Tractable Algorithms for Robust Model Estimation
Enqvist, Olof LU ; Ask, Erik LU ; Kahl, Fredrik LU and Åström, Karl LU
(2015)
In International Journal of Computer Vision
112(1).
p.115-129
- Abstract
- What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for... (More)
- What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5142569
- author
- Enqvist, Olof
LU
; Ask, Erik
LU
; Kahl, Fredrik
LU
and Åström, Karl
LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Outliers Geometry Optimization 3D reconstruction Image registration
- in
- International Journal of Computer Vision
- volume
- 112
- issue
- 1
- pages
- 115 - 129
- publisher
- Springer
- external identifiers
-
- wos:000350361500006
- scopus:84924022008
- ISSN
- 1573-1405
- DOI
- 10.1007/s11263-014-0760-2
- language
- English
- LU publication?
- yes
- id
- 8bbe9fb5-f855-43e7-a348-cdb2d86ecb48 (old id 5142569)
- date added to LUP
- 2016-04-01 10:19:12
- date last changed
- 2022-05-13 07:43:08
@article{8bbe9fb5-f855-43e7-a348-cdb2d86ecb48,
abstract = {{What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated L2-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.}},
author = {{Enqvist, Olof and Ask, Erik and Kahl, Fredrik and Åström, Karl}},
issn = {{1573-1405}},
keywords = {{Outliers Geometry Optimization 3D reconstruction Image registration}},
language = {{eng}},
number = {{1}},
pages = {{115--129}},
publisher = {{Springer}},
series = {{International Journal of Computer Vision}},
title = {{Tractable Algorithms for Robust Model Estimation}},
url = {{http://dx.doi.org/10.1007/s11263-014-0760-2}},
doi = {{10.1007/s11263-014-0760-2}},
volume = {{112}},
year = {{2015}},
}