imwip.functions

imwip.functions.functions_dvf

file: functions_dvf.py
brief: Image warping functions using a DVF
author: Jens Renders

imwip.functions.functions_dvf.warp(image, u, v, w=None, out=None, degree=3, backend=None)

Warps a 2D or 3D image along a DVF.

This function is linear in terms of the input image (even if degree 3 is used for the splines). Therefore it has an adjoint function which is computed by adjoint_warp().

Parameters

image (numpy.ndarray) – Input image
u (numpy.ndarray) – First component of the DVF describing the warp
v (numpy.ndarray) – Second component of the DVF describing the warp
w (numpy.ndarray, optional) – Third component of the DVF describing the warp. Leave empty for a 2D warp
out (numpy.ndarray, optional) – Array to write the output image in. If None, an output array will be allocated.
degree (1 or 3, optional) – Degree of the splines used for interpolation
backend (cpp or numba, optional) – Whether to use the cpp or numba backend. If None, cpp will be used if available, else numba

Returns

The warped image

Return type

numpy.ndarray

imwip.functions.functions_dvf.adjoint_warp(image, u, v, w=None, out=None, degree=3, backend=None): The function warp() is a linear function of the input image (even if degree 3 is used for the splines). Therefore it has an adjoint function which is computed by this function, as described by Renders et al. [RSDB21]. See warp() for the description of parameters and return value.

imwip.functions.functions_dvf.diff_warp(image, u, v, w=None, diff_x=None, diff_y=None, diff_z=None, backend=None)

The derivative of warp() towards the DVF. This function assumes splines of degree 3, to ensure differentiability.

Parameters

image (numpy.ndarray) – Input image
u (numpy.ndarray) – First component of the DVF describing the warp
v (numpy.ndarray) – Second component of the DVF describing the warp
w (numpy.ndarray, optional) – Third component of the DVF describing the warp. Leave empty for a 2D warp
diff_x (numpy.ndarray, optional) – Array to write the derivative to the first component in. If None, an output array will be allocated.
diff_y (numpy.ndarray, optional) – Array to write the derivative to the first component in. If None, an output array will be allocated.
diff_z (numpy.ndarray, optional) – Array to write the derivative to the first component in. If None, an output array will be allocated.
backend (cpp or numba, optional) – Whether to use the cpp or numba backend. If None, cpp will be used if available, else numba

Returns

diff_x, diff_y, diff_z

Return type

numpy.ndarray, numpy.ndarray, numpy.ndarray,

imwip.functions.functions_affine

file: functions_affine.py
brief: Image warping functions using an affine transformation
author: Jens Renders

imwip.functions.functions_affine.affine_warp(image, A, b, out=None, degree=3, indexing='ij', backend=None)

Warps a 2D or 3D image according to an affine transformation Ax + b.

This function is linear in terms of the input image (even if degree 3 is used for the splines). Therefore it has an adjoint function which is computed by adjoint_affine_warp().

Parameters

image (numpy.ndarray) – Input image
A (numpy.ndarray) – Matrix A of the affine transformation Ax + b. It shoud be an 2x2 for 2D warp and 3x3 for a 3D warp.
b (numpy.ndarray) – Vector b of the affine transformation Ax + b. It should have length 2 for a 2D warp and length 3 for a 3D warp.
out (numpy.ndarray, optional) – Array to write the output image in. If None, an output array will be allocated.
degree (1 or 3, optional) – Degree of the splines used for interpolation
indexing (ij or xy, optional) – ij uses standard numpy array indexing. “xy” reversed the order of the indexes, making the vertical axis the first index. This can be more intuitive for 2D arrays. Defaults to ij.
backend (cpp or numba, optional) – Whether to use the cpp or numba backend. If None, cpp will be used if available, else numba

Returns

The warped image

Return type

numpy.ndarray

imwip.functions.functions_affine.adjoint_affine_warp(image, A, b, out=None, degree=3, indexing='ij', backend=None): The function affine_warp() is a linear function of the input image (even if degree 3 is used for the splines). Therefore it has an adjoint function which is computed by this function, as described by Renders et al. [RSDB21]. See affine_warp() for the description of parameters and return value.

imwip.functions.functions_affine.diff_affine_warp(image, A, b, diff_x=None, diff_y=None, diff_z=None, indexing='ij', backend=None)

The derivative of affine_warp() towards the DVF describing the affine warp. This function assumes splines of degree 3, to ensure differentiability.

Parameters

image (numpy.ndarray) – Input image
A (numpy.ndarray) – Matrix A of the affine transformation Ax + b. It shoud be an 2x2 for 2D warp and 3x3 for a 3D warp.
b (numpy.ndarray) – Vector b of the affine transformation Ax + b. It should have length 2 for a 2D warp and length 3 for a 3D warp.
diff_x – Array to write the derivative to the first component in. If None, an output array will be allocated.
diff_y – Array to write the derivative to the first component in. If None, an output array will be allocated.
diff_z – Array to write the derivative to the first component in. If None, an output array will be allocated.
indexing (ij or xy, optional) – ij uses standard numpy array indexing. “xy” reversed the order of the indexes, making the vertical axis the first index. This can be more intuitive for 2D arrays. Defaults to ij.
backend (cpp or numba, optional) – Whether to use the cpp or numba backend. If None, cpp will be used if available, else numba

Returns

diff_x, diff_y, diff_z

Return type

numpy.ndarray, numpy.ndarray, numpy.ndarray,