétrica o también conocido como estimación por núcleos. La unión de estas dos estrategias conduce a la definición de un nuevo estimador de máximo a posteriori (MAP) basado en la minimización de la entropía de la fdp estimada de la función de verosimilitud y el CAM simultáneamente, al cual se le ha denominado estimador MAP de la entropía (MAPEE). Se realizaron una serie de experimentos con diferentes tipos de imágenes degradadas con ruido impulsivo y los resultados de segmentación obtenidos fueron bastante satisfactorios y prometedores

Spatio-Temporal Mixed Models for Diffusion Tensor Magnetic Resonance Imaging

Diffusion tensor imaging (DTI) is a magnetic resonance imaging modality that provides useful in vivo information about the microstructure of human brain tissue, particularly the white matter structures that comprise the 'wiring' of the brain. DTI holds great promise for enhancing our understanding of white matter disorders, which comprise public health burdens in a variety of medical domains. Due to its relatively complex structure, however, extracting useful information from DTI data presents a number of statistical challenges. More effective statistical methodologies will improve the sensitivity of DTI data analyses and increases their clinical relevance, a goal of substantial public health significance. In this dissertation, I propose a series of analytic approaches to DTI data analysis based on linear mixed effects models (LMEs). These models provide a number of advantages over several expedient DTI data analyses in current use. I demonstrate the applicability and advantages of my LME-based approaches in an analysis that compares white matter microstructure in a group of children and young adults with autism spectrum disorders (ASDs) to typically developing controls.I first identify a class of LMEs for DTI data analyses for which closed-form maximum likelihood estimators of all parameters exist. By avoiding iteration, these models enable practitioners to perform exploratory and confirmatory analyses of large DTI datasets in clinically feasible time. This family of models incorporates group heterogeneity in variance-covariance structure. I then compare the results of my approach with other approaches currently in practice in an analysis of white matter abnormalities associated with ASDs. I also introduce a data analytic framework that incorporates the entire multivariate tensor in a single analysis. I last describe a unified likelihood-based approach to addressing reliability with a new estimator of a generalized intraclass correlation coefficient. I establish the robustness of this approach to model perturbations with a series of theoretical and simulation results and apply it to quantify local spatial reliability in the ASDs example