Sheung, Hoi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 65-70). / Abstract also in Chinese. / Abstract --- p.v / Acknowledgements --- p.ix / List of Figures --- p.xiii / List of Tables --- p.xv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main Contributions --- p.3 / Chapter 1.2 --- Outline --- p.3 / Chapter 2 --- Related Work --- p.5 / Chapter 2.1 --- Volumetric reconstruction --- p.5 / Chapter 2.2 --- Combinatorial approaches --- p.6 / Chapter 2.3 --- Robust statistics in surface reconstruction --- p.6 / Chapter 2.4 --- Down-sampling of massive points --- p.7 / Chapter 2.5 --- Streaming and parallel computing --- p.7 / Chapter 3 --- Robust Normal Estimation and Point Projection --- p.9 / Chapter 3.1 --- Robust Estimator --- p.9 / Chapter 3.2 --- Mean Shift Method --- p.11 / Chapter 3.3 --- Normal Estimation and Projection --- p.11 / Chapter 3.4 --- Moving Least Squares Surfaces --- p.14 / Chapter 3.4.1 --- Step 1: local reference domain --- p.14 / Chapter 3.4.2 --- Step 2: local bivariate polynomial --- p.14 / Chapter 3.4.3 --- Simpler Implementation --- p.15 / Chapter 3.5 --- Robust Moving Least Squares by Forward Search --- p.16 / Chapter 3.6 --- Comparison with RMLS --- p.17 / Chapter 3.7 --- K-Nearest Neighborhoods --- p.18 / Chapter 3.7.1 --- Octree --- p.18 / Chapter 3.7.2 --- Kd-Tree --- p.19 / Chapter 3.7.3 --- Other Techniques --- p.19 / Chapter 3.8 --- Principal Component Analysis --- p.19 / Chapter 3.9 --- Polynomial Fitting --- p.21 / Chapter 3.10 --- Highly Parallel Implementation --- p.22 / Chapter 4 --- Error Controlled Subsampling --- p.23 / Chapter 4.1 --- Centroidal Voronoi Diagram --- p.23 / Chapter 4.2 --- Energy Function --- p.24 / Chapter 4.2.1 --- Distance Energy --- p.24 / Chapter 4.2.2 --- Shape Prior Energy --- p.24 / Chapter 4.2.3 --- Global Energy --- p.25 / Chapter 4.3 --- Lloyd´ةs Algorithm --- p.26 / Chapter 4.4 --- Clustering Optimization and Subsampling --- p.27 / Chapter 5 --- Mesh Generation --- p.29 / Chapter 5.1 --- Tight Cocone Triangulation --- p.29 / Chapter 5.2 --- Clustering Based Local Triangulation --- p.30 / Chapter 5.2.1 --- Initial Surface Reconstruction --- p.30 / Chapter 5.2.2 --- Cleaning Process --- p.32 / Chapter 5.2.3 --- Comparisons --- p.33 / Chapter 5.3 --- Computing Dual Graph --- p.34 / Chapter 6 --- Results and Discussion --- p.37 / Chapter 6.1 --- Results of Mesh Reconstruction form Noisy Point Cloud --- p.37 / Chapter 6.2 --- Results of Clustering Based Local Triangulation --- p.47 / Chapter 7 --- Conclusions --- p.55 / Chapter 7.1 --- Key Contributions --- p.55 / Chapter 7.2 --- Factors Affecting Our Algorithm --- p.55 / Chapter 7.3 --- Future Work --- p.56 / Chapter A --- Building Neighborhood Table --- p.59 / Chapter A.l --- Building Neighborhood Table in Streaming --- p.59 / Chapter B --- Publications --- p.63 / Bibliography --- p.65

Xue, Tianfan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 52-55). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Previous Approaches on Face Identification --- p.3 / Chapter 1.1.1 --- Face Identification --- p.3 / Chapter 1.1.2 --- General Objects --- p.4 / Chapter 1.1.3 --- Manifold Objects --- p.7 / Chapter 1.2 --- Previous Approaches on 3D Reconstruction --- p.9 / Chapter 1.3 --- Our approach for Face Identification --- p.11 / Chapter 1.4 --- Our approach for 3D Reconstruction --- p.13 / Chapter 2 --- Face Detection --- p.14 / Chapter 2.1 --- GAFI and its Face Identification Results --- p.15 / Chapter 2.2 --- Our Face Identification Approach --- p.17 / Chapter 2.2.1 --- Real Face Detection --- p.18 / Chapter 2.2.2 --- The Weak Face Adjacency Theorem --- p.20 / Chapter 2.2.3 --- Searching for Type 1 Lost Faces --- p.22 / Chapter 2.2.4 --- Searching for Type 2 Lost Faces --- p.23 / Chapter 2.3 --- Experimental Results --- p.25 / Chapter 3 3 --- D Reconstruction --- p.30 / Chapter 3.1 --- Assumption and Terminology --- p.30 / Chapter 3.2 --- Finding Cuts from a Line Drawing --- p.34 / Chapter 3.2.1 --- Propositions for Finding Cuts --- p.34 / Chapter 3.2.2 --- Searching for Good Cuts --- p.35 / Chapter 3.3 --- Separation of a Line Drawing from Cuts --- p.38 / Chapter 3.4 3 --- D Reconstruction from a Line Drawing --- p.45 / Chapter 3.5 --- Experiments --- p.45 / Chapter 4 --- Conclusion --- p.50

An image is a two-dimensional representation of the three-dimensional world. Recovering the information which is lost in the process of image formation is one of the fundamental problems in Computer Vision. One approach to this problem involves generating and evaluating a succession of surface hypotheses, with the best hypothesis selected as the final estimate. The fitness of each hypothesis can be evaluated by comparing the reference images against synthetic images of the hypothesised surface rendered with the reference cameras. An infinite number of surfaces can recreate any set of reference images, so many approaches to the reconstruction problem recover the largest from this set of surfaces. In contrast, the approach we present here accommodates prior structural information about the scene, thereby reducing ambiguity and finding a reconstruction which reflects the requirements of the user. The user describes structural information by defining a set of primitives and relating them by parameterised transformations. The reconstruction problem then becomes one of estimating the parameter values that transform the primitives such that the hypothesised surface best recreates the reference images. Two appearance-based likelihoods which measure the hypothesised surface against the reference images are described. The first likelihood compares each reference image against an image synthesised from the same viewpoint by rendering a projection of a second image onto the surface. The second likelihood finds the ‘optimal’ surface texture given the hypothesised scene configuration. Not only does this process maximise photo-consistency with respect to all reference images, but it prohibits incorrect reconstructions by allowing the use of prior information about occlusion. The second likelihood is able to reconstruct scenes in cases where the first is biased. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1330993 / Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 2008

Image reconstruction, in common with many other inverse problems, is often mathematically ill-posed in the sense that solutions are neither stable nor unique. Ultrasonic image reconstruction is particularly notorious in this regard, with narrow transducer bandwidths and limited - sometimes sparsely sampled apertures posing formidable difficulties for conventional signal processing. To overcome these difficulties, some form of regularisation is mandatory, whereby the ill-posed problem is restated as a closely related, well-posed problem, and then solved uniquely. This thesis explores the application of maximum entropy (MaxEnt) regularisation to the problem of reconstructing complex-valued imagery from sparsely sampled coherent ultrasonic field data, with particular emphasis on three-dimensional problems in the non-destructive evaluation (NDE) of materials. MaxEnt has not previously been applied to this class of problem, and yet in comparison with many other approaches to image reconstruction, it emerges as the clear leader in terms of resolution and overall image quality. To account for this performance, it is argued that the default image model used with MaxEnt is particularly meaningful in cases of ultrasonic scattering by objects embedded in homogeneous media. To establish physical and mathematical insights into the forward problem, linear equations describing scattering from both penetrable and impenetrable objects are first derived using the Born and physical optics approximations respectively. These equations are then expressed as a shift-invariant computational model that explicitly incorporates sparse sampling. To validate this model, time-domain scattering responses are computed and compared with analytical solutions for a simple canonical test case drawn from the field of NDE. The responses computed via the numerical model are shown to accurately reproduce the analytical responses. To solve inverse scattering problems via MaxEnt, the robust Cambridge algorithm is generalised to the complex domain and extended to handle broadband (multiple-frequency) data. Two versions of the augmented algorithm are then compared with a range of other algorithms, including several linearly regularised algorithms and lastly, due to its acknowledged status as a competitor with MaxEnt in radio-astronomy, the non-linear CLEAN algorithm. These comparisons are made through simulated 3-D imaging experiments under conditions of both complete and sparse aperture sampling with low and high levels of additive Gaussian noise. As required in any investigation of inverse problems, the experimental confirmation of algorithmic performance is emphasised, and two common imaging geometries relevant to NDE are selected for this purpose. In monostatic synthetic aperture imaging experiments involving side-drilled holes in an aluminium plate and test objects immersed in H2O, MaxEnt image reconstruction is demonstrated to be robust against grating-lobe and side-lobe formation, in addition to temporal bandwidth restriction. This enables efficient reconstruction of 2-D and 3-D images from small numbers of discrete samples in the spatial and frequency domains. The thesis concludes with a description of the design and testing of a novel polyvinylidene fluoride (PVDF) bistatic array transducer that offers advantages over conventional point-sampled arrays in terms of construction simplicity and signal-to-noise ratio. This ultra-sparse orthogonal array is the only one of its kind yet demonstrated, and was made possible by MaxEnt signal processing.

Thesis (Ph. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

<p>3D Models of botanical trees are very important in video games, simulation, virtual reality, digital city modeling and other fields of computer graphics. However, since the early days of computer graphics, the modeling of trees has been challenging, because of the huge dynamical range between its smallest and largest structures and their geometrical complexity. Trees are also ubiquitous which makes it even hard to model them in a realistic way, Current techniques are limited in that they model a tree either in a rule-based way or in an approximated way. These methods emphasize appearance while sacrificing its real structure. Recent development in range scanners are making 3D aquisition feasible for large and complex objects. This report presents the semi-automatic technique developed for modeling laser-scanned trees. First, the user draws a few strokes on the depth image plane generated from the dataset. Branches are then extracted through the 2D Curve detection algorithm originally developed. Afterwards, those short branches are connected together to generate the skeleton of the tree by forming a Minimum Spanning Tree (MST). Finally, the geometry of the tree skeleton is produced using allometric rules for branch thickness and branching angles.</p>

In magnetic resonance imaging (MRI), sampling methods that lead to incomplete data coverage of k-space are used to accelerate imaging and reduce overall scan time. Non-Cartesian sampling trajectories such as radial, spiral, and random trajectories are employed to facilitate advanced imaging techniques, such as compressed sensing, or to provide more efficient coverage of k-space for a shorter scan period. When k-space is undersampled or unevenly sampled, traditional methods of transforming Fourier data to obtain the desired image, such as the FFT, may no longer be applicable. The Fourier reconstruction of optical interferometer data (FROID) algorithm is a novel reconstruction method developed by A. R. Hajian that has been successful in the field of optical interferometry in reconstructing images from sparsely and unevenly sampled data. It is applicable to cases where the collected data is a Fourier representation of the desired image or spectrum. The framework presented allows for a priori information, such as the positions of the sampled points, to be incorporated into the reconstruction of images. Initially, FROID assumes a guess of the real-valued spectrum or image in the form of an interpolated function and calculates the corresponding integral Fourier transform. Amplitudes are then sampled in the Fourier space at locations corresponding to the acquired measurements to form a model dataset. The guess spectrum or image is then adjusted such that the model dataset in the Fourier space is least squares fitted to measured values. In this thesis, FROID has been adapted and implemented for use in MRI where k-space is the Fourier transform of the desired image. By forming a continuous mapping of the image and modelling data in the Fourier space, a comparison and optimization with respect to data acquired in k-space that is either undersampled or irregularly sampled can be performed as long as the sampling positions are known. To apply FROID to the reconstruction of magnetic resonance images, an appropriate objective function that expresses the desired least squares fit criteria was defined and the model for interpolating Fourier data was extended to include complex values of an image. When an image with two Gaussian functions was tested, FROID was able to reconstruct images from data randomly sampled in k-space and was not restricted to data sampled evenly on a Cartesian grid. An MR image of a bone with complex values was also reconstructed using FROID and the magnitude image was compared to that reconstructed by the FFT. It was found that FROID outperformed the FFT in certain cases even when data were rectilinearly sampled.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 110-120). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 110-120). Also available on the Internet.

D. Tech. Electrical Engineering