Browsing Department of Applied Mathematics by browse.metadata.advisor "Du Preez, J. A."
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- ItemA probabilistic graphical model approach to solving the structure and motion problem(Stellenbosch : Stellenbosch University, 2016-03) Streicher, Simon Frederik; Brink, Willie; Du Preez, J. A.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT: Probabilistic graphical models show great promise in resolving uncertainty within large systems by using probability theory. However, the focus is usually on problems with a discrete representation, or problems with linear dependencies. The focus of this study is on graphical models as a means to solve a nonlinear system, specifically the structure and motion problem. For a given system, our proposed solution makes use of multivariate Gaussians to model parameters as random variables, and sigma point linearisation to capture all interrelationships as covariances. This technique does not need in-depth knowledge about given nonlinearities (such as Jacobian matrices) and can therefore be used as part of a general solution. The aim of structure and motion is to generate a 3D reconstruction of a scene and camera poses, using 2D images as input. We discuss the typical feature based structure and motion pipeline along with the underlying multiview geometry, and use this theory to find relationships between variables. We test our approach by building a probabilistic graphical model for the structure and motion problem and evaluating it on different types of synthetic datasets. Furthermore, we test our approach on two real-world datasets. From this study we conclude that, for structure and motion, there is clear promise in the performance of our system, especially on small datasets. The required runtime quickly increases, and the accuracy of results decreases, as the number of feature points and camera poses increase or the noise in the inputs increase. However, we believe that further developments can improve the system to the point where it can be used as a practical and robust solution for a wide range of real-world image sets. We further conclude that this method can be a great aid in solving similar types of nonlinear problems where uncertainty needs to be dealt with, especially those without well-known solutions.