scipy.spatial.transform.Rotation.mean#

Rotation.mean(self, weights=None)#

Get the mean of the rotations.

The mean used is the chordal L2 mean (also called the projected or induced arithmetic mean) [1]. If A is a set of rotation matrices, then the mean M is the rotation matrix that minimizes the following loss function:

\[L(M) = \sum_{i = 1}^{n} w_i \lVert \mathbf{A}_i - \mathbf{M} \rVert^2 ,\]

where \(w_i\)’s are the weights corresponding to each matrix.

Parameters:

weightsarray_like shape (N,), optional: Weights describing the relative importance of the rotations. If None (default), then all values in weights are assumed to be equal.

Returns:

meanRotation instance: Object containing the mean of the rotations in the current instance.

References

[1]

Hartley, Richard, et al., “Rotation Averaging”, International Journal of Computer Vision 103, 2013, pp. 267-305.

Examples

>>> from scipy.spatial.transform import Rotation as R
>>> r = R.from_euler('zyx', [[0, 0, 0],
...                          [1, 0, 0],
...                          [0, 1, 0],
...                          [0, 0, 1]], degrees=True)
>>> r.mean().as_euler('zyx', degrees=True)
array([0.24945696, 0.25054542, 0.24945696])