mirror of
https://github.com/wassname/scikit-image.git
synced 2026-07-10 01:40:01 +08:00
Juan Nunez-Iglesias
406 lines
13 KiB
Python
406 lines
13 KiB
Python
"""
|
|
Grayscale morphological operations
|
|
"""
|
|
import numpy as np
|
|
from scipy import ndimage as nd
|
|
from .misc import default_selem
|
|
|
|
__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 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 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
|
|
`nd.grey_morphology` [1].
|
|
|
|
Parameters
|
|
----------
|
|
selem : array
|
|
The input structuring element.
|
|
|
|
Returns
|
|
-------
|
|
inverted : array
|
|
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
|
|
|
|
|
|
@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.filter.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)
|
|
nd.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
|
|
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.filter.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)
|
|
# invert the structuring element to patch the same thing happening inside
|
|
# ndimage.grey_dilation
|
|
# 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)
|
|
nd.grey_dilation(image, footprint=selem, output=out)
|
|
return out
|
|
|
|
|
|
@default_selem
|
|
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
|
|
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
|
|
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
|
|
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
|
|
The result of the morphological white top hat.
|
|
|
|
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)
|
|
out -= opened
|
|
return out
|
|
elif out is None:
|
|
out = np.empty_like(image)
|
|
out = nd.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
|
|
-------
|
|
opening : uint8 array
|
|
The result of the black top filter.
|
|
|
|
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)
|
|
out -= original
|
|
return out
|