The objective of the proposed research is to develop high performance, low computational complexity resolution enhancement and demosaicing algorithms. Our approach to both problems is to find creative ways to incorporate edge information into the algorithm design. However, in contrast with the usual edge directed approaches, we do not try to detect edge presence and orientation explicitly. For the image interpolation problem, we study the relationship between low resolution and high resolution pixels, and derive a general interpolation formula to be used on all pixels. This simple interpolation algorithm is able to generate sharp edges in any orientation. We also propose a simple 3 by 3 filter that quantifies local luminance transition and apply it to the demosaicing problem. Additionally, we propose a gradient based directional demosaicing method that does not require setting any thresholds. We show that the performance of this algorithm can be improved by using multiscale gradients. Finally, we address the low spectral correlation demosaicing problem by proposing a new family of hybrid color filter array (CFA) patterns and a local algorithm that is two orders of magnitude faster than a comparable non-local solution while offering the same level of performance.

<p>The main part of this thesis is concerned with detailed explanation of a newly proposed Markov random field-based de-interlacing algorithm. Previous works, assume a first or higher-order Markovian spatial inter-dependency between the pixel intensity values. In accord with the specific interpolation problem in hand, they try to approximate the Markov random field parameters using available original pixels. Then using the approximate model, they define an objective function such as energy function of the MRF to be optimized. The efficiency and accuracy of the optimization step is as important as the effectiveness of definition of the cost (objective function) as well as the MRF model.\\ \indent The major concept that distinguishes the newly proposed algorithm with the aforementioned MRF-based models is the definition of the MRF not over the intensity domain but over interpolator (interpolation method) domain. Unlike previous MRF-based models which try to estimate a two-dimensional array of pixel values, this new method estimates an MRF of interpolation function (interpolators) associated with the 2-D array of pixel intensity values.\\ \indent With some modifications, one can utilize the proposed model in different related fields such as image and video up-conversion, view interpolation and frame-rate up-conversion. To prove this potential of the proposed MRF-based model, we extend it to an image up-scaling algorithm. This algorithm uses a simplified version of the proposed MRF-based model for the purpose of image up-scaling by a factor of two in each spatial direction. Simulation results prove that the proposed model obtains competing performance results when applied in the two interpolation problems of video de-interlacing and image up-scaling.</p> / Master of Applied Science (MASc)

Various methods describes an image by specific shapes, which are called basis or frames. With these basis can be transformed the image into a representation by transformation coefficients. The aim is that the image can be described by a small number of coefficients to obtain so-called sparse representation. This feature can be used for example for image compression. But basis are not able to describe all the shapes that may appear in the image. This lack increases the number of transformation coefficients describing the image. The aim of this thesis is to study the general principle of calculating the transformation coefficients and to compare classical methods of image analysis with some of the new methods of image analysis. Compares effectiveness of method for image reconstruction from a limited number of coefficients and a noisy image. Also, compares image interpolation method using characteristics of two different transformations with bicubic transformation. Theoretical part describes the transformation methods. Describes some methods from aspects of multi/resolution, localization in time and frequency domains, redundancy and directionality. Furthermore, gives examples of transformations on a particular image. The practical part of the thesis compares efficiency of the Fourier, Wavelet, Contourlet, Ridgelet, Radon, Wavelet Packet and WaveAtom transform in image recontruction from a limited number of the most significant transformation coefficients. Besides, ability of image denoising using these methods with thresholding techniques applied to transformation coefficients. The last section deals with the interpolation of image interpolation by combining of two methods and compares the results with the classical bicubic interpolation.

<p>In this thesis we present new methods for image and video super resolution and video deinterlacing. For image super resolution a new approach for finding a High Resolution (HR) image from a single Low Resolution (LR) image has been introduced. We have done this by employing Compressive Sensing (CS) theory. In CS framework images are assumed to be sparse in a transform domain such as wavelets or contourlets. Using this fact we have developed an approach in which the contourlet domain is considered as the transform domain and a CS algorithm is used to find the high resolution image. Following that, we extend our image super resolution scheme to video super resolution. Our video super resolution method has two steps, the first step consists of our image super resolution method which is applied on each frame separately. Then a post processing step is performed on estimated outputs to increase the video quality. The post processing step consists of a deblurring and a Bilateral Total Variation (BTV) filtering for increasing the video consistency. Experimental results show significant improvement over existing image and video super resolution methods both objectively and subjectively.</p> <p>For video deinterlacing problem a method has been proposed which is also a two step approach. At first 6 interpolators are applied to each missing line and the interpolator which gives the minimum error is selected. An initial deinterlaced frame is constructed using selected interpolator. In the next step this initial deinterlaced frame is fed into a post processing step. The post processing step is a modified version of 2-D Bilateral Total Variation filter. The proposed deinterlacing technique outperforms many existing deinterlacing algorithms.</p> / Master of Science (MSc)

The techniques of surface deformation and mapping are useful tools for the visualization of medical surfaces, especially for highly undulated or branched surfaces. In this thesis, two algorithms are presented for flattened visualizations of multi-branched medical surfaces, such as vessels. The first algorithm is an angle preserving approach, which is based on conformal analysis. The mapping function is obtained by minimizing two Dirichlet functionals. On a triangulated representation of vessel surfaces, this algorithm can be implemented efficiently using a finite element method. The second algorithm adjusts the result from conformal mapping to produce a flattened representation of the original surface while preserving areas. It employs the theory of optimal mass transport via a gradient descent approach. A new class of image morphing algorithms is also considered based on the theory of optimal mass transport. The mass moving energy functional is revised by adding an intensity penalizing term, in order to reduce the undesired "fading" effects. It is a parameter free approach. This technique has been applied on several natural and medical images to generate in-between image sequences.

The visualization of a 3D image obtained from computerized tomography examinations has shown itself to be an important factor for increasing the quality of medical diagnoses and, consequently, treatment efficacy. There already exist on the market, several visualization softwares, which use different techniques to show the 3D tomography image. However, to show a high quality 3D image, sophisticated devices must be used to obtain slices, close to one another, thus increasing the incidence of X-ray given to the patient. An interpolation slice method which resulted from the TC examination produces good results, and is able to reduce the X-ray incidence upon the patient. This method must reconstruct the curvature from the patient s internal structures without using slices in close proximity. This work proposes a method of 3D image interpolation, composed of a juxtaposition of the slices from CT examination results. The goal of this method is to increase the quality of 3D visualization through the production of sharp and precise structure contours. This thesis proposes the division of the interpolation method into two steps. In the first step, the goal is to obtain an initial representation of the image in 3D, which is composed of real slices as well as virtual slices which are referred to in this work as initial virtual slices. In the second step, the empty spaces of the structure are recovered by the 3D image inpainting process. This work also proposes a method to obtain the initial virtual slice and two different methods for inpainting the 3D image. These inpainting methods are the transversal slice line prolongation method and the transportation and diffusion of information. Both methods use the differential equation theory. The transportation and diffusion of information method shows better results than other methods proposed in this work, besides this, this method presents better results than the linear interpolation and Goshtasby et al. [1] methods also implemented in this work. Visual and numerical comparisons are used to obtain this conclusion. The numerical measures used are statistical correlation, the PSNR and the Hausdorff distance [2]. The transportation and diffusion of information method shows itself able to produce better results than all the other tested methods. Besides this principal contribution, this work also developed a KIT to implement 2D and 3D CT visualize applications. / A visualização de imagens resultantes de exame de tomografia computadorizada (TC) em 3D ´e um fator importante para o aumento da precisão nos diagnósticos médicos e, consequentemente, na eficácia dos tratamentos. Atualmente existem diversos produtos no mercado, que fazem uso de várias técnicas existentes para apresentação de imagens tomográficas em 3D. Contudo, para se obter maior suavidade e precisão nos contornos das estruturas visualizadas em 3D, utiliza-se equipamentos capazes de produzir fatias paralelas do corpo humano muito próximas uma das outras, aumentando a exposição dos pacientes aos raios X. Um método de interpolação de fatias resultantes de exame de TC que forneça bons resultados, pode reduzir a incidência de raios X no paciente, pois esse método pode recuperar a curvatura das estruturas sem a necessidade de uma grande proximidade entre as fatias. Este trabalho propõe um método para a interpolação de imagem em 3D, formada pela justaposição de fatias de resultados de exames de tomografia computadorizada. O objetivo desse método ´e obter contornos suaves e precisos, melhorando os processos de visualização em 3D. Para isso, esta tese propõe a divisão do processo de interpolação em duas etapas. Na primeira etapa obtém-se uma representação inicial da imagem em 3D composta por fatias reais e por fatias denominadas de fatias virtuais iniciais e, na segunda etapa, restaura-se essas estruturas geradas com um processo de retoque de imagem em 3D. Este trabalho propõe também um método para obtenção da fatia virtual inicial e dois métodos diferentes para a realização do passo de retoque da imagem em 3D resultante da justaposição das fatias reais e virtuais iniciais. Esses métodos são o prolongamento de linhas nas fatias transversais e transporte e difusão de informações. Ambos os métodos utilizam a teoria de equações diferenciais. O método de transporte e difusão de informações demonstrou melhores resultados do que outro método proposto neste trabalho, além de obter melhores resultados do que os métodos de interpolação linear e Goshtasby e outros [1] implementados neste trabalho. Comparações visuais e comparações numéricas utilizando a correlação estatística, a PSNR e a distância de Haussdorff [2] foram realizadas para se obter essas conclusões. O método de transporte e difusão de informações é capaz de gerar contornos mais suaves e precisos que esses outros métodos testados. Além dessa contribuição principal, este trabalho também desenvolveu um KIT para a construção de aplicações visualizadoras de tomografias computadorizadas em 2D e em 3D. / Mestre em Ciências

Úkolem této diplomové práce je navrhnout vlastní metodu pro zvýšení rozlišení v obraze scény, pokud je k dispozici více snímků dané scény. V teoretické části diplomové práce jsou jako nejlepší metody pro zvýšení rozlišení v obraze vybrány ty, které jsou založeny na principech zpracování signálu. Dále jsou popsány základní požadavky metod pro zvýšení rozlišení v obraze při přítomnosti více snímků stejné scény a jejich typická struktura. Následuje stručný přehled těchto metod a jejich vzájemné porovnání podle optimálních kritérií. Praktická část diplomové práce se zabývá samotným návrhem metody pro zvýšení rozlišení v obraze, pokud je k dispozici více snímků této scény. První navržená metoda je naimplementována a otestována. Při testování této metody je však  zjištěna její špatná funkčnost pro snímky scény s nízkým rozlišením, které vznikly vzájemnou rotací. Z toho důvodu je navržena vylepšená metoda pro zvýšení rozlišení v obraze. Tato metoda využívá při svém výpočtu robustních technik. Díky tomu je již vylepšená metoda nezávislá na rotaci mezi snímky scény s nízkým rozlišením. I tato metoda je řádně otestována a její výsledky jsou porovnány s výsledky první navržené metody pro zvýšení rozlišení v obraze. V porovnání výpočetních časů je lepší první navrhovaná metoda, avšak její výsledky pro obrazy obsahující rotace nejsou kvalitní. Oproti tomu pro obrazy, které vznikly pouze posunem při snímání scény, jsou tyto výsledky velice dobré. Vylepšená metoda je tedy využitelná zejména pro obrazy obsahující rotace. V závěru této práce je ještě navrženo jedno vylepšení, které by mohlo zlepšit výsledky druhé navrhnuté metody pro zvýšení rozlišení v obraze scény.