deepfold.losses.procrustes.kabsch

deepfold.losses.procrustes.kabsch(x: Tensor, y: Tensor, weights: Tensor | None = None, compute_scaling: bool = False) → Tuple[Tensor, Tensor, float | None]

Returns the rigid transformation and the optimal scaling that best align an input list of points x to a target list of points y, by minimizing the sum of square distance.

Parameters:

• x – […, N, D] list of N points of dimension D.

• y – […, N, D] list of corresponding target points.

• weights – […, N] optional list of weights associated to each point.

Returns:

a triplet (R, t, s) consisting of a rotation matrix r, a translational vector t and a scaling s if compute scaling is true.