Dissertations / Theses on the topic 'Wavelets (Mathematics) Image processing Surfaces'

Thesis (Ph.D.)--Tufts University, 2003.
Adviser: Joseph P. Noonan. Submitted to the Dept. of Electrical Engineering. Includes bibliographical references (leaves 149-149). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Stereo vision is a means of obtaining three-dimensional information by considering the same scene from two different positions. Stereo correspondence has long been and will continue to be the active research topic in computer vision. The requirement of dense disparity map output is great demand motivated by modern applications of stereo such as three-dimensional high-resolution object reconstruction and view synthesis, which require disparity estimates in all image regions. Stereo correspondence algorithms usually require significant computation. The challenges are computational economy, accuracy and robustness. While a large number of algorithms for stereo matching have been developed, there still leaves the space for improvement especially when a new mathematical tool such as wavelet analysis becomes mature. The aim of the thesis is to investigate the stereo matching approach using wavelet transform with a view to producing efficient and dense disparity map outputs. After the shift invariance property of various wavelet transforms is identified, the main contributions of the thesis are made in developing and evaluating two wavelet approaches (the dyadic wavelet transform and complex wavelet transform) for solving the standard correspondence problem. This comprises an analysis of the applicability of dyadic wavelet transform to disparity map computation, the definition of a waveletbased similarity measure for matching, the combination of matching results from different scales based on the detectable minimum disparity at each scale and the application of complex wavelet transform to stereo matching. The matching method using the dyadic wavelet transform is through SSD correlation comparison and is in particular detailed. A new measure using wavelet coefficients is defined for similarity comparison. The approach applying a dual tree of complex wavelet transform to stereo matching is formulated through phase information. A multiscale matching scheme is applied for both the matching methods. Imaging testing has been made with various synthesised and real image pairs. Experimental results with a variety of stereo image pairs exhibit a good agreement with ground truth data, where available, and are qualitatively similar to published results for other stereo matching approaches. Comparative results show that the dyadic wavelet transform-based matching method is superior in most cases to the other approaches considered.

Orientador: Yuzo Iano
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: A área que trata de compressão de imagem com perdas é, atualmente, de grande importância. Isso se deve ao fato de que as técnicas de compressão permitem representar de uma forma eficiente uma imagem reduzindo assim, o espaço necessário para armazenamento ou um posterior envio da imagem através de um canal de comunicações. Em particular, o algoritmo SPIHT (Set Partitioning of Hierarchical Trees) muito usado em compressão de imagens é de implementação simples e pode ser aproveitado em aplicações onde se requer uma baixa complexidade. Este trabalho propõe um esquema de compressão de imagens utilizando uma forma personalizada de armazenamento da transformada DWT (Discrete Wavelet Transform), codificação flexível da ROI (Region Of Interest) e a compressão de imagens usando o algoritmo SPIHT. A aplicação consiste na transmissão dos dados correspondentes usando-se codificação turbo. A forma personalizada de armazenamento da DWT visa um melhor aproveitamento da memória por meio do uso de algoritmo SPIHT. A codificação ROI genérica é aplicada em um nível alto da decomposição DWT. Nesse ponto, o algoritmo SPIHT serve para ressaltar e transmitir com prioridade as regiões de interesse. Os dados a serem transmitidos, visando o menor custo de processamento, são codificados com um esquema turbo convolucional. Isso porque esse esquema é de implementação simples no que concerne à codificação. A simulação é implementada em módulos separados e reutilizáveis para esta pesquisa. Os resultados das simulações mostram que o esquema proposto é uma solução que diminui a quantidade de memória utilizada bem como o custo computacional para aplicações de envio de imagens em aplicações como transmissão de imagens via satélite, radiodifusão e outras mídias
Abstract: Nowadays, the area that comes to lossy image compression is really important. This is due to the fact that compression techniques allow an efficient way to represent an image thereby reducing the space required for storage or subsequent submission of an image through a communications channel. In particular, the algorithm SPIHT (Set Partitioning of Hierarchical Trees) widely used in image compression is simple to implement and can be used in applications where a low complexity is required. This study proposes an image compression scheme using a personalized storage transform DWT (Discrete Wavelet Transform), encoding flexible ROI (Region Of Interest) and image compression algorithm using SPIHT. The application consists in a transmission of the corresponding data using turbo coding. The shape of the custom storage DWT aims to make better use of memory by reducing the amount of memory through the use of SPIHT algorithm. ROI coding is applied in a generic high-level DWT decomposition. At this point, the algorithm serves to highlight SPITH and transmit the priority areas of interest. The data to be transmitted in order to lower the cost of processing are encoded with a turbo convolutional scheme. This is due this scheme is simple to implement with regard to coding. The simulation is implemented in separate modules and reusable for this research. The simulations and analysis show that the proposed scheme is a solution that decreases the amount of memory used and the computational cost for applications to send images in applications such as image transmission via satellite, broadcasting and others medias
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica

Les problèmes inverses consistent à retrouver une donnée qui a été transformée ou perturbée. Ils nécessitent une régularisation puisque mal posés. En traitement d'images, la variation totale en tant qu'outil de régularisation a l'avantage de préserver les discontinuités tout en créant des zones lisses, résultats établis dans cette thèse dans un cadre continu et pour des énergies générales. En outre, nous proposons et étudions une variante de la variation totale. Nous établissons une formulation duale qui nous permet de démontrer que cette variante coïncide avec la variation totale sur des ensembles de périmètre fini. Ces dernières années les méthodes non-locales exploitant les auto-similarités dans les images ont connu un succès particulier. Nous adaptons cette approche au problème de complétion de spectre pour des problèmes inverses généraux. La dernière partie est consacrée aux aspects algorithmiques inhérents à l'optimisation des énergies convexes considérées. Nous étudions la convergence et la complexité d'une famille récente d'algorithmes dits Primal-Dual.

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Na área de processamento de sinais e, particularmente, em processamento de imagens, pesquisas recentes priorizam o desenvolvimento de novas técnicas e métodos que possam ser empregados em um amplo domínio de aplicações. As pirâmides de imagens constituem uma técnica bastante importante na criação de decomposições multirresolução em visão computacional e processamento de imagens. As transformadas de Wavelets podem ser vistas como mecanismos para decompor sinais nas suas partes constituintes, permitindo analisar os dados em diferentes domínios de frequência com a resolução de cada componente relacionada à sua escala. Além disso, na análise de wavelets, pode-se usar funções que estão contidas em regiões finitas, tornando-as convenientes na aproximação de dados com descontinuidades. Neste contexto, o presente trabalho apresentou uma técnica piramidal baseada nas transformações dos Polinômios Potências de Sigmóide (PPS) e suas famílias PPS-Wavelet, para tratamento em imagens digitais. Foram reaizados experimentos utilizando as novas técnicas piramidais e métricas para a avaliação de qualidade imagem, apresentando resultados promissores em relação à acurácia
In the signal processing and image processing fields, recent research give priority to develop new techniques and methods that can be used in a wide field of applications. The pyramids of images are important techniques used in multiresolution decompositions, applied to computer vision and image processing. The wavelet transforms can be viewed as tools to decompose signals into component parts, allowing to analyze the data in different frequency domains with resolution of each component related to your own scale. Furthermore, in the wavelet analysis, can be used functions which are contained in limited areas, making them suitable approximation of the data discontinuities. In this research presents a technique based on pyramid transforms the PPS and PPS-Wavelet families applied to digital images. The experiments using new techniques and pyramidal metrics for evaluation of image quality presents promising results about accuracy

Orientador: João Fernando Marar
Banca: José Remo Ferreira Brega
Banca: Edson Costa de Barros Carvalho Filho
Banca: Antonio Carlos Sementille
Resumo: Na área de processamento de sinais e, particularmente, em processamento de imagens, pesquisas recentes priorizam o desenvolvimento de novas técnicas e métodos que possam ser empregados em um amplo domínio de aplicações. As pirâmides de imagens constituem uma técnica bastante importante na criação de decomposições multirresolução em visão computacional e processamento de imagens. As transformadas de Wavelets podem ser vistas como mecanismos para decompor sinais nas suas partes constituintes, permitindo analisar os dados em diferentes domínios de frequência com a resolução de cada componente relacionada à sua escala. Além disso, na análise de wavelets, pode-se usar funções que estão contidas em regiões finitas, tornando-as convenientes na aproximação de dados com descontinuidades. Neste contexto, o presente trabalho apresentou uma técnica piramidal baseada nas transformações dos Polinômios Potências de Sigmóide (PPS) e suas famílias PPS-Wavelet, para tratamento em imagens digitais. Foram reaizados experimentos utilizando as novas técnicas piramidais e métricas para a avaliação de qualidade imagem, apresentando resultados promissores em relação à acurácia
Abstract: In the signal processing and image processing fields, recent research give priority to develop new techniques and methods that can be used in a wide field of applications. The pyramids of images are important techniques used in multiresolution decompositions, applied to computer vision and image processing. The wavelet transforms can be viewed as tools to decompose signals into component parts, allowing to analyze the data in different frequency domains with resolution of each component related to your own scale. Furthermore, in the wavelet analysis, can be used functions which are contained in limited areas, making them suitable approximation of the data discontinuities. In this research presents a technique based on pyramid transforms the PPS and PPS-Wavelet families applied to digital images. The experiments using new techniques and pyramidal metrics for evaluation of image quality presents promising results about accuracy
Mestre

Orientador: Yuzo Iano
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Segmentação de texturas é um ponto crucial em muitas aplicações da área de visão computacional e processamento digital de imagens. Muitas são as aplicações que utilizam imagens com texturas, como: sensoriamento remoto, análise de imagens médicas, inspeção industrial, etc. Para análise de texturas, é essencial o uso de um extrator de características capaz de representar bem cada textura presente na imagem. A transformada wavelet packet fornece a caracterização necessária para discriminação de texturas, oferecendo também uma representação multi-escala, ferramenta muito importante na análise de texturas. Outro ponto importante neste trabalho, é o fato da metodologia aqui proposta ser não supervisionada. Para tal, é utilizado o algoritmo de clusterização ARIA, que determina automaticamente o número de clusters presentes no conjunto de dados. A eficiência do método desenvolvido é comprovada aplicando-o em diversas imagens, como: mosaicos de Brodatz, imagens naturais, imagens médicas e outras aplicações.
Abstract:Texture segmentation is a crucial aspect in many computer vision and digital image processing applications. Several of these applications use texture images, such as remote sensing, medical image analysis, industrial inspection, etc. For texture analysis, it is essential to use a feature-extractor that can represent precisely each of the textures present in the picture. The wavelet packet transform provides the characteristics required for discrimination of the textures, as well as offering a multi-scale representation, which is a very important tool in texture analysis. Another important aspect in this work is that the proposed methodology is unsupervised. To achieve that, the clustering algorithm ARIA is used, which automatically determines the number of clusters present in the data set. The efficiency of the developed method is clear in the application of the method on several types of images, such as mosaics of Brodatz, natural images, medical images and other applications.
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica

Orientadores: Yuzo Iano, Ana Lucia Mendes Cruz Silvestre da Silva
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: O campo de análise e compressão de imagens tem recebido especial atenção da comunidade científica recentemente por abranger os principais sistemas de TV digital, comunicações via satélite e comunicações móveis. Neste contexto, as Transformadas Wavelets Discretas (TWD) surgem como uma ferramenta poderosa e suas inúmeras vantagens permitiram sua inserção em importantes padrões tais como JPEG2000, MPEG4 e MPEG7. O método lifting realiza a TWD sub-amostrando o sinal antes do processo de filtragem, implicando em rápido processamento por fazer uso das similaridades entre filtros passa-alta e passa-baixa, acelerando o cálculo dos coeficientes. Na literatura, ganhos aritméticos teóricos de diferentes proporções foram obtidos sobre o método tradicional, destacando-se os trabalhos de Daubechies e Sweldens e de Reichel. O objetivo desta pesquisa consiste em estender esta discussão de resultados teóricos quando implementados através de ferramentas, interpretada e compilada, focando no tempo de processamento necessário para a realização (decomposição e reconstrução) de diferentes imagens estáticas empregando wavelets pertencentes às famílias de Daubechies, Symlets e Biortogonais. Medidas de PSNR foram utilizadas de forma a corroborar a perfeita implementação do lifting, dado que o mesmo não pode implicar em deterioração na imagem reconstruída.
Abstract: The field of analysis and compression of images has been received special attention of the scientific community because of including in the main systems of digital TV, satellite communications and mobile communications. In this context, the Discrete Transform Wavelet (TWD) arise how a powerful tool and its many advantages allowed your insertion in important standards such as JPEG2000, MPEG4 and MPEG7. The lifting method realizes the TWD sub-sampling the signal before the filtering, resulting in faster processing by using the similarities between high and low pass filters, speeding up the calculation of coefficients. In the literature, arithmetic theoretical gains of different proportions were obtained on the traditional method, especially the works of Daubechies and Sweldens and of Reichel. The objective of this research is to extend this discussion of theoretical results when implemented through tools, interpreted and compiled, targeting the processing time required to perform (decomposition and reconstruction) of different images using wavelets belonging to the families of Daubechies, and Symlets Biortogonais. Measures of PSNR were used to corroborate the perfect implementation of the lifting, since that cannot result in deterioration in the reconstructed image.
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica

Most applications in computer vision suffer from two major difficulties. The first is they are notoriously ridden with sub-optimal local minima. The second is that they typically require high computational cost to be solved robustly. The reason for these two drawbacks is that most problems in computer vision, even when well-defined, typically require finding a solution in a very large high-dimensional space. It is for these two reasons that multiscale methods are particularly well-suited to problems in computer vision. Multiscale methods, by way of looking at the coarse scale nature of a problem before considering the fine scale nature, often have the ability to avoid sub-optimal local minima and obtain a more globally optimal solution. In addition, multiscale methods typically enjoy reduced computational cost. This thesis applies novel multiscale active contour methods to several problems in computer vision, especially in simultaneous segmentation and reconstruction of tomography images. In addition, novel multiscale methods are applied to contour registration using minimal surfaces and to the computation of non-linear rotationally invariant optical flow. Finally, a methodology for fast robust image segmentation is presented that relies on a lower dimensional image basis derived from an image scale space. The specific advantages of using multiscale methods in each of these problems is highlighted in the various simulations throughout the thesis, particularly their ability to avoid sub-optimal local minima and their ability to solve the problems at a lower overall computational cost.

Adaptive optics (AO) systems are used to increase the spatial resolution achieved by ground-based telescopes, which are limited by the atmospheric motion of air layers above them. Therefore, the real cut-off frequency is extended closer to the theoretical diffraction limit of the telescope thus allowing more high-frequency information from the object to be present in the image. Nevertheless, although the goal of image reconstruction and deconvolution algorithms is basically the same (i.e., to recover a “real” diffracted limit image, free of noise, from the object), and since the correction of AO is not complete (i.e., the effective cut-off frequency achieved by AO is still below the theoretical diffraction limit), the simultaneous use of such deconvolution algorithms over dataset acquired with AO is possible and desirable to further enhance their contrast. On the other hand, multiresolution tools like the wavelet transform (WT) have been historically introduced into multiple deconvolution schemes improving their performance with respect to their non-wavelet counterparts. The ability of such transforms to separate image components depending on their frequency content results in solutions that are generally closer to the real object. On the other hand, AO community generally states that, due to the high variability of AO PSFs is necessary to update the PSF estimate during the reconstruction process. Hence, the use of blind and myopic deconvolution algorithms should be unavoidable and yields to better results than those obtained by the static-PSFs codes. Therefore, being the aforementioned paragraphs the current state-of-art of AO imaging, this thesis yields the following topics/goals: 1. The static-PSF algorithm AMWLE has been applied over binary systems simulated for the 3-m Shane telescope to evaluate the photometric accuracy of the reconstruction. Its performance is compared with the PSF-fitting algorithm StarFinder, commonly used by the AO community, as well as other algorithms like FITSTAR, PDF deconvolution and IDAC. Results shown that AWMLE is able to produce better results than StarFinder and FITSTAR, and very similar results with respect to the rest of codes, especially for high Strehl ratios (SR) and matched PSFs. 2. A new deconvolution algorithm called ACMLE, based on the curvelet transform (CT) and a maximum likelihood estimator (MLE), has been designed for the reconstruction of extended and/or elongated objects. ACMLE has been tested together with AMWLE and blind/myopic codes such as MISTRAL and IDAC over Saturn and galaxy simulated images for the 5-m. Hale telescope. It is shown that the performance in the presence of noise of the multiresolution static-PSF algorithms is better than myopic and blind algorithms, thus showing that the control of noise is as important as the update of the PSF estimate during the reconstruction process. 3. A unidimensional WT has been applied in the spectral deconvolution of integral field spectroscopy (IFS) datacubes for direct imaging of exoplanets with EPICS instrument, which will be installed at the forthcoming 39-m E-ELT telescope. When this approach is compared with the classical non-wavelet one, an improvement of 1 mag from angle separations equal to 73 mas is devised. Furthermore, detection of close-in planets, between 43 and 58 mas also benefit of the application of wavelets. The use of WT allows the APLC chronograph to obtain similar results with respect to the apodizer-only solution, especially with increasing Talbot length, thus showing that WT classify planet frequency components and chromatic aberrations in different scales. Preliminary results for HARMONI spectrograph are also shown. This thesis opens several lines of research that will be addressed in future: - The world of multiresolution transforms is extremely huge and has produced dozens of new mathematical tools. Among many other, it is worthwhile to mention the shearlet transform, which is an extension/improvement of CT, and the waveatom tool, which is intended to classify textures in the image. They should be studied and compared to establish their best performance and their best field of application over AO images. - Blind and myopic algorithms have proved their ability for large mismatches between the “real” PSF that has created the image and the PSF that is used as a first estimate in the reconstruction process. However, their performance in the presence of noise is highly affected. Hence, it is convenient to investigate if it is possible to introduce (and how to do it) multiresolution transforms into these algorithms to improve their behavior. - For the study of IFS datacubes, other father scaling functions with different shapes could be proposed, in particular, it can be considered a “dynamic” scaling function with the ability to modulate its shape according to the low frequency signal to be removed from the spaxel. This could potentially improved the final photometry of the detected faint source. Besides, the design of a dictionary of wavelets, which increase the decomposing resolution across the spaxel, instead of a single dyadic decomposition, can improve the photometric accuracy of detected planets as well as their spectral characterizations, taking full advantage of the information contained in the IFS datacubes.

L'objet de ce mémoire est l'analyse des schémas de subdivision, outil de modélisation de surface lisse multi-résolution. Nos travaux se sont tout d'abord consacrés à l'étude du comportement géométrique de ces surfaces au voisinage des sommets extraordinaires du maillage de contrôle. La géométrie d'une surface de subdivision présente un comportement complexe au voisinage de ces sommets, et ces effets parfois néfastes sont pour certains encore mal connus. Nous avons proposé un cadre d'évaluation du comportement géométrique d'une surface de subdivision à travers une mesure de qualité adaptée : le gradient de courbure absolue. Nous avons ensuite proposé un espace de visualisation adapté à l'analyse du voisinage d'un sommet extraordinaire.Celui-ci étant indépendant du schéma de subdivision utilisé, ce cadre d'analyse nous permet de les comparer. Nos travaux se sont alors portés sur une analyse fréquentielle polaire des comportements géométriques, en tenant compte de leurs caractéristiques radiales et angulaires par rapport à la topologie du voisinage d'un sommet extraordinaire. Notre analyse étend les études existantes pour l'évaluation des comportements géométriques de cet outil de modélisation. De plus, nous avons proposé un systàme de description de la phase de subdivision topologique d'un schéma de subdivision. Notre systàme prend la forme d'un codage compact et flexible, il généralise les descriptions existantes. Ce codage permet la description des phases topologiques de tous les schémas de subdivision connus, ainsi que de nombreuses autres.

随着3D 图形学技术的快速发展，基于细分小波的多分辨率方法受到了越来越多的关注。为了提高运算效率， 一些细分小波采用了厅局部提升用的方法以避免解全局方程组的庞大开销。这种方法虽然极大地提高了小波分解的速度，但也使得这些小波较之一些经典的细分小波在生成曲面的质量上有所不如。在本篇论文里，我们提出了一组新型细分小波。这些小波变换不但保留了"局部提升"波运算速度快，节省内存的优点，在生成模型的质量上也大大提高，接近了经典的全局优化小波。
我们构造了极细分小波用于极结构快速简化和重构。极细分小波变换有效地避免Catmull -Clark 细分小波用于极结构时所造成的"皱裙"和鞍点，可以在高度数的异常点区域生成非常自然的二次连续曲面。为了更好的应用于普通的四边形网格曲面，我们还改进了极细分小波使之生成的曲面可以在边界处与Catmull-Clark 细分小波曲面光滑地融合。实验表明我们构造的混合极细分小波不但运算效率高，节省内存，还具有良好的稳定性，生成的曲面质量良好。基于矩阵值细分，我们还构造了一组近似和插值类型的矩阵值小波。由于矩阵值小波变换直接作用于向量，我们可以利用向量中额外的项作为参数以控制生成的多分辨率由面的形状。通过优化这些形状控制参数，我们在保持高效低内存消耗的同时，还可以进一步提高"局部提升"小波曲面的质量。
我们还将矩阵值小波应用于3D 模型的几何压缩。为了避免存储形状控制参数所带来的额外消耗，我们采用固定的形状控制参数从而将矩阵值小波简化为一种特殊的标量值小波。实验表明采用我们的小波的压缩方法，其压缩率接近于经典的全局优化小波，远高于"局部提升"小波。其压缩速度则接近于"局部提升"小波，远高于经典的采用全局优化小波。在未来的研究工作中，我们会进一步优化形状控制参数的选择策略，并尝试将其应用范围从目前三角形网格由面扩展到四边形曲面， T 样条曲面以及混合曲面。我们还将研究如何应用己有的小波变换提高多分辨率编辑与动画技术。
During the rapid development of 3D graphics applications, the wavelet-based multiresolution approaches have attracted more attention because they can effectively reduce the process/storage costs of high-detailed models. For the efficiency, many wavelets are constructed by using local lifting, which makes the fitting quality of results are not good as the usual wavelets with global optimization. On the other hand, once the wavelet transforms were constructed, the multiresolution meshes got by them cannot be adjusted any more. It is important to develop the new adaptive wavelets with better fitting quality, while keeping the high efficiency. In this dissertation, we provide several secondgeneration wavelets with improved fitting qualities, which include the compound biorthogonal wavelets for the hybrid quadrilateral meshes, and the efficient matrix-valued wavelets for complex triangular meshes.
We propose the novel polar subdivision wavelet, which efficiently generate multiresolution the polar structures. Polar structures are the natural representations of the self-revolution structures or high-valence regions of quadrilateral grids. The traditional multiresolution methods for the polar structures often generate deficits caused by high valence vertices. By adopting the polar subdivision and the special lifting operations on the polar structures, our wavelet transforms can generate smooth multiresolution surfaces without ripples and saddle points. To process the hybrid meshes made of quadrilaterals and polar structures, we extend the polar wavelet to the vertices in the circular layers, which makes it possible to fuse the surfaces generated by different wavelet transforms seamlessly. To improve the fitting quality of local lifting wavelets, we extend wavelet constructions from the scalar-valued scheme to the matrix-valued scheme, and propose a family of novel approximate and interpolatory matrix-valued subdivision wavelets. The matrix-valued wavelets are constructed from the refinable basis function vectors, which deal with the additional parameters to the geometric position of vertices. Since the final results of wavelet transforms are sensitive to the parameters, these parameters can be used to adjust the shape of multiresolution surfaces. By applying the lifting scheme, the computations of wavelet transform are local and in-placed. We also discuss the strategy of better shape controls for improving the fitting quality of simplified surfaces. The experiments showed that these novel wavelet transforms were sufficiently stable and performed well for noise reduction. With the suitable shape control parameters, the fitting quality of multiresolution surfaces can be further improved.
We study how to apply the efficient compression approach to the real applications, such as the compression of meshes. Since the shape control parameters need the additional storage, they will decrease the compression ratio if we apply the original versions of matrix-valued wavelets. We revise the construction of the matrix-valued wavelet transform and proposed the parameterized scalar-valued wavelet transform. With the special optimization of wavelet construction and suitable parameters, our compression approach has the high compression ratio close to the well-known approaches using the global orthogonal wavelets, and much higher compression ratio than the compression using the local lifting wavelets, while keeping the good efficiency. In the future work, we plan to extend the matrix-valued wavelets from triangular meshes to quadrilateral, normal and hybrid meshes. We will study how to apply the matrix-valued wavelets to the applications, such as multiresolution editing and animations. Further optimization of the shape control parameters for mobile and online applications is also an important issue.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Zhao, Chong.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 136-149).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
Abstract --- p.i
Acknowledgement --- p.v
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Introduction --- p.1
Chapter 1.2 --- Wavelet Transform --- p.4
Chapter 1.2.1 --- Wavelets and Multiresolution Analysis --- p.4
Chapter 1.2.2 --- Continuous Wavelet Transforms --- p.7
Chapter 1.2.3 --- Discrete Wavelet Transform --- p.8
Chapter 1.3 --- Second Generation Wavelets --- p.9
Chapter 1.3.1 --- Lifting Scheme --- p.9
Chapter 1.3.2 --- Subdivision --- p.11
Chapter 1.3.3 --- Subdivision Wavelets --- p.13
Chapter 1.4 --- Main Contributions --- p.15
Chapter 1.5 --- Chapter Summary --- p.16
Chapter 2 --- Compound Wavelets on Quadrilaterals --- p.18
Chapter 2.1 --- Introduction --- p.18
Chapter 2.2 --- Related Work --- p.19
Chapter 2.3 --- Polar Subdivision --- p.20
Chapter 2.3.1 --- Subdivision in radial layers --- p.21
Chapter 2.3.2 --- Subdivision in circular layers --- p.24
Chapter 2.4 --- Subdivision Wavelets Using Lifting --- p.25
Chapter 2.4.1 --- Lifting wavelets --- p.25
Chapter 2.4.2 --- Wavelet transforms --- p.29
Chapter 2.5 --- Compound Subdivision Wavelets --- p.32
Chapter 2.6 --- Experimental Results --- p.34
Chapter 2.7 --- Chapter Summary --- p.38
Chapter 3 --- Matrix-valued Loop Wavelets --- p.40
Chapter 3.1 --- Introduction --- p.40
Chapter 3.2 --- Related Work --- p.41
Chapter 3.3 --- Matrix-valued Loop Subdivision --- p.43
Chapter 3.4 --- Matrix-valued Loop Subdivision Wavelet --- p.46
Chapter 3.4.1 --- Lazy Wavelet --- p.46
Chapter 3.4.2 --- Inner Product --- p.49
Chapter 3.4.3 --- Wavelet Transform --- p.54
Chapter 3.4.4 --- Shape Control Parameters --- p.55
Chapter 3.5 --- Experiments and Discussion --- p.57
Chapter 3.6 --- Chapter Summary --- p.61
Chapter 4 --- Matrix-valued Interpolatory Wavelets --- p.63
Chapter 4.1 --- Introduction --- p.63
Chapter 4.2 --- Matrix-valued Interpolatory Subdivision --- p.64
Chapter 4.3 --- Matrix-valued 1-ring Wavelets --- p.67
Chapter 4.3.1 --- Biorthogonal Wavelet Transform --- p.67
Chapter 4.3.2 --- Extraordinary Points Treatment --- p.74
Chapter 4.3.3 --- Shape Control Parameters --- p.75
Chapter 4.4 --- Matrix-valued 2-ring Wavelets --- p.81
Chapter 4.5 --- Experiments and Discussion --- p.86
Chapter 4.5.1 --- 1-ring Wavelet Transform --- p.86
Chapter 4.5.2 --- 2-ring Wavelet Transform --- p.92
Chapter 4.6 --- Chapter Summary --- p.98
Chapter 5 --- Geometry compression using wavelets. --- p.100
Chapter 5.1 --- Introduction --- p.100
Chapter 5.2 --- Related Work --- p.101
Chapter 5.3 --- Matrix-valued Wavelet Transform --- p.105
Chapter 5.3.1 --- Matrix-valued Loop Subdivision --- p.105
Chapter 5.3.2 --- Lazy Wavelet --- p.108
Chapter 5.3.3 --- Inner Product --- p.109
Chapter 5.3.4 --- Wavelet Transform --- p.112
Chapter 5.3.5 --- Coding --- p.113
Chapter 5.4 --- Experiments and discussion --- p.114
Chapter 5.4.1 --- Stability --- p.117
Chapter 5.4.2 --- Efficiency --- p.118
Chapter 5.4.3 --- Compressions --- p.120
Chapter 5.5 --- Chapter Summary --- p.124
Chapter 6 --- Conclusions --- p.125
Chapter 6.1 --- Research Summary --- p.125
Chapter 6.2 --- Future Work --- p.127
Chapter A --- Inner Products of Wavelets in Radial Layers --- p.130
Chapter B --- Publication List --- p.133
Bibliography --- p.134

Jianhua Chen.
Thesis (Ph.D.)--Chinese University of Hong kong, 1998.
Includes bibliographical references (p. 127-[134]).
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.

This thesis has two related goals: the first involves the concept of self-similarity of images. Image self-similarity is important because it forms the basis for many imaging techniques such as non-local means denoising and fractal image coding. Research so far has been focused largely on self-similarity in the pixel domain. That is, examining how well different regions in an image mimic each other. Also, most works so far concerning self-similarity have utilized only the mean squared error (MSE). In this thesis, self-similarity is examined in terms of the pixel and wavelet representations of images. In each of these domains, two ways of measuring similarity are considered: the MSE and a relatively new measurement of image fidelity called the Structural Similarity (SSIM) Index. We show that the MSE and SSIM Index give very different answers to the question of how self-similar images really are. The second goal of this thesis involves non-local image processing. First, a generalization of the well known non-local means denoising algorithm is proposed and examined. The groundwork for this generalization is set by the aforementioned results on image self-similarity with respect to the MSE. This new method is then extended to the wavelet representation of images. Experimental results are given to illustrate the applications of these new ideas.

This thesis presents an algorithm that estimates motion in image sequence using wavelet transform. The motion detection is performed under unfavorable conditions of background movement, change of brightness, and noise. The algorithm is tolerant to brightness changes, noise, and small movement in the background. The false alarm rate of motion detection is reduced as compared to standard techniques. Using wavelet transform is numerically efficient and the storage requirements are significantly reduced. Also, a more accurate motion detection is achieved. Tests performed on real images show the effectiveness of this algorithm. Practical results of motion detection are presented.
Graduation date: 2003

Wen, Chengfeng.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 77-83).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.

Pun Chi Man.
"July 2002."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (p. 119-127).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.

The first part of this thesis studies advanced wavelet transform techniques for scalable still image object coding. In order to adapt to the content of a given signal and obtain more flexible adaptive representation, two advanced wavelet transform techniques, wavelet packet transform and directional wavelet transform, are developed for object-based image coding. Extensive experiments demonstrate that the new wavelet image coding systems perform comparable to or better than state-of-the-art in image compression while possessing some attractive features such as object-based coding functionality and high coding scalability.
The objective of this thesis is to develop an object-based coding framework built upon a family of wavelet coding techniques for a variety of arbitrarily shaped visual object scalable coding applications. Two kinds of arbitrarily shaped visual object scalable coding techniques are investigated in this thesis. One is object-based scalable wavelet still image coding; another is object-based scalable wavelet video coding.
The second part of this thesis investigates various components of object-based scalable wavelet video coding. A generalized 3-D object-based directional threading, which unifies the concepts of temporal motion threading and spatial directional threading, is seamlessly incorporated into 3-D shape-adaptive directional wavelet transform to exploit the spatio-temporal correlation inside the 3-D video object. To improve the computational efficiency of multi-resolution motion estimation (MRME) in shift-invariant wavelet domain, two fast MRME algorithms are proposed for wavelet-based scalable video coding. As demonstrated in the experiments, the proposed 3-D object-based wavelet video coding techniques consistently outperform MPEG-4 and other wavelet-based schemes for coding arbitrarily shaped video object, while providing full spatio-temporal-quality scalability with non-redundant 3-D subband decomposition.
Liu, Yu.
Adviser: King Ngi Ngan.
Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3693.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references (leaves 166-173).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.

As the electronic industry advances rapidly, the dimensions of the semiconductor products keep on being shrunk and that leads to more stringent requirement on process control and quality assurance. In particular, area array packages like BGA, CSP, flip chips, wafer bumping and wafer-level packaging need to have the 3D quality of some micro-surfaces inspected accurately and efficiently. An example of the micro-surfaces is the solder bumps for direct die-to-die bonding, which are of size as small as 60 to 600 microns in diameter. However, the tiny size and often highly specular and textureless nature of the surfaces make the inspection difficult. In addition, the size of the inspection system is required to be small so as to minimize restraint, on the operation of the various moving parts involved in the manufacturing process.
Experimental results with image data of a variety of objects have positively demonstrated the feasibility of the proposed methodology.
In the mechanism the inspection speed is governed by the number of needed images which also equals the number of spatial shiftings of the grating. This thesis also addresses how the grating, as well as its spatial shifting, can be designed optimally for minimizing this image number for faster inspection speed. An optimal solution to shifting strategy optimization is proposed that is applicable to any pattern on the fringe grating. A design method is also introduced for optimal pattern design, which has higher efficiency than brute-force searching. To reduce image number furthermore, bit-pairing codification mechanism and color-encoded pattern are proposed and verified to be more efficient.
In this thesis, I propose a new methodology for reconstructing micro-surfaces in 3D. The mechanism is based upon the familiar concept of binary structured-light, projection, but adapted, for the purpose of greatly reducing the system size, from the traditional setup of an array of multiple light sources to one with a single light source. The mechanism consists of a single light source in combination with a binary grating for projecting a binary pattern onto the target surface, and of a camera for capturing image of the illuminated scene. By shifting the binary grating in space and in every drifting taking a separate image of the illuminated surface, each position on the illuminated surface will be attached with a string of binary code over the sequence of captured images. With a suitable design of the binary grating, the binary code string can be made unique for each bump surface position, allowing exact correspondence between the binary pattern and image data, and subsequently 3D determination through triangulation. With such a bright-or-dark world for each image position, the issues of image saturation, image noise, and textureless nature of the target surfaces are avoided.
Jun Cheng.
"June 2006."
Adviser: Ronald Chi-kit Chung.
Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6499.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (p. 107-117).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.

by Lam Chi Wah.
Thesis submitted in: December 1997.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.
Includes bibliographical references (leaves 89-91).
Abstract also in Chinese.
Chapter Chapter 1 --- Introduction to Data Compression and Image Coding --- p.1
Chapter 1.1 --- Introduction --- p.1
Chapter 1.2 --- Fundamental Principle of Data Compression --- p.2
Chapter 1.3 --- Some Data Compression Algorithms --- p.3
Chapter 1.4 --- Image Coding Overview --- p.4
Chapter 1.5 --- Image Transformation --- p.5
Chapter 1.6 --- Quantization --- p.7
Chapter 1.7 --- Lossless Coding --- p.8
Chapter Chapter 2 --- Subband Coding and Wavelet Transform --- p.9
Chapter 2.1 --- Subband Coding Principle --- p.9
Chapter 2.2 --- Perfect Reconstruction --- p.11
Chapter 2.3 --- Multi-Channel System --- p.13
Chapter 2.4 --- Discrete Wavelet Transform --- p.13
Chapter Chapter 3 --- Vector Quantization (VQ) --- p.16
Chapter 3.1 --- Introduction --- p.16
Chapter 3.2 --- Basic Vector Quantization Procedure --- p.17
Chapter 3.3 --- Codebook Searching and the LBG Algorithm --- p.18
Chapter 3.3.1 --- Codebook --- p.18
Chapter 3.3.2 --- LBG Algorithm --- p.19
Chapter 3.4 --- Problem of VQ and Variations of VQ --- p.21
Chapter 3.4.1 --- Classified VQ (CVQ) --- p.22
Chapter 3.4.2 --- Finite State VQ (FSVQ) --- p.23
Chapter 3.5 --- Vector Quantization on Wavelet Coefficients --- p.24
Chapter Chapter 4 --- Vector Wavelet Transform-Linear Predictor Coding --- p.26
Chapter 4.1 --- Image Coding Using Wavelet Transform with Vector Quantization --- p.26
Chapter 4.1.1 --- Future Standard --- p.26
Chapter 4.1.2 --- Drawback of DCT --- p.27
Chapter 4.1.3 --- "Wavelet Coding and VQ, the Future Trend" --- p.28
Chapter 4.2 --- Mismatch between Scalar Transformation and VQ --- p.29
Chapter 4.3 --- Vector Wavelet Transform (VWT) --- p.30
Chapter 4.4 --- Example of Vector Wavelet Transform --- p.34
Chapter 4.5 --- Vector Wavelet Transform - Linear Predictive Coding (VWT-LPC) --- p.36
Chapter 4.6 --- An Example of VWT-LPC --- p.38
Chapter Chapter 5 --- Vector Quantizaton with Inter-band Bit Allocation (IBBA) --- p.40
Chapter 5.1 --- Bit Allocation Problem --- p.40
Chapter 5.2 --- Bit Allocation for Wavelet Subband Vector Quantizer --- p.42
Chapter 5.2.1 --- Multiple Codebooks --- p.42
Chapter 5.2.2 --- Inter-band Bit Allocation (IBBA) --- p.42
Chapter Chapter 6 --- Parental Finite State Vector Quantizers (PFSVQ) --- p.45
Chapter 6.1 --- Introduction --- p.45
Chapter 6.2 --- Parent-Child Relationship Between Subbands --- p.46
Chapter 6.3 --- Wavelet Subband Vector Structures for VQ --- p.48
Chapter 6.3.1 --- VQ on Separate Bands --- p.48
Chapter 6.3.2 --- InterBand Information for Intraband Vectors --- p.49
Chapter 6.3.3 --- Cross band Vector Methods --- p.50
Chapter 6.4 --- Parental Finite State Vector Quantization Algorithms --- p.52
Chapter 6.4.1 --- Scheme I: Parental Finite State VQ with Parent Index Equals Child Class Number --- p.52
Chapter 6.4.2 --- Scheme II: Parental Finite State VQ with Parent Index Larger than Child Class Number --- p.55
Chapter Chapter 7 --- Simulation Result --- p.58
Chapter 7.1 --- Introduction --- p.58
Chapter 7.2 --- Simulation Result of Vector Wavelet Transform (VWT) --- p.59
Chapter 7.3 --- Simulation Result of Vector Wavelet Transform - Linear Predictive Coding (VWT-LPC) --- p.61
Chapter 7.3.1 --- First Test --- p.61
Chapter 7.3.2 --- Second Test --- p.61
Chapter 7.3.3 --- Third Test --- p.61
Chapter 7.4 --- Simulation Result of Vector Quantization Using Inter-band Bit Allocation (IBBA) --- p.62
Chapter 7.5 --- Simulation Result of Parental Finite State Vector Quantizers (PFSVQ) --- p.63
Chapter Chapter 8 --- Conclusion --- p.86
REFERENCE --- p.89

Indiana University-Purdue University Indianapolis (IUPUI)
Multiresolution image fusion is an emerging area of research for use in military and commercial applications. While many methods for image fusion have been developed, improvements can still be made. In many cases, image fusion methods are tailored to specific applications and are limited as a result. In order to make improvements to general image fusion, novel methods have been developed based on the wavelet transform and empirical variance. One particular novelty is the use of directional filtering in conjunction with wavelet transforms. Instead of treating the vertical, horizontal, and diagonal sub-bands of a wavelet transform the same, each sub-band is handled independently by applying custom filter windows. Results of the new methods exhibit better performance across a wide range of images highlighting different situations.

Tsang, Man Ho.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 57-60).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.