Дисертації з теми "Digital image restoration"

Digital image restoration is a fundamental image processing problem with underlying physical motivations. A digital imaging system is unable to generate a continuum of ideal pointwise measurements of the input scene. Instead, the acquired digital image is an array of measured values. Generally, algorithms can be developed to remove a significant part of the error associated with these measure image values provided a proper model of the image acquisition system is used as the basis for the algorithm development. The continuous/discrete/continuous (C/D/C) model has proven to be a better alternative compared to the relatively incomplete image acquisition models commonly used in image restoration. Because it is more comprehensive, the C/D/C model offers a basis for developing significantly better restoration filters. The C/D/C model uses Fourier domain techniques to account for system blur at the image formation level, for the potentially important effects of aliasing, for additive noise and for blur at the image reconstruction level.;This dissertation develops a wavelet-based representation for the C/D/C model, including a theoretical treatment of convolution and sampling. This wavelet-based C/D/C model representation is used to formulate the image restoration problem as a generalized least squares problem. The use of wavelets discretizes the image acquisition kernel, and in this way the image restoration problem is also discrete. The generalized least squares problem is solved using the singular value decomposition. Because image restoration is only meaningful in the presence of noise, restoration solutions must deal with the issue of noise amplification. In this dissertation the treatment of noise is addressed with a restoration parameter related to the singular values of the discrete image acquisition kernel. The restoration procedure is assessed using simulated scenes and real scenes with various degrees of smoothness, in the presence of noise. All these scenes are restoration-challenging because they have a considerable amount of spatial detail at small scale. An empirical procedure that provides a good initial guess of the restoration parameter is devised.

The design of a digital image restoration filter must address four concerns: the completeness of the underlying imaging system model, the validity of the restoration metric used to derive the filter, the computational efficiency of the algorithm for computing the filter values and the ability to apply the filter in the spatial domain. Consistent with these four concerns, this dissertation presents a constrained least-squares (CLS) restoration filter for digital image restoration. The CLS restoration filter is based on a comprehensive, continuous-input/discrete- processing/continuous-output (c/d/c) imaging system model that accounts for acquisition blur, spatial sampling, additive noise and imperfect image reconstruction. The c/d/c model-based CLS restoration filter can be applied rigorously and is easier to compute than the corresponding c/d/c model-based Wiener restoration filter. The CLS restoration filter can be efficiently implemented in the spatial domain as a small convolution kernel. Simulated restorations are used to illustrate the CLS filter's performance for a range of imaging conditions. Restoration studies based, in part, on an actual Forward Looking Infrared (FLIR) imaging system, show that the CLS restoration filter can be used for effective range reduction. The CLS restoration filter is also successfully tested on blurred and noisy radiometric images of the earth's outgoing radiation field from a satellite-borne scanning radiometer used by the National Aeronautics and Space Administration (NASA) for atmospheric research.

All atomic force microscope (AFM) images suffer from distortions, which are principally produced by the interaction between the measured sample and the AFM tip. If the three-dimensional shape of the tip is known, the distorted image can be processed and the original surface form ' restored' typically by deconvolution approaches. This restored image gives a better representation of the real 3D surface or the measured sample than the original distorted image. In this thesis, a quantitative investigation of using morphological deconvolution has been used to restore AFM images via computer simulation using various computer simulated tips and objects. This thesis also presents the systematic quantitative study of the blind tip estimation algorithm via computer simulation using various computer simulated tips and objects. This thesis proposes a new method for estimating the impulse response of the AFM by measuring a micro-cylinder with a-priori known dimensions using contact mode AFM. The estimated impulse response is then used to restore subsequent AFM images, when measured with the same tip, under similar measurement conditions. Significantly, an approximation to what corresponds to the impulse response of the AFM can be deduced using this method. The suitability of this novel approach for restoring AFM images has been confirmed using both computer simulation and also with real experimental AFM images. This thesis suggests another new approach (impulse response technique) to estimate the impulse response of the AFM. this time from a square pillar sample that is measured using contact mode AFM. Once the impulse response is known, a deconvolution process is carried out between the estimated impulse response and typical 'distorted' raw AFM images in order to reduce the distortion effects. The experimental results and the computer simulations validate the performance of the proposed approach, in which it illustrates that the AFM image accuracy has been significantly improved. A new approach has been implemented in this research programme for the restoration of AFM images enabling a combination of cantilever and feedback signals at different scanning speeds. In this approach, the AFM topographic image is constructed using values obtained by summing the height image that is used for driving the Z-scanner and the deflection image with a weight function oc that is close to 3. The value of oc has been determined experimentally using tri al and error. This method has been tested 3t ten different scanning speeds and it consistently gives more faithful topographic images than the original AFM images.

The problems of noise removal, and simultaneous noise removal and deblurring of imagery are common to many areas of science. An approach which allows for the unified treatment of both problems involves modeling imagery as a sample of a random process. Various nonstationary image models are explored in this context. Attention is directed to identifying the model parameters from imagery which has been corrupted by noise and possibly blur, and the use of the model to form an optimal reconstruction of the image. Throughout the work, emphasis is placed on both theoretical development and practical considerations involved in achieving this reconstruction. The results indicate that the use of nonstationary image models offers considerable improvement over traditional techniques.

The problem of restoring an image distorted by a system consisting of a stochastic impulse response in conjuction with additive noise is investigated. The method of constrained least squares is extended to this problem, and leads to the development of a new technique based on the minimization of a weighted error function. Results obtained using the new method are compared with those obtained by constrained least squares, and by the Wiener filter and approximations thereof. It is found that the new technique, "Weighted Least Squares", gives superior results if the noise in the impulse response is comparable to or greater than the additive noise.
Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate

This dissertation examines the suitability of Display-Processor (DP) image computers for image enhancement and restoration tasks. Because the major architectural feature of the DP devices is their ability to rapidly evaluate finite impulse response (FIR) convolutions, much of the study focusses on the use of spatial-domain FIR convolutions to approximate Fourier-domain filtering. When the enhancement task requires the evaluation of only a single convolution, it is important that the FIR kernel used to implement the convolution is designed so that the resulting output is a good approximation of the desired output. A Minimum-Mean-Squared-Error design criterion is introduced for the purpose of FIR kernel design and its usefulness is demonstrated by showing some results of its use. If the restoration or enhancement task requires multiple convolutions in an iterative algorithm, it is important to understand how the truncation of the kernel to a finite region of support will affect the convergence properties of an algorithm and the output of the iterative sequence. These questions are examined for a limited class of nonlinear restoration algorithms. Because FIR convolutions are most efficiently performed on computing machines that have limited precision and are usually limited to performing fixed-point arithmetic, the dissertation also examines the effects of roundoff error on output images that have been computed using fixed point math. The number of bits that are needed to represent the data during a computation is algorithm dependent, but for a limited class of algorithms, it is shown that 12 bits are sufficient. Finally, those architectural features in a DP that are necessary for useful enhancement and restoration operations are identified.

This dissertation describes the application of maximum entropy image restoration to envelope-detected ultrasonic sector scans. The maximum entropy restoration of the image of a point target (phantom) test object is shown to be superior to results obtained from the more familiar Wiener filter. The subsequent application of maximum entropy to an in-vivo clinical ultrasound image, however, illustrates the pitfalls associated with determining the relative merit of an ultrasonic image restoration technique from test object results alone. Since the resolution of sector scan images is substantially worse in the lateral (azimuthal) scan direction than the axial scan direction, the deconvolution filters described in this thesis were applied in the lateral direction only. The maximum entropy method is shown to have certain inherent advantages over linear frequency-domain techniques for the restoration of ultrasonic sector scan images. The positivity constraint inherent in the maximum entropy method is shown to produce restorations with substantially fewer oscillatory artifacts than those produced by Wiener filtering. In addition, the iterative nature of the maximum entropy algorithm is shown to be compatible with the restoration of the undersampled regions in the far field of sector scan images. The restoration of sector scan images is complicated by the spatially varying degradation associated with such images. A novel approach to the restoration of this class of image degradation is presented in this thesis. The widespread use of maximum entropy image restoration has been inhibited by the technique's demanding computational requirements. This problem can be alleviated by the use of high speed computer hardware, and the final chapters of this thesis describe the design and construction of a microcomputer-based array processor. The advantages inherent in the use of such hardware are demonstrated with reference to the maximum entropy restoration of ultrasonic images.

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Inpainting Digital é uma técnica recente que permite completar a falta de informação em imagens, seja por falha ou por remoção intencional de alguma área ou objeto. Uma das atribuições importantes do inpainting digital é de que deve ser capaz de alterar uma imagem, de forma que não seja simples perceber que esta alteração foi feita; caracteriza uma modificação indetectável. Os métodos para determinar como esta falta de informação será preenchida variam desde a criação do primeiro modelo de inpainting digital. Contudo, sempre deve ser mantida uma coerência no preenchimento, que fará com que a região preenchida automaticamente aparente como parte da imagem verdadeira. As técnicas atuais tratam este preenchimento como uma propagação da estrutura da área que está ao redor da região a ser preenchida, trabalhando diretamente no domímio das cores, utilizando abordagens como Variação Total e Equações Diferenciais Parciais. Neste trabalho, é feito o uso de transformada Wavelet para a aplicação de inpainting digita
Digital Inpainting is a recent techinique that allows the filling of missing information in images. One important attribute of a digital inpainting technique is the ability of altering an image in such a way that it is not simple for the human observer to detect the modification, characterizing an undetectable modification. The strategies for filling missing parts vary since the first inpainting model, but one thing that remains is the fact that the filled area must be coherent with the original part of the image. Current techniques handle the filling as a structure propagation problem, working directly in the image color domain, and based on concepts like Total Variation or Partial Diferential Equations. In this work, we present a digital inpainting model that works exclusively in Wavelet domain,filling the target area with a texture synthesis mechanism using the properties of the Wavelet Transform

Energy minimization approach is widely used in image processing applications.Many image processing problems can be modelled in a form of a minimizationproblem. This thesis deals with two crucial tasks of image analysis workflows:image restoration and segmentation of images corrupted by blur and noise. Bothimage restoration and segmentation are modelled as energy minimizationproblems, where energy function is composed of two parts: data fidelity term andregularization term. The main contribution of this thesis is development of newdata fidelity and regularization terms for both image restoration andsegmentation tasks.Image restoration methods (non-blind and blind deconvolution and superresolutionreconstruction) developed within this thesis are suited for mixedPoisson-Gaussian noise which is encountered in many realistic imagingconditions. We use generalized Anscombe variance stabilization transformationfor removing signal-dependency of noise. We propose novel data fidelity termwhich incorporates variance stabilization transformation process into account.Turning our attention to the regularization term for image restoration, weinvestigate how sparsity promoting regularization in the gradient domainformulated as Total Variation, can be improved in the presence of blur and mixedPoisson-Gaussian noise. We found that Huber potential function leads tosignificant improvement of restoration performance.In this thesis we propose new segmentation method, the so called coveragesegmentation, which estimates the relative coverage of each pixel in a sensedimage by each image component. Its data fidelity term takes into accountblurring and down-sampling processes and in that way it provides robustsegmentation in the presence of blur, allowing at the same time segmentation atincreased spatial resolution. In addition, new sparsity promoting regularizationterms are suggested: (i) Huberized Total Variation which provides smooth objectboundaries and noise removal, and (ii) non-edge image fuzziness, whichresponds to an assumption that imaged objects are crisp and that fuzziness ismainly due to the imaging and digitization process.The applicability of here proposed restoration and coverage segmentationmethods is demonstrated for Transmission Electron Microscopy imageenhancement and segmentation of micro-computed tomography andhyperspectral images.
Поступак минимизације функције енергије је често коришћен зарешавање проблема у обради дигиталне слике. Предмет истраживањатезе су два круцијална задатка дигиталне обраде слике: рестаурација исегментација слика деградираних шумом и замагљењем. И рестaурацијаи сегментација су моделовани као проблеми минимизације функцијеенергије која представља збир две функције: функције фитовањаподатака и регуларизационе функције. Главни допринос тезе је развојнових функција фитовања података и нових регуларизационих функцијаза рестаурацију и сегментацију.Методе за рестаурацију (оне код којих је функција замагљења позната икод којих је функцију замагљења потребно оценити на основу датихподатака као и методе за реконструкцију слике у супер-резолуцији)развијене у оквиру ове тезе третирају мешавину Поасоновог и Гаусовогшума који се појављује у многобројним реалистичним сценаријима. Затретирање такве врсте шума користили смо нелинеарну трансформацијуи предложили смо нову функцију фитовања података која узима у обзиртакву трансформацију. У вези са регуларизационим функцијама смотестирали хипотезу да се функција Тоталне Варијације која промовишеретку слику у градијентном домену може побољшати уколико се користетзв. потенцијалне функције. Показали смо да се употребом Хуберовепотенцијалне функције може значајно побољшати квалитет рестауриранеслике која је деградирана замагљењем и мешавином Поасоновог иГаусовог шума.У оквиру тезе смо предложили нову методу сегментације која допуштаделимичну покривеност пиксела објектом. Функција фитовања податакаове методе укључује и модел замагљења и смањења резолуције. На тајначин је постигнута робустност сегментације у присуству замагљења идобијена могућност сегментирања слике у супер-резолуцији. Додатно,нове регуларизационе функције које промовишу ретке репрезентацијеслике су предложене.Предложене методе рестаурације и сегментације која допушта делимичнупокривеност пиксела објектом су примењене на слике добијене помоћуелектронског микроскопа, хиперспектралне слике и медицинске ЦТ слике.
Postupak minimizacije funkcije energije je često korišćen zarešavanje problema u obradi digitalne slike. Predmet istraživanjateze su dva krucijalna zadatka digitalne obrade slike: restauracija isegmentacija slika degradiranih šumom i zamagljenjem. I restauracijai segmentacija su modelovani kao problemi minimizacije funkcijeenergije koja predstavlja zbir dve funkcije: funkcije fitovanjapodataka i regularizacione funkcije. Glavni doprinos teze je razvojnovih funkcija fitovanja podataka i novih regularizacionih funkcijaza restauraciju i segmentaciju.Metode za restauraciju (one kod kojih je funkcija zamagljenja poznata ikod kojih je funkciju zamagljenja potrebno oceniti na osnovu datihpodataka kao i metode za rekonstrukciju slike u super-rezoluciji)razvijene u okviru ove teze tretiraju mešavinu Poasonovog i Gausovogšuma koji se pojavljuje u mnogobrojnim realističnim scenarijima. Zatretiranje takve vrste šuma koristili smo nelinearnu transformacijui predložili smo novu funkciju fitovanja podataka koja uzima u obzirtakvu transformaciju. U vezi sa regularizacionim funkcijama smotestirali hipotezu da se funkcija Totalne Varijacije koja promovišeretku sliku u gradijentnom domenu može poboljšati ukoliko se koristetzv. potencijalne funkcije. Pokazali smo da se upotrebom Huberovepotencijalne funkcije može značajno poboljšati kvalitet restauriraneslike koja je degradirana zamagljenjem i mešavinom Poasonovog iGausovog šuma.U okviru teze smo predložili novu metodu segmentacije koja dopuštadelimičnu pokrivenost piksela objektom. Funkcija fitovanja podatakaove metode uključuje i model zamagljenja i smanjenja rezolucije. Na tajnačin je postignuta robustnost segmentacije u prisustvu zamagljenja idobijena mogućnost segmentiranja slike u super-rezoluciji. Dodatno,nove regularizacione funkcije koje promovišu retke reprezentacijeslike su predložene.Predložene metode restauracije i segmentacije koja dopušta delimičnupokrivenost piksela objektom su primenjene na slike dobijene pomoćuelektronskog mikroskopa, hiperspektralne slike i medicinske CT slike.

In x-ray imaging, the x-ray radiation must be the minimum necessary to achieve the required diagnostic objective, to ensure the patients safety. However, low-dose acquisitions yield images with low quality, which affect the radiologists image interpretation. Therefore, there is a compromise between image quality and radiation dose. This work proposes an image restoration framework capable of restoring low-dose acquisitions to achieve the quality of full-dose acquisitions. The contribution of the new method includes the capability of restoring images with quantum and electronic noise, pixel offset and variable detector gain. To validate the image processing chain, a simulation algorithm was proposed. The simulation generates low-dose DBT projections, starting from fulldose images. To investigate the feasibility of reducing the radiation dose in breast cancer screening programs, a simulated pre-clinical trial was conducted using the simulation and the image processing pipeline proposed in this work. Digital breast tomosynthesis (DBT) images from 72 patients were selected, and 5 human observers were invited for the experiment. The results suggested that a reduction of up to 30% in radiation dose could not be perceived by the human reader after the proposed image processing pipeline was applied. Thus, the image processing algorithm has the potential to decrease radiation levels in DBT, also decreasing the cancer induction risks associated with the exam.
Em programas de rastreamento de câncer de mama, a dose de radiação deve ser mantida o mínimo necessário para se alcançar o diagnóstico, para garantir a segurança dos pacientes. Entretanto, imagens adquiridas com dose de radiação reduzida possuem qualidade inferior. Assim, existe um equilíbrio entre a dose de radiação e a qualidade da imagem. Este trabalho propõe um algoritmo de restauração de imagens capaz de recuperar a qualidade das imagens de tomossíntese digital mamária, adquiridas com doses reduzidas de radiação, para alcançar a qualidade de imagens adquiridas com a dose de referência. As contribuições do trabalho incluem a melhoria do modelo de ruído, e a inclusão das características do detector, como o ganho variável do ruído quântico. Para a validação a cadeia de processamento, um método de simulação de redução de dose de radiação foi proposto. Para investigar a possibilidade de redução de dose de radiação utilizada na tomossíntese, um estudo pré-clínico foi conduzido utilizando o método de simulação proposto e a cadeia de processamento. Imagens clínicas de tomossíntese mamária de 72 pacientes foram selecionadas e cinco observadores foram convidados para participar do estudo. Os resultados sugeriram que, após a utilização do processamento proposto, uma redução de 30% de dose de radiação pôde ser alcançada sem que os observadores percebessem diferença nos níveis de ruído e borramento. Assim, o algoritmo de processamento tem o potencial de reduzir os níveis de radiação na tomossíntese mamária, reduzindo também os riscos de indução do câncer de mama.

The generation of urban digital elevation models from satellite images using stereo reconstruction techniques poses several challenges due to its precision requirements. In this thesis we study three problems related to the reconstruction of urban models using stereo images in a low baseline disposition. They were motivated by the MISS project, launched by the CNES (Centre National d'Etudes Spatiales), in order to develop a low baseline acquisition model. The first problem is the restoration of irregularly sampled images and image fusion using a band limited interpolation model. A novel restoration algorithm is proposed, which incorporates the image formation model as a set of local constraints, and uses of a family of regularizers that allow to control the spectral behavior of the solution. Secondly, the problem of interpolating sparsely sampled images is addressed using a self-similarity prior. The related problem of image inpainting is also considered, and a novel framework for exemplar-based image inpainting is proposed. This framework is then extended to consider the interpolation of sparsely sampled images. The third problem is the regularization and interpolation of digital elevation models imposing geometric restrictions. The geometric restrictions come from a reference image. For this problem three different regularization models are studied: an anisotropic minimal surface regularizer, the anisotropic total variation and a new piecewise affine interpolation algorithm.
La generación de modelos urbanos de elevación a partir de imágenes de satélite mediante técnicas de reconstrucción estereoscópica presenta varios retos debido a sus requisitos de precisión. En esta tesis se estudian tres problemas vinculados a la generación de estos modelos partiendo de pares estereoscópicos adquiridos por satélites en una configuración con baseline pequeño. Estos problemas fueron motivados por el proyecto MISS, lanzado por el CNES (Centre National d'Etudes Spatiales) con el objetivo de desarrollar las técnicas de reconstrucción para imágenes adquiridas con baseline pequeños. El primer problema es la restauración de imágenes muestreadas irregularmente y la fusión de imágenes usando un modelo de interpolación de banda limitada. Se propone un nuevo método de restauración, el cual usa una familia de regularizadores que permite controlar el decaimiento espectral de la solución e incorpora el modelo de formación de imagen como un conjunto de restricciones locales. El segundo problema es la interpolación de imágenes muestreadas en forma dispersa usando un prior de auto similitud, se considera también el problema relacionado de inpainting de imágenes. Se propone un nuevo framework para inpainting basado en ejemplares, el cual luego es extendido a la interpolación de imágenes muestreadas en forma dispersa. El tercer problema es la regularización e interpolación de modelos digitales de elevación imponiendo restricciones geométricas las cuales se extraen de una imagen de referencia. Para este problema se estudian tres modelos de regularización: un regularizador anisótropo de superficie mínima, la variación total anisótropa y un nuevo algoritmo de interpolación afín a trozos.

Orientador: Maurílio Boaventura
Banca: Evanildo Castro Silva Júnior
Banca: Alagacone Sri Ranga
Resumo: Neste trabalho propomos quatro novas abordagens para tratar o problema de restauração de imagens reais contendo texturas sob a perspectiva dos temas: reconstrução de regiões danificadas, remoção de objetos, e eliminação de ruídos. As duas primeiras abor dagens são designadas para recompor partes perdias ou remover objetos de uma imagem real a partir de formulações envolvendo decomposiçãode imagens e inpainting por exem- plar, enquanto que as duas últimas são empregadas para remover ruído, cujas formulações são baseadas em decomposição de três termos e equações diferenciais parciais não lineares. Resultados experimentais atestam a boa performace dos protótipos apresentados quando comparados à modelagens correlatas da literatura.
Abstract: In this paper we propose four new approaches to address the problem of restoration of real images containing textures from the perspective of reconstruction of damaged areas, object removal, and denoising topics. The first two approaches are designed to reconstruct missing parts or to remove objects of a real image using formulations based on image de composition and exemplar based inpainting, while the last two other approaches are used to remove noise, whose formulations are based on decomposition of three terms and non- linear partial di®erential equations. Experimental results attest to the good performance of the presented prototypes when compared to modeling related in literature.
Mestre

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Neste trabalho propomos quatro novas abordagens para tratar o problema de restauração de imagens reais contendo texturas sob a perspectiva dos temas: reconstrução de regiões danificadas, remoção de objetos, e eliminação de ruídos. As duas primeiras abor dagens são designadas para recompor partes perdias ou remover objetos de uma imagem real a partir de formulações envolvendo decomposiçãode imagens e inpainting por exem- plar, enquanto que as duas últimas são empregadas para remover ruído, cujas formulações são baseadas em decomposição de três termos e equações diferenciais parciais não lineares. Resultados experimentais atestam a boa performace dos protótipos apresentados quando comparados à modelagens correlatas da literatura.
In this paper we propose four new approaches to address the problem of restoration of real images containing textures from the perspective of reconstruction of damaged areas, object removal, and denoising topics. The first two approaches are designed to reconstruct missing parts or to remove objects of a real image using formulations based on image de composition and exemplar based inpainting, while the last two other approaches are used to remove noise, whose formulations are based on decomposition of three terms and non- linear partial di®erential equations. Experimental results attest to the good performance of the presented prototypes when compared to modeling related in literature.

Técnicas baseadas na Equação de Fluxo Bem-Balanceada têm sido muitas vezes empregadas como eficientes ferramentas para eliminação de ruídos e preservação de arestas em imagens digitais. Embora efetivas, essas técnicas demandam alto custo computacional. Este trabalho objetiva propor uma técnica baseada na abordagem multigrid para acelerar a solução numérica da Equação de Fluxo Bem-Balanceada. A equação de difusão é resolvida em uma malha grossa e uma correção do erro na malha grossa para as mais finas é aplicada para gerar a solução desejada. A transferência entre malhas grossas e finas é feita pelo filtro de Mitchell, um esquema bem conhecido que é projetado para preservação de arestas. Além disso, a equação do transporte e a Equação do Fluxo de Curvatura são adaptadas à nossa técnica para retoque em imagens e eliminação de ruí?dos. Resultados numéricos são comparados quantitativamente e qualitativamente com outras abordagens, mostrando que o método aqui introduzido produz qualidade de imagens similares com muito menos tempo computacional.
Techniques based on the Well-Balanced Flow Equation have been employed as an efficient tool for edge preserving noise removal. Although effective, this technique demands high computational effort, rendering it not practical in several applications. This work aims at proposing a multigrid-like technique for speeding up the solution of the Well- Balanced Flow equation. In fact, the diffusion equation is solved in a coarse grid and a coarse-to-fine error correction is applied in order to generate the desired solution. The transfer between coarser and finer grids is made by the Mitchell-Filter, a well known interpolation scheme that is designed for preserving edges. Furthermore, the solution of the transport and the Mean Curvature Flow equations is adapted to the multigrid like technique for image inpainting and denoising. Numerical results are compared quantitative and qualitatively with other approaches, showing that our method produces similar image quality with much lower computational time.

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Problemas durante o processo de aquisição de imagens de AFM têm feito com que pesquisas na área de nanotecnologia busquem a utilização de ferramentas para minimizar esses efeitos degenerativos. Neste sentido, foram desenvolvidas ferramentas computacionais de restauração destas imagens degradadas. Neste trabalho é utilizado o método baseado na Regularização de Tikhonov, cuja aplicação está concentrada principalmente em restaurações de imagens biológicas. A proposta deste trabalho é a utilização deste regularizador também em imagens de interesse em engenharia. Em alguns casos, um pré-processamento anteriormente à aplicação do algoritmo, apresenta boa resposta na restauração das imagens. Na fase de préprocessamento foram utilizados alguns filtros como, filtro de média, filtro de mediana, filtro laplaciano e filtro de média pontual. Com a aplicação deste regularizador em imagens foi possível obter perfis de distribuição dos pixels onde é mostrado que na medida em que se aumenta a carga de dissolução de ferro puro em ácido sulfúrico, percebe-se que a razão de aspecto aumenta e características de superfície ficam mais visíveis.
Problems during the process of acquisition of images of AFM have been doing with that research in the nanotechnology searchs the use of tools to minimize those degenerative effects. Computational tools for restoration of these degraded images have developed, in this work the method is used based on Regularization of Tikhonov. This method is usually used for restoration of biological images. It is proposed the use of this regularization functional also in images of interest in engineering. In some cases, a previously processing to the application of the algorithm, it presents good answer in the restoration of the images. The previously processing phase some were used filters as, average filter, median filter, laplacian filter and filter of punctual average, besides combination of filters. With the application of this regularizator it was possible to obtain profiles of distribution of the pixels where is shown that in the measure in that he increases the dissolution charge of iron in sulphuric acid, it is noticed that the aspect reason increases and surface characteristics are more visible.

Image restoration consists in recovering a high quality image estimate based only on observations. This is considered an ill-posed inverse problem, which implies non-unique unstable solutions. Regularization methods allow the introduction of constraints in such problems and assure a stable and unique solution. One of these methods is Total Variation, which has been broadly applied in signal processing tasks such as image denoising, image deconvolution, and image inpainting for multiple noise scenarios. Total Variation features a regularization parameter which defines the solution regularization impact, a crucial step towards its high quality level. Therefore, an optimal selection of the regularization parameter is required. Furthermore, while the classic Total Variation applies its constraint to the entire image, there are multiple scenarios in which this approach is not the most adequate. Defining different regularization levels to different image elements benefits such cases. In this work, an optimal regularization parameter selection framework for Total Variation image restoration is proposed. It covers two noise scenarios: Impulse noise and Impulse over Gaussian Additive noise. A broad study of the state of the art, which covers noise estimation algorithms, risk estimation methods, and Total Variation numerical solutions, is included. In order to approach the optimal parameter estimation problem, several adaptations are proposed in order to create a local-fashioned regularization which requires no a-priori information about the noise level. Quality and performance results, which include the work covered in two recently published articles, show the effectivity of the proposed regularization parameter selection and a great improvement over the global regularization framework, which attains a high quality reconstruction comparable with the state of the art algorithms.
Tesis

Orientador: Heloisa Helena Marino Silva
Banca: Antonio Castelo Filho
Banca: Maurílio Boaventura
Resumo: O objetivo deste trabalho þe apresentar um estudo sobre a aplicação de métodos numéricos para a resolução do modelo proposto por Barcelos, Boaventura e Silva Jr. [7], para a eliminação de ruídos em imagens digitais por meio de uma equação diferencial parcial, e propor uma anþalise da estabilidade do mþetodo iterativo comumente aplicado a este modelo. Uma anþalise comparativa entre os vários mþetodos abordados þe realizada atravþes de resultados experimentais em imagens sintéticas e imagens da vida real.
Abstract: The purpose of this work is to present a study on the application of numerical methods for the resolution of model considered by Barcelos, Boaventura and Silva Jr [7], for image denoising through a partial di erential equation, and to consider a stability analysis of an iterative method usually applied to this model. A comparative analysis among various considered methods is carried out through experimental results for synthetic and real images.
Mestre

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Dentre os problemas e desafios que permeiam o processo de digitalização de documentos e todos os passos subsequentes até a transposição da informação para o meio digital, dois pontos específicos são focados: o texto partido ou degradado e texto escrito em tamanha proximidade que geram sobreposições dos traços. Assim, métodos para solucionar tais problemas, foram pesquisados e desenvolvidos. Baseamos nossa abordagem na emulação de forças físicas de inércia e centrípeta pois entendemos que estas podem ser bem utilizadas para o processamento de imagens de caracteres manuscritos. Para o problema de dígitos partidos, foi desenvolvida uma solução para a restauração de dígitos isolados quebrados e de cadeias de dígitos quebrados através da emulação das forças centrípeta e de inércia. Esta solução tem como princípio gerar uma reconstrução da quebra de modo que se assemelhe à escrita do dígito em questão. Também é abordado a sobreposição de pares de dígitos, problema para o qual foi proposta uma solução de segmentação. Esta solução de segmentação se baseia no conceito de uma bola deformável que tem seus movimentos regidos pela emulação da força de inércia e pela deformação que lhe é permitida receber. Ainda, para desenvolvimento e experimentação dos métodos, foram formadas bases de imagens pertinentes a cada aplicação. Os resultados obtidos mostram desempenhos promissores. Ao aplicar a reconstrução, obtivemos um ganho de aproximadamente seis pontos percentuais em taxa de reconhecimento em relação ao reconhecimento dos dígitos partidos. Já a segmentação provou que supera outros dois métodos de segmentação quando aplicamos o reconhecimento aos dígitos segmentados. Também deve-se ressaltar a questão do custo computacional, especificamente a solução voltada para a segmentação de dígitos sobrepostos, onde seu custo se apresenta mais baixo em relação aos métodos similares pesquisados e testados. Assim, mostramos que os métodos propostos atingem seus objetivos, aliando bons desempenhos com custos computacionais baixos.
Among the problems and challenges that surround the process of document digitization and all subsequent steps until the conversion of the information to a digital medium, two specific steps are focused: broken text and text written in such proximity that cause overlapping of strokes. Methods to solve these problems were researched and developed. We base our approach on the emulation of physical forces of inertia and centripetal force, since it is our understanding that the emulation of such forces can be used for the processing of images of handwritten characters and digits. For the problem of broken digits, a solution for the restoration of isolated broken digits and chains of broken digits through the emulations of inertia and centripetal force was developed. This solution has as principle to generate a reconstruction of the break in such a way that it resembles closely the writing style of the digit in question. We also tackle overlapping pairs of digits, problem for which we propose a segmentation solution. This segmentation is based on the concept of a deformable ball that has its movements governed by the emulation of inertia and the degree of deformation the ball is allowed to have. For development and experimentation of the created methods, image databases pertinent to each application were formed. The obtained results show promising performance. When applying the reconstruction, we obtained a gain of approximately six percentage points in recognition rates when compared to rates obtained for broken digits. In regards to segmentation, it proved to outperform two other methods when recognition is applied to the output segmented digits. The computational cost of the methods should also be pointed out, specifically regarding the solution created for the segmentation of overlapped digits, which is lower when compared to other similar methods that were researched and tested. Therefore, we show that the proposed methods reach their goals, coupling performance with low computational costs.

Vast collections of historical photographs are being digitally archived and placed online, providing an objective record of the last two centuries that remains largely untapped. We propose that time-varying 3D models can pull together and index large collections of images while also serving as a tool of historical discovery, revealing new information about the locations, dates, and contents of historical images. In particular, our goal is to use computer vision techniques to tie together a large set of historical photographs of a given city into a consistent 4D model of the city: a 3D model with time as an additional dimension. To extract 4D city models from historical images, we must perform inference about the position of cameras and scene structure in both space and time. Traditional structure from motion techniques can be used to deal with the spatial problem, while here we focus on the problem of inferring temporal information: a date for each image and a time interval for which each structural element in the scene persists. We first formulate this task as a constraint satisfaction problem based on the visibility of structural elements in each image, resulting in a temporal ordering of images. Next, we present methods to incorporate real date information into the temporal inference solution. Finally, we present a general probabilistic framework for estimating all temporal variables in structure from motion problems, including an unknown date for each camera and an unknown time interval for each structural element. Given a collection of images with mostly unknown or uncertain dates, we can use this framework to automatically recover the dates of all images by reasoning probabilistically about the visibility and existence of objects in the scene. We present results for image collections consisting of hundreds of historical images of cities taken over decades of time, including Manhattan and downtown Atlanta.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
O objetivo deste trabalho þe apresentar um estudo sobre a aplicação de métodos numéricos para a resolução do modelo proposto por Barcelos, Boaventura e Silva Jr. [7], para a eliminação de ruídos em imagens digitais por meio de uma equação diferencial parcial, e propor uma anþalise da estabilidade do mþetodo iterativo comumente aplicado a este modelo. Uma anþalise comparativa entre os vários mþetodos abordados þe realizada atravþes de resultados experimentais em imagens sintéticas e imagens da vida real.
The purpose of this work is to present a study on the application of numerical methods for the resolution of model considered by Barcelos, Boaventura and Silva Jr [7], for image denoising through a partial di erential equation, and to consider a stability analysis of an iterative method usually applied to this model. A comparative analysis among various considered methods is carried out through experimental results for synthetic and real images.

Bengala passou por enormes experiências de desenvolvimento sócio‐cultural, de estabilidade económica e de avanço da literatura e das artes. Durante o reinado Budista, Hindu e do Sultanato, a sociedade foi‐se valorizando e enriquecendo com estes diferentes valores e a amálgama cultural que representaram. Esta coexistência foi evoluindo e as pessoas começaram a dedicar‐se ao comércio, mas foram organizando e reformando a própria sociedade. O verdadeiro "renascimento" desta política económica e cultural Bengali seguiu um determinado caminho entre os possíveis. Para se manter e para proteger o território dos inimigos e de todas as ameaças externas, os “heróis” antigos foram previdentes, desenvolvendo uma forte capacidade em reforçar território fortificado, que designamos por cidade‐fortaleza. Esta tipo de cidade histórica planeada foi implantada, com variações, neste delta Bengali; por isso, os padrões de instalação e ocupação antigos foram observados na sua relação com as margens ribeirinhas e os recursos de água adjacentes e centrados em torno de uma estrutura religiosa. Uma cronologia popular no país ajuda a compreender a formação de um povoado ou de uma cidade. Na era Budista, a comunidade religiosa, o bazar e as vias marítimas eram o ponto central que concentram a mistura de pessoas e nações. Este sítio não foi excepção do delta de Bengali, embora esta tese fosse sinuosa e estivesse no meio de uma grande rede fluvial; os antigos dirigentes face à necessidade de criar sistemas de protecção territorial foram gerando os diversos padrões de assentamento e ocupação, com mega‐estruturas, infraestruturas e uma arquitectura público que se foram tornando os elementos característicos do domínio do espaço. Essas fortalezas ribeirinhas foram organizando padrões de assentamento cujas características variavam em função das percepções estratégicas e da morfologia do sítio; afinal estas foram as cidades do Delta que, além do perfil do rio, muitas vezes dependeram de influências locais e tradicionais. Neste delta Bengal, a cidade podia obedecer a tipos diferentes, mas, no geral, havia um padrão geral de ocupação das cidades que os administradores budistas antigos concebiam com um planejamento estratégico e uma morfologia que ía além da muralha do forte. O objectivo desta investigação é, em primeiro lugar, identificar e analisar a morfologia das antigas cidades‐fortaleza e os padrões de assentamentos em termos das suas estratégias de defesa e da arquitectura que organizava a ligação ao rio da terra Bengali. Em segundo lugar, o contexto e a organização do planeamento e lugar das estruturas fortificadas, abordando‐as numa perspectiva de conjectura, através do trabalho pictográfico e ilustrado. O antigo assentamento e a própria arquitectura de MAHASTHAN, um sítio datado do século VIII AD é um local ideal para essa investigação, dado ser um local de memória, de um espaço evocativo, ter um "sentido de lugar" e, claro, um padrão espacial tradicional flexível em relação as condições regionais e às construção tradicionais deste delta Bengali. Por fim, o estudo irá explorar a imagem (restauração conjectural) da escala da cidade, do espaço, da função e do sentido cultural do próprio bairro da antiga povoação ribeirinha, através da revisão crítica da literatura, do conhecimento das sucessivas escavações arqueológicas e com a ajuda da informação histórica pictográfica. O estudo irá explorar ainda o significado desses antigos assentamentos no subcontinente e a sua transformação em Bengali, focando as estratégias actuais de defesa e a sua manifestação física, bem como o papel que pode ter o Património Digital; Riverine Fortress city of `MAHASTHAN´ in Deltaic Bengal: In search for the traditional settlement pattern of ancient cities Abstract: Bengal had passed through enormous experiences of socio‐cultural development, economical stabilities, advancement in literature and arts. During the reign of Buddhist, Hindu and Sultanate Bengal the society was cherished and enriched with full of values and cultural amalgamation. Co‐existence in the society evolved up and people started occupying time in trade‐transaction and society reformation. The ‘rebirth’ of the Bengali cultural consistency took a way forward to immense possible trails. To remain retain established and to protect the territory from external forces as well as the enemies, the ancient heroes had prepared themselves, besides invented with strong capability to reinforce fortified territory or the fortress city. The historic city planning implanted with different characteristics, and prolonged with variations in this delta land of Bengal. Ancient Bengal was focused with their settlement pattern by the bank of the river or by the watery sources. Settlement in the ancient time used to develop centering a religious structure. Eventually; it is the popular chronology for deriving a hamlet or a town. For the Buddhist era, religious community, bazaar and the maritime route came to focus with the mixture of various people and the nation. Simply, it was no exception for the case of the delta land Bengal, although this mainland is curved and chiseled with cress cross river networks; the ancient heroes contributed outposts for territorial protection and thoroughly generated the pattern of settlement. Mega structures, infrastructures and public welfare architecture were becoming the notion of the domain. That river fort architecture and the settlement patterns had the strategic and morphological characteristics, which got different from other purpose built forts, nonetheless‐was in consistence with the local city context. Bengali riverine fortress cities experienced lots of local and traditional influences only for being the river fort and their settlement around it, stating from the component, elements of forts and formal profile of the river. So, undoubtedly Bengal conceived unique kind of riverine oriented fortress settlement pattern, which has distinct typescripts. Even in the case of this fort formation the ancient Buddhist administrators had some strategic planning, morphology for spread city beyond the fort wall. The objective of the research is firstly to identify and to analyse the morphology of the ancient fortress cities1 and settlements in terms of their defence strategies and river fort architecture of Bengal. Secondly the context and the planning organization and positioning the sites for fortification addressing pictographic and conjectural restoration2 includes ancient city formation through river‐fort architecture in Bengal. The ancient settlement and architecture, dated back 8th Century AD of a specific site of MAHASTHAN would be the intensive area of the research, its memory, space, ‘sense of place’ and the traditional spatial pattern would be the intensive area of the study that would remind flexible towards regional conditions and building tradition as happened in riverine ancient Bengal. Lastly the study will explore the image (conjectural restoration) of the scale of the city, space, function and cultural longing of the neighbourhood pattern of ancient riverine settlement, through the critical literature reviewing, progressive archaeological excavation and by the referencing of historic pictographic information. The study will explore for meaning of ancient settlements in the subcontinent and its transformation in Bengal with a focus on defence strategies and its physical manifestation as well as the Digital Heritage phenomenon.

稀疏性在最近的圖像恢復技術發展中起到了重要作用。在這個碩士研究中，我們專注於兩種通過信號稀疏性假設相聯繫的圖像恢復問題。具體來講，在第一個圖像恢復問題中，信號本身在某些變換域是稀疏的，例如小波變換。在本研究的第二部分，信號並非傳統意義上的稀疏，但它可以用很少的幾個參數來表示--亦即信號具有稀疏的表示。我們希望通過講述一個「雙城記」，聯繫起這兩個稀疏圖像重建問題。
在第二章中，我們提出了一種創新的算法框架，用於解決信號稀疏假設下的圖像恢復問題。重建圖像的目標函數，由一個數據保真項和`1正則項組成。然而，我們不是直接估計重建的圖像，而是專注於如何獲得重建的這個過程。我們的策略是將這個重建過程表示成基本閾值函數的線性組合（LET）：這些線性係數可以通過最小化目標函數解得。然後，可以更新閾值函數并迭代這個過程（i-LET）。這種線性參數化的主要優點是可以大幅降低問題的規模-每次我們只需解決一個線性係數維度大小的優化問題（通常小於十），而不是整個圖像大小的問題。如果閾值函滿足一定的條件，迭代LET算法可以保證全局的收斂性。多個測試圖像在不同噪音水平和不同卷積核類型的測試清楚地表明，我們提出的框架在所需運算時間和迭代循環次數方面，通常超越當今最好水平。
在第三章中，我們擴展了有限創新率採樣框架至某一種特定二維曲線。我們用掩模函數的解來間接定義這個二維曲線。這裡，掩模函數可以表示為有限數目的正弦信號加權求和。因此，從這個角度講，我們定義的二維曲線具有「有限創新率」（FRI）。由於與定義曲線相關聯的指示器圖像沒有帶寬限制，因而根據經典香農採樣定理，不能在有限數量的採樣基礎上獲得完全重建。然而，我們證明，仍然可以設計一個針對指示器圖像採樣的框架，實現完美重構。此外，對於這一方法的空間域解釋，使我們能夠拓展嚴格的FRI曲線模型用於描述自然圖像的邊緣，可以在各種圖像處理的問題中保持圖像的邊緣。我們用一個潛在的在圖像上採樣中的應用作為示例。
Sparsity has played an important role in recent developments of various image restoration techniques. In this MPhil study, we focus on two different types of image restoration problems, which are related by the sparsity assumptions. Specifically, in the first image restoration problem, the signal (i.e. the restored image) itself is sparse in some transformation domain, e.g. wavelet. While in the second part of this study, the signal is not sparse in the traditional sense but that it can be parametrized with a few parameters hence having a sparse representation. Our goal is to tell a "tale of two cities" and to show the connections between the two sparse image restoration problems in this thesis.
In Chapter 2, we proposed a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an ℓ₁ regularization. However, instead of estimating the reconstructed image that minimizes the objective functional directly, we focus on the restoration process that maps the degraded measurements to the reconstruction. Our idea amounts to parameterizing the process as a linear combination of few elementary thresholding functions (LET) and solve for the linear weighting coefficients by minimizing the objective functional. It is then possible to update the thresholding functions and to iterate this process (i-LET). The key advantage of such a linear parametrization is that the problem size reduces dramatically--each time we only need to solve an optimization problem over the dimension of the linear coefficients (typically less than 10) instead of the whole image dimensio . With the elementary thresholding functions satisfying certain constraints, global convergence of the iterated LET algorithm is guaranteed. Experiments on several test images over a wide range of noise levels and different types of convolution kernels clearly indicate that the proposed framework usually outperform state-of-theart algorithms in terms of both CPU time and number of iterations.
In Chapter 3, we extended the sampling framework for signals with finite rate of innovation to a specific class of two-dimensional curves, which are defined implicitly as the roots of a mask function. Here the mask function has a parametric representation as weighted summation of a finite number of sinusoids, and therefore, has finite rate of innovation [1]. The associated indicator image of the defined curve is not bandlimited and cannot be perfectly reconstructed based on the classical Shannon's sampling theorem. Yet, we show that it is possible to devise a sampling scheme and have a perfect reconstruction from finite number of (noiseless) samples of the indicator image with the annihilating filter method (also known as Prony's method). Robust reconstruction algorithms with noisy samples are also developed. Furthermore, the new spatial domain interpretation of the annihilating filter enables us to generalize the exact FRI curve model to characterize edges of a natural image. We can impose the annihilation constraint to preserve edges in various image processing problems. We exemplified the effectiveness of the annihilation constraint with a potential application in image up-sampling.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Pan, Hanjie.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 69-74).
Abstracts also in Chinese.
Acknowledgments --- p.iii
Abstract --- p.vii
Contents --- p.xii
List of Figures --- p.xv
List of Tables --- p.xvii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Sampling Sparse Signals --- p.1
Chapter 1.2 --- Thesis Organizations and Contributions --- p.3
Chapter 2 --- An Iterated Linear Expansion of Thresholds for ℓ₁-based Image Restoration --- p.5
Chapter 2.1 --- Introduction --- p.5
Chapter 2.1.1 --- Problem Description --- p.5
Chapter 2.1.2 --- Approaches to Solve the Problem --- p.6
Chapter 2.1.3 --- Proposed Approach --- p.8
Chapter 2.1.4 --- Organization of the Chapter --- p.9
Chapter 2.2 --- Basic Ingredients --- p.9
Chapter 2.2.1 --- Iterative Reweighted Least Square Methods --- p.9
Chapter 2.2.2 --- Linear Expansion of Thresholds (LET) --- p.11
Chapter 2.3 --- Iterative LET Restoration --- p.15
Chapter 2.3.1 --- Selection of i-LET Bases --- p.15
Chapter 2.3.2 --- Convergence of the i-LET Scheme --- p.16
Chapter 2.3.3 --- Examples of i-LET Bases --- p.18
Chapter 2.4 --- Experimental Results --- p.23
Chapter 2.4.1 --- Deconvolution with Decimated Wavelet Transform --- p.24
Chapter 2.4.2 --- Deconvolution with Redundant Wavelet Transform --- p.28
Chapter 2.4.3 --- Algorithm Complexity Analysis --- p.29
Chapter 2.4.4 --- Choice of Regularization Weight λ --- p.30
Chapter 2.4.5 --- Deconvolution with Cycle Spinnings --- p.30
Chapter 2.5 --- Summary --- p.31
Chapter 3 --- Sampling Curves with Finite Rate of Innovation --- p.33
Chapter 3.1 --- Introduction --- p.33
Chapter 3.2 --- Two-dimensional Curves with Finite Rate of Innovation --- p.34
Chapter 3.2.1 --- FRI Curves --- p.34
Chapter 3.2.2 --- Interior Indicator Image --- p.35
Chapter 3.2.3 --- Acquisition of Indicator Image Samples --- p.36
Chapter 3.3 --- Reconstruction of the Annihilable Curves --- p.37
Chapter 3.3.1 --- Annihilating Filter Method --- p.37
Chapter 3.3.2 --- Relate Fourier Transform with Spatial Domain Samples --- p.39
Chapter 3.3.3 --- Reconstruction of Annihilation Coe cients --- p.39
Chapter 3.3.4 --- Reconstruction with Model Mismatch --- p.42
Chapter 3.3.5 --- Retrieval of the Annihilable Curve Amplitudes --- p.46
Chapter 3.4 --- Dealing with Non-ideal Low-pass Filtered Samples --- p.48
Chapter 3.5 --- Generalization of the FRI Framework for Natural Images --- p.49
Chapter 3.5.1 --- Spatial Domain Interpretation of the Annihilation Equation --- p.50
Chapter 3.5.2 --- Annihilable Curve Approximation of Image Edges --- p.51
Chapter 3.5.3 --- Up-sampling with Annihilation Constraint --- p.53
Chapter 3.6 --- Conclusion --- p.57
Chapter 4 --- Conclusions --- p.59
Chapter 4.1 --- Thesis Summary --- p.59
Chapter 4.2 --- Perspectives --- p.60
Chapter A --- Proofs and Derivations --- p.61
Chapter A.1 --- Proof of Lemma 3 --- p.61
Chapter A.2 --- Proof of Theorem 2 --- p.62
Chapter A.3 --- Efficient Implementation of IRLS Inner Loop with Matlab --- p.63
Chapter A.4 --- Derivations of the Sampling Formula (3.7) --- p.64
Chapter A.5 --- Correspondence between the Spatial and Fourier Domain Samples --- p.65
Chapter A.6 --- Optimal Post-filter Applied to Non-ideal Samples --- p.66
Bibliography --- p.69

by Man-Ching Auyeung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.
Includes bibliographical references (leaves 86-93).
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Transform coding and the JPEG scheme --- p.2
Chapter 1.2 --- Motivation --- p.5
Chapter 1.3 --- Thesis outline --- p.6
Chapter 2 --- MED and DC Coefficient Restoration scheme --- p.8
Chapter 2.1 --- Introduction --- p.8
Chapter 2.2 --- MED and DC Coefficient Restoration scheme --- p.10
Chapter 2.2.1 --- Definition --- p.10
Chapter 2.2.2 --- Existing schemes --- p.11
Chapter 2.3 --- DC Coefficient Restoration scheme using block selection scheme --- p.14
Chapter 2.4 --- Joint optimization technique --- p.16
Chapter 2.4.1 --- Lagrange multiplier method --- p.17
Chapter 2.4.2 --- Algorithm description --- p.18
Chapter 2.5 --- Experimental results --- p.20
Chapter 2.6 --- Summary --- p.32
Chapter 3 --- Low Frequency Walsh Transform Coefficient Restoration scheme --- p.34
Chapter 3.1 --- Introduction --- p.34
Chapter 3.2 --- Restoration of low frequency coefficient using Walsh transform --- p.35
Chapter 3.3 --- Selection of quantization table optimized for Walsh transform --- p.37
Chapter 3.3.1 --- Image model used --- p.39
Chapter 3.3.2 --- Infinite uniform quantization --- p.40
Chapter 3.3.3 --- Search for an optimized quantization matrix --- p.42
Chapter 3.4 --- Walsh transform-based LFCR scheme --- p.44
Chapter 3.5 --- Experimental results --- p.46
Chapter 3.6 --- Summary --- p.56
Chapter 4 --- Low Frequency DCT Coefficient Prediction --- p.57
Chapter 4.1 --- Introduction --- p.57
Chapter 4.2 --- Low Frequency Coefficient Prediction scheme with negligible side information --- p.58
Chapter 4.2.1 --- Selection of threshold --- p.63
Chapter 4.2.2 --- Representation of the AC component --- p.63
Chapter 4.3 --- Experimental results --- p.67
Chapter 4.4 --- Summary --- p.84
Chapter 5 --- Conclusions --- p.86
Appendix A --- p.89
Bibliography --- p.90

by Tse, Fu Wing.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.
Includes bibliographical references (leaves 155-[63]).
Acknowledgment --- p.iii
Abstract --- p.iv
Contents --- p.vi
List of Tables --- p.x
List of Figures --- p.xii
Notations --- p.xvii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- DC coefficient restoration --- p.1
Chapter 1.2 --- Model based image compression --- p.5
Chapter 1.3 --- The minimum edge difference criterion and the existing estima- tion schemes --- p.7
Chapter 1.3.1 --- Fundamental definitions --- p.8
Chapter 1.3.2 --- The minimum edge difference criterion --- p.9
Chapter 1.3.3 --- The existing estimation schemes --- p.10
Chapter 1.4 --- Thesis outline --- p.14
Chapter 2 --- A mathematical description of the DC coefficient restoration problem --- p.17
Chapter 2.1 --- Introduction --- p.17
Chapter 2.2 --- Mathematical formulation --- p.18
Chapter 2.3 --- Properties of H --- p.22
Chapter 2.4 --- Analysis of the DC coefficient restoration problem --- p.22
Chapter 2.5 --- The MED criterion as an image model --- p.25
Chapter 2.6 --- Summary --- p.27
Chapter 3 --- The global estimation scheme --- p.29
Chapter 3.1 --- Introduction --- p.29
Chapter 3.2 --- the global estimation scheme --- p.30
Chapter 3.3 --- Theory of successive over-relaxation --- p.34
Chapter 3.3.1 --- Introduction --- p.34
Chapter 3.3.2 --- Gauss-Seidel iteration --- p.35
Chapter 3.3.3 --- Theory of successive over-relaxation --- p.38
Chapter 3.3.4 --- Estimation of optimal relaxation parameter --- p.41
Chapter 3.4 --- Using successive over-relaxation in the global estimation scheme --- p.43
Chapter 3.5 --- Experiments --- p.48
Chapter 3.6 --- Summary --- p.49
Chapter 4 --- The block selection scheme --- p.52
Chapter 4.1 --- Introduction --- p.52
Chapter 4.2 --- Failure of the minimum edge difference criterion --- p.53
Chapter 4.3 --- The block selection scheme --- p.55
Chapter 4.4 --- Using successive over-relaxation with the block selection scheme --- p.57
Chapter 4.5 --- Practical considerations --- p.58
Chapter 4.6 --- Experiments --- p.60
Chapter 4.7 --- Summary --- p.61
Chapter 5 --- The edge selection scheme --- p.65
Chapter 5.1 --- Introduction --- p.65
Chapter 5.2 --- Edge information and the MED criterion --- p.66
Chapter 5.3 --- Mathematical formulation --- p.70
Chapter 5.4 --- Practical Considerations --- p.74
Chapter 5.5 --- Experiments --- p.76
Chapter 5.6 --- Discussion of edge selection scheme --- p.78
Chapter 5.7 --- Summary --- p.79
Chapter 6 --- Performance Analysis --- p.81
Chapter 6.1 --- Introduction --- p.81
Chapter 6.2 --- Mathematical derivations --- p.82
Chapter 6.3 --- Simulation results --- p.92
Chapter 6.4 --- Summary --- p.96
Chapter 7 --- The DC coefficient restoration scheme with baseline JPEG --- p.97
Chapter 7.1 --- Introduction --- p.97
Chapter 7.2 --- General specifications --- p.97
Chapter 7.3 --- Simulation results --- p.101
Chapter 7.3.1 --- The global estimation scheme with the block selection scheme --- p.101
Chapter 7.3.2 --- The global estimation scheme with the edge selection scheme --- p.113
Chapter 7.3.3 --- Performance comparison at the same bit rate --- p.121
Chapter 7.4 --- Computation overhead using the DC coefficient restoration scheme --- p.134
Chapter 7.5 --- Summary --- p.134
Chapter 8 --- Conclusions and Discussions --- p.136
Chapter A --- Fundamental definitions --- p.144
Chapter B --- Irreducibility by associated directed graph --- p.146
Chapter B.1 --- Irreducibility and associated directed graph --- p.146
Chapter B.2 --- Derivation of irreducibility --- p.147
Chapter B.3 --- Multiple blocks selection --- p.149
Chapter B.4 --- Irreducibility with edge selection --- p.151
Chapter C --- Sample images --- p.153
Bibliography --- p.155

Tse Fu Wing.
"June 2000."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (p. 172-177).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.

Lu Yang.
Thesis submitted in: November 2004.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 96-103).
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgement --- p.iv
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Motivation --- p.1
Chapter 1.2 --- Our Contributions --- p.3
Chapter 1.3 --- Thesis Outline --- p.5
Chapter 2 --- Background Study --- p.7
Chapter 2.1 --- MPEG-7 Introduction --- p.8
Chapter 2.2 --- Image Analysis in CBIR Systems --- p.11
Chapter 2.2.1 --- Color Information --- p.13
Chapter 2.2.2 --- Color Layout --- p.19
Chapter 2.2.3 --- Texture Information --- p.20
Chapter 2.2.4 --- Shape Information --- p.24
Chapter 2.2.5 --- CBIR Systems --- p.26
Chapter 2.3 --- Image Processing in JPEG Frequency Domain --- p.30
Chapter 2.4 --- Photo Album Clustering --- p.33
Chapter 3 --- Feature Extraction and Similarity Analysis --- p.38
Chapter 3.1 --- Feature Set in Frequency Domain --- p.38
Chapter 3.1.1 --- JPEG Frequency Data --- p.39
Chapter 3.1.2 --- Our Feature Set --- p.42
Chapter 3.2 --- Digital Photo Similarity Analysis --- p.43
Chapter 3.2.1 --- Energy Histogram --- p.43
Chapter 3.2.2 --- Photo Distance --- p.45
Chapter 4 --- 1-Dimensional Photo Album Management Techniques --- p.49
Chapter 4.1 --- Photo Album Sorting --- p.50
Chapter 4.2 --- Photo Album Clustering --- p.52
Chapter 4.3 --- Photo Album Compression --- p.56
Chapter 4.3.1 --- Variable IBP frames --- p.56
Chapter 4.3.2 --- Adaptive Search Window --- p.57
Chapter 4.3.3 --- Compression Flow --- p.59
Chapter 4.4 --- Experiments and Performance Evaluations --- p.60
Chapter 5 --- High Dimensional Photo Clustering --- p.67
Chapter 5.1 --- Traditional Clustering Techniques --- p.67
Chapter 5.1.1 --- Hierarchical Clustering --- p.68
Chapter 5.1.2 --- Traditional K-means --- p.71
Chapter 5.2 --- Multidimensional Scaling --- p.74
Chapter 5.2.1 --- Introduction --- p.75
Chapter 5.2.2 --- Classical Scaling --- p.77
Chapter 5.3 --- Our Interactive MDS-based Clustering --- p.80
Chapter 5.3.1 --- Principal Coordinates from MDS --- p.81
Chapter 5.3.2 --- Clustering Scheme --- p.82
Chapter 5.3.3 --- Layout Scheme --- p.84
Chapter 5.4 --- Experiments and Results --- p.87
Chapter 6 --- Conclusions --- p.94
Bibliography --- p.96

碩士
國立中興大學
土木工程學系
87
Image Matching theory of conjugate points on digitial aerial images has been developed since 1950’s,and it tends to be matured today. But there are often faultly matching happening in practical applications. This is because of poor image quality,uniform tones of matching areas and casting shadow. Especially when casting shadow exists,it varies large gray value of image and causes extra diffculty of matching conjugate points on shadow areas. Even though we apply image matching on shadow areas,we are not necessarily get accurate conjugate points. And that is to say nothing of the ability to match accurate conjugate points by automatic Image Matching method. The objectives of this paper are to detect the shadow regions of aerial images,to restore gray value of shadow regions in no shadow-casting conditions,and simultaneously enhance the accuracy of matching. First,we choose shadow areas by manual operations,and then find exact shadow regions in these areas by applying to Image Segmentation method cooperating with Mathematical Morphology theory. Second,we adjust image histograms of shadow regions and restore their gray value in no shadow-casiting conditions by Image Histogram Matching method. Finally,we apply image matching of conjugate points in shadow regions of two stereo overlapping imges respectively before and after shadow restoration processes. That will assist us to examine the ability of enhancing accuracy of image matching in aerial shadow areas,and it can also demostrate the objectives of this paper.