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

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

published_or_final_version / abstract / toc / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Zernike moments are sets of mathematical quantities that uniquely characterize an image. It is known that they are invariant under rotation and reflection and robust to noise. In this thesis several other algorithms have been used to calculate these moments. The intent of this thesis is: 1. to use the classical method and the algorithms to reconstruct an image using Zernike moments and study their accuracy and 2. to examine if the invariance and noise insensitivity property of the calculated Zernike moments are upheld by these procedures. It is found that the constructed images using these algorithms do not resemble the original image. This prevents us from carrying out further study of these algorithms. The classical method has been successfully used to reconstruct an image when the height and width are equal. The classical method is also shown to be invariant under rotation and reflection and robust to Poisson noise. xxxvii

Zernike moments are sets of mathematical quantities that uniquely characterize an image. It is known that they are invariant under rotation and reflection and robust to noise. In this thesis several other algorithms have been used to calculate these moments. The intent of this thesis is: 1. to use the classical method and the algorithms to reconstruct an image using Zernike moments and study their accuracy and 2. to examine if the invariance and noise insensitivity property of the calculated Zernike moments are upheld by these procedures. It is found that the constructed images using these algorithms do not resemble the original image. This prevents us from carrying out further study of these algorithms. The classical method has been successfully used to reconstruct an image when the height and width are equal. The classical method is also shown to be invariant under rotation and reflection and robust to Poisson noise. xxxvii