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Homography-Based Positioning and Planar Motion Recovery

Wadenbäck, Mårten LU (2017)
Abstract
Planar motion is an important and frequently occurring situation in mobile robotics applications. This thesis concerns estimation of ego-motion and pose of a single downwards oriented camera under the assumptions of planar motion and known internal camera parameters. The so called essential matrix (or its uncalibrated counterpart, the fundamental matrix) is frequently used in computer vision applications to compute a reconstruction in 3D of the camera locations and the observed scene. However, if the observed points are expected to lie on a plane - e.g. the ground plane - this makes the determination of these matrices an ill-posed problem. Instead, methods based on homographies are better suited to this situation.

One section of... (More)
Planar motion is an important and frequently occurring situation in mobile robotics applications. This thesis concerns estimation of ego-motion and pose of a single downwards oriented camera under the assumptions of planar motion and known internal camera parameters. The so called essential matrix (or its uncalibrated counterpart, the fundamental matrix) is frequently used in computer vision applications to compute a reconstruction in 3D of the camera locations and the observed scene. However, if the observed points are expected to lie on a plane - e.g. the ground plane - this makes the determination of these matrices an ill-posed problem. Instead, methods based on homographies are better suited to this situation.

One section of this thesis is concerned with the extraction of the camera pose and ego-motion from such homographies. We present both a direct SVD-based method and an iterative method, which both solve this problem. The iterative method is extended to allow simultaneous determination of the camera tilt from several homographies obeying the same planar motion model. This extension improves the robustness of the original method, and it provides consistent tilt estimates for the frames that are used for the estimation. The methods are evaluated using experiments on both real and synthetic data.

Another part of the thesis deals with the problem of computing the homographies from point correspondences. By using conventional homography estimation methods for this, the resulting homography is of a too general class and is not guaranteed to be compatible with the planar motion assumption. For this reason, we enforce the planar motion model at the homography estimation stage with the help of a new homography solver using a number of polynomial constraints on the entries of the homography matrix. In addition to giving a homography of the right type, this method uses only \num{2.5} point correspondences instead of the conventional four, which is good \eg{} when used in a RANSAC framework for outlier removal. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Doktor Kannala, Juho, Aalto University, Finland
organization
publishing date
type
Thesis
publication status
published
subject
pages
131 pages
publisher
Lund University
defense location
lecture hall MH:Hörmander, Matematikhuset, Sölvegatan 18, Lund University, Faculty of Engineering LTH, Lund
defense date
2017-04-07 13:15
ISBN
978-91-7753-153-1
978-91-7753-154-8
language
English
LU publication?
yes
id
0b51882d-44ee-4a24-94bb-8af3a24681cc
date added to LUP
2017-03-08 14:11:22
date last changed
2018-03-01 15:05:16
@phdthesis{0b51882d-44ee-4a24-94bb-8af3a24681cc,
  abstract     = {Planar motion is an important and frequently occurring situation in mobile robotics applications. This thesis concerns estimation of ego-motion and pose of a single downwards oriented camera under the assumptions of planar motion and known internal camera parameters. The so called essential matrix (or its uncalibrated counterpart, the fundamental matrix) is frequently used in computer vision applications to compute a reconstruction in 3D of the camera locations and the observed scene. However, if the observed points are expected to lie on a plane - e.g. the ground plane - this makes the determination of these matrices an ill-posed problem. Instead, methods based on homographies are better suited to this situation.<br/><br/>One section of this thesis is concerned with the extraction of the camera pose and ego-motion from such homographies. We present both a direct SVD-based method and an iterative method, which both solve this problem. The iterative method is extended to allow simultaneous determination of the camera tilt from several homographies obeying the same planar motion model. This extension improves the robustness of the original method, and it provides consistent tilt estimates for the frames that are used for the estimation. The methods are evaluated using experiments on both real and synthetic data.<br/><br/>Another part of the thesis deals with the problem of computing the homographies from point correspondences. By using conventional homography estimation methods for this, the resulting homography is of a too general class and is not guaranteed to be compatible with the planar motion assumption. For this reason, we enforce the planar motion model at the homography estimation stage with the help of a new homography solver using a number of polynomial constraints on the entries of the homography matrix. In addition to giving a homography of the right type, this method uses only \num{2.5} point correspondences instead of the conventional four, which is good \eg{} when used in a RANSAC framework for outlier removal.},
  author       = {Wadenbäck, Mårten},
  isbn         = {978-91-7753-153-1},
  language     = {eng},
  pages        = {131},
  publisher    = {Lund University},
  school       = {Lund University},
  title        = {Homography-Based Positioning and Planar Motion Recovery},
  year         = {2017},
}