unageek / similarity-transformation

Find parameters of similarity transformation (rotation, translation, and scaling)

similarity-transformation

Given two lists of points $(𝐩_i)_{i=1}^N$ and $(𝐪_i)_{i=1}^N$, SimilarityTransformation::estimate finds the common similarity transformation (rotation, translation, and scaling) that maps each $𝐩_i$ to $𝐪_i$.

Usage

This library consists of a single header file similarity_transformation.h.

The following dependencies are required:

• Eigen
• artivis/manif
• TartanLlama/optional

See tests/test.cc for usage.

Implementation

The Gauss–Newton method is used to minimize the sum of squared errors $∑_{i=1}^N ‖𝐪_i - f(𝐩_i)‖^2$.

References

1. C. Hertzberg, R. Wagner, U. Frese, and L. Schröder, Integrating Generic Sensor Fusion Algorithms with Sound State Representations through Encapsulation of Manifolds. https://doi.org/10.48550/arXiv.1107.1119

2. J. Solà, J. Deray, and D. Atchuthan, A micro Lie theory for state estimation in robotics. https://doi.org/10.48550/arXiv.1812.01537