Esta dissertação apresenta os principais métodos estatísticos para analisar as séries temporais de fMRI com o objetivo de detectar regiões ativadas e caracterizar o erro envolvido nessa decisão. Na análise de imagens funcionais, devido à baixa razão sinal-ruído, torna-se necessário o uso de técnicas elaboradas de processamento. O resultado da aplicação de técnicas estatísticas sobre as séries temporais obtidas da imagem de fMRI, é um mapa estatístico paramétrico, (Statistical Parametric Map), (SPM), uma imagem 3-D que permite determinar o estado do voxel, ativado ou não ativado, e a significância estatística do resultado. Propomos um novo método baseado na Difusão Anisotrópica Robusta, (Robust Anisotropic Diffusion), (RAD), que explora uma característica fundamental da imagem funcional, a correlação espacial das regiões ativadas do cérebro humano. O método proposto permite obter mapas estatísticos que melhoram a determinação das áreas ativadas a partir de dados fMRI ruidosos. Os novos mapas estatísticos paramétricos, baseados na correlação espacial da imagem fMRI, reduzem os erros do processo de classificação dos voxels, melhorando assim o mapeamento das regiões ativadas no cérebro. Aplicamos a técnica proposta em dados gerados artificialmente, simulando ruído e sinal, e avaliamos o novo método proposto e um método clássico de processamento de fMRI. Apresentamos resultados comparativos entre um método clássico, o método de correlação e o novo método. Calculamos os erros envolvidos e apresentamos a curvas características de operação de um receptor, (Receiver Operating Characteristics), (ROC), para ambos métodos, comparando os parâmetros mais importantes. Também avaliamos o novo método em dados reais de fMRI de um experimento em blocos com estímulo visual. / This dissertation presents the main statistical methods to analyse fMRI temporal series to detect activated regions and to characterise the error involved in this decision. Due to low signal to noise ratio, elaborate processing techniques are necessary to analyse functional images. Statistical techniques are usually applied on the temporal series obtained from fMRI, resulting in a Statistical Parametric Map (SPM), a 3-D image that makes it possible to determine the state of a voxel, as activated or not activated, and the statistical significance of the result. We proposed a new, simple an elegant method based on Robust Anisotropic Diffusion (RAD) to exploit the spatial correlation of activated regions of the human brain. The new method, named Robust Anisotropic Diffusion of Statistical Parametric Maps (RADSPM), allows one to obtain statistical maps that improve the determination of activated areas from noisy fMRI data. The new parametric statistical maps, based on the voxel spatial correlation of the fMRI image, reduce the classification error thus improving the significance of the results. We have tested the new technique in both simulated and real fMRI, obtaining sharp and noiseless SPMs with increased statistical significance. We compare results of the new RADSPM method with those of a classic method, the conventional correlation method. We calculate the involved errors and we present Receiver Operating Characteristics (ROC) curves for both methods, comparing the most important parameters for simulated fMRI data. We also evaluate the new method on real data of a visual fMRI experiment.

Esta dissertação apresenta os principais métodos estatísticos para analisar as séries temporais de fMRI com o objetivo de detectar regiões ativadas e caracterizar o erro envolvido nessa decisão. Na análise de imagens funcionais, devido à baixa razão sinal-ruído, torna-se necessário o uso de técnicas elaboradas de processamento. O resultado da aplicação de técnicas estatísticas sobre as séries temporais obtidas da imagem de fMRI, é um mapa estatístico paramétrico, (Statistical Parametric Map), (SPM), uma imagem 3-D que permite determinar o estado do voxel, ativado ou não ativado, e a significância estatística do resultado. Propomos um novo método baseado na Difusão Anisotrópica Robusta, (Robust Anisotropic Diffusion), (RAD), que explora uma característica fundamental da imagem funcional, a correlação espacial das regiões ativadas do cérebro humano. O método proposto permite obter mapas estatísticos que melhoram a determinação das áreas ativadas a partir de dados fMRI ruidosos. Os novos mapas estatísticos paramétricos, baseados na correlação espacial da imagem fMRI, reduzem os erros do processo de classificação dos voxels, melhorando assim o mapeamento das regiões ativadas no cérebro. Aplicamos a técnica proposta em dados gerados artificialmente, simulando ruído e sinal, e avaliamos o novo método proposto e um método clássico de processamento de fMRI. Apresentamos resultados comparativos entre um método clássico, o método de correlação e o novo método. Calculamos os erros envolvidos e apresentamos a curvas características de operação de um receptor, (Receiver Operating Characteristics), (ROC), para ambos métodos, comparando os parâmetros mais importantes. Também avaliamos o novo método em dados reais de fMRI de um experimento em blocos com estímulo visual. / This dissertation presents the main statistical methods to analyse fMRI temporal series to detect activated regions and to characterise the error involved in this decision. Due to low signal to noise ratio, elaborate processing techniques are necessary to analyse functional images. Statistical techniques are usually applied on the temporal series obtained from fMRI, resulting in a Statistical Parametric Map (SPM), a 3-D image that makes it possible to determine the state of a voxel, as activated or not activated, and the statistical significance of the result. We proposed a new, simple an elegant method based on Robust Anisotropic Diffusion (RAD) to exploit the spatial correlation of activated regions of the human brain. The new method, named Robust Anisotropic Diffusion of Statistical Parametric Maps (RADSPM), allows one to obtain statistical maps that improve the determination of activated areas from noisy fMRI data. The new parametric statistical maps, based on the voxel spatial correlation of the fMRI image, reduce the classification error thus improving the significance of the results. We have tested the new technique in both simulated and real fMRI, obtaining sharp and noiseless SPMs with increased statistical significance. We compare results of the new RADSPM method with those of a classic method, the conventional correlation method. We calculate the involved errors and we present Receiver Operating Characteristics (ROC) curves for both methods, comparing the most important parameters for simulated fMRI data. We also evaluate the new method on real data of a visual fMRI experiment.

In this thesis we study Sobolev gradient flows for Perona-Malik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. We show that these flows are well-posed in the forward and reverse directions which yields an effective linear sharpening algorithm. We furthermore establish a number of maximum principles for the forward flow and show that edges are preserved for a finite period of time. We then go on to study isotropic Sobolev gradient flows with respect to higher order Sobolev metrics. As the Sobolev order is increased, we observe an increasing reluctance to destroy fine details and texture. We then consider Sobolev gradient flows for non-linear anisotropic diffusion functionals of arbitrary order. We establish existence, uniqueness and continuous dependence on initial data for a broad class of such equations. The well-posedness of these new anisotropic gradient flows opens the door to a wide variety of sharpening and diffusion techniques which were previously impossible under L2 gradient descent. We show how one can easily use this framework to design an anisotropic sharpening algorithm which can sharpen image features while suppressing noise. We compare our sharpening algorithm to the well-known shock filter and show that Sobolev sharpening produces natural looking images without the "staircasing" artifacts that plague the shock filter. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-08-25 10:44:12.23

Neste trabalho são apresentadas, complementadas e melhoradas duas técnicas de restauração de imagens: uma abordando o problema de retoque digital/remoção de objetos enquanto a segunda é direcionada ao problema deneliminação de ruído. Em ambas as técnicas, a ideia é trabalhar com imagens contendo texturas e outras características de interesse para um observador humano como a preservação de padrões, bordas, estruturas e regiões de natureza oscilatória. A técnica descrita sobre retoque digital de imagens combina difusão anisotrópica, síntese de texturas, busca dinâmica e um novo termo empregado no mecanismo de atribuição da ordem de prioridade durante o processo de reconstrução. Assim, dada uma imagem com regiões a serem recompostas, uma técnica de difusão anisotrópica é aplicada à imagem afim de se obter um mapa de saliência contendo bordas, estruturas e demais informações de baixa frequência da imagem. Na sequência, um mecanismo de prioridade baseado em um novo termo de confiabilidade regularizado é calculado a partir da combinação do mapa anteriormente gerado com a equação do transporte. Tal mecanismo é utilizado para determinar a ordem de preenchimento das partes faltantes da imagem. Para essa tarefa, a abordagem apresentada utiliza uma nova medida de similaridade entre blocos de pixels(amostrados dinamicamente para acelerar o processo), afim de encontrar os melhores candidatos a serem alocados nas regiões danificadas. A técnica destinada à remoção de ruídos alia a teoria da difusão anisotrópica, técnicas de análise harmônica e modelos numéricos de discretização de EDPs não-lineares em uma equação diferencial parcial regularizada, a qual atua de forma incisiva em regiões mais homogêneas da imagem e de forma mais suave em regiões caracterizadas como textura e bordas, preservando, assim, essas regiões. Além da natureza anisotrópica, a EDP procura recompor partes texturizadas perdidas no processo de eliminação de ruído através da aplicação de técnicas robustas de análise harmônica. Uma validação teórica e experimental para esta EDP e um estudo do ajuste paramétrico do método de eliminação de ruído baseado nesta EDP foram realizados neste trabalho. A eficiência e a performance das técnicas propostas são atestadas por meio das análises experimentais quantitativas e qualitativas com outras abordagens clássicas da literatura. / In this work two techniques of image restoration are presented, complemented and improved: one approaching the problem of image inpainting/object removal problem while the second one dealing with the image denoising problem. In both cases, the core idea is to process images containing textures and other features perceptible to a human observer such as patterns, contours, structures and oscillatory information. The image inpainting technique combines anisotropic diffusion, texture synthesis, dynamic search and a mechanism to set the order of priority during the image completion process. More precisely, given an image and target region to be inpainted, an anisotropic diffusion technique is applied in order to generate a saliency map containing edges, structures and other low frequency parts of the image. Next, apriority mechanism based on a new biased confidence term is computed from the map previously generated with the transport equation to define the level of priority of the pixels during the filling procedure. To accomplish this task, the presented approach employs a novel measure of similarity wich measures the distance between blocks of pixels (sampled dynamically to speed up the process) in order to find the best candidates to be allocated in the damaged regions. The technique devoted to denoising an image combines the theory of anisotropic diffusion, harmonic analysis techniques and numerical models into a regularized partial differential equation, which diffuses the pixels more incisively on homogeneous regions of the image while still seeking to attenuate regions formed by textures and patterns, thus preserving those information. Moreover, the proposed PDE aims at recovering texturized regions which have been degraded during the denoising process by employing harmonic analysis tools. A theoretical and experimental validation for this EDP and a study of the parametric adjustment of the image denoising method based on this EDP were performed in this work. The effectivenss and performance of the proposed approaches are attested through a comprehensive set of comparisons against other representative techniques in the literature.

In my time at the Laboratory of Membrane and Protein Dynamics at McMaster University, it has been our goal to investigate the fundamental properties of model membranes and how some common membrane molecules, namely water, ethanol, and cholesterol, interact with the bilayer. Our studies employ highly-oriented, solid-supported membranes in order to extract unambiguous structural information perpendicular to and in the plane of the membranes, with the exception of the hydrated powder samples used in probing the effects on ethanol. Both X-ray and neutron scattering were employed to investigate the structural properties of the membranes and neutron scattering was used to infer the dynamical properties. A variety of neutron scattering techniques were used to determine the properties of hydrated lipid bilayers, as described in the first two publications listed. Instruments including a neutron backscattering spectrometer, reflectometer, and time-of-flight spectrometer were used to observe bilayer structure, lipid/water coupling, and water diffusion. We found that hydrated, solid-supported single-bilayers showed no strong coupling between hydration water and lipid tails and the out-of-plane structure of stacked fluid bilayers as well as the anisotropic and anomalous behaviour of hydration water compared to bulk water. Both X-ray and neutron scattering experiments were done to determine the effect of a 2mol% concentration of ethanol on a hydrated lipid powder. X-ray scattering was used to determine the structural changes due to the addition of ethanol and the location of ethanol within the bilayer. This was accomplished by determining areas of increased electron density in the head group and among the acyl tails. The presence of ethanol also attributed to a decrease in lateral lipid diffusion constant in the gel phase, while no significant change was found in fluid bilayers. In the final study outlined in this thesis, the result of a 32.5% concentration of cholesterol in a hydrated, fluid phospholipid membrane is discussed. Coarse-grained molecular simulations and measurements of the lateral structure of the membrane via neutron spectrometry were able to determine the heterogeneous nature of the liquid-ordered phase and the structure of each of the domains in the membrane. The following thesis will introduce model membranes, their relevant components and the scattering of X-rays and neutrons from such matter. Next, experimental techniques, sample constituents, sample preparations, and instruments used in experiments will be described. Then, each study will be introduced and discussed which will showcase the progress made in the field of model membranes. Lastly, an overview of the studies will lead in to future directions for each model system in terms of suggested experiments and general path. / Thesis / Doctor of Philosophy (PhD)

Security cameras installed in public spaces or in private organizations continuously record video data with the aim of detecting and preventing crime. For that reason, video content analysis applications, either for real time (i.e. analytic) or post-event (i.e. forensic) analysis, have gained high interest in recent years. In this thesis, the primary focus is on two key aspects of video analysis, reliable moving object segmentation and carried object detection & identification. A novel moving object segmentation scheme by background subtraction is presented in this thesis. The scheme relies on background modelling which is based on multi-directional gradient and phase congruency. As a post processing step, the detected foreground contours are refined by classifying the edge segments as either belonging to the foreground or background. Further contour completion technique by anisotropic diffusion is first introduced in this area. The proposed method targets cast shadow removal, gradual illumination change invariance, and closed contour extraction. A state of the art carried object detection method is employed as a benchmark algorithm. This method includes silhouette analysis by comparing human temporal templates with unencumbered human models. The implementation aspects of the algorithm are improved by automatically estimating the viewing direction of the pedestrian and are extended by a carried luggage identification module. As the temporal template is a frequency template and the information that it provides is not sufficient, a colour temporal template is introduced. The standard steps followed by the state of the art algorithm are approached from a different extended (by colour information) perspective, resulting in more accurate carried object segmentation. The experiments conducted in this research show that the proposed closed foreground segmentation technique attains all the aforementioned goals. The incremental improvements applied to the state of the art carried object detection algorithm revealed the full potential of the scheme. The experiments demonstrate the ability of the proposed carried object detection algorithm to supersede the state of the art method.

Ultrasound imaging is widely used in medical examination. However, the interpretation of images is not trivial and requires much experience. In this thesis, various techniques for enhancement of visual quality of ultrasound images are presented. Several basic and advanced methods that may simplify the visual diagnosis are described. Finally, an interactive application is designed and implemented for simple usage of presented methods.

No description available.

The master thesis is focused on the principle of ultrasonographs and their modes, and ways of denoising data obtained by ultrasonographs. This project will also concentrate on removing the speckle noise, because the speckle noise has the largest share of the noise in the measured data in ultrasonographs. The other main objective was to describe advanced methods of filtration, especially the modifications of the median filter, such as the modified hybrid median filter and modification of the anisotropic diffusion, namely generalizing Perona-Malik anisotropic diffusion using restricted dissimilarity functions. These two filters were tested on images with artificial noise and on data captured using the ultrasound system GE VingMed System FiVe. Also, the program for filtering and display filtered ultrasound data captured by GE VingMed System FiVe is described.

A textura de uma imagem apresenta informações importantes sobre as características de um objeto. Usar essa informação para reconhecimento de padrões vem sendo uma tarefa bastante pesquisada na área de processamento de imagens e aplicado em atividades como indústria têxtil, biologia, análise de imagens médicas, imagens de satélite, análise de peças industriais, entre outros. Muitos pesquisadores focam em criar mecanismos que convertam a imagem em um vetor de características a fim de utilizar um classificador sobre esse vetores. No entanto, as imagens podem ser transformadas para que que características peculiares sejam evidenciadas fazendo com que extratores de características já existentes explorem melhor as imagens. Esse trabalho tem como objetivo estudar a influência da aplicação de métodos de pré-processamento em imagens de textura para a posterior análise das imagens. Os métodos escolhidos são seis: difusão isotrópica, difusão anisotrópica clássica, dois métodos de regularização da difusão anisotrópica, um método de difusão morfológica e a transformada de distância. Além disso, os métodos foram aliados a sete descritores já conhecidos da literatura para que as características das imagens tranformadas sejam extraídas. Resultados mostram um aumento significativo no desempenho dos classificadores KNN e Naive Bayes quando utilizados nas imagens transformadas de quatro bases de textura: Brodatz, Outex, Usptex e Vistex. / The texture of an image plays an important source of information of the image content. The use of this information to pattern recognition became very popular in image processing area and has applications such in textile industry, biology, medical image analysis, satelite images analysis, industrial equipaments analysis, among others. Many researchers focus on creating different methods to convert the input image to a feature vector to the able to classify the image based on these vectors. However, images can be modified in different ways such that important features are enhanced. Therefore, descriptors are able to extract features easily to perform a better representation of the image. This project aims to apply six different preprocessing methods to analyze their power of enhancement on the texture extraction. The methods are: isotropic diffusion, the classic anisotropic diffusion, two regularizations of the anisotropic diffusion, a morphologic diffusion and the distance transform. To extract the features of these modified images, seven texture analysis algorithms are used along KNN and Naive Bayes to classify the textures. Results show a significant increase when datasets Brodatz, Vistex, Usptex and Outex are transformed prior to texture analysis and classification.