In Part I of the thesis, we study the problems of image denoising and de-blurring under impulse noise. We consider two-phase methods for solving these problems. In the first phase, efficient detectors are applied to detect the outliers. In the second phase, variational methods utilizing the outputs of the first phase are performed. For denoising, we prove that the functionals to be minimized in the second phase have many good properties such as maximum principle, Lipschitz continuity and etc. Based on the results, we propose conjugate gradient methods and quasi-Newton methods to minimize the functional efficiently. For deblurring, we propose a two-phase method combining the median-type filters and a variational method with Mumford-Shah regularization term. The experiments show that the two-phase methods give much better results than both the median-type filters and full variational methods. / In this thesis, we study two aspects in image processing. Part I is about image denoising and deblurring under impulse noise, and Part II is about framelet-based methods for image reconstruction. / Part II of the thesis focuses on framelet-based methods for image reconstruction. In particular, we consider framelet-based methods for chopped and nodded image reconstruction and image inpainting. By interpreting both the problems as recovery of missing data, framelet, a generalization of wavelet, is applied to solve the problems. We incorporate sophisticated thresholding schemes into the algorithm, hence the regularities of the restored images can be guaranteed. By the theory of convex analysis, we prove the convergence of the framelet-based methods. We find that the limits of the framelet-based methods satisfy some minimization properties, hence connections with variational methods are established. / Cai, Jianfeng. / "March 2007." / Adviser: Raymond H. Chan. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0350. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 119-129). / 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.

No description available.

by Lo Kwok-tung. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references. / ABSTRACT --- p.i / ACKNOWLEDGEMENTS --- p.iii / LIST OF PRINCIPLE SYMBOLS AND ABBREVIATIONS --- p.iv / LIST OF FIGURES --- p.vii / LIST OF TABLES --- p.ix / TABLE OF CONTENTS --- p.x / Chapter CHAPTER 1 --- Introduction / Chapter 1.1 --- Background - The Need for Image Compression --- p.1-1 / Chapter 1.2 --- Image Compression - An Overview --- p.1-2 / Chapter 1.2.1 --- Predictive Coding - DPCM --- p.1-3 / Chapter 1.2.2 --- Sub-band Coding --- p.1-5 / Chapter 1.2.3 --- Transform Coding --- p.1-6 / Chapter 1.2.4 --- Vector Quantization --- p.1-8 / Chapter 1.2.5 --- Block Truncation Coding --- p.1-10 / Chapter 1.3 --- Block Based Image Coding Techniques --- p.1-11 / Chapter 1.4 --- Goal of the Work --- p.1-13 / Chapter 1.5 --- Organization of the Thesis --- p.1-14 / Chapter CHAPTER 2 --- Block-Based Image Coding Techniques / Chapter 2.1 --- Statistical Model of Image --- p.2-1 / Chapter 2.1.1 --- One-Dimensional Model --- p.2-1 / Chapter 2.1.2 --- Two-Dimensional Model --- p.2-2 / Chapter 2.2 --- Image Fidelity Criteria --- p.2-3 / Chapter 2.2.1 --- Objective Fidelity --- p.2-3 / Chapter 2.2.2 --- Subjective Fidelity --- p.2-5 / Chapter 2.3 --- Transform Coding Theroy --- p.2-6 / Chapter 2.3.1 --- Transformation --- p.2-6 / Chapter 2.3.2 --- Quantization --- p.2-10 / Chapter 2.3.3 --- Coding --- p.2-12 / Chapter 2.3.4 --- JPEG International Standard --- p.2-14 / Chapter 2.4 --- Vector Quantization Theory --- p.2-18 / Chapter 2.4.1 --- Codebook Design and the LBG Clustering Algorithm --- p.2-20 / Chapter 2.5 --- Block Truncation Coding Theory --- p.2-22 / Chapter 2.5.1 --- Optimal MSE Block Truncation Coding --- p.2-24 / Chapter CHAPTER 3 --- Development of New Orthogonal Transforms / Chapter 3.1 --- Introduction --- p.3-1 / Chapter 3.2 --- Weighted Cosine Transform --- p.3-4 / Chapter 3.2.1 --- Development of the WCT --- p.3-6 / Chapter 3.2.2 --- Determination of a and β --- p.3-9 / Chapter 3.3 --- Simplified Cosine Transform --- p.3-10 / Chapter 3.3.1 --- Development of the SCT --- p.3-11 / Chapter 3.4 --- Fast Computational Algorithms --- p.3-14 / Chapter 3.4.1 --- Weighted Cosine Transform --- p.3-14 / Chapter 3.4.2 --- Simplified Cosine Transform --- p.3-18 / Chapter 3.4.3 --- Computational Requirement --- p.3-19 / Chapter 3.5 --- Performance Evaluation --- p.3-21 / Chapter 3.5.1 --- Evaluation using Statistical Model --- p.3-21 / Chapter 3.5.2 --- Evaluation using Real Images --- p.3-28 / Chapter 3.6 --- Concluding Remarks --- p.3-31 / Chapter 3.7 --- Note on Publications --- p.3-32 / Chapter CHAPTER 4 --- Pruning in Transform Coding of Images / Chapter 4.1 --- Introduction --- p.4-1 / Chapter 4.2 --- "Direct Fast Algorithms for DCT, WCT and SCT" --- p.4-3 / Chapter 4.2.1 --- Discrete Cosine Transform --- p.4-3 / Chapter 4.2.2 --- Weighted Cosine Transform --- p.4-7 / Chapter 4.2.3 --- Simplified Cosine Transform --- p.4-9 / Chapter 4.3 --- Pruning in Direct Fast Algorithms --- p.4-10 / Chapter 4.3.1 --- Discrete Cosine Transform --- p.4-10 / Chapter 4.3.2 --- Weighted Cosine Transform --- p.4-13 / Chapter 4.3.3 --- Simplified Cosine Transform --- p.4-15 / Chapter 4.4 --- Operations Saved by Using Pruning --- p.4-17 / Chapter 4.4.1 --- Discrete Cosine Transform --- p.4-17 / Chapter 4.4.2 --- Weighted Cosine Transform --- p.4-21 / Chapter 4.4.3 --- Simplified Cosine Transform --- p.4-23 / Chapter 4.4.4 --- Generalization Pruning Algorithm for DCT --- p.4-25 / Chapter 4.5 --- Concluding Remarks --- p.4-26 / Chapter 4.6 --- Note on Publications --- p.4-27 / Chapter CHAPTER 5 --- Efficient Encoding of DC Coefficient in Transform Coding Systems / Chapter 5.1 --- Introduction --- p.5-1 / Chapter 5.2 --- Minimum Edge Difference (MED) Predictor --- p.5-3 / Chapter 5.3 --- Performance Evaluation --- p.5-6 / Chapter 5.4 --- Simulation Results --- p.5-9 / Chapter 5.5 --- Concluding Remarks --- p.5-14 / Chapter 5.6 --- Note on Publications --- p.5-14 / Chapter CHAPTER 6 --- Efficient Encoding Algorithms for Vector Quantization of Images / Chapter 6.1 --- Introduction --- p.6-1 / Chapter 6.2 --- Sub-Codebook Searching Algorithm (SCS) --- p.6-4 / Chapter 6.2.1 --- Formation of the Sub-codebook --- p.6-6 / Chapter 6.2.2 --- Premature Exit Conditions in the Searching Process --- p.6-8 / Chapter 6.2.3 --- Sub-Codebook Searching Algorithm --- p.6-11 / Chapter 6.3 --- Predictive Sub-Codebook Searching Algorithm (PSCS) --- p.6-13 / Chapter 6.4 --- Simulation Results --- p.6-17 / Chapter 6.5 --- Concluding Remarks --- p.5-20 / Chapter 6.6 --- Note on Publications --- p.6-21 / Chapter CHAPTER 7 --- Predictive Classified Address Vector Quantization of Images / Chapter 7.1 --- Introduction --- p.7-1 / Chapter 7.2 --- Optimal Three-Level Block Truncation Coding --- p.7-3 / Chapter 7.3 --- Predictive Classified Address Vector Quantization --- p.7-5 / Chapter 7.3.1 --- Classification of Images using Three-level BTC --- p.7-6 / Chapter 7.3.2 --- Predictive Mean Removal Technique --- p.7-8 / Chapter 7.3.3 --- Simplified Address VQ Technique --- p.7-9 / Chapter 7.3.4 --- Encoding Process of PCAVQ --- p.7-13 / Chapter 7.4 --- Simulation Results --- p.7-14 / Chapter 7.5 --- Concluding Remarks --- p.7-18 / Chapter 7.6 --- Note on Publications --- p.7-18 / Chapter CHAPTER 8 --- Recapitulation and Topics for Future Investigation / Chapter 8.1 --- Recapitulation --- p.8-1 / Chapter 8.2 --- Topics for Future Investigation --- p.8-3 / REFERENCES --- p.R-1 / APPENDICES / Chapter A. --- Statistics of Monochrome Test Images --- p.A-l / Chapter B. --- Statistics of Color Test Images --- p.A-2 / Chapter C. --- Fortran Program Listing for the Pruned Fast DCT Algorithm --- p.A-3 / Chapter D. --- Training Set Images for Building the Codebook of Standard VQ Scheme --- p.A-5 / Chapter E. --- List of Publications --- p.A-7

Another objective of this work is to study the perceptual optimized video object coding. Since MPEG-4 treats a scene as a composition of video objects that are separately encoded and decoded, such a flexible video coding framework makes it possible to code different video objects with different priorities. It is necessary to analyze the priorities of video objects according to their intrinsic properties and psycho-visual characteristics such that the bit budget can be distributed properly to video objects to improve the perceptual quality of the compressed video. An object-level visual attention model is developed to automatically obtain the visual attention information of video objects. The visual attention values of video objects are calculated and incorporated in the newly developed dynamic bit allocation mechanism to improve the objective quality of the high priority objects such that the perceptual quality of the overall picture can be maximized. / As strict rate control algorithms used in video coding sacrifice the quality consistency, the rate distortion tradeoff is important to achieve a balance between the bit rate and quality. A novel separable rate distortion modeling method is proposed to analyze the rate distortion characteristics of the color video signal. This method provides higher estimation accuracy when compared to the non-separable modeling method. To achieve rate distortion tradeoff in H.264/AVC, a new control strategy is presented. The feedback from the encoder buffer is analyzed by a control-theoretic adaptation approach to avoid buffer overflow and underflow. A novel rate distortion tradeoff controller is designed by considering both the quality variation and buffer fluctuation. Smooth video quality is achieved and the relevant constraints are satisfied. / Due to the unique features of the video object coding such as both texture and shape introducing distortions and video objects being of arbitrarily shapes, the rate distortion analysis and optimization strategies are different from the traditional rectangular frame-based techniques. Two new rate distortion modeling methods are proposed for the shape coding. The first one is a linear rate distortion modeling method. The computational complexity is low and the estimation is accurate. To further improve the modeling performance, a novel statistical learning based method is proposed by incorporating shape features to provide rate distortion analysis for the shape coding. Therefore, a joint texture-shape rate distortion modeling approach is derived by integrating the texture and shape rate distortion models. The new joint texture-shape distortion models provide the basis for optimal bit allocation for the video object coding to minimize the coding distortion with the bit rate constraint and stabilize the buffer fullness. The major contribution of this optimal bit allocation scheme is to provide a unified solution for the following two problems: how to allocate bits between the texture and shape and how to distribute the hit budget for multiple video objects, simultaneously. / This thesis addresses rate distortion analysis, optimization, and control problems in video coding. These rate distortion issues not only provide the theoretical background but also are concerned with the practical design for video coding systems. The main objective of this thesis is to consider the problems associated with analyzing the rate distortion characteristics of the video source and providing optimal solutions or tradeoffs for the rate and distortion in video coding systems. More specifically this thesis focuses on both the object-based video coding system, MPEG-4, and the rectangular frame-based video coding system, H.264/AVC. / Chen, Zhenzhong. / "July 2007." / Adviser: King Ngi Ngan. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1194. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 225-247). / 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. / Abstract in English and Chinese. / School code: 1307.

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.

A primary investigation on the selection of texture representations for the appearance modeling is also enclosed in this thesis, as a useful piece of work toward the automatic construction of deformable appearance models. / For both methods, the model generalization errors---the criteria directly evaluating deformable models, are adopted to quantitatively evaluate the registration results. The proposed methods are compared with state-of-the-art ones on both synthetic and real biomedical data. Their abilities to construct 2D and 3D shape models with better quality are demonstrated. Based on the STS method, an Active Boundary Model is also proposed for 3D images segmentation. / In recent years, the deformable shape models have been playing important roles in medical image analysis. A key problem involved in their construction is the shape registration: to establish dense correspondences across a group of different shapes. / So the second method, named STS (Segments tied to splines), is further proposed. It can directly take point sets as input shapes, which is able to handle shapes of complicated topologies in high dimensions. STS employs the same number of segments to gradually and concurrently model different point sets, achieving their registration by maintaining a correspondence that is naturally established at the coarsest stage of modeling. It formulates the registration problem in a Bayesian framework, where a constrained Gaussian Mixture Model (GMM) is taken to measure the likelihood, and an item derived from the bending energy of the Thin Plate Spline (TPS) is assumed to be the prior. This problem is efficiently solved by an Expectation-Maximum (EM) algorithm, which is embedded in a coarse-to-fine scheme. / The first method, called CAP (Coding all the points), employs a set of landmarks along the shape contours to establish the correspondence between shapes. Shape registration is formulated as an optimal coding problem, where not only the position of landmarks, but also the shape contours themselves are coded. The resultant description length is minimized by a new optimization approach, which utilizes multiple optimization techniques and a propagation scheme. However, CAP has difficulty to handle shapes in high dimensions, especially with complicated topologies. This is because it needs to parameterize the shapes under registration, so as to manipulate the trajectories of landmarks. / Two basic elements are normally embedded in a shape registration algorithm: a shape representation model and a transformation model. To our best knowledge, most existing methods treat them separately, where the representations for each shape are obtained first, and then the correspondence is established by only optimizing transformations. From the view of building deformable shape models, this leads to sub-optimal results, because a shape model is a coupled one of both representation and transformation. In this thesis, two new methods have been developed, both achieving the registration by simultaneously optimizing the shape representation and transformation, and thus have the potential to build optimal deformable shape models. Neither of them depend on any specific feature detection. / Jiang, Yifeng. / "September 2007." / Advisers: Hung-Tat Tsui; Qing-Hu Max Meng. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 4844. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 161-172). / 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.

Most of the existing research on mathematical morphology is restricted to the deterministic case. This thesis addresses the void in the results on the stochastic properties of morphological filters. The primary results include analysis of the stochastic properties of morphological operations, such as dilation, erosion, closing and opening. Two unbiased morphological filters are introduced and a quantitative description of the probability distribution function of morphological operations on independent, identically distributed random signals is obtained. Design of an optimal morphological filter in the sense of a criterion proposed here is also discussed. A brief, but systematic description of the definitions and properties of deterministic morphological operations on sets is presented to establish the necessary background for the analysis of the filter stochastic properties. / Graduation date: 1992

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Five algorithms in different applications are proposed in this thesis. All of them are formulated as smoothness based labeling problems, including single image segmentation, video object cutout, image/video completion, image denoising, and image matting. According to different definitions, different optimization approaches are used in these algorithms. In single image segmentation and video object cutout, the graph-cut algorithms are used; in image/video completion, belief propagation is used; and in image denoising and image matting, closed form optimization is implemented. / Many applications in computer vision can be formulated as labeling problems of assigning each pixel a label where the labels represent some local quantities. If all pixels are regarded as independent, i.e., the label of each pixel has nothing to do with the labels of other pixels, such labeling problems are seriously sensitive to noise. On the other hand, for applications in videos, if the inter-frame information is neglected, the performance of the algorithms will be degraded. / Successful performance of the five proposed algorithms, with comparisons to related methods, demonstrates that the proposed models of the labeling problems using the smoothness-based priors work very well in these computer vision applications. / Such labeling problems with smoothness-based priors can be solved by minimizing a Markov energy. According to different definitions of the energy functions, different optimization tools can be used to obtain the results. In this thesis, three optimization approaches are used due to their good performance: graph cuts, belief propagation, and optimization with a closed form solution. / To improve results of these labeling problems, smoothness-based priors can be enforced in the formulations. For a single image, the smoothness is the spatial coherence, which means that spatially close pixels trend to have similar labels. For a video, an additional temporal coherence is enforced, which means that the corresponding pixels in different frames should have similar labels. The spatial coherence constraint makes algorithms robust to noise and the temporal coherence constraint utilizes the inter-frame information for better video-based applications. / Chen, Shifeng. / Adviser: Liu Jian Zhuang. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3594. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 130-145). / 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.

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