Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/82702
Type: Thesis
Title: Constrained parameter estimation in multiple view geometry.
Author: Szpak, Zygmunt Ladyslaw
Issue Date: 2013
School/Discipline: School of Computer Science
Abstract: Multiple view geometry is a branch of computer vision devoted entirely to the study of the relationship between images generated from a fixed three-dimensional scene. Thanks to the body of knowledge generated in this domain some of the most exciting developments in navigation have recently been realised. Google's release of Street-view maps is the most remarkable example. Currently there is a growing demand for new insight and knowledge originating from multiple view geometry, as two of the most popular technological companies, Google and Apple, embark on a mission to generate three-dimensional maps. The research conducted in this thesis makes a direct contribution to two specific problems that arise frequently in the context of multiple view geometry: homography estimation and ellipse fitting. A homography is used to establish a relationship between two images of a scene, whenever the scene consists of a flat surface. If the scene consists of several at surfaces, such as walls of buildings in urban environments, then multiple homographies are required to adequately represent the relationship between a pair of images. But when multiple homographies are required, computer vision practitioners typically estimate homographies separately. This thesis demonstrates that multiple homographies must not be estimated separately, because additional interhomography constraints need to be satisfied in order for a collection of homographies to accurately reflect the three-dimensional geometry of the scene. This thesis offers a comprehensive account of a variety of subtleties that arise in the estimation of multiple homographies, and presents detailed novel algorithms for fulfilling the estimation task. A central contribution is the development of a new framework for jointly estimating multiple homographies. The new framework leads to considerably more accurate homography estimates than previous approaches. The second major contribution of this thesis relates to another frequently encountered task in multiple view geometry: ellipse fitting. Recently many new cost functions promising unbiasedness, consistency or hyperaccuracy have been reported to improve the state-of-the-art in fitting ellipses to data. Unfortunately, the new cost functions have not been substantiated with thorough experimental comparisons. This thesis offers an extensive evaluation of both new and old ellipse fitting methods with the aid of comprehensive simulations. The findings suggest that there is not much difference between the newer and more established estimators. There is, however, a significant difference between the sole estimator that guarantees an ellipse fit, and other estimators which are prone to occasionally producing hyperbolas. The estimator that guarantees an ellipse fit is significantly less accurate. To remedy this undesirable discovery, a new ellipse estimator is proposed that shares a similar statistical accuracy to the unbiased, consistent or hyper-accurate estimators, but unlike all of these, still guarantees an ellipse fit.
Advisor: van den Hengel, Anton John
Dick, Anthony Robert
Eriksson, Anders Per
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 2013
Keywords: homography estimation; consistency constraints; ellipse fitting; parameter estimation; computer vision
Provenance: Copyright material removed from digital thesis. See print copy in University of Adelaide Library for full text.
Copyright material removed from digital thesis. See print copy in University of Adelaide Library for full text.
Appears in Collections:Research Theses

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