Revisiting Sampson Approximations for Geometric Estimation Problems
(2024) 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024 p.4990-4998- Abstract
Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations. This necessitates some measure of how much an observation 'agrees' with a given model. A natural choice is to consider the smallest perturbation that makes the observation exactly satisfy the constraints. However, for many problems, this metric is expensive or otherwise intractable to compute. The so-called Sampson error approximates this geometric error through a linearization scheme. For epipolar geometry, the Sampson error is a popular choice and in practice known to yield very tight approximations... (More)
Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations. This necessitates some measure of how much an observation 'agrees' with a given model. A natural choice is to consider the smallest perturbation that makes the observation exactly satisfy the constraints. However, for many problems, this metric is expensive or otherwise intractable to compute. The so-called Sampson error approximates this geometric error through a linearization scheme. For epipolar geometry, the Sampson error is a popular choice and in practice known to yield very tight approximations of the corresponding geometric residual (the reprojection error). In this paper we revisit the Sampson approximation and provide new theoretical insights as to why and when this approximation works, as well as provide explicit bounds on the tightness under some mild assumptions. Our theoretical results are validated in several experiments on real data and in the context of different geometric estimation tasks.
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- author
- Rydell, Felix ; Torres, Angélica and Larsson, Viktor LU
- organization
- publishing date
- 2024
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- geometric estimation, Sampson approximation
- host publication
- Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- pages
- 9 pages
- conference name
- 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2024
- conference location
- Seattle, United States
- conference dates
- 2024-06-16 - 2024-06-22
- external identifiers
-
- scopus:85218180644
- DOI
- 10.1109/CVPR52733.2024.00477
- language
- English
- LU publication?
- yes
- id
- d82d58ac-f8a2-4936-9f5e-6797b82ccb9f
- date added to LUP
- 2025-06-05 10:51:42
- date last changed
- 2025-06-05 10:53:00
@inproceedings{d82d58ac-f8a2-4936-9f5e-6797b82ccb9f,
abstract = {{<p>Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations. This necessitates some measure of how much an observation 'agrees' with a given model. A natural choice is to consider the smallest perturbation that makes the observation exactly satisfy the constraints. However, for many problems, this metric is expensive or otherwise intractable to compute. The so-called Sampson error approximates this geometric error through a linearization scheme. For epipolar geometry, the Sampson error is a popular choice and in practice known to yield very tight approximations of the corresponding geometric residual (the reprojection error). In this paper we revisit the Sampson approximation and provide new theoretical insights as to why and when this approximation works, as well as provide explicit bounds on the tightness under some mild assumptions. Our theoretical results are validated in several experiments on real data and in the context of different geometric estimation tasks.</p>}},
author = {{Rydell, Felix and Torres, Angélica and Larsson, Viktor}},
booktitle = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}},
keywords = {{geometric estimation; Sampson approximation}},
language = {{eng}},
pages = {{4990--4998}},
title = {{Revisiting Sampson Approximations for Geometric Estimation Problems}},
url = {{http://dx.doi.org/10.1109/CVPR52733.2024.00477}},
doi = {{10.1109/CVPR52733.2024.00477}},
year = {{2024}},
}