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Grayscale morphological operations
"""
import numpy as np
from scipy import ndimage as ndi
from .footprints import _footprint_is_sequence, mirror_footprint, pad_footprint
from .misc import default_footprint
__all__ = ['erosion', 'dilation', 'opening', 'closing', 'white_tophat', 'black_tophat']
def _iterate_gray_func(gray_func, image, footprints, out, mode, cval):
"""Helper to call `gray_func` for each footprint in a sequence.
`gray_func` is a morphology function that accepts `footprint`, `output`,
`mode` and `cval` keyword arguments (e.g. `scipy.ndimage.grey_erosion`).
"""
fp, num_iter = footprints[0]
gray_func(image, footprint=fp, output=out, mode=mode, cval=cval)
for _ in range(1, num_iter):
gray_func(out.copy(), footprint=fp, output=out, mode=mode, cval=cval)
for fp, num_iter in footprints[1:]:
# Note: out.copy() because the computation cannot be in-place!
for _ in range(num_iter):
gray_func(out.copy(), footprint=fp, output=out, mode=mode, cval=cval)
return out
def _min_max_to_constant_mode(dtype, mode, cval):
"""Replace 'max' and 'min' with appropriate 'cval' and 'constant' mode."""
if mode == "max":
mode = "constant"
if np.issubdtype(dtype, bool):
cval = True
elif np.issubdtype(dtype, np.integer):
cval = np.iinfo(dtype).max
else:
cval = np.inf
elif mode == "min":
mode = "constant"
if np.issubdtype(dtype, bool):
cval = False
elif np.issubdtype(dtype, np.integer):
cval = np.iinfo(dtype).min
else:
cval = -np.inf
return mode, cval
_SUPPORTED_MODES = {
"reflect",
"constant",
"nearest",
"mirror",
"wrap",
"max",
"min",
"ignore",
}
@default_footprint
def erosion(
image,
footprint=None,
out=None,
*,
mode="reflect",
cval=0.0,
):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarrays, optional
The array to store the result of the morphology. If None is
passed, a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'.
If 'max' or 'ignore', pixels outside the image domain are assumed
to be the maximum for the image's dtype, which causes them to not
influence the result. Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
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 :func:`skimage.filters.rank.minimum`
function more efficient for larger images and footprints.
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
For even-sized footprints, :func:`skimage.morphology.binary_erosion` and
this function produce an output that differs: one is shifted by one pixel
compared to the other. :func:`skimage.morphology.pad_footprint` is available
to account for this.
Examples
--------
>>> # Erosion shrinks bright regions
>>> import numpy as np
>>> from skimage.morphology import footprint_rectangle
>>> 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, footprint_rectangle((3, 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)
"""
if out is None:
out = np.empty_like(image)
if mode not in _SUPPORTED_MODES:
raise ValueError(f"unsupported mode, got {mode!r}")
if mode == "ignore":
mode = "max"
mode, cval = _min_max_to_constant_mode(image.dtype, mode, cval)
footprint = pad_footprint(footprint, pad_end=False)
if not _footprint_is_sequence(footprint):
footprint = [(footprint, 1)]
out = _iterate_gray_func(
gray_func=ndi.grey_erosion,
image=image,
footprints=footprint,
out=out,
mode=mode,
cval=cval,
)
return out
@default_footprint
def dilation(
image,
footprint=None,
out=None,
*,
mode="reflect",
cval=0.0,
):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarray, optional
The array to store the result of the morphology. If None is
passed, a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'.
If 'min' or 'ignore', pixels outside the image domain are assumed
to be the maximum for the image's dtype, which causes them to not
influence the result. Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
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 :func:`skimage.filters.rank.maximum`
function more efficient for larger images and footprints.
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
For non-symmetric footprints, :func:`skimage.morphology.binary_dilation`
and :func:`skimage.morphology.dilation` produce an output that differs:
`binary_dilation` mirrors the footprint, whereas `dilation` does not.
:func:`skimage.morphology.mirror_footprint` is available to correct for this.
Examples
--------
>>> # Dilation enlarges bright regions
>>> import numpy as np
>>> from skimage.morphology import footprint_rectangle
>>> 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, footprint_rectangle((3, 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)
"""
if out is None:
out = np.empty_like(image)
if mode not in _SUPPORTED_MODES:
raise ValueError(f"unsupported mode, got {mode!r}")
if mode == "ignore":
mode = "min"
mode, cval = _min_max_to_constant_mode(image.dtype, mode, cval)
footprint = pad_footprint(footprint, pad_end=False)
# Note that `ndi.grey_dilation` mirrors the footprint and this
# additional inversion should be removed in skimage2, see gh-6676.
footprint = mirror_footprint(footprint)
if not _footprint_is_sequence(footprint):
footprint = [(footprint, 1)]
out = _iterate_gray_func(
gray_func=ndi.grey_dilation,
image=image,
footprints=footprint,
out=out,
mode=mode,
cval=cval,
)
return out
@default_footprint
def opening(image, footprint=None, out=None, *, mode="reflect", cval=0.0):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'.
If 'ignore', pixels outside the image domain are assumed
to be the maximum for the image's dtype in the erosion, and minimum
in the dilation, which causes them to not influence the result.
Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
Returns
-------
opening : array, same shape and type as `image`
The result of the morphological opening.
Notes
-----
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
Examples
--------
>>> # Open up gap between two bright regions (but also shrink regions)
>>> import numpy as np
>>> from skimage.morphology import footprint_rectangle
>>> 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, footprint_rectangle((3, 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)
"""
footprint = pad_footprint(footprint, pad_end=False)
eroded = erosion(image, footprint, mode=mode, cval=cval)
out = dilation(eroded, mirror_footprint(footprint), out=out, mode=mode, cval=cval)
return out
@default_footprint
def closing(image, footprint=None, out=None, *, mode="reflect", cval=0.0):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarray, optional
The array to store the result of the morphology. If None,
a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'.
If 'ignore', pixels outside the image domain are assumed
to be the maximum for the image's dtype in the erosion, and minimum
in the dilation, which causes them to not influence the result.
Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
Returns
-------
closing : array, same shape and type as `image`
The result of the morphological closing.
Notes
-----
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
Examples
--------
>>> # Close a gap between two bright lines
>>> import numpy as np
>>> from skimage.morphology import footprint_rectangle
>>> 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, footprint_rectangle((3, 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)
"""
footprint = pad_footprint(footprint, pad_end=False)
dilated = dilation(image, footprint, mode=mode, cval=cval)
out = erosion(dilated, mirror_footprint(footprint), out=out, mode=mode, cval=cval)
return out
@default_footprint
def white_tophat(image, footprint=None, out=None, *, mode="reflect", cval=0.0):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'. See :func:`skimage.morphology.opening`.
Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
Returns
-------
out : array, same shape and type as `image`
The result of the morphological white top hat.
Notes
-----
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
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 footprint_rectangle
>>> 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, footprint_rectangle((3, 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:
# We need a temporary image
opened = opening(image, footprint, mode=mode, cval=cval)
if np.issubdtype(opened.dtype, bool):
np.logical_xor(out, opened, out=out)
else:
out -= opened
return out
# Else write intermediate result into output image
out = opening(image, footprint, out=out, mode=mode, cval=cval)
if np.issubdtype(out.dtype, bool):
np.logical_xor(image, out, out=out)
else:
np.subtract(image, out, out=out)
return out
@default_footprint
def black_tophat(image, footprint=None, out=None, *, mode="reflect", cval=0.0):
"""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 or tuple, optional
The neighborhood expressed as a 2-D array of 1's and 0's.
If None, use a cross-shaped footprint (connectivity=1). The footprint
can also be provided as a sequence of smaller footprints as described
in the notes below.
out : ndarray, optional
The array to store the result of the morphology. If None
is passed, a new array will be allocated.
mode : str, optional
The `mode` parameter determines how the array borders are handled.
Valid modes are: 'reflect', 'constant', 'nearest', 'mirror', 'wrap',
'max', 'min', or 'ignore'. See :func:`skimage.morphology.closing`.
Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
.. versionadded:: 0.23
`mode` and `cval` were added in 0.23.
Returns
-------
out : array, same shape and type as `image`
The result of the morphological black top hat.
Notes
-----
The footprint can also be a provided as a sequence of 2-tuples where the
first element of each 2-tuple is a footprint ndarray and the second element
is an integer describing the number of times it should be iterated. For
example ``footprint=[(np.ones((9, 1)), 1), (np.ones((1, 9)), 1)]``
would apply a 9x1 footprint followed by a 1x9 footprint resulting in a net
effect that is the same as ``footprint=np.ones((9, 9))``, but with lower
computational cost. Most of the builtin footprints such as
:func:`skimage.morphology.disk` provide an option to automatically generate
a footprint sequence of this type.
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 footprint_rectangle
>>> 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, footprint_rectangle((3, 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:
# We need a temporary image
closed = closing(image, footprint, mode=mode, cval=cval)
if np.issubdtype(closed.dtype, bool):
np.logical_xor(closed, out, out=out)
else:
np.subtract(closed, out, out=out)
return out
out = closing(image, footprint, out=out, mode=mode, cval=cval)
if np.issubdtype(out.dtype, np.bool_):
np.logical_xor(out, image, out=out)
else:
out -= image
return out
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