scipy.spatial.transform.Rotation.

mean#

Rotation.mean(weights=None, axis=None)[source]#

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. If given, the shape of weights must be broadcastable to the rotation shape. Weights must be non-negative.
axisNone, int, or tuple of ints, optional: Axis or axes along which the means are computed. The default is to compute the mean of all rotations.

Returns:

meanRotation instance: Single rotation 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])