can-song / umeyama-python

Python Umeyama's Algorithm - Transformation between two sets of points

Python Umeyama's algorithm

A python implementation of Umeyama's algorithm presented in Least-Squares Estimation of Transformation Parameters Between Two Point Patterns (Shinji Umeyama, 1991).

Description

Let X be a set of n m-dimensional points in a given frame. Let Y be a set of the same m-dimensional points in another frame. We have X = {x1, x2, ..., xn}, Y = {y1, y2, ..., yn} where xi and yi are m-dimenstional points. We want to find the transformation from one frame to another such as it minimizes the mean square error between the two sets of points.
More specifically, we want to find [c, R, t] ∈ Sim(3) given the minimum value of MSE(Y, c * R · X + t).
Notations in the code are consistent with the paper.

Usage

Let X and Y be 3D numpy arrays with shape (m, n) where m is the dimension of the points and n is the number of points in the point set. Let X and Y have consistent indexes, that is, Y[:, i] must be the m-dimensional point corresponding to X[:, i].

from umeyama import umeyama
c, R, t = umeyama(X, Y)

The function returns c, R and t such as Y ~ c * R @ X + t.

Example

We provide an example in the IPython notebook example.ipynb.