A Comparison of Four Algorithms for Estimating 3-D Rigid Transformations.
Abstract
A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points for which corresponding pairs have been determined. In this paper a comparative analysis of four popular and efficient algorithms is given. Each computes the translational and rotational components of the transform in closed-form as the solution to a least squares formulation of the problem. They differ in terms of the representation of the transform and the method of solution, using respectively: singular value decomposition of a matrix, orthonormal matrices, unit quaternions and dual quaternions. This comparison presents results of several experiments designed to determine the (1) accuracy in the presence of noise, (2) stability with respect to degenerate data sets, and (3) relative computation time of each approach.
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In rigid transformation estimation, a closed-form least-squares solution exists if three or more distinct non-collinear pairs of correspondences are given, and can be solved by SVD, quaternions, orthonormal matrices or dual quaternions.
“In rigid transformation estimation, a closed-form least-squares solution (preferable for efficiency and robustness) exists if three or more distinct non-collinear pairs of correspondences are given [100], which can be solved by SVD, quaternions, orthonormal matrices or dual quaternions.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [100]
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Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
Tam, G. K. L., Cheng, Z.-Q., Lai, Y.-K., Langbein, F. C., Liu, Y., Marshall, D., Martin, R. R., Sun, X.-F., & Rosin, P. L. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2012.310 · Cited by 679 · see citing works
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- Authors
- Larusso, A., Eggert, D., & Fisher, R.
- Venue
- Procedings of the British Machine Vision Conference 1995
- Publisher
- British Machine Vision Association
- Published
- 1995
- Pages
- 24.1-24.10
- OpenAlex
- W1991202364
- Cited by
- 141
- References
- 10
- Citations by year
- 2024: 1 · 2022: 1 · 2021: 2 · 2020: 6 · 2019: 3 · 2018: 4 · 2017: 7 · 2016: 4 · 2015: 3 · 2014: 3 · 2013: 2 · 2012: 6
- FWCI
- 2.92
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- British Machine Vision Conference (BMVC) (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Keywords
- rigid registration, point matching, least squares, singular value decomposition, unit quaternions, dual quaternions, analytical solution, numerical stability, noise robustness, computational time, machine vision
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