https://github.com/xclud/rust-umeyama
An algorithm for finding the optimal translation, rotation, and scaling that aligns two sets of points with minimum root-mean-square deviation (RMSD).
https://github.com/xclud/rust-umeyama
data-science machine-learning machine-learning-algorithms point-set-registration umeyama
Last synced: 2 months ago
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An algorithm for finding the optimal translation, rotation, and scaling that aligns two sets of points with minimum root-mean-square deviation (RMSD).
- Host: GitHub
- URL: https://github.com/xclud/rust-umeyama
- Owner: xclud
- Created: 2024-02-26T07:14:29.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-02-26T07:20:40.000Z (over 2 years ago)
- Last Synced: 2024-04-29T19:44:08.704Z (about 2 years ago)
- Topics: data-science, machine-learning, machine-learning-algorithms, point-set-registration, umeyama
- Language: Rust
- Homepage: https://docs.rs/crate/umeyama
- Size: 2.93 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Umeyama
The Kabsch-Umeyama algorithm is a method for finding the optimal translation, rotation, and scaling that aligns two sets of points with minimum root-mean-square deviation (RMSD). It is named after Wolfgang Kabsch and Shinji Umeyama, who independently developed the algorithm for different applications. It is useful for comparing molecular and protein structures, point-set registration, and physics simulation.
Some of the main steps of the algorithm are:
* Calculate the centroids of the two sets of points and translate them to the origin.
* Compute the covariance matrix of the translated points and perform singular value decomposition on it.
* Determine the optimal rotation matrix and scale factor using the singular values and the sign of the determinant of the orthogonal matrices.
* Apply the translation, rotation, and scaling to the second set of points to align it with the first set.