Umeyama

Umeyama is a Python library implementing the Umeyama method for estimating the optimal similarity transformation (rotation, translation, and uniform scaling) between two sets of corresponding points.

pip install umeyama

Quick Start

from umeyama import umeyama
import numpy as np

src = np.array([[0, 0], [1, 0], [1, 1], [0, 1]], dtype=float)
dst = np.array([[1, 1], [1, 2], [2, 2], [2, 1]], dtype=float)

result = umeyama(src, dst)

print(result.rotation)  # Rotation matrix
print(result.translation)  # Translation vector
print(result.scale)  # Scale factor

transformed = result.apply(src)
print(result.rmse(src, dst))  # Root mean square error

References

• Umeyama, Shinji. "Least-Squares Estimation of Transformation Parameters Between Two Point Patterns." IEEE Transactions on Pattern Analysis and Machine Intelligence 13, no. 4 (April 1991): 376–80. https://doi.org/10.1109/34.88573.