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Robust Estimation of Motion Parameters and Scene Geometry : Minimal Solvers and Convexification of Regularisers for Low-Rank Approximation

Valtonen Örnhag, Marcus LU (2021)
Abstract
In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. The more you know about the object you wish to track—through sensors or mechanical construction—the more likely you are to get good positioning estimates. In the first part of this thesis, we explore new ways of improving positioning for vehicles travelling on a planar surface. This is done in several different ways: first, we generalise the work done for monocular vision to include two cameras, we propose ways of speeding... (More)
In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. The more you know about the object you wish to track—through sensors or mechanical construction—the more likely you are to get good positioning estimates. In the first part of this thesis, we explore new ways of improving positioning for vehicles travelling on a planar surface. This is done in several different ways: first, we generalise the work done for monocular vision to include two cameras, we propose ways of speeding up the estimation time with polynomial solvers, and we develop an auto-calibration method to cope with radially distorted images, without enforcing pre-calibration procedures.

We continue to investigate the case of constrained motion—this time using auxiliary data from inertial measurement units (IMUs) to improve positioning of unmanned aerial vehicles (UAVs). The proposed methods improve the state-of-the-art for partially calibrated cases (with unknown focal length) for indoor navigation. Furthermore, we propose the first-ever real-time compatible minimal solver for simultaneous estimation of radial distortion profile, focal length, and motion parameters while utilising the IMU data.

In the third and final part of this thesis, we develop a bilinear framework for low-rank regularisation, with global optimality guarantees under certain conditions. We also show equivalence between the linear and the bilinear framework, in the sense that the objectives are equal. This enables users of alternating direction method of multipliers (ADMM)—or other subgradient or splitting methods—to transition to the new framework, while being able to enjoy the benefits of second order methods. Furthermore, we propose a novel regulariser fusing two popular methods. This way we are able to combine the best of two worlds by encouraging bias reduction while enforcing low-rank solutions. (Less)
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author
supervisor
opponent
  • Dr. Fitzgibbon, Andrew, Microsoft Research Cambridge, UK.
organization
alternative title
Robust skattning av rörelseparametrar och 3D-geometri : Minimala lösare och konvexifiering av minimerare för långrangsapproximation
publishing date
type
Thesis
publication status
published
subject
keywords
Computer Vision, Visual Odometry, Simultaneous Localization and Mapping, minimal solvers, Convex relaxations, Structure from motion
pages
387 pages
publisher
Lund University Faculty of Engineering, Lund, Sweden
defense location
Lecture hall MH:Hörmander, Centre of Mathematical Sciences, Sölvegatan 18, Faculty of Engineering LTH, Lund University, Lund
defense date
2021-05-14 13:15:00
ISSN
1404-0034
ISBN
978-91-7895-770-5
978-91-7895-769-9
language
English
LU publication?
yes
id
5e1c6c74-12c3-4706-9313-5ea211a7fc3e
date added to LUP
2021-04-16 15:09:42
date last changed
2021-04-20 09:39:10
@phdthesis{5e1c6c74-12c3-4706-9313-5ea211a7fc3e,
  abstract     = {In the dawning age of autonomous driving, accurate and robust tracking of vehicles is a quintessential part. This is inextricably linked with the problem of Simultaneous Localisation and Mapping (SLAM), in which one tries to determine the position of a vehicle relative to its surroundings without prior knowledge of them. The more you know about the object you wish to track—through sensors or mechanical construction—the more likely you are to get good positioning estimates. In the first part of this thesis, we explore new ways of improving positioning for vehicles travelling on a planar surface. This is done in several different ways: first, we generalise the work done for monocular vision to include two cameras, we propose ways of speeding up the estimation time with polynomial solvers, and we develop an auto-calibration method to cope with radially distorted images, without enforcing pre-calibration procedures.<br/><br/>We continue to investigate the case of constrained motion—this time using auxiliary data from inertial measurement units (IMUs) to improve positioning of unmanned aerial vehicles (UAVs). The proposed methods improve the state-of-the-art for partially calibrated cases (with unknown focal length) for indoor navigation. Furthermore, we propose the first-ever real-time compatible minimal solver for simultaneous estimation of radial distortion profile, focal length, and motion parameters while utilising the IMU data.<br/><br/>In the third and final part of this thesis, we develop a bilinear framework for low-rank regularisation, with global optimality guarantees under certain conditions. We also show equivalence between the linear and the bilinear framework, in the sense that the objectives are equal. This enables users of alternating direction method of multipliers (ADMM)—or other subgradient or splitting methods—to transition to the new framework, while being able to enjoy the benefits of second order methods. Furthermore, we propose a novel regulariser fusing two popular methods. This way we are able to combine the best of two worlds by encouraging bias reduction while enforcing low-rank solutions.},
  author       = {Valtonen Örnhag, Marcus},
  isbn         = {978-91-7895-770-5},
  issn         = {1404-0034},
  language     = {eng},
  publisher    = {Lund University Faculty of Engineering, Lund, Sweden},
  school       = {Lund University},
  title        = {Robust Estimation of Motion Parameters and Scene Geometry : Minimal Solvers and Convexification of Regularisers for Low-Rank Approximation},
  url          = {https://lup.lub.lu.se/search/ws/files/96755564/phd_thesis_marcus_valtonen_ornhag.pdf},
  year         = {2021},
}