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Recovering Planar Motion from Homographies Obtained using a 2.5-Point Solver for a Polynomial System

Wadenbäck, Mårten LU ; Åström, Karl LU and Heyden, Anders LU (2016) The 23rd IEEE International Conference on Image Processing In IEEE International Conference on Image Processing (ICIP), 2016 p.2966-2970
Abstract
We present a minimal solver for a special kind of homography arising in applications with planar camera motion (e.g. mobile robotics applications). Since the camera motion we consider only has five degrees of freedom, an explicit parametrisation allows us to reduce the required number of point correspondences to 2.5. Using fewer point correspondences is beneficial when used together with RANSAC, but more importantly, the proposed special solver ensures that the estimated homography is of the correct type (in contrast to the DLT, which estimates a general homography). Our method works by enforcing eleven independent polynomial constraints on the elements of this kind of homography matrix, through the framework of the action matrix method... (More)
We present a minimal solver for a special kind of homography arising in applications with planar camera motion (e.g. mobile robotics applications). Since the camera motion we consider only has five degrees of freedom, an explicit parametrisation allows us to reduce the required number of point correspondences to 2.5. Using fewer point correspondences is beneficial when used together with RANSAC, but more importantly, the proposed special solver ensures that the estimated homography is of the correct type (in contrast to the DLT, which estimates a general homography). Our method works by enforcing eleven independent polynomial constraints on the elements of this kind of homography matrix, through the framework of the action matrix method for solving polynomial equations. Some analytical investigation using symbolic software has been conducted in order to understand the properties of the polynomial system, and these results have been used to help guide our design of the solver. Additionally, we provide a direct method to recover the sought motion parameters from the homography matrix. We demonstrate that it is possible to recover both the homography and its generating parameters efficiently and accurately. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
planar motion, polynomial solver, homography, action matrix
in
IEEE International Conference on Image Processing (ICIP), 2016
pages
5 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
The 23rd IEEE International Conference on Image Processing
external identifiers
  • scopus:85006705702
ISBN
978-1-4673-9961-6
DOI
10.1109/ICIP.2016.7532903
language
English
LU publication?
yes
id
df237e6f-35dd-40df-8c0d-0a293c8f3b2c
date added to LUP
2016-08-31 23:09:33
date last changed
2017-01-15 04:42:37
@inproceedings{df237e6f-35dd-40df-8c0d-0a293c8f3b2c,
  abstract     = {We present a minimal solver for a special kind of homography arising in applications with planar camera motion (e.g. mobile robotics applications). Since the camera motion we consider only has five degrees of freedom, an explicit parametrisation allows us to reduce the required number of point correspondences to 2.5. Using fewer point correspondences is beneficial when used together with RANSAC, but more importantly, the proposed special solver ensures that the estimated homography is of the correct type (in contrast to the DLT, which estimates a general homography). Our method works by enforcing eleven independent polynomial constraints on the elements of this kind of homography matrix, through the framework of the action matrix method for solving polynomial equations. Some analytical investigation using symbolic software has been conducted in order to understand the properties of the polynomial system, and these results have been used to help guide our design of the solver. Additionally, we provide a direct method to recover the sought motion parameters from the homography matrix. We demonstrate that it is possible to recover both the homography and its generating parameters efficiently and accurately.},
  author       = {Wadenbäck, Mårten and Åström, Karl and Heyden, Anders},
  booktitle    = { IEEE International Conference on Image Processing (ICIP), 2016 },
  isbn         = {978-1-4673-9961-6 },
  keyword      = {planar motion,polynomial solver,homography,action matrix},
  language     = {eng},
  month        = {08},
  pages        = {2966--2970},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Recovering Planar Motion from Homographies Obtained using a 2.5-Point Solver for a Polynomial System},
  url          = {http://dx.doi.org/10.1109/ICIP.2016.7532903},
  year         = {2016},
}