490 lines
16 KiB
Python
490 lines
16 KiB
Python
"""
|
|
Grayscale morphological operations
|
|
"""
|
|
import functools
|
|
import numpy as np
|
|
from scipy import ndimage as ndi
|
|
from .misc import default_selem
|
|
from ..util import crop
|
|
|
|
__all__ = ['erosion', 'dilation', 'opening', 'closing', 'white_tophat',
|
|
'black_tophat']
|
|
|
|
|
|
def _shift_selem(selem, shift_x, shift_y):
|
|
"""Shift the binary image `selem` in the left and/or up.
|
|
|
|
This only affects 2D structuring elements with even number of rows
|
|
or columns.
|
|
|
|
Parameters
|
|
----------
|
|
selem : 2D array, shape (M, N)
|
|
The input structuring element.
|
|
shift_x, shift_y : bool
|
|
Whether to move `selem` along each axis.
|
|
|
|
Returns
|
|
-------
|
|
out : 2D array, shape (M + int(shift_x), N + int(shift_y))
|
|
The shifted structuring element.
|
|
"""
|
|
if selem.ndim != 2:
|
|
# do nothing for 1D or 3D or higher structuring elements
|
|
return selem
|
|
m, n = selem.shape
|
|
if m % 2 == 0:
|
|
extra_row = np.zeros((1, n), selem.dtype)
|
|
if shift_x:
|
|
selem = np.vstack((selem, extra_row))
|
|
else:
|
|
selem = np.vstack((extra_row, selem))
|
|
m += 1
|
|
if n % 2 == 0:
|
|
extra_col = np.zeros((m, 1), selem.dtype)
|
|
if shift_y:
|
|
selem = np.hstack((selem, extra_col))
|
|
else:
|
|
selem = np.hstack((extra_col, selem))
|
|
return selem
|
|
|
|
|
|
def _invert_selem(selem):
|
|
"""Change the order of the values in `selem`.
|
|
|
|
This is a patch for the *weird* footprint inversion in
|
|
`ndi.grey_morphology` [1]_.
|
|
|
|
Parameters
|
|
----------
|
|
selem : array
|
|
The input structuring element.
|
|
|
|
Returns
|
|
-------
|
|
inverted : array, same shape and type as `selem`
|
|
The structuring element, in opposite order.
|
|
|
|
Examples
|
|
--------
|
|
>>> selem = np.array([[0, 0, 0], [0, 1, 1], [0, 1, 1]], np.uint8)
|
|
>>> _invert_selem(selem)
|
|
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
|
|
"""
|
|
inverted = selem[(slice(None, None, -1),) * selem.ndim]
|
|
return inverted
|
|
|
|
|
|
def pad_for_eccentric_selems(func):
|
|
"""Pad input images for certain morphological operations.
|
|
|
|
Parameters
|
|
----------
|
|
func : callable
|
|
A morphological function, either opening or closing, that
|
|
supports eccentric structuring elements. Its parameters must
|
|
include at least `image`, `selem`, 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, selem, out=None, *args, **kwargs):
|
|
pad_widths = []
|
|
padding = False
|
|
if out is None:
|
|
out = np.empty_like(image)
|
|
for axis_len in selem.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, selem, out=out_temp, *args, **kwargs)
|
|
if padding:
|
|
out[:] = crop(out_temp, pad_widths)
|
|
else:
|
|
out = out_temp
|
|
return out
|
|
return func_out
|
|
|
|
@default_selem
|
|
def erosion(image, selem=None, out=None, shift_x=False, shift_y=False):
|
|
"""Return greyscale 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.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as an array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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 structuring element about center point. This only affects
|
|
eccentric structuring elements (i.e. selem 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 structuring elements.
|
|
|
|
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)
|
|
|
|
"""
|
|
selem = np.array(selem)
|
|
selem = _shift_selem(selem, shift_x, shift_y)
|
|
if out is None:
|
|
out = np.empty_like(image)
|
|
ndi.grey_erosion(image, footprint=selem, output=out)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
def dilation(image, selem=None, out=None, shift_x=False, shift_y=False):
|
|
"""Return greyscale morphological dilation of an image.
|
|
|
|
Morphological dilation sets a pixel at (i,j) to the maximum over all pixels
|
|
in the neighborhood centered at (i,j). Dilation enlarges bright regions
|
|
and shrinks dark regions.
|
|
|
|
Parameters
|
|
----------
|
|
|
|
image : ndarray
|
|
Image array.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as a 2-D array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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 structuring element about center point. This only affects
|
|
eccentric structuring elements (i.e. selem 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 structuring elements.
|
|
|
|
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)
|
|
|
|
"""
|
|
selem = np.array(selem)
|
|
selem = _shift_selem(selem, shift_x, shift_y)
|
|
# Inside ndimage.grey_dilation, the structuring element is inverted,
|
|
# eg. `selem = selem[::-1, ::-1]` for 2D [1]_, for reasons unknown to
|
|
# this author (@jni). To "patch" this behaviour, we invert our own
|
|
# selem before passing it to `ndi.grey_dilation`.
|
|
# [1] https://github.com/scipy/scipy/blob/ec20ababa400e39ac3ffc9148c01ef86d5349332/scipy/ndimage/morphology.py#L1285
|
|
selem = _invert_selem(selem)
|
|
if out is None:
|
|
out = np.empty_like(image)
|
|
ndi.grey_dilation(image, footprint=selem, output=out)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
@pad_for_eccentric_selems
|
|
def opening(image, selem=None, out=None):
|
|
"""Return greyscale morphological opening of an image.
|
|
|
|
The morphological opening on 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.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as an array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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, selem)
|
|
# note: shift_x, shift_y do nothing if selem side length is odd
|
|
out = dilation(eroded, selem, out=out, shift_x=True, shift_y=True)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
@pad_for_eccentric_selems
|
|
def closing(image, selem=None, out=None):
|
|
"""Return greyscale morphological closing of an image.
|
|
|
|
The morphological closing on 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.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as an array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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
|
|
-------
|
|
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, selem)
|
|
# note: shift_x, shift_y do nothing if selem side length is odd
|
|
out = erosion(dilated, selem, out=out, shift_x=True, shift_y=True)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
def white_tophat(image, selem=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 structuring element.
|
|
|
|
Parameters
|
|
----------
|
|
image : ndarray
|
|
Image array.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as an array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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 grey background from bright peak
|
|
>>> import numpy as np
|
|
>>> from skimage.morphology import square
|
|
>>> bright_on_grey = 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_grey, 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)
|
|
|
|
"""
|
|
selem = np.array(selem)
|
|
if out is image:
|
|
opened = opening(image, selem)
|
|
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)
|
|
# work-around for NumPy deprecation warning for arithmetic
|
|
# operations on bool arrays
|
|
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=selem, output=out_)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
def black_tophat(image, selem=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 structuring element. Note that dark spots in the
|
|
original image are bright spots after the black top hat.
|
|
|
|
Parameters
|
|
----------
|
|
image : ndarray
|
|
Image array.
|
|
selem : ndarray, optional
|
|
The neighborhood expressed as a 2-D array of 1's and 0's.
|
|
If None, use cross-shaped structuring element (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_grey = 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_grey, 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, selem, out=out)
|
|
if np.issubdtype(out.dtype, np.bool_):
|
|
np.logical_xor(out, original, out=out)
|
|
else:
|
|
out -= original
|
|
return out
|