Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, June 2003. / Thesis advisor(s): Phillip E. Pace, Don Brutzman. Includes bibliographical references (p. 129-130). Also available online.

This work focuses on developing an inversion scheme to estimate water-column sound-speed fields in three dimensions. The inversion scheme is based on a linearized perturbative technique which utilizes estimates of modal travel times. The technique is appropriate in the littoral ocean where measurements are made across range and cross-range distances greater than 10 km to ensure sufficient modal dispersion. Previous applications of then inversion technique has been limited to one or two dimensions and/or focused primarily on the seabed. Compared to past applications, the accuracy and uncertainty of the solution is improved by employing approximate equality constraints within the context of \textit{a priori} estimates of model and data covariances. The effectiveness of the constrained technique is explored through a one-dimensional example. The robustness of the technique is illustrated by introducing different types of errors into the inversion and considering the accuracy. A further examination of the technique is given by exploring a three-dimensional example. Several case studies are presented to investigate the effects of different levels of environmental variability and spatial sampling. / text

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

This thesis is concerned with three-dimensional (3D) reconstruction and point registration, which are fundamental topics of numerous applications in the area of computer vision. First, we propose the multiple epipolar lines (MEL) shape recovery method for 3D reconstruction from an image sequence captured under circular motion. This method involves recovering the 3D shape by reconstructing a set of 3D rim curves. The position of each point on a 3D rim curve is estimated by using three or more views. Two or more of these views are chosen close to each other to guarantee good image point matching, while one or more views are chosen far from these views to properly compensate for the error introduced in the triangulation scheme by the short baseline of the close views. Image point matching among all views is performed using a new method that suitably combines epipolar geometry and cross-correlation. Second, we develop the one line search (OLS) method for estimating the 3D model of an object from a sequence of images. The recovered object comprises a set of 3D rim curves. The OLS method determines the image point correspondences of each 3D point through a single line search along the ray defined by the camera center and each two-dimensional (2D) point where a photo-consistency index is maximized. In accordance with the approach, the search area is independently reduced to a line segment on the number of views. The key advantage of the proposed method is that only one variable is focused on in defining the corresponding 3D point, whereas the approaches for multiple-view stereo typically exploit multiple epipolar lines and hence require multiple variables. Third, we propose the expectation conditional maximization for point registration (ECMPR) algorithm to solve the rigid point registration problem by fitting the problem into the framework of maximum likelihood with missing data. The unknown correspondences are handled via mixture models. We derive a maximization criterion based on the expected complete-data log-likelihood. Then, the point registration problem can be solved by an instance of the expectation conditional maximization algorithm, that is, the ECMPR algorithm. Experiments with synthetic and real data are presented in each section. The proposed approaches provide satisfactory and promising results. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

　　Image-based rendering (IBR) is an emerging technology for rendering photo-realistic views of scenes from a collection of densely sampled images or videos. It provides a framework for developing revolutionary virtual reality and immersive viewing systems. There has been considerable progress recently in the capturing, storage and transmission of image-based representations. This thesis proposes two image-based rendering (IBR) systems for improving the viewing freedom and environmental modeling capability of conventional static IBR systems. The first system consists of a circular array with 13 still cameras (Canon 550D) for capturing ancient Chinese artifacts at high resolution. The second one is constructed by mounting a linear array of 8 video cameras (Sony HDR-TGIE) on an electrically controllable wheel chair with its motion being controllable manually or remotely through wireless local area network (LAN) by means of additional hardware circuitry. 　　Both systems support object-based rendering and 3D reconstruction capability and consist of two main components. 1) A novel view synthesis algorithm using a new segmentation and mutual information (MI)-based algorithm for dense depth map estimation, which relies on segmentation, local polynomial regression (LPR)-based depth map smoothing and MI-based matching algorithm to iteratively estimate the depth map. The method is very flexible and both semi-automatic and automatic segmentation methods can be employed. They rank fourth and sixth, respectively, in the Middlebury comparison of existing depth estimation methods. This allows high quality renderings of outdoor and indoor scenes with improved mobility/freedom to be obtained. This algorithm can also be extended to object tracking. Experimental results also show that the proposed MI-based algorithms are applicable to robust registration in noisy dynamic ultrasound images. 2) A new 3D reconstruction algorithm which utilizes sequential-structure-from-motion (S-SFM) technique and the dense depth maps estimated previously. It relies on a new iterative point cloud refinement algorithm based on Kalman filter (KF) for outlier removal and the segmentation-MI-based algorithm to further refine the correspondences and the projection matrices. The mobility of our system allows us to recover more conveniently 3D model of static objects from the improved point cloud using a new robust radial basis function (RBF)-based modeling algorithm to further suppress possible outliers and generate smooth 3D meshes of objects. Moreover, a new rendering technique named view dependent texture mapping is used to enhance the final rendering effect. Experimental results show that the proposed 3D reconstruction algorithm significantly reduces the adverse effect of the outliers and produces high quality renderings using view dependent texture mapping and the model reconstructed. 　　Overall, this study provides a framework for designing IBR systems with improved viewing freedom and ability to cope with moving and static objects in indoor and outdoor environment. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Recovering 3D structure from multiple 2D images is a fundamental problem in computer vision. Most of existing methods focus on the reconstruction of static points in 3D space; however, the reconstruction of trajectories which are resulted from moving points should also have our full attention due to its high efficiency in structure modeling and description. Depending on whether points are moving in spatial domain or in time domain, trajectory recovery turns out to be a curve reconstruction problem or a non-rigid structure recovery problem respectively. This thesis addresses several issues that were not considered in existing approaches in both of the two problems. For the curve reconstruction problem, we propose a dedicated method for planar curve reconstruction and an optimization method for general curve reconstruction. In the planar curve reconstruction method, measured projected curves that are typically represented by sequences of points are fitted using B-splines before reconstruction, enabling the occlusion problem to be handled naturally. Also, an optimization algorithm is developed to match the fitted curves across images while enforcing the planarity constraint, and the algorithm is guaranteed to converge. In the general curve reconstruction method, Non-Uniform Rational B-Spline (NURBS) is employed for curve representation in 3D space, which improves the flexibility in curve description while maintaining the smoothness of a curve at the same time. Starting with measured point sequences of projected curves, a complete set of algorithms are developed and evaluated, including curve initialization and optimization of the initialized curve by minimizing the 2D reprojection error that is defined to be the 2D Euclidean distance from measured points to reprojected curves. Experiments show that the proposed methods are robust and efficient, and are excellent in producing high-quality reconstruction results. For the non-rigid structure recovery problem, we proposed two methods for the recovery of non-rigid structures together with a strategy that automates the process of non-rigid structure recovery. Compared with existing methods using synthetic datasets, both of the two proposed methods perform significantly better than existing methods when there are noise contaminations in measurements, and are capable to recover the ground truth solution when the measurements are noise free whereas no existing method is capable of achieving this so far. In the first method, namely factorization-based method, the available constraints in non-rigid structure from motion are analyzed and the ambiguity of the solution space of the proposed method is clarified, leading to a straightforward approach that requires only solution to several linear equations in least-squares sense instead of having to solve non-linear optimization problems in existing methods. In the second method, namely bundle adjustment method, a modified trajectory basis model that is demonstrated to be more flexible for non-rigid structure description is proposed. The method seeks for optimal non-rigid structure and camera matrices by alternately solving a set of linear equations in least square sense. Experiments on real non-rigid motions show that the method improves the quality of reconstruction significantly. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Three-dimensional (3D) sonography is regarded as a further development of ultrasound imaging technology and its application has greatly increased in recent years. This thesis summarizes the original research findings of the application of 3D ultrasonography for biometry measurement, morphology screening, prenatal diagnosis of abnormalities, ultrasound training and the application of 3D volumetry in the early diagnosis of homozygous α-thalassemia and birth weight prediction in term pregnancy. In a study involving 50 singleton pregnancies at 17-34 weeks' gestation, fetal biometric measurements obtained by an inexperienced operator using both two-dimensional (2D) and 3D ultrasound were reproducible and showed good agreement with those obtained by an experienced operator (all intraclass correlation coefficients were ≥ 0.991). The use of 3D ultrasound by an inexperienced operator allowed faster measurement of fetal biometric parameters than the use of 2D ultrasound, and also seemed to facilitate the acquisition of higher-quality images for the measurement of abdominal circumference. In basic central nervous system and cardiac screening examination, for the inexperienced operator, 3D/four-dimensional(4D) volume acquisition yielded a quicker but less optimal anatomic examination of the fetal central nervous system and heart structures compared to 2D. The diagnostic accuracy of 3D ultrasonography in central nervous system abnormalities was also investigated. The results illustrated that 3D agreed with 2D ultrasonography in the prenatal diagnosis of intracranial malformations. Homozygous α0-thalassemia is very common in South-east Asia and its prenatal diagnosis is essential due to increased fetal and maternal mortality and morbidity. Placental volume/CRL quotient measured by 3D volumetry was significantly higher in pregnancies with α0-thalassemia major cases, and 1.49 may be regarded as a cut-off for early prediction of α0-thalassemia major. In a cross-sectional study of 290 Hong Kong Chinese women with a singleton pregnancy at 37-42 weeks of gestation, the birth weight prediction models based on 3D thigh volume and conventional 2D biometric measurements were developed. It was found that with 3D thigh model, the precision of birth weight prediction to within 5 and 10% of actual birth weight in a Chinese population at term gestation could be achieved. Previous studies have shown that there is a difference in the learning curve of fetal biometry measurement by 2D ultrasound among trainees. Whether there is any difference in the learning curve between 2D and 3D ultrasound is unknown. The study included three trainees and each of them performed 90 scans in biometry measurements. By using cumulative sum analysis graphs, it could be shown that there was no difference in the learning curve between 2D and 3D ultrasound. In conclusion, the above studies have demonstrated that the use of 3D ultrasound has diversified and provided much additional information in selected indications. / published_or_final_version / Obstetrics and Gynaecology / Doctoral / Doctor of Philosophy

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