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"""
Grayscale morphological operations
"""
import functools
import numpy as np
from scipy import ndimage as ndi
from .._shared.utils import deprecate_kwarg
from ..util import crop
from .misc import default_footprint
__all__ = ['erosion', 'dilation', 'opening', 'closing', 'white_tophat',
'black_tophat']
def _shift_footprint(footprint, shift_x, shift_y):
"""Shift the binary image `footprint` in the left and/or up.
This only affects 2D footprints with even number of rows
or columns.
Parameters
----------
footprint : 2D array, shape (M, N)
The input footprint.
shift_x, shift_y : bool
Whether to move `footprint` along each axis.
Returns
-------
out : 2D array, shape (M + int(shift_x), N + int(shift_y))
The shifted footprint.
"""
if footprint.ndim != 2:
# do nothing for 1D or 3D or higher footprints
return footprint
m, n = footprint.shape
if m % 2 == 0:
extra_row = np.zeros((1, n), footprint.dtype)
if shift_x:
footprint = np.vstack((footprint, extra_row))
else:
footprint = np.vstack((extra_row, footprint))
m += 1
if n % 2 == 0:
extra_col = np.zeros((m, 1), footprint.dtype)
if shift_y:
footprint = np.hstack((footprint, extra_col))
else:
footprint = np.hstack((extra_col, footprint))
return footprint
def _invert_footprint(footprint):
"""Change the order of the values in `footprint`.
This is a patch for the *weird* footprint inversion in
`ndi.grey_morphology` [1]_.
Parameters
----------
footprint : array
The input footprint.
Returns
-------
inverted : array, same shape and type as `footprint`
The footprint, in opposite order.
Examples
--------
>>> footprint = np.array([[0, 0, 0], [0, 1, 1], [0, 1, 1]], np.uint8)
>>> _invert_footprint(footprint)
array([[1, 1, 0],
[1, 1, 0],
[0, 0, 0]], dtype=uint8)
References
----------
.. [1] https://github.com/scipy/scipy/blob/ec20ababa400e39ac3ffc9148c01ef86d5349332/scipy/ndimage/morphology.py#L1285 # noqa
"""
inverted = footprint[(slice(None, None, -1),) * footprint.ndim]
return inverted
def pad_for_eccentric_footprints(func):
"""Pad input images for certain morphological operations.
Parameters
----------
func : callable
A morphological function, either opening or closing, that
supports eccentric footprints. Its parameters must
include at least `image`, `footprint`, and `out`.
Returns
-------
func_out : callable
The same function, but correctly padding the input image before
applying the input function.
See Also
--------
opening, closing.
"""
@functools.wraps(func)
def func_out(image, footprint, out=None, *args, **kwargs):
pad_widths = []
padding = False
if out is None:
out = np.empty_like(image)
for axis_len in footprint.shape:
if axis_len % 2 == 0:
axis_pad_width = axis_len - 1
padding = True
else:
axis_pad_width = 0
pad_widths.append((axis_pad_width,) * 2)
if padding:
image = np.pad(image, pad_widths, mode='edge')
out_temp = np.empty_like(image)
else:
out_temp = out
out_temp = func(image, footprint, out=out_temp, *args, **kwargs)
if padding:
out[:] = crop(out_temp, pad_widths)
else:
out = out_temp
return out
return func_out
@default_footprint
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
def erosion(image, footprint=None, out=None, shift_x=False, shift_y=False):
"""Return grayscale morphological erosion of an image.
Morphological erosion sets a pixel at (i,j) to the minimum over all pixels
in the neighborhood centered at (i,j). Erosion shrinks bright regions and
enlarges dark regions.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as an array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarrays, optional
The array to store the result of the morphology. If None is
passed, a new array will be allocated.
shift_x, shift_y : bool, optional
shift footprint about center point. This only affects
eccentric footprints (i.e. footprint with even numbered
sides).
Returns
-------
eroded : array, same shape as `image`
The result of the morphological erosion.
Notes
-----
For ``uint8`` (and ``uint16`` up to a certain bit-depth) data, the
lower algorithm complexity makes the `skimage.filters.rank.minimum`
function more efficient for larger images and footprints.
Examples
--------
>>> # Erosion shrinks bright regions
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_square = np.array([[0, 0, 0, 0, 0],
... [0, 1, 1, 1, 0],
... [0, 1, 1, 1, 0],
... [0, 1, 1, 1, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> erosion(bright_square, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
footprint = np.array(footprint)
footprint = _shift_footprint(footprint, shift_x, shift_y)
if out is None:
out = np.empty_like(image)
ndi.grey_erosion(image, footprint=footprint, output=out)
return out
@default_footprint
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
def dilation(image, footprint=None, out=None, shift_x=False, shift_y=False):
"""Return grayscale morphological dilation of an image.
Morphological dilation sets the value of a pixel to the maximum over all
pixel values within a local neighborhood centered about it. The values
where the footprint is 1 define this neighborhood.
Dilation enlarges bright regions and shrinks dark regions.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as an array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarray, optional
The array to store the result of the morphology. If None is
passed, a new array will be allocated.
shift_x, shift_y : bool, optional
Shift footprint about center point. This only affects 2D
eccentric footprints (i.e., footprints with even-numbered
sides).
Returns
-------
dilated : uint8 array, same shape and type as `image`
The result of the morphological dilation.
Notes
-----
For `uint8` (and `uint16` up to a certain bit-depth) data, the lower
algorithm complexity makes the `skimage.filters.rank.maximum` function more
efficient for larger images and footprints.
Examples
--------
>>> # Dilation enlarges bright regions
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_pixel = np.array([[0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0],
... [0, 0, 1, 0, 0],
... [0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> dilation(bright_pixel, square(3))
array([[0, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
footprint = np.array(footprint)
footprint = _shift_footprint(footprint, shift_x, shift_y)
# Inside ndi.grey_dilation, the footprint is inverted,
# e.g. `footprint = footprint[::-1, ::-1]` for 2D [1]_, for reasons unknown
# to this author (@jni). To "patch" this behaviour, we invert our own
# footprint before passing it to `ndi.grey_dilation`.
# [1] https://github.com/scipy/scipy/blob/ec20ababa400e39ac3ffc9148c01ef86d5349332/scipy/ndimage/morphology.py#L1285 # noqa
footprint = _invert_footprint(footprint)
if out is None:
out = np.empty_like(image)
ndi.grey_dilation(image, footprint=footprint, output=out)
return out
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
@default_footprint
@pad_for_eccentric_footprints
def opening(image, footprint=None, out=None):
"""Return grayscale morphological opening of an image.
The morphological opening of an image is defined as an erosion followed by
a dilation. Opening can remove small bright spots (i.e. "salt") and connect
small dark cracks. This tends to "open" up (dark) gaps between (bright)
features.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as an array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
Returns
-------
opening : array, same shape and type as `image`
The result of the morphological opening.
Examples
--------
>>> # Open up gap between two bright regions (but also shrink regions)
>>> import numpy as np
>>> from skimage.morphology import square
>>> bad_connection = np.array([[1, 0, 0, 0, 1],
... [1, 1, 0, 1, 1],
... [1, 1, 1, 1, 1],
... [1, 1, 0, 1, 1],
... [1, 0, 0, 0, 1]], dtype=np.uint8)
>>> opening(bad_connection, square(3))
array([[0, 0, 0, 0, 0],
[1, 1, 0, 1, 1],
[1, 1, 0, 1, 1],
[1, 1, 0, 1, 1],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
eroded = erosion(image, footprint)
# note: shift_x, shift_y do nothing if footprint side length is odd
out = dilation(eroded, footprint, out=out, shift_x=True, shift_y=True)
return out
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
@default_footprint
@pad_for_eccentric_footprints
def closing(image, footprint=None, out=None):
"""Return grayscale morphological closing of an image.
The morphological closing of an image is defined as a dilation followed by
an erosion. Closing can remove small dark spots (i.e. "pepper") and connect
small bright cracks. This tends to "close" up (dark) gaps between (bright)
features.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as an array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarray, optional
The array to store the result of the morphology. If None,
a new array will be allocated.
Returns
-------
closing : array, same shape and type as `image`
The result of the morphological closing.
Examples
--------
>>> # Close a gap between two bright lines
>>> import numpy as np
>>> from skimage.morphology import square
>>> broken_line = np.array([[0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0],
... [1, 1, 0, 1, 1],
... [0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> closing(broken_line, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[1, 1, 1, 1, 1],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
dilated = dilation(image, footprint)
# note: shift_x, shift_y do nothing if footprint side length is odd
out = erosion(dilated, footprint, out=out, shift_x=True, shift_y=True)
return out
@default_footprint
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
def white_tophat(image, footprint=None, out=None):
"""Return white top hat of an image.
The white top hat of an image is defined as the image minus its
morphological opening. This operation returns the bright spots of the image
that are smaller than the footprint.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as an array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
Returns
-------
out : array, same shape and type as `image`
The result of the morphological white top hat.
See Also
--------
black_tophat
References
----------
.. [1] https://en.wikipedia.org/wiki/Top-hat_transform
Examples
--------
>>> # Subtract gray background from bright peak
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_on_gray = np.array([[2, 3, 3, 3, 2],
... [3, 4, 5, 4, 3],
... [3, 5, 9, 5, 3],
... [3, 4, 5, 4, 3],
... [2, 3, 3, 3, 2]], dtype=np.uint8)
>>> white_tophat(bright_on_gray, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 5, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
footprint = np.array(footprint)
if out is image:
opened = opening(image, footprint)
if np.issubdtype(opened.dtype, bool):
np.logical_xor(out, opened, out=out)
else:
out -= opened
return out
elif out is None:
out = np.empty_like(image)
# promote bool to a type that allows arithmetic operations
if isinstance(image, np.ndarray) and image.dtype == bool:
image_ = image.view(dtype=np.uint8)
else:
image_ = image
if isinstance(out, np.ndarray) and out.dtype == bool:
out_ = out.view(dtype=np.uint8)
else:
out_ = out
out_ = ndi.white_tophat(image_, footprint=footprint, output=out_)
return out
@default_footprint
@deprecate_kwarg(kwarg_mapping={'selem': 'footprint'}, removed_version="1.0",
deprecated_version="0.19")
def black_tophat(image, footprint=None, out=None):
"""Return black top hat of an image.
The black top hat of an image is defined as its morphological closing minus
the original image. This operation returns the dark spots of the image that
are smaller than the footprint. Note that dark spots in the
original image are bright spots after the black top hat.
Parameters
----------
image : ndarray
Image array.
footprint : ndarray, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use cross-shaped footprint (connectivity=1).
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
Returns
-------
out : array, same shape and type as `image`
The result of the morphological black top hat.
See Also
--------
white_tophat
References
----------
.. [1] https://en.wikipedia.org/wiki/Top-hat_transform
Examples
--------
>>> # Change dark peak to bright peak and subtract background
>>> import numpy as np
>>> from skimage.morphology import square
>>> dark_on_gray = np.array([[7, 6, 6, 6, 7],
... [6, 5, 4, 5, 6],
... [6, 4, 0, 4, 6],
... [6, 5, 4, 5, 6],
... [7, 6, 6, 6, 7]], dtype=np.uint8)
>>> black_tophat(dark_on_gray, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 5, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
"""
if out is image:
original = image.copy()
else:
original = image
out = closing(image, footprint, out=out)
if np.issubdtype(out.dtype, np.bool_):
np.logical_xor(out, original, out=out)
else:
out -= original
return out