def transform_affine(volume, ref_shape, affine, order=1):
from cupyimg.scipy.ndimage._kernels import interp
ndim = volume.ndim
legacy_mode = interp.const_legacy_mode
interp.const_legacy_mode = False
try:
affine = cupy.asarray(affine)
if True:
out = ndi.affine_transform(
volume,
matrix=affine,
order=order,
mode="constant",
output_shape=tuple(ref_shape),
)
else:
# use map_coordinates instead of affine_transform
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=volume.dtype) for s in ref_shape],
indexing="ij",
sparse=True,
)
coords = _apply_affine_to_field(
xcoords,
affine[:ndim, :],
include_translations=True,
coord_axis=0,
)
out = ndi.map_coordinates(volume, coords, order=1)
finally:
interp.const_legacy_mode = legacy_mode
return out
def profile_line(
image,
src,
dst,
linewidth=1,
order=None,
mode=None,
cval=0.0,
*,
reduce_func=cp.mean,
):
"""Return the intensity profile of an image measured along a scan line.
Parameters
----------
image : ndarray, shape (M, N[, C])
The image, either grayscale (2D array) or multichannel
(3D array, where the final axis contains the channel
information).
src : array_like, shape (2, )
The coordinates of the start point of the scan line.
dst : array_like, shape (2, )
The coordinates of the end point of the scan
line. The destination point is *included* in the profile, in
contrast to standard numpy indexing.
linewidth : int, optional
Width of the scan, perpendicular to the line
order : int in {0, 1, 2, 3, 4, 5}, optional
The order of the spline interpolation, default is 0 if
image.dtype is bool and 1 otherwise. The order has to be in
the range 0-5. See `skimage.transform.warp` for detail.
mode : {'constant', 'nearest', 'reflect', 'mirror', 'wrap'}, optional
How to compute any values falling outside of the image.
cval : float, optional
If `mode` is 'constant', what constant value to use outside the image.
reduce_func : callable, optional
Function used to calculate the aggregation of pixel values
perpendicular to the profile_line direction when `linewidth` > 1.
If set to None the unreduced array will be returned.
Returns
-------
return_value : array
The intensity profile along the scan line. The length of the profile
is the ceil of the computed length of the scan line.
Examples
--------
>>> import cupy as cp
>>> x = cp.asarray([[1, 1, 1, 2, 2, 2]])
>>> img = cp.vstack([cp.zeros_like(x), x, x, x, cp.zeros_like(x)])
>>> img
array([[0, 0, 0, 0, 0, 0],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[1, 1, 1, 2, 2, 2],
[0, 0, 0, 0, 0, 0]])
>>> profile_line(img, (2, 1), (2, 4))
array([1., 1., 2., 2.])
>>> profile_line(img, (1, 0), (1, 6), cval=4)
array([1., 1., 1., 2., 2., 2., 4.])
The destination point is included in the profile, in contrast to
standard numpy indexing.
For example:
>>> profile_line(img, (1, 0), (1, 6)) # The final point is out of bounds
array([1., 1., 1., 2., 2., 2., 0.])
>>> profile_line(img, (1, 0), (1, 5)) # This accesses the full first row
array([1., 1., 1., 2., 2., 2.])
For different reduce_func inputs:
>>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=cp.mean)
array([0.66666667, 0.66666667, 0.66666667, 1.33333333])
>>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=cp.max)
array([1, 1, 1, 2])
>>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=cp.sum)
array([2, 2, 2, 4])
The unreduced array will be returned when `reduce_func` is None or when
`reduce_func` acts on each pixel value individually.
>>> profile_line(img, (1, 2), (4, 2), linewidth=3, order=0,
... reduce_func=None)
array([[1, 1, 2],
[1, 1, 2],
[1, 1, 2],
[0, 0, 0]])
>>> profile_line(img, (1, 0), (1, 3), linewidth=3, reduce_func=cp.sqrt)
array([[1. , 1. , 0. ],
[1. , 1. , 0. ],
[1. , 1. , 0. ],
[1.41421356, 1.41421356, 0. ]])
"""
order = _validate_interpolation_order(image.dtype, order)
if mode is None:
warn(
"Default out of bounds interpolation mode 'constant' is "
"deprecated. In version 0.19 it will be set to 'reflect'. "
"To avoid this warning, set `mode=` explicitly.",
FutureWarning,
stacklevel=2,
)
mode = "constant"
perp_lines = _line_profile_coordinates(src, dst, linewidth=linewidth)
if image.ndim == 3:
pixels = [
ndi.map_coordinates(
image[..., i],
perp_lines,
prefilter=order > 1,
order=order,
mode=mode,
cval=cval,
) for i in range(image.shape[2])
]
pixels = cp.transpose(cp.asarray(pixels), (1, 2, 0))
else:
pixels = ndi.map_coordinates(
image,
perp_lines,
prefilter=order > 1,
order=order,
mode=mode,
cval=cval,
)
# The outputted array with reduce_func=None gives an array where the
# row values (axis=1) are flipped. Here, we make this consistent.
pixels = np.flip(pixels, axis=1)
if reduce_func is None:
intensities = pixels
else:
try:
intensities = reduce_func(pixels, axis=1)
except TypeError: # function doesn't allow axis kwarg
intensities = cnp.apply_along_axis(reduce_func, arr=pixels, axis=1)
return intensities
def test_warp_coords_example():
image = cp.asarray(astronaut().astype(np.float32))
assert 3 == image.shape[2]
tform = SimilarityTransform(translation=(0, -10), xp=cp)
coords = warp_coords(tform, (30, 30, 3))
map_coordinates(image[:, :, 0], coords[:2])
def warp(
image,
inverse_map,
map_args={},
output_shape=None,
order=None,
mode="constant",
cval=0.0,
clip=True,
preserve_range=False,
):
"""Warp an image according to a given coordinate transformation.
Parameters
----------
image : ndarray
Input image.
inverse_map : transformation object, callable ``cr = f(cr, **kwargs)``, or ndarray
Inverse coordinate map, which transforms coordinates in the output
images into their corresponding coordinates in the input image.
There are a number of different options to define this map, depending
on the dimensionality of the input image. A 2-D image can have 2
dimensions for gray-scale images, or 3 dimensions with color
information.
- For 2-D images, you can directly pass a transformation object,
e.g. `skimage.transform.SimilarityTransform`, or its inverse.
- For 2-D images, you can pass a ``(3, 3)`` homogeneous
transformation matrix, e.g.
`skimage.transform.SimilarityTransform.params`.
- For 2-D images, a function that transforms a ``(M, 2)`` array of
``(col, row)`` coordinates in the output image to their
corresponding coordinates in the input image. Extra parameters to
the function can be specified through `map_args`.
- For N-D images, you can directly pass an array of coordinates.
The first dimension specifies the coordinates in the input image,
while the subsequent dimensions determine the position in the
output image. E.g. in case of 2-D images, you need to pass an array
of shape ``(2, rows, cols)``, where `rows` and `cols` determine the
shape of the output image, and the first dimension contains the
``(row, col)`` coordinate in the input image.
See `scipy.ndimage.map_coordinates` for further documentation.
Note, that a ``(3, 3)`` matrix is interpreted as a homogeneous
transformation matrix, so you cannot interpolate values from a 3-D
input, if the output is of shape ``(3,)``.
See example section for usage.
map_args : dict, optional
Keyword arguments passed to `inverse_map`.
output_shape : tuple (rows, cols), optional
Shape of the output image generated. By default the shape of the input
image is preserved. Note that, even for multi-band images, only rows
and columns need to be specified.
order : int, optional
The order of interpolation. The order has to be in the range 0-5:
- 0: Nearest-neighbor
- 1: Bi-linear (default)
- 2: Bi-quadratic
- 3: Bi-cubic
- 4: Bi-quartic
- 5: Bi-quintic
Default is 0 if image.dtype is bool and 1 otherwise.
mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional
Points outside the boundaries of the input are filled according
to the given mode. Modes match the behaviour of `numpy.pad`.
cval : float, optional
Used in conjunction with mode 'constant', the value outside
the image boundaries.
clip : bool, optional
Whether to clip the output to the range of values of the input image.
This is enabled by default, since higher order interpolation may
produce values outside the given input range.
preserve_range : bool, optional
Whether to keep the original range of values. Otherwise, the input
image is converted according to the conventions of `img_as_float`.
Also see
https://scikit-image.org/docs/dev/user_guide/data_types.html
Returns
-------
warped : double ndarray
The warped input image.
Notes
-----
- The input image is converted to a `double` image.
- In case of a `SimilarityTransform`, `AffineTransform` and
`ProjectiveTransform` and `order` in [0, 3] this function uses the
underlying transformation matrix to warp the image with a much faster
routine.
Examples
--------
>>> from skimage.transform import warp
>>> from skimage import data
>>> image = data.camera()
The following image warps are all equal but differ substantially in
execution time. The image is shifted to the bottom.
Use a geometric transform to warp an image (fast):
>>> from skimage.transform import SimilarityTransform
>>> tform = SimilarityTransform(translation=(0, -10))
>>> warped = warp(image, tform)
Use a callable (slow):
>>> def shift_down(xy):
... xy[:, 1] -= 10
... return xy
>>> warped = warp(image, shift_down)
Use a transformation matrix to warp an image (fast):
>>> import cupy as cp
>>> matrix = cp.asarray([[1, 0, 0], [0, 1, -10], [0, 0, 1]])
>>> warped = warp(image, matrix)
>>> from skimage.transform import ProjectiveTransform
>>> warped = warp(image, ProjectiveTransform(matrix=matrix))
You can also use the inverse of a geometric transformation (fast):
>>> warped = warp(image, tform.inverse)
For N-D images you can pass a coordinate array, that specifies the
coordinates in the input image for every element in the output image. E.g.
if you want to rescale a 3-D cube, you can do:
>>> cube_shape = cp.asarray([30, 30, 30])
>>> cube = cp.random.rand(*cube_shape)
Setup the coordinate array, that defines the scaling:
>>> scale = 0.1
>>> output_shape = (scale * cube_shape).astype(int)
>>> coords0, coords1, coords2 = cp.mgrid[:output_shape[0],
... :output_shape[1], :output_shape[2]]
>>> coords = cp.asarray([coords0, coords1, coords2])
Assume that the cube contains spatial data, where the first array element
center is at coordinate (0.5, 0.5, 0.5) in real space, i.e. we have to
account for this extra offset when scaling the image:
>>> coords = (coords + 0.5) / scale - 0.5
>>> warped = warp(cube, coords)
"""
if image.size == 0:
raise ValueError("Cannot warp empty image with dimensions", image.shape)
order = _validate_interpolation_order(image.dtype, order)
if image.dtype.kind == "c":
if not preserve_range:
raise NotImplementedError("TODO")
else:
image = convert_to_float(image, preserve_range)
input_shape = np.array(image.shape)
if output_shape is None:
output_shape = input_shape
else:
output_shape = safe_as_int(output_shape)
warped = None
if order == 2:
# When fixing this issue, make sure to fix the branches further
# below in this function
warn(
"Bi-quadratic interpolation behavior has changed due "
"to a bug in the implementation of scikit-image. "
"The new version now serves as a wrapper "
"around SciPy's interpolation functions, which itself "
"is not verified to be a correct implementation. Until "
"skimage's implementation is fixed, we recommend "
"to use bi-linear or bi-cubic interpolation instead."
)
if warped is None:
# use ndi.map_coordinates
if isinstance(inverse_map, cp.ndarray) and inverse_map.shape == (3, 3,):
# inverse_map is a transformation matrix as numpy array,
# this is only used for order >= 4.
inverse_map = ProjectiveTransform(matrix=inverse_map)
if isinstance(inverse_map, cp.ndarray):
# inverse_map is directly given as coordinates
coords = inverse_map
else:
# inverse_map is given as function, that transforms (N, 2)
# destination coordinates to their corresponding source
# coordinates. This is only supported for 2(+1)-D images.
if image.ndim < 2 or image.ndim > 3:
raise ValueError(
"Only 2-D images (grayscale or color) are "
"supported, when providing a callable "
"`inverse_map`."
)
def coord_map(*args):
return inverse_map(*args, **map_args)
if len(input_shape) == 3 and len(output_shape) == 2:
# Input image is 2D and has color channel, but output_shape is
# given for 2-D images. Automatically add the color channel
# dimensionality.
output_shape = (
output_shape[0],
output_shape[1],
input_shape[2],
)
coords = warp_coords(coord_map, output_shape)
# Pre-filtering not necessary for order 0, 1 interpolation
prefilter = order > 1
ndi_mode = _to_ndimage_mode(mode)
warped = ndi.map_coordinates(
image,
coords,
prefilter=prefilter,
mode=ndi_mode,
order=order,
cval=cval,
)
_clip_warp_output(image, warped, order, mode, cval, clip)
return warped
def resize(
image,
output_shape,
order=None,
mode="reflect",
cval=0,
clip=True,
preserve_range=False,
anti_aliasing=None,
anti_aliasing_sigma=None,
):
"""Resize image to match a certain size.
Performs interpolation to up-size or down-size N-dimensional images. Note
that anti-aliasing should be enabled when down-sizing images to avoid
aliasing artifacts. For down-sampling with an integer factor also see
`skimage.transform.downscale_local_mean`.
Parameters
----------
image : ndarray
Input image.
output_shape : tuple or ndarray
Size of the generated output image `(rows, cols[, ...][, dim])`. If
`dim` is not provided, the number of channels is preserved. In case the
number of input channels does not equal the number of output channels a
n-dimensional interpolation is applied.
Returns
-------
resized : ndarray
Resized version of the input.
Other parameters
----------------
order : int, optional
The order of the spline interpolation, default is 0 if
image.dtype is bool and 1 otherwise. The order has to be in
the range 0-5. See `skimage.transform.warp` for detail.
mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}, optional
Points outside the boundaries of the input are filled according
to the given mode. Modes match the behaviour of `numpy.pad`.
cval : float, optional
Used in conjunction with mode 'constant', the value outside
the image boundaries.
clip : bool, optional
Whether to clip the output to the range of values of the input image.
This is enabled by default, since higher order interpolation may
produce values outside the given input range.
preserve_range : bool, optional
Whether to keep the original range of values. Otherwise, the input
image is converted according to the conventions of `img_as_float`.
Also see https://scikit-image.org/docs/dev/user_guide/data_types.html
anti_aliasing : bool, optional
Whether to apply a Gaussian filter to smooth the image prior
to down-scaling. It is crucial to filter when down-sampling
the image to avoid aliasing artifacts. If input image data
type is bool, no anti-aliasing is applied.
anti_aliasing_sigma : {float, tuple of floats}, optional
Standard deviation for Gaussian filtering to avoid aliasing artifacts.
By default, this value is chosen as (s - 1) / 2 where s is the
down-scaling factor, where s > 1. For the up-size case, s < 1, no
anti-aliasing is performed prior to rescaling.
Notes
-----
Modes 'reflect' and 'symmetric' are similar, but differ in whether the edge
pixels are duplicated during the reflection. As an example, if an array
has values [0, 1, 2] and was padded to the right by four values using
symmetric, the result would be [0, 1, 2, 2, 1, 0, 0], while for reflect it
would be [0, 1, 2, 1, 0, 1, 2].
Examples
--------
>>> from skimage import data
>>> from skimage.transform import resize
>>> image = data.camera()
>>> resize(image, (100, 100)).shape
(100, 100)
"""
output_shape = tuple(output_shape)
output_ndim = len(output_shape)
input_shape = image.shape
if output_ndim > image.ndim:
# append dimensions to input_shape
input_shape = input_shape + (1,) * (output_ndim - image.ndim)
image = cp.reshape(image, input_shape)
elif output_ndim == image.ndim - 1:
# multichannel case: append shape of last axis
output_shape = output_shape + (image.shape[-1],)
elif output_ndim < image.ndim - 1:
raise ValueError(
"len(output_shape) cannot be smaller than the image " "dimensions"
)
if anti_aliasing is None:
anti_aliasing = not image.dtype == bool
if image.dtype == bool and anti_aliasing:
warn(
"Input image dtype is bool. Gaussian convolution is not defined "
"with bool data type. Please set anti_aliasing to False or "
"explicitely cast input image to another data type. Starting "
"from version 0.19 a ValueError will be raised instead of this "
"warning.",
FutureWarning,
stacklevel=2,
)
factors = np.asarray(input_shape, dtype=float) / np.asarray(
output_shape, dtype=float
)
if anti_aliasing:
if anti_aliasing_sigma is None:
anti_aliasing_sigma = np.maximum(0, (factors - 1) / 2)
else:
anti_aliasing_sigma = np.atleast_1d(
anti_aliasing_sigma
) * np.ones_like(factors)
if np.any(anti_aliasing_sigma < 0):
raise ValueError(
"Anti-aliasing standard deviation must be "
"greater than or equal to zero"
)
elif np.any((anti_aliasing_sigma > 0) & (factors <= 1)):
warn(
"Anti-aliasing standard deviation greater than zero but "
"not down-sampling along all axes"
)
# Translate modes used by np.pad to those used by ndi.gaussian_filter
np_pad_to_ndimage = {
"constant": "constant",
"edge": "nearest",
"symmetric": "reflect",
"reflect": "mirror",
"wrap": "wrap",
}
try:
ndi_mode = np_pad_to_ndimage[mode]
except KeyError:
raise ValueError(
"Unknown mode, or cannot translate mode. The "
"mode should be one of 'constant', 'edge', "
"'symmetric', 'reflect', or 'wrap'. See the "
"documentation of numpy.pad for more info."
)
image = ndi.gaussian_filter(
image, anti_aliasing_sigma, cval=cval, mode=ndi_mode
)
# 2-dimensional interpolation
if len(output_shape) == 2 or (
len(output_shape) == 3 and output_shape[2] == input_shape[2]
):
rows = output_shape[0]
cols = output_shape[1]
input_rows = input_shape[0]
input_cols = input_shape[1]
if rows == 1 and cols == 1:
tform = AffineTransform(
translation=(input_cols / 2.0 - 0.5, input_rows / 2.0 - 0.5),
xp=np,
)
else:
# 3 control points necessary to estimate exact AffineTransform
src_corners = np.array([[1, 1], [1, rows], [cols, rows]]) - 1
dst_corners = np.zeros(src_corners.shape, dtype=np.double)
# take into account that 0th pixel is at position (0.5, 0.5)
dst_corners[:, 0] = factors[1] * (src_corners[:, 0] + 0.5) - 0.5
dst_corners[:, 1] = factors[0] * (src_corners[:, 1] + 0.5) - 0.5
tform = AffineTransform(xp=np)
tform.estimate(src_corners, dst_corners)
# Make sure the transform is exactly metric, to ensure fast warping.
tform.params[2] = np.asarray((0, 0, 1))
tform.params[0, 1] = 0
tform.params[1, 0] = 0
# transfer the Affine to the GPU
tform.params = cp.asarray(tform.params)
out = warp(
image,
tform,
output_shape=output_shape,
order=order,
mode=mode,
cval=cval,
clip=clip,
preserve_range=preserve_range,
)
else: # n-dimensional interpolation
order = _validate_interpolation_order(image.dtype, order)
coord_arrays = [
factors[i] * (cp.arange(d) + 0.5) - 0.5
for i, d in enumerate(output_shape)
]
coord_map = cp.stack(
cp.meshgrid(*coord_arrays, sparse=False, indexing="ij")
)
image = convert_to_float(image, preserve_range)
ndi_mode = _to_ndimage_mode(mode)
out = ndi.map_coordinates(
image, coord_map, order=order, mode=ndi_mode, cval=cval
)
_clip_warp_output(image, out, order, mode, cval, clip)
return out
def warp(
volume,
d1,
affine_idx_in=None,
affine_idx_out=None,
affine_disp=None,
out_shape=None,
*,
order=1,
mode="constant",
coord_axis=-1,
):
"""
Deforms the input volume under the given transformation. The warped volume
is computed using is given by:
(1) warped[i] = volume[ C * d1[A*i] + B*i ]
where:
A = affine_idx_in
B = affine_idx_out
C = affine_disp
"""
A = affine_idx_in
B = affine_idx_out
C = affine_disp
if out_shape is None:
out_shape = volume.shape
if A is not None:
A = cupy.asarray(A)
if B is not None:
B = cupy.asarray(B)
if C is not None:
C = cupy.asarray(C)
# TODO: reduce number of temporary arrays
coord_dtype = cupy.promote_types(volume.dtype, np.float32)
ndim = volume.ndim
if d1.shape[coord_axis] != ndim:
raise ValueError("expected a displacement field with shape "
"{} along axis {}".format(ndim, coord_axis))
if A is None:
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=coord_dtype) for s in out_shape],
indexing="ij",
sparse=True,
)
Z = cupy.ascontiguousarray(cupy.moveaxis(d1, -1, 0))
else:
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=coord_dtype) for s in out_shape],
indexing="ij",
sparse=True,
)
# Y = mul0(A, xcoords, sh, cupy, lastcol=1)
Y = _apply_affine_to_field(
xcoords,
A[:ndim, :],
out=None,
include_translations=True,
coord_axis=0,
)
# for CuPy with non-legacy linear interpolation, don't need to extend d1
Z = cupy.empty_like(Y)
if coord_axis == -1:
for n in range(ndim):
Z[n, ...] = ndi.map_coordinates(d1[..., n],
Y,
order=1,
mode=mode)
else:
for n in range(ndim):
Z[n, ...] = ndi.map_coordinates(d1[n], Y, order=1, mode=mode)
if C is not None:
# Z = mul0(C, Z, sh, cupy, out=Z, lastcol=0)
Z = _apply_affine_to_field(
Z,
C[:ndim, :ndim],
out=None,
include_translations=False,
coord_axis=0,
)
if B is not None:
# Z += mul0(B, xcoords, sh, cupy, lastcol=1)
Z += _apply_affine_to_field(
xcoords,
B[:ndim, :],
out=None,
include_translations=True,
coord_axis=0,
)
else:
if A is None:
for n in range(ndim):
Z[n, ...] += xcoords[n]
else:
Z += Y
return ndi.map_coordinates(volume, Z, order=order, mode=mode)
def simplify_warp_function(
d,
affine_idx_in,
affine_idx_out,
affine_disp,
out_shape,
*,
mode="constant",
coord_axis=-1,
):
"""
Simplifies a nonlinear warping function combined with an affine transform
Modifies the given deformation field by incorporating into it
an affine transformation and voxel-to-space transforms associated with
the discretization of its domain and codomain.
The resulting transformation may be regarded as operating on the
image spaces given by the domain and codomain discretization.
More precisely, the resulting transform is of the form:
(1) T[i] = W * d[U * i] + V * i
Where U = affine_idx_in, V = affine_idx_out, W = affine_disp.
Parameters
----------
d : array, shape (S', R', C', 3)
the non-linear part of the transformation (displacement field)
affine_idx_in : array, shape (4, 4)
the matrix U in eq. (1) above
affine_idx_out : array, shape (4, 4)
the matrix V in eq. (1) above
affine_disp : array, shape (4, 4)
the matrix W in eq. (1) above
out_shape : array, shape (3,)
the number of slices, rows and columns of the sampling grid
Returns
-------
out : array, shape = out_shape
the deformation field `out` associated with `T` in eq. (1) such that:
T[i] = i + out[i]
Notes
-----
Both the direct and inverse transforms of a DiffeomorphicMap can be written
in this form:
Direct: Let D be the voxel-to-space transform of the domain's
discretization, P be the pre-align matrix, Rinv the space-to-voxel
transform of the reference grid (the grid the displacement field
is defined on) and Cinv be the space-to-voxel transform of the
codomain's discretization. Then, for each i in the domain's grid,
the direct transform is given by
(2) T[i] = Cinv * d[Rinv * P * D * i] + Cinv * P * D * i
and we identify U = Rinv * P * D, V = Cinv * P * D, W = Cinv
Inverse: Let C be the voxel-to-space transform of the codomain's
discretization, Pinv be the inverse of the pre-align matrix, Rinv
the space-to-voxel transform of the reference grid (the grid the
displacement field is defined on) and Dinv be the space-to-voxel
transform of the domain's discretization. Then, for each j in the
codomain's grid, the inverse transform is given by
(3) Tinv[j] = Dinv * Pinv * d[Rinv * C * j] + Dinv * Pinv * C * j
and we identify U = Rinv * C, V = Dinv * Pinv * C, W = Dinv * Pinv
"""
if coord_axis not in [0, -1]:
raise ValueError("coord_axis must be 0 or -1")
ndim = d.shape[coord_axis]
U = affine_idx_in
V = affine_idx_out
W = affine_disp
# TODO: reduce number of temporary arrays
coord_dtype = cupy.promote_types(d.dtype, np.float32)
if U is None:
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=coord_dtype) for s in d.shape[:-1]],
indexing="ij",
sparse=True,
)
if coord_axis == 0:
Z = d.copy()
else:
Z = cupy.ascontiguousarray(cupy.moveaxis(d, -1, 0))
else:
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=coord_dtype) for s in d.shape[:-1]],
indexing="ij",
sparse=True,
)
# Y = mul0(A, xcoords, sh, cupy, lastcol=1)
Y = _apply_affine_to_field(
xcoords,
U[:ndim, :],
out=None,
include_translations=True,
coord_axis=0,
)
# for CuPy with non-legacy linear interpolation, don't need to extend d
Z = cupy.empty_like(Y)
if coord_axis == 0:
for n in range(ndim):
Z[n, ...] = ndi.map_coordinates(d[n], Y, order=1, mode=mode)
else:
for n in range(ndim):
Z[n, ...] = ndi.map_coordinates(d[..., n],
Y,
order=1,
mode=mode)
if W is not None:
# Z = mul0(C, Z, sh, cupy, out=Z, lastcol=0)
Z = _apply_affine_to_field(
Z,
W[:ndim, :ndim],
out=None,
include_translations=False,
coord_axis=0,
)
if V is not None:
Z += _apply_affine_to_field(
xcoords,
V[:ndim, :],
out=None,
include_translations=True,
coord_axis=0,
)
for n in range(ndim):
Z[n, ...] -= xcoords[
n] # TODO: just subtract one from last column of V instead?
if coord_axis == -1:
Z = cupy.moveaxis(Z, 0, -1)
if not Z.flags.c_contiguous:
Z = cupy.ascontiguousarray(Z)
return Z
def compose_vector_fields(
d1,
d2,
premult_index,
premult_disp,
time_scaling,
comp=None,
order=1,
*,
coord_axis=-1,
omit_stats=False,
xcoords=None,
Y=None,
Z=None,
):
if comp is None:
comp = cupy.empty_like(d1, order="C")
# need vector elements on first axis, not last
if coord_axis != 0:
d1 = cupy.ascontiguousarray(cupy.moveaxis(d1, -1, 0))
d2 = cupy.ascontiguousarray(cupy.moveaxis(d2, -1, 0))
else:
if not d1.flags.c_contiguous:
d1 = cupy.ascontiguousarray(d1)
if not d2.flags.c_contiguous:
d2 = cupy.ascontiguousarray(d2)
ndim = d1.shape[0]
B = premult_disp
A = premult_index
t = time_scaling
if xcoords is None:
xcoords = cupy.meshgrid(
*[cupy.arange(s, dtype=d1.real.dtype) for s in d1.shape[1:]],
indexing="ij",
sparse=True,
)
# TODO: reduce number of temporary arrays
if ndim in [2, 3]:
if Y is None:
Y = cupy.empty_like(d1)
if A is None:
if B is None:
if ndim == 3:
composeNone_3d(
d1[0],
d1[1],
d1[2],
xcoords[0],
xcoords[1],
xcoords[2],
Y[0],
Y[1],
Y[2],
)
else:
composeNone_2d(d1[0], d1[1], xcoords[0], xcoords[1], Y[0],
Y[1])
else:
B = cupy.asarray(B[:ndim, :ndim], dtype=d1.dtype, order="C")
if ndim == 3:
composeB_3d(
d1[0],
d1[1],
d1[2],
xcoords[0],
xcoords[1],
xcoords[2],
B,
Y[0],
Y[1],
Y[2],
)
else:
composeB_2d(d1[0], d1[1], xcoords[0], xcoords[1], B, Y[0],
Y[1])
elif B is None:
A = cupy.asarray(A[:ndim, :], dtype=d1.dtype, order="C")
if ndim == 3:
composeA_3d(xcoords[0], xcoords[1], xcoords[2], A, Y[0], Y[1],
Y[2])
else:
composeA_2d(xcoords[0], xcoords[1], A, Y[0], Y[1])
else:
A = cupy.asarray(A[:ndim, :], dtype=d1.dtype, order="C")
B = cupy.asarray(B[:ndim, :ndim], dtype=d1.dtype, order="C")
if ndim == 3:
composeAB_3d(
d1[0],
d1[1],
d1[2],
xcoords[0],
xcoords[1],
xcoords[2],
B,
A,
Y[0],
Y[1],
Y[2],
)
else:
composeAB_2d(d1[0], d1[1], xcoords[0], xcoords[1], B, A, Y[0],
Y[1])
else:
if B is None:
d1tmp = d1.copy() # have to copy to avoid modification of d1
else:
d1tmp = _apply_affine_to_field(d1,
B[:ndim, :ndim],
include_translations=False,
coord_axis=0)
if A is None:
Y = d1tmp
for n in range(ndim):
Y[n] += xcoords[n]
else:
# Y = mul0(A, xcoords, sh, cupy, lastcol=1)
Y = _apply_affine_to_field(xcoords,
A[:ndim, :],
include_translations=True,
coord_axis=0)
Y += d1tmp
from cupyimg.scipy.ndimage._kernels import interp
# TODO: things outside the domain should be set to zero
legacy_mode_pre = interp.const_legacy_mode
try:
interp.const_legacy_mode = True
if Z is None:
Z = cupy.empty_like(Y)
for n in range(ndim):
Z[n, ...] = ndi.map_coordinates(d2[n], Y, order=1, mode="constant")
finally:
interp.const_legacy_mode = legacy_mode_pre
if coord_axis == 0:
res = comp
else:
res = cupy.empty_like(Z)
if omit_stats and ndim in [2, 3]:
_shape = cupy.asarray([d1.shape[1 + n] - 1 for n in range(ndim)],
dtype=cupy.int32)
if ndim == 3:
_comp_apply_masked_time_scaling_3d(
d1[0],
d1[1],
d1[2],
Y[0],
Y[1],
Y[2],
Z[0],
Z[1],
Z[2],
t,
_shape,
res[0],
res[1],
res[2],
)
else:
_comp_apply_masked_time_scaling_2d(d1[0], d1[1], Y[0], Y[1], Z[0],
Z[1], t, _shape, res[0], res[1])
else:
# TODO: declare count as boolean?
count = cupy.zeros(Z.shape[1:], dtype=np.int32)
# We now compute:
# res = d1 + t * Z
# except that res = 0 where either coordinate in
# interpolating Y was outside the displacement extent
for n in range(ndim):
_comp_apply_masked_time_scaling_nd(d1[n], Y[n], Z[n], t,
d1.shape[1 + n] - 1, res[n],
count)
# nnz corresponds to the number of points in comp inside the domain
count = count > 0 # remove after init count as boolean
if not omit_stats:
nnz = res.size // ndim - cupy.count_nonzero(count)
res *= ~count[np.newaxis, ...]
if omit_stats:
stats = None
else:
# compute the stats
stats = cupy.empty((3, ), dtype=float)
nn = res[0] * res[0]
for n in range(1, ndim):
nn += res[n] * res[n]
# TODO: do we want stats to be a GPU array or CPU array?
stats[0] = cupy.sqrt(nn.max())
mean_norm = nn.sum() / nnz
stats[1] = cupy.sqrt(mean_norm)
nn *= nn
stats[2] = cupy.sqrt(nn.sum() / nnz - mean_norm * mean_norm)
if coord_axis != 0:
res = cupy.moveaxis(res, 0, -1)
comp[...] = res
return comp, stats