invert_warping

skfda.preprocessing.registration.invert_warping(warping, *, output_points=None)

Compute the inverse of a diffeomorphism.

Let \(\gamma : [a,b] \rightarrow [a,b]\) be a function strictly increasing, calculates the corresponding inverse \(\gamma^{-1} : [a,b] \rightarrow [a,b]\) such that \(\gamma^{-1} \circ \gamma = \gamma \circ \gamma^{-1} = \gamma_{id}\).

Uses a PCHIP interpolator to compute approximately the inverse.

Parameters:

• warping (FDataGrid) – Functions to be inverted.

• output_points (Optional[ArrayLike]) – Set of points where the functions are interpolated to obtain the inverse, by default uses the sample points of the fdatagrid.

Returns:

Inverse of the original functions.

Raises:

ValueError – If the functions are not strictly increasing or are multidimensional.

Return type:

FDataGrid

Examples

>>> import numpy as np
>>> from skfda import FDataGrid

We will construct the warping \(\gamma : [0,1] \rightarrow [0,1]\) wich maps t to t^3.

>>> t = np.linspace(0, 1)
>>> gamma = FDataGrid(t**3, t)
>>> gamma
FDataGrid(...)

We will compute the inverse.

>>> inverse = invert_warping(gamma)
>>> inverse
FDataGrid(...)

The result of the composition should be approximately the identity function .

>>> identity = gamma.compose(inverse)
>>> identity([0, 0.25, 0.5, 0.75, 1]).round(3)
array([[[ 0.  ],
        [ 0.25],
        [ 0.5 ],
        [ 0.75],
        [ 1.  ]]])

Examples using skfda.preprocessing.registration.invert_warping

Pairwise alignment

Pairwise alignment