No description available.

Die vorliegende Arbeit beschäftigt sich mit den finiten matriziellen Momentenproblemen von Stieltjes-Typ und beschreibt unter Verwendung der Methode der Fundamentalen Matrixungleichungen die Lösungsmenge durch gebrochen lineare Transformationen.

It is obvious that differential equations can be used to model real-life problems. Although it is possible to obtain analytical solutions of some of them, it is in general difficult to find closed form solutions of differential equations. Finding thus approximate solutions has been the subject of many researchers from different areas. In this thesis, we propose a new approach to Variational Iteration Method (VIM) to obtain the solutions of systems of first-order differential equations. The main contribution of the thesis to VIM is that proposed approach uses restricted variations only for the nonlinear terms and builds up a matrix-valued Lagrange multiplier that leads to the extension of the method (EVIM). Close relation between the matrix-valued Lagrange multipliers and fundamental solutions of the differential equations highlights the relation between the extended version of the variational iteration method and the classical variation of parameters formula. It has been proved that the exact solution of the initial value problems for (nonhomogenous) linear differential equations can be obtained by such a generalisation using only a single variational step. Since higher-order equations can be reduced to first-order systems, the proposed approach is capable of solving such equations too / indeed, without such a reduction, variational iteration method is also extended to higher-order scalar equations. Further, the close connection with the associated first-order systems is presented. Such extension of the method to higher-order equations is then applied to solve boundary value problems: linear and nonlinear ones. Although the corresponding Lagrange multiplier resembles the Green&rsquo / s function, without the need of the latter, the extended approach to the variational iteration method is systematically applied to solve boundary value problems, surely in the nonlinear case as well. In order to show the applicability of the method, we have applied the EVIM to various real-life problems: the classical Sturm-Liouville eigenvalue problems, Brusselator reaction-diffusion, and chemical master equations. Results show that the method is simple, but powerful and effective.

The recent advances in the field of computer vision have brought many of the laboratory algorithms into the realm of industry. However, one problem that still remains open in the field of 3D vision is the problem of noise. The challenging problem of 3D structure recovery from images is highly sensitive to the presence of input data that are contaminated by errors that do not conform to ideal assumptions. Tackling the problem of extreme data, or outliers has led to many robust methods in the field that are able to handle moderate levels of outliers and still provide accurate outputs. However, this problem remains open, especially for higher noise levels and so it has been the goal of this thesis to address the issue of robustness with respect to two central problems in 3D computer vision. The two problems are highly related and they have been presented together within a Structure from Motion (SfM) context. The first, is the problem of robustly estimating the fundamental matrix from images whose correspondences contain high outlier levels. Even though this area has been extensively studied, two algorithms have been proposed that significantly speed up the computation of the fundamental matrix and achieve accurate results in scenarios containing more than 50% outliers. The presented algorithms rely on ideas from the field of robust statistics in order to develop guided sampling techniques that rely on information inferred from residual analysis. The second, problem addressed in this thesis is the robust estimation of camera intrinsic parameters from fundamental matrices, or self-calibration. Self-calibration algorithms are notoriously unreliable for general cases and it is shown that the existing methods are highly sensitive to noise. In spite of this, robustness in self-calibration has received little attention in the literature. Through experimental results, it is shown that it is essential for a real-world self-calibration algorithm to be robust. In order to introduce robustness to the existing methods, three robust algorithms have been proposed that utilize existing constraints for self-calibration from the fundamental matrix. However, the resulting algorithms are less affected by noise than existing algorithms based on these constraints. This is an important milestone since self-calibration offers many possibilities by providing estimates of camera parameters without requiring access to the image acquisition device. The proposed algorithms rely on perturbation theory, guided sampling methods and a robust root finding method for systems of higher order polynomials. By adding robustness to self-calibration it is hoped that this idea is one step closer to being a practical method of camera calibration rather than merely a theoretical possibility.

The recent advances in the field of computer vision have brought many of the laboratory algorithms into the realm of industry. However, one problem that still remains open in the field of 3D vision is the problem of noise. The challenging problem of 3D structure recovery from images is highly sensitive to the presence of input data that are contaminated by errors that do not conform to ideal assumptions. Tackling the problem of extreme data, or outliers has led to many robust methods in the field that are able to handle moderate levels of outliers and still provide accurate outputs. However, this problem remains open, especially for higher noise levels and so it has been the goal of this thesis to address the issue of robustness with respect to two central problems in 3D computer vision. The two problems are highly related and they have been presented together within a Structure from Motion (SfM) context. The first, is the problem of robustly estimating the fundamental matrix from images whose correspondences contain high outlier levels. Even though this area has been extensively studied, two algorithms have been proposed that significantly speed up the computation of the fundamental matrix and achieve accurate results in scenarios containing more than 50% outliers. The presented algorithms rely on ideas from the field of robust statistics in order to develop guided sampling techniques that rely on information inferred from residual analysis. The second, problem addressed in this thesis is the robust estimation of camera intrinsic parameters from fundamental matrices, or self-calibration. Self-calibration algorithms are notoriously unreliable for general cases and it is shown that the existing methods are highly sensitive to noise. In spite of this, robustness in self-calibration has received little attention in the literature. Through experimental results, it is shown that it is essential for a real-world self-calibration algorithm to be robust. In order to introduce robustness to the existing methods, three robust algorithms have been proposed that utilize existing constraints for self-calibration from the fundamental matrix. However, the resulting algorithms are less affected by noise than existing algorithms based on these constraints. This is an important milestone since self-calibration offers many possibilities by providing estimates of camera parameters without requiring access to the image acquisition device. The proposed algorithms rely on perturbation theory, guided sampling methods and a robust root finding method for systems of higher order polynomials. By adding robustness to self-calibration it is hoped that this idea is one step closer to being a practical method of camera calibration rather than merely a theoretical possibility.

Die vorliegende Arbeit beschäftigt sich mit den finiten matriziellen Momentenproblemen von Stieltjes-Typ und beschreibt unter Verwendung der Methode der Fundamentalen Matrixungleichungen die Lösungsmenge durch gebrochen lineare Transformationen.

A smart phone camera based indoor guidance system to aid the visually impaired is presented. Most proposed systems for aiding the visually impaired with indoor navigation are not feasible for widespread use due to cost, usability, or portability. We use a smart phone vision based system to create an indoor guidance system that is simple, accessible, inexpensive, and discrete to aid the visually impaired to navigate unfamiliar environments such as public buildings. The system consists of a smart phone and a server. The smart phone transmits pictures of the user's location to the server. The server processes the images and matches them to a database of stored images of the building. After matching features, the location and orientation of the person is calculated using 3D location correspondence data stored for features of each image. Positional information is then transmitted back to the smart phone and communicated to the user via text-to-speech. This thesis focuses on developing the vision technology for this unique application rather than building the complete system. Experimental results demonstrate the ability of the system to quickly and accurately determine the pose of the user in a university building.

No / An algorithm for the rectification of uncalibrated images is presented and applied to a variety of cases. The algorithm generates the rectifying transformations directly from the geometrical relationship between the images, using any three correspondences in the images to define a reference plane. A small set of correspondences is used to calculate an initial rectification. Additional correspondences are introduced semi-automatically, by correlating regions of the rectified images. Since the rectified images of surfaces in the reference plane have no relative distortion, features can be matched very accurately by correlation, allowing small changes in disparity to be detected. In the 3-d reconstruction of an architectural scene, differences in depth are resolved to about 0.001 of the distance from camera to subject.

No description available.

This thesis deals with the reconstruction of the scene using two or more images. It describes the whole reconstruction process consisting of detecting points in images, finding the appropriate geometry between images and resulting projection of these points into the space of scene. The thesis also includes a description of the application, which demonstrates the described methods.