import numpy as np
from scipy import ndimage as ndi
from ._geometric import SimilarityTransform, AffineTransform, ProjectiveTransform
from ._warps_cy import _warp_fast
from ..measure import block_reduce
from .._shared.utils import (
get_bound_method_class,
safe_as_int,
warn,
convert_to_float,
_to_ndimage_mode,
_validate_interpolation_order,
channel_as_last_axis,
)
HOMOGRAPHY_TRANSFORMS = (SimilarityTransform, AffineTransform, ProjectiveTransform)
def _preprocess_resize_output_shape(image, output_shape):
"""Validate resize output shape according to input image.
Parameters
----------
image: ndarray
Image to be resized.
output_shape: iterable
Size of the generated output image `(rows, cols[, ...][, dim])`. If
`dim` is not provided, the number of channels is preserved.
Returns
-------
image: ndarray
The input image, but with additional singleton dimensions appended in
the case where ``len(output_shape) > input.ndim``.
output_shape: tuple
The output image converted to tuple.
Raises
------
ValueError:
If output_shape length is smaller than the image number of
dimensions
Notes
-----
The input image is reshaped if its number of dimensions is not
equal to output_shape_length.
"""
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 += (1,) * (output_ndim - image.ndim)
image = np.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:
raise ValueError(
"output_shape length cannot be smaller than the "
"image number of dimensions"
)
return image, output_shape
[文档]
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 downsampling with an integer factor also see
`skimage.transform.downscale_local_mean`.
Parameters
----------
image : ndarray
Input image.
output_shape : iterable
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 downsampling. It is crucial to filter when downsampling
the image to avoid aliasing artifacts. If not specified, it is set to
True when downsampling an image whose data type is not bool.
It is also set to False when using nearest neighbor interpolation
(``order`` == 0) with integer input data type.
anti_aliasing_sigma : {float, tuple of floats}, optional
Standard deviation for Gaussian filtering used when anti-aliasing.
By default, this value is chosen as (s - 1) / 2 where s is the
downsampling 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)
"""
image, output_shape = _preprocess_resize_output_shape(image, output_shape)
input_shape = image.shape
input_type = image.dtype
if input_type == np.float16:
image = image.astype(np.float32)
if anti_aliasing is None:
anti_aliasing = (
not input_type == bool
and not (np.issubdtype(input_type, np.integer) and order == 0)
and any(x < y for x, y in zip(output_shape, input_shape))
)
if input_type == bool and anti_aliasing:
raise ValueError("anti_aliasing must be False for boolean images")
factors = np.divide(input_shape, output_shape)
order = _validate_interpolation_order(input_type, order)
if order > 0:
image = convert_to_float(image, preserve_range)
# Translate modes used by np.pad to those used by scipy.ndimage
ndi_mode = _to_ndimage_mode(mode)
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"
)
filtered = ndi.gaussian_filter(
image, anti_aliasing_sigma, cval=cval, mode=ndi_mode
)
else:
filtered = image
zoom_factors = [1 / f for f in factors]
out = ndi.zoom(
filtered, zoom_factors, order=order, mode=ndi_mode, cval=cval, grid_mode=True
)
_clip_warp_output(image, out, mode, cval, clip)
return out
[文档]
@channel_as_last_axis()
def rescale(
image,
scale,
order=None,
mode='reflect',
cval=0,
clip=True,
preserve_range=False,
anti_aliasing=None,
anti_aliasing_sigma=None,
*,
channel_axis=None,
):
"""Scale image by a certain factor.
Performs interpolation to up-scale or down-scale 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 : (M, N[, ...][, C]) ndarray
Input image.
scale : {float, tuple of floats}
Scale factors for spatial dimensions. Separate scale factors can be defined as
(m, n[, ...]).
Returns
-------
scaled : ndarray
Scaled 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.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
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 rescale
>>> image = data.camera()
>>> rescale(image, 0.1).shape
(51, 51)
>>> rescale(image, 0.5).shape
(256, 256)
"""
scale = np.atleast_1d(scale)
multichannel = channel_axis is not None
if len(scale) > 1:
if (not multichannel and len(scale) != image.ndim) or (
multichannel and len(scale) != image.ndim - 1
):
raise ValueError("Supply a single scale, or one value per spatial " "axis")
if multichannel:
scale = np.concatenate((scale, [1]))
orig_shape = np.asarray(image.shape)
output_shape = np.maximum(np.round(scale * orig_shape), 1)
if multichannel: # don't scale channel dimension
output_shape[-1] = orig_shape[-1]
return resize(
image,
output_shape,
order=order,
mode=mode,
cval=cval,
clip=clip,
preserve_range=preserve_range,
anti_aliasing=anti_aliasing,
anti_aliasing_sigma=anti_aliasing_sigma,
)
[文档]
def rotate(
image,
angle,
resize=False,
center=None,
order=None,
mode='constant',
cval=0,
clip=True,
preserve_range=False,
):
"""Rotate image by a certain angle around its center.
Parameters
----------
image : ndarray
Input image.
angle : float
Rotation angle in degrees in counter-clockwise direction.
resize : bool, optional
Determine whether the shape of the output image will be automatically
calculated, so the complete rotated image exactly fits. Default is
False.
center : iterable of length 2
The rotation center. If ``center=None``, the image is rotated around
its center, i.e. ``center=(cols / 2 - 0.5, rows / 2 - 0.5)``. Please
note that this parameter is (cols, rows), contrary to normal skimage
ordering.
Returns
-------
rotated : ndarray
Rotated 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
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 rotate
>>> image = data.camera()
>>> rotate(image, 2).shape
(512, 512)
>>> rotate(image, 2, resize=True).shape
(530, 530)
>>> rotate(image, 90, resize=True).shape
(512, 512)
"""
rows, cols = image.shape[0], image.shape[1]
if image.dtype == np.float16:
image = image.astype(np.float32)
# rotation around center
if center is None:
center = np.array((cols, rows)) / 2.0 - 0.5
else:
center = np.asarray(center)
tform1 = SimilarityTransform(translation=center)
tform2 = SimilarityTransform(rotation=np.deg2rad(angle))
tform3 = SimilarityTransform(translation=-center)
tform = tform3 + tform2 + tform1
output_shape = None
if resize:
# determine shape of output image
corners = np.array([[0, 0], [0, rows - 1], [cols - 1, rows - 1], [cols - 1, 0]])
corners = tform.inverse(corners)
minc = corners[:, 0].min()
minr = corners[:, 1].min()
maxc = corners[:, 0].max()
maxr = corners[:, 1].max()
out_rows = maxr - minr + 1
out_cols = maxc - minc + 1
output_shape = np.around((out_rows, out_cols))
# fit output image in new shape
translation = (minc, minr)
tform4 = SimilarityTransform(translation=translation)
tform = tform4 + tform
# Make sure the transform is exactly affine, to ensure fast warping.
tform.params[2] = (0, 0, 1)
return warp(
image,
tform,
output_shape=output_shape,
order=order,
mode=mode,
cval=cval,
clip=clip,
preserve_range=preserve_range,
)
[文档]
def downscale_local_mean(image, factors, cval=0, clip=True):
"""Down-sample N-dimensional image by local averaging.
The image is padded with `cval` if it is not perfectly divisible by the
integer factors.
In contrast to interpolation in `skimage.transform.resize` and
`skimage.transform.rescale` this function calculates the local mean of
elements in each block of size `factors` in the input image.
Parameters
----------
image : (M[, ...]) ndarray
Input image.
factors : array_like
Array containing down-sampling integer factor along each axis.
cval : float, optional
Constant padding value if image is not perfectly divisible by the
integer factors.
clip : bool, optional
Unused, but kept here for API consistency with the other transforms
in this module. (The local mean will never fall outside the range
of values in the input image, assuming the provided `cval` also
falls within that range.)
Returns
-------
image : ndarray
Down-sampled image with same number of dimensions as input image.
For integer inputs, the output dtype will be ``float64``.
See :func:`numpy.mean` for details.
Examples
--------
>>> a = np.arange(15).reshape(3, 5)
>>> a
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
>>> downscale_local_mean(a, (2, 3))
array([[3.5, 4. ],
[5.5, 4.5]])
"""
return block_reduce(image, factors, np.mean, cval)
def _swirl_mapping(xy, center, rotation, strength, radius):
x, y = xy.T
x0, y0 = center
rho = np.sqrt((x - x0) ** 2 + (y - y0) ** 2)
# Ensure that the transformation decays to approximately 1/1000-th
# within the specified radius.
radius = radius / 5 * np.log(2)
theta = rotation + strength * np.exp(-rho / radius) + np.arctan2(y - y0, x - x0)
xy[..., 0] = x0 + rho * np.cos(theta)
xy[..., 1] = y0 + rho * np.sin(theta)
return xy
[文档]
def swirl(
image,
center=None,
strength=1,
radius=100,
rotation=0,
output_shape=None,
order=None,
mode='reflect',
cval=0,
clip=True,
preserve_range=False,
):
"""Perform a swirl transformation.
Parameters
----------
image : ndarray
Input image.
center : (column, row) tuple or (2,) ndarray, optional
Center coordinate of transformation.
strength : float, optional
The amount of swirling applied.
radius : float, optional
The extent of the swirl in pixels. The effect dies out
rapidly beyond `radius`.
rotation : float, optional
Additional rotation applied to the image.
Returns
-------
swirled : ndarray
Swirled version of the input.
Other parameters
----------------
output_shape : tuple (rows, cols), optional
Shape of the output image generated. By default the shape of the input
image is preserved.
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, with 'reflect' used as the default. 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
"""
if center is None:
center = np.array(image.shape)[:2][::-1] / 2
warp_args = {
'center': center,
'rotation': rotation,
'strength': strength,
'radius': radius,
}
return warp(
image,
_swirl_mapping,
map_args=warp_args,
output_shape=output_shape,
order=order,
mode=mode,
cval=cval,
clip=clip,
preserve_range=preserve_range,
)
def _stackcopy(a, b):
"""Copy b into each color layer of a, such that::
a[:,:,0] = a[:,:,1] = ... = b
Parameters
----------
a : (M, N) or (M, N, P) ndarray
Target array.
b : (M, N)
Source array.
Notes
-----
Color images are stored as an ``(M, N, 3)`` or ``(M, N, 4)`` arrays.
"""
if a.ndim == 3:
a[:] = b[:, :, np.newaxis]
else:
a[:] = b
[文档]
def warp_coords(coord_map, shape, dtype=np.float64):
"""Build the source coordinates for the output of a 2-D image warp.
Parameters
----------
coord_map : callable like GeometricTransform.inverse
Return input coordinates for given output coordinates.
Coordinates are in the shape (P, 2), where P is the number
of coordinates and each element is a ``(row, col)`` pair.
shape : tuple
Shape of output image ``(rows, cols[, bands])``.
dtype : np.dtype or string
dtype for return value (sane choices: float32 or float64).
Returns
-------
coords : (ndim, rows, cols[, bands]) array of dtype `dtype`
Coordinates for `scipy.ndimage.map_coordinates`, that will yield
an image of shape (orows, ocols, bands) by drawing from source
points according to the `coord_transform_fn`.
Notes
-----
This is a lower-level routine that produces the source coordinates for 2-D
images used by `warp()`.
It is provided separately from `warp` to give additional flexibility to
users who would like, for example, to re-use a particular coordinate
mapping, to use specific dtypes at various points along the the
image-warping process, or to implement different post-processing logic
than `warp` performs after the call to `ndi.map_coordinates`.
Examples
--------
Produce a coordinate map that shifts an image up and to the right:
>>> from skimage import data
>>> from scipy.ndimage import map_coordinates
>>>
>>> def shift_up10_left20(xy):
... return xy - np.array([-20, 10])[None, :]
>>>
>>> image = data.astronaut().astype(np.float32)
>>> coords = warp_coords(shift_up10_left20, image.shape)
>>> warped_image = map_coordinates(image, coords)
"""
shape = safe_as_int(shape)
rows, cols = shape[0], shape[1]
coords_shape = [len(shape), rows, cols]
if len(shape) == 3:
coords_shape.append(shape[2])
coords = np.empty(coords_shape, dtype=dtype)
# Reshape grid coordinates into a (P, 2) array of (row, col) pairs
tf_coords = np.indices((cols, rows), dtype=dtype).reshape(2, -1).T
# Map each (row, col) pair to the source image according to
# the user-provided mapping
tf_coords = coord_map(tf_coords)
# Reshape back to a (2, M, N) coordinate grid
tf_coords = tf_coords.T.reshape((-1, cols, rows)).swapaxes(1, 2)
# Place the y-coordinate mapping
_stackcopy(coords[1, ...], tf_coords[0, ...])
# Place the x-coordinate mapping
_stackcopy(coords[0, ...], tf_coords[1, ...])
if len(shape) == 3:
coords[2, ...] = range(shape[2])
return coords
def _clip_warp_output(input_image, output_image, mode, cval, clip):
"""Clip output image to range of values of input image.
Note that this function modifies the values of `output_image` in-place
and it is only modified if ``clip=True``.
Parameters
----------
input_image : ndarray
Input image.
output_image : ndarray
Output image, which is modified in-place.
Other parameters
----------------
mode : {'constant', 'edge', 'symmetric', 'reflect', 'wrap'}
Points outside the boundaries of the input are filled according
to the given mode. Modes match the behaviour of `numpy.pad`.
cval : float
Used in conjunction with mode 'constant', the value outside
the image boundaries.
clip : bool
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.
"""
if clip:
min_val = np.min(input_image)
if np.isnan(min_val):
# NaNs detected, use NaN-safe min/max
min_func = np.nanmin
max_func = np.nanmax
min_val = min_func(input_image)
else:
min_func = np.min
max_func = np.max
max_val = max_func(input_image)
# Check if cval has been used such that it expands the effective input
# range
preserve_cval = (
mode == 'constant'
and not min_val <= cval <= max_val
and min_func(output_image) <= cval <= max_func(output_image)
)
# expand min/max range to account for cval
if preserve_cval:
# cast cval to the same dtype as the input image
cval = input_image.dtype.type(cval)
min_val = min(min_val, cval)
max_val = max(max_val, cval)
# Convert array-like types to ndarrays (gh-7159)
min_val, max_val = np.asarray(min_val), np.asarray(max_val)
np.clip(output_image, min_val, max_val, out=output_image)
[文档]
def warp(
image,
inverse_map,
map_args=None,
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):
>>> matrix = np.array([[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 = np.array([30, 30, 30])
>>> rng = np.random.default_rng()
>>> cube = rng.random(cube_shape)
Setup the coordinate array, that defines the scaling:
>>> scale = 0.1
>>> output_shape = (scale * cube_shape).astype(int)
>>> coords0, coords1, coords2 = np.mgrid[:output_shape[0],
... :output_shape[1], :output_shape[2]]
>>> coords = np.array([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 map_args is None:
map_args = {}
if image.size == 0:
raise ValueError("Cannot warp empty image with dimensions", image.shape)
order = _validate_interpolation_order(image.dtype, order)
if order > 0:
image = convert_to_float(image, preserve_range)
if image.dtype == np.float16:
image = image.astype(np.float32)
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 order in (1, 3) and not map_args:
# use fast Cython version for specific interpolation orders and input
matrix = None
if isinstance(inverse_map, np.ndarray) and inverse_map.shape == (3, 3):
# inverse_map is a transformation matrix as numpy array
matrix = inverse_map
elif isinstance(inverse_map, HOMOGRAPHY_TRANSFORMS):
# inverse_map is a homography
matrix = inverse_map.params
elif (
hasattr(inverse_map, '__name__')
and inverse_map.__name__ == 'inverse'
and get_bound_method_class(inverse_map) in HOMOGRAPHY_TRANSFORMS
):
# inverse_map is the inverse of a homography
matrix = np.linalg.inv(inverse_map.__self__.params)
if matrix is not None:
matrix = matrix.astype(image.dtype)
ctype = 'float32_t' if image.dtype == np.float32 else 'float64_t'
if image.ndim == 2:
warped = _warp_fast[ctype](
image,
matrix,
output_shape=output_shape,
order=order,
mode=mode,
cval=cval,
)
elif image.ndim == 3:
dims = []
for dim in range(image.shape[2]):
dims.append(
_warp_fast[ctype](
image[..., dim],
matrix,
output_shape=output_shape,
order=order,
mode=mode,
cval=cval,
)
)
warped = np.dstack(dims)
if warped is None:
# use ndi.map_coordinates
if isinstance(inverse_map, np.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, np.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, mode, cval, clip)
return warped
def _linear_polar_mapping(output_coords, k_angle, k_radius, center):
"""Inverse mapping function to convert from cartesian to polar coordinates
Parameters
----------
output_coords : (M, 2) ndarray
Array of `(col, row)` coordinates in the output image.
k_angle : float
Scaling factor that relates the intended number of rows in the output
image to angle: ``k_angle = nrows / (2 * np.pi)``.
k_radius : float
Scaling factor that relates the radius of the circle bounding the
area to be transformed to the intended number of columns in the output
image: ``k_radius = ncols / radius``.
center : tuple (row, col)
Coordinates that represent the center of the circle that bounds the
area to be transformed in an input image.
Returns
-------
coords : (M, 2) ndarray
Array of `(col, row)` coordinates in the input image that
correspond to the `output_coords` given as input.
"""
angle = output_coords[:, 1] / k_angle
rr = ((output_coords[:, 0] / k_radius) * np.sin(angle)) + center[0]
cc = ((output_coords[:, 0] / k_radius) * np.cos(angle)) + center[1]
coords = np.column_stack((cc, rr))
return coords
def _log_polar_mapping(output_coords, k_angle, k_radius, center):
"""Inverse mapping function to convert from cartesian to polar coordinates
Parameters
----------
output_coords : (M, 2) ndarray
Array of `(col, row)` coordinates in the output image.
k_angle : float
Scaling factor that relates the intended number of rows in the output
image to angle: ``k_angle = nrows / (2 * np.pi)``.
k_radius : float
Scaling factor that relates the radius of the circle bounding the
area to be transformed to the intended number of columns in the output
image: ``k_radius = width / np.log(radius)``.
center : 2-tuple
`(row, col)` coordinates that represent the center of the circle that bounds the
area to be transformed in an input image.
Returns
-------
coords : ndarray, shape (M, 2)
Array of `(col, row)` coordinates in the input image that
correspond to the `output_coords` given as input.
"""
angle = output_coords[:, 1] / k_angle
rr = ((np.exp(output_coords[:, 0] / k_radius)) * np.sin(angle)) + center[0]
cc = ((np.exp(output_coords[:, 0] / k_radius)) * np.cos(angle)) + center[1]
coords = np.column_stack((cc, rr))
return coords
[文档]
@channel_as_last_axis()
def warp_polar(
image,
center=None,
*,
radius=None,
output_shape=None,
scaling='linear',
channel_axis=None,
**kwargs,
):
"""Remap image to polar or log-polar coordinates space.
Parameters
----------
image : (M, N[, C]) ndarray
Input image. For multichannel images `channel_axis` has to be specified.
center : 2-tuple, optional
`(row, col)` coordinates of the point in `image` that represents the center of
the transformation (i.e., the origin in Cartesian space). Values can be of
type `float`. If no value is given, the center is assumed to be the center point
of `image`.
radius : float, optional
Radius of the circle that bounds the area to be transformed.
output_shape : tuple (row, col), optional
scaling : {'linear', 'log'}, optional
Specify whether the image warp is polar or log-polar. Defaults to
'linear'.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
**kwargs : keyword arguments
Passed to `transform.warp`.
Returns
-------
warped : ndarray
The polar or log-polar warped image.
Examples
--------
Perform a basic polar warp on a grayscale image:
>>> from skimage import data
>>> from skimage.transform import warp_polar
>>> image = data.checkerboard()
>>> warped = warp_polar(image)
Perform a log-polar warp on a grayscale image:
>>> warped = warp_polar(image, scaling='log')
Perform a log-polar warp on a grayscale image while specifying center,
radius, and output shape:
>>> warped = warp_polar(image, (100,100), radius=100,
... output_shape=image.shape, scaling='log')
Perform a log-polar warp on a color image:
>>> image = data.astronaut()
>>> warped = warp_polar(image, scaling='log', channel_axis=-1)
"""
multichannel = channel_axis is not None
if image.ndim != 2 and not multichannel:
raise ValueError(
f'Input array must be 2-dimensional when '
f'`channel_axis=None`, got {image.ndim}'
)
if image.ndim != 3 and multichannel:
raise ValueError(
f'Input array must be 3-dimensional when '
f'`channel_axis` is specified, got {image.ndim}'
)
if center is None:
center = (np.array(image.shape)[:2] / 2) - 0.5
if radius is None:
w, h = np.array(image.shape)[:2] / 2
radius = np.sqrt(w**2 + h**2)
if output_shape is None:
height = 360
width = int(np.ceil(radius))
output_shape = (height, width)
else:
output_shape = safe_as_int(output_shape)
height = output_shape[0]
width = output_shape[1]
if scaling == 'linear':
k_radius = width / radius
map_func = _linear_polar_mapping
elif scaling == 'log':
k_radius = width / np.log(radius)
map_func = _log_polar_mapping
else:
raise ValueError("Scaling value must be in {'linear', 'log'}")
k_angle = height / (2 * np.pi)
warp_args = {'k_angle': k_angle, 'k_radius': k_radius, 'center': center}
warped = warp(
image, map_func, map_args=warp_args, output_shape=output_shape, **kwargs
)
return warped
def _local_mean_weights(old_size, new_size, grid_mode, dtype):
"""Create a 2D weight matrix for resizing with the local mean.
Parameters
----------
old_size: int
Old size.
new_size: int
New size.
grid_mode : bool
Whether to use grid data model of pixel/voxel model for
average weights computation.
dtype: dtype
Output array data type.
Returns
-------
weights: (new_size, old_size) array
Rows sum to 1.
"""
if grid_mode:
old_breaks = np.linspace(0, old_size, num=old_size + 1, dtype=dtype)
new_breaks = np.linspace(0, old_size, num=new_size + 1, dtype=dtype)
else:
old, new = old_size - 1, new_size - 1
old_breaks = np.pad(
np.linspace(0.5, old - 0.5, old, dtype=dtype),
1,
'constant',
constant_values=(0, old),
)
if new == 0:
val = np.inf
else:
val = 0.5 * old / new
new_breaks = np.pad(
np.linspace(val, old - val, new, dtype=dtype),
1,
'constant',
constant_values=(0, old),
)
upper = np.minimum(new_breaks[1:, np.newaxis], old_breaks[np.newaxis, 1:])
lower = np.maximum(new_breaks[:-1, np.newaxis], old_breaks[np.newaxis, :-1])
weights = np.maximum(upper - lower, 0)
weights /= weights.sum(axis=1, keepdims=True)
return weights
[文档]
def resize_local_mean(
image, output_shape, grid_mode=True, preserve_range=False, *, channel_axis=None
):
"""Resize an array with the local mean / bilinear scaling.
Parameters
----------
image : ndarray
Input image. If this is a multichannel image, the axis corresponding
to channels should be specified using `channel_axis`.
output_shape : iterable
Size of the generated output image. When `channel_axis` is not None,
the `channel_axis` should either be omitted from `output_shape` or the
``output_shape[channel_axis]`` must match
``image.shape[channel_axis]``. If the length of `output_shape` exceeds
image.ndim, additional singleton dimensions will be appended to the
input ``image`` as needed.
grid_mode : bool, optional
Defines ``image`` pixels position: if True, pixels are assumed to be at
grid intersections, otherwise at cell centers. As a consequence,
for example, a 1d signal of length 5 is considered to have length 4
when `grid_mode` is False, but length 5 when `grid_mode` is True. See
the following visual illustration:
.. code-block:: text
| pixel 1 | pixel 2 | pixel 3 | pixel 4 | pixel 5 |
|<-------------------------------------->|
vs.
|<----------------------------------------------->|
The starting point of the arrow in the diagram above corresponds to
coordinate location 0 in each mode.
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
-------
resized : ndarray
Resized version of the input.
See Also
--------
resize, downscale_local_mean
Notes
-----
This method is sometimes referred to as "area-based" interpolation or
"pixel mixing" interpolation [1]_. When `grid_mode` is True, it is
equivalent to using OpenCV's resize with `INTER_AREA` interpolation mode.
It is commonly used for image downsizing. If the downsizing factors are
integers, then `downscale_local_mean` should be preferred instead.
References
----------
.. [1] http://entropymine.com/imageworsener/pixelmixing/
Examples
--------
>>> from skimage import data
>>> from skimage.transform import resize_local_mean
>>> image = data.camera()
>>> resize_local_mean(image, (100, 100)).shape
(100, 100)
"""
if channel_axis is not None:
if channel_axis < -image.ndim or channel_axis >= image.ndim:
raise ValueError("invalid channel_axis")
# move channels to last position
image = np.moveaxis(image, channel_axis, -1)
nc = image.shape[-1]
output_ndim = len(output_shape)
if output_ndim == image.ndim - 1:
# insert channels dimension at the end
output_shape = output_shape + (nc,)
elif output_ndim == image.ndim:
if output_shape[channel_axis] != nc:
raise ValueError(
"Cannot reshape along the channel_axis. Use "
"channel_axis=None to reshape along all axes."
)
# move channels to last position in output_shape
channel_axis = channel_axis % image.ndim
output_shape = (
output_shape[:channel_axis] + output_shape[channel_axis:] + (nc,)
)
else:
raise ValueError(
"len(output_shape) must be image.ndim or (image.ndim - 1) "
"when a channel_axis is specified."
)
resized = image
else:
resized, output_shape = _preprocess_resize_output_shape(image, output_shape)
resized = convert_to_float(resized, preserve_range)
dtype = resized.dtype
for axis, (old_size, new_size) in enumerate(zip(image.shape, output_shape)):
if old_size == new_size:
continue
weights = _local_mean_weights(old_size, new_size, grid_mode, dtype)
product = np.tensordot(resized, weights, [[axis], [-1]])
resized = np.moveaxis(product, -1, axis)
if channel_axis is not None:
# restore channels to original axis
resized = np.moveaxis(resized, -1, channel_axis)
return resized
