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 # Copyright (C) 2003-2005 Peter J. Verveer
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
#
# 3. The name of the author may not be used to endorse or promote
# products derived from this software without specific prior
# written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import warnings
import operator
import numpy
from . import _ni_support
from . import _nd_image
from . import _filters
__all__ = ['iterate_structure', 'generate_binary_structure', 'binary_erosion',
'binary_dilation', 'binary_opening', 'binary_closing',
'binary_hit_or_miss', 'binary_propagation', 'binary_fill_holes',
'grey_erosion', 'grey_dilation', 'grey_opening', 'grey_closing',
'morphological_gradient', 'morphological_laplace', 'white_tophat',
'black_tophat', 'distance_transform_bf', 'distance_transform_cdt',
'distance_transform_edt']
def _center_is_true(structure, origin):
structure = numpy.array(structure)
coor = tuple([oo + ss // 2 for ss, oo in zip(structure.shape,
origin)])
return bool(structure[coor])
def iterate_structure(structure, iterations, origin=None):
"""
Iterate a structure by dilating it with itself.
Parameters
----------
structure : array_like
Structuring element (an array of bools, for example), to be dilated with
itself.
iterations : int
number of dilations performed on the structure with itself
origin : optional
If origin is None, only the iterated structure is returned. If
not, a tuple of the iterated structure and the modified origin is
returned.
Returns
-------
iterate_structure : ndarray of bools
A new structuring element obtained by dilating `structure`
(`iterations` - 1) times with itself.
See Also
--------
generate_binary_structure
Examples
--------
>>> from scipy import ndimage
>>> struct = ndimage.generate_binary_structure(2, 1)
>>> struct.astype(int)
array([[0, 1, 0],
[1, 1, 1],
[0, 1, 0]])
>>> ndimage.iterate_structure(struct, 2).astype(int)
array([[0, 0, 1, 0, 0],
[0, 1, 1, 1, 0],
[1, 1, 1, 1, 1],
[0, 1, 1, 1, 0],
[0, 0, 1, 0, 0]])
>>> ndimage.iterate_structure(struct, 3).astype(int)
array([[0, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[1, 1, 1, 1, 1, 1, 1],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 1, 0, 0, 0]])
"""
structure = numpy.asarray(structure)
if iterations < 2:
return structure.copy()
ni = iterations - 1
shape = [ii + ni * (ii - 1) for ii in structure.shape]
pos = [ni * (structure.shape[ii] // 2) for ii in range(len(shape))]
slc = tuple(slice(pos[ii], pos[ii] + structure.shape[ii], None)
for ii in range(len(shape)))
out = numpy.zeros(shape, bool)
out[slc] = structure != 0
out = binary_dilation(out, structure, iterations=ni)
if origin is None:
return out
else:
origin = _ni_support._normalize_sequence(origin, structure.ndim)
origin = [iterations * o for o in origin]
return out, origin
def generate_binary_structure(rank, connectivity):
"""
Generate a binary structure for binary morphological operations.
Parameters
----------
rank : int
Number of dimensions of the array to which the structuring element
will be applied, as returned by `np.ndim`.
connectivity : int
`connectivity` determines which elements of the output array belong
to the structure, i.e., are considered as neighbors of the central
element. Elements up to a squared distance of `connectivity` from
the center are considered neighbors. `connectivity` may range from 1
(no diagonal elements are neighbors) to `rank` (all elements are
neighbors).
Returns
-------
output : ndarray of bools
Structuring element which may be used for binary morphological
operations, with `rank` dimensions and all dimensions equal to 3.
See Also
--------
iterate_structure, binary_dilation, binary_erosion
Notes
-----
`generate_binary_structure` can only create structuring elements with
dimensions equal to 3, i.e., minimal dimensions. For larger structuring
elements, that are useful e.g., for eroding large objects, one may either
use `iterate_structure`, or create directly custom arrays with
numpy functions such as `numpy.ones`.
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> struct = ndimage.generate_binary_structure(2, 1)
>>> struct
array([[False, True, False],
[ True, True, True],
[False, True, False]], dtype=bool)
>>> a = np.zeros((5,5))
>>> a[2, 2] = 1
>>> a
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.]])
>>> b = ndimage.binary_dilation(a, structure=struct).astype(a.dtype)
>>> b
array([[ 0., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 0., 0.]])
>>> ndimage.binary_dilation(b, structure=struct).astype(a.dtype)
array([[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 1., 1., 1., 1., 1.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.]])
>>> struct = ndimage.generate_binary_structure(2, 2)
>>> struct
array([[ True, True, True],
[ True, True, True],
[ True, True, True]], dtype=bool)
>>> struct = ndimage.generate_binary_structure(3, 1)
>>> struct # no diagonal elements
array([[[False, False, False],
[False, True, False],
[False, False, False]],
[[False, True, False],
[ True, True, True],
[False, True, False]],
[[False, False, False],
[False, True, False],
[False, False, False]]], dtype=bool)
"""
if connectivity < 1:
connectivity = 1
if rank < 1:
return numpy.array(True, dtype=bool)
output = numpy.fabs(numpy.indices([3] * rank) - 1)
output = numpy.add.reduce(output, 0)
return output <= connectivity
def _binary_erosion(input, structure, iterations, mask, output,
border_value, origin, invert, brute_force):
try:
iterations = operator.index(iterations)
except TypeError as e:
raise TypeError('iterations parameter should be an integer') from e
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if structure is None:
structure = generate_binary_structure(input.ndim, 1)
else:
structure = numpy.asarray(structure, dtype=bool)
if structure.ndim != input.ndim:
raise RuntimeError('structure and input must have same dimensionality')
if not structure.flags.contiguous:
structure = structure.copy()
if numpy.prod(structure.shape, axis=0) < 1:
raise RuntimeError('structure must not be empty')
if mask is not None:
mask = numpy.asarray(mask)
if mask.shape != input.shape:
raise RuntimeError('mask and input must have equal sizes')
origin = _ni_support._normalize_sequence(origin, input.ndim)
cit = _center_is_true(structure, origin)
if isinstance(output, numpy.ndarray):
if numpy.iscomplexobj(output):
raise TypeError('Complex output type not supported')
else:
output = bool
output = _ni_support._get_output(output, input)
temp_needed = numpy.may_share_memory(input, output)
if temp_needed:
# input and output arrays cannot share memory
temp = output
output = _ni_support._get_output(output.dtype, input)
if iterations == 1:
_nd_image.binary_erosion(input, structure, mask, output,
border_value, origin, invert, cit, 0)
elif cit and not brute_force:
changed, coordinate_list = _nd_image.binary_erosion(
input, structure, mask, output,
border_value, origin, invert, cit, 1)
structure = structure[tuple([slice(None, None, -1)] *
structure.ndim)]
for ii in range(len(origin)):
origin[ii] = -origin[ii]
if not structure.shape[ii] & 1:
origin[ii] -= 1
if mask is not None:
mask = numpy.asarray(mask, dtype=numpy.int8)
if not structure.flags.contiguous:
structure = structure.copy()
_nd_image.binary_erosion2(output, structure, mask, iterations - 1,
origin, invert, coordinate_list)
else:
tmp_in = numpy.empty_like(input, dtype=bool)
tmp_out = output
if iterations >= 1 and not iterations & 1:
tmp_in, tmp_out = tmp_out, tmp_in
changed = _nd_image.binary_erosion(
input, structure, mask, tmp_out,
border_value, origin, invert, cit, 0)
ii = 1
while ii < iterations or (iterations < 1 and changed):
tmp_in, tmp_out = tmp_out, tmp_in
changed = _nd_image.binary_erosion(
tmp_in, structure, mask, tmp_out,
border_value, origin, invert, cit, 0)
ii += 1
if temp_needed:
temp[...] = output
output = temp
return output
def binary_erosion(input, structure=None, iterations=1, mask=None, output=None,
border_value=0, origin=0, brute_force=False):
"""
Multidimensional binary erosion with a given structuring element.
Binary erosion is a mathematical morphology operation used for image
processing.
Parameters
----------
input : array_like
Binary image to be eroded. Non-zero (True) elements form
the subset to be eroded.
structure : array_like, optional
Structuring element used for the erosion. Non-zero elements are
considered True. If no structuring element is provided, an element
is generated with a square connectivity equal to one.
iterations : int, optional
The erosion is repeated `iterations` times (one, by default).
If iterations is less than 1, the erosion is repeated until the
result does not change anymore.
mask : array_like, optional
If a mask is given, only those elements with a True value at
the corresponding mask element are modified at each iteration.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
border_value : int (cast to 0 or 1), optional
Value at the border in the output array.
origin : int or tuple of ints, optional
Placement of the filter, by default 0.
brute_force : boolean, optional
Memory condition: if False, only the pixels whose value was changed in
the last iteration are tracked as candidates to be updated (eroded) in
the current iteration; if True all pixels are considered as candidates
for erosion, regardless of what happened in the previous iteration.
False by default.
Returns
-------
binary_erosion : ndarray of bools
Erosion of the input by the structuring element.
See Also
--------
grey_erosion, binary_dilation, binary_closing, binary_opening,
generate_binary_structure
Notes
-----
Erosion [1]_ is a mathematical morphology operation [2]_ that uses a
structuring element for shrinking the shapes in an image. The binary
erosion of an image by a structuring element is the locus of the points
where a superimposition of the structuring element centered on the point
is entirely contained in the set of non-zero elements of the image.
References
----------
.. [1] https://en.wikipedia.org/wiki/Erosion_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[1:6, 2:5] = 1
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.binary_erosion(a).astype(a.dtype)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> #Erosion removes objects smaller than the structure
>>> ndimage.binary_erosion(a, structure=np.ones((5,5))).astype(a.dtype)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
"""
return _binary_erosion(input, structure, iterations, mask,
output, border_value, origin, 0, brute_force)
def binary_dilation(input, structure=None, iterations=1, mask=None,
output=None, border_value=0, origin=0,
brute_force=False):
"""
Multidimensional binary dilation with the given structuring element.
Parameters
----------
input : array_like
Binary array_like to be dilated. Non-zero (True) elements form
the subset to be dilated.
structure : array_like, optional
Structuring element used for the dilation. Non-zero elements are
considered True. If no structuring element is provided an element
is generated with a square connectivity equal to one.
iterations : int, optional
The dilation is repeated `iterations` times (one, by default).
If iterations is less than 1, the dilation is repeated until the
result does not change anymore. Only an integer of iterations is
accepted.
mask : array_like, optional
If a mask is given, only those elements with a True value at
the corresponding mask element are modified at each iteration.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
border_value : int (cast to 0 or 1), optional
Value at the border in the output array.
origin : int or tuple of ints, optional
Placement of the filter, by default 0.
brute_force : boolean, optional
Memory condition: if False, only the pixels whose value was changed in
the last iteration are tracked as candidates to be updated (dilated)
in the current iteration; if True all pixels are considered as
candidates for dilation, regardless of what happened in the previous
iteration. False by default.
Returns
-------
binary_dilation : ndarray of bools
Dilation of the input by the structuring element.
See Also
--------
grey_dilation, binary_erosion, binary_closing, binary_opening,
generate_binary_structure
Notes
-----
Dilation [1]_ is a mathematical morphology operation [2]_ that uses a
structuring element for expanding the shapes in an image. The binary
dilation of an image by a structuring element is the locus of the points
covered by the structuring element, when its center lies within the
non-zero points of the image.
References
----------
.. [1] https://en.wikipedia.org/wiki/Dilation_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((5, 5))
>>> a[2, 2] = 1
>>> a
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.]])
>>> ndimage.binary_dilation(a)
array([[False, False, False, False, False],
[False, False, True, False, False],
[False, True, True, True, False],
[False, False, True, False, False],
[False, False, False, False, False]], dtype=bool)
>>> ndimage.binary_dilation(a).astype(a.dtype)
array([[ 0., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 0., 0.]])
>>> # 3x3 structuring element with connectivity 1, used by default
>>> struct1 = ndimage.generate_binary_structure(2, 1)
>>> struct1
array([[False, True, False],
[ True, True, True],
[False, True, False]], dtype=bool)
>>> # 3x3 structuring element with connectivity 2
>>> struct2 = ndimage.generate_binary_structure(2, 2)
>>> struct2
array([[ True, True, True],
[ True, True, True],
[ True, True, True]], dtype=bool)
>>> ndimage.binary_dilation(a, structure=struct1).astype(a.dtype)
array([[ 0., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 0., 0.]])
>>> ndimage.binary_dilation(a, structure=struct2).astype(a.dtype)
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.]])
>>> ndimage.binary_dilation(a, structure=struct1,\\
... iterations=2).astype(a.dtype)
array([[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 1., 1., 1., 1., 1.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.]])
"""
input = numpy.asarray(input)
if structure is None:
structure = generate_binary_structure(input.ndim, 1)
origin = _ni_support._normalize_sequence(origin, input.ndim)
structure = numpy.asarray(structure)
structure = structure[tuple([slice(None, None, -1)] *
structure.ndim)]
for ii in range(len(origin)):
origin[ii] = -origin[ii]
if not structure.shape[ii] & 1:
origin[ii] -= 1
return _binary_erosion(input, structure, iterations, mask,
output, border_value, origin, 1, brute_force)
def binary_opening(input, structure=None, iterations=1, output=None,
origin=0, mask=None, border_value=0, brute_force=False):
"""
Multidimensional binary opening with the given structuring element.
The *opening* of an input image by a structuring element is the
*dilation* of the *erosion* of the image by the structuring element.
Parameters
----------
input : array_like
Binary array_like to be opened. Non-zero (True) elements form
the subset to be opened.
structure : array_like, optional
Structuring element used for the opening. Non-zero elements are
considered True. If no structuring element is provided an element
is generated with a square connectivity equal to one (i.e., only
nearest neighbors are connected to the center, diagonally-connected
elements are not considered neighbors).
iterations : int, optional
The erosion step of the opening, then the dilation step are each
repeated `iterations` times (one, by default). If `iterations` is
less than 1, each operation is repeated until the result does
not change anymore. Only an integer of iterations is accepted.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
origin : int or tuple of ints, optional
Placement of the filter, by default 0.
mask : array_like, optional
If a mask is given, only those elements with a True value at
the corresponding mask element are modified at each iteration.
.. versionadded:: 1.1.0
border_value : int (cast to 0 or 1), optional
Value at the border in the output array.
.. versionadded:: 1.1.0
brute_force : boolean, optional
Memory condition: if False, only the pixels whose value was changed in
the last iteration are tracked as candidates to be updated in the
current iteration; if true all pixels are considered as candidates for
update, regardless of what happened in the previous iteration.
False by default.
.. versionadded:: 1.1.0
Returns
-------
binary_opening : ndarray of bools
Opening of the input by the structuring element.
See Also
--------
grey_opening, binary_closing, binary_erosion, binary_dilation,
generate_binary_structure
Notes
-----
*Opening* [1]_ is a mathematical morphology operation [2]_ that
consists in the succession of an erosion and a dilation of the
input with the same structuring element. Opening, therefore, removes
objects smaller than the structuring element.
Together with *closing* (`binary_closing`), opening can be used for
noise removal.
References
----------
.. [1] https://en.wikipedia.org/wiki/Opening_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((5,5), dtype=int)
>>> a[1:4, 1:4] = 1; a[4, 4] = 1
>>> a
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, 1]])
>>> # Opening removes small objects
>>> ndimage.binary_opening(a, structure=np.ones((3,3))).astype(int)
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]])
>>> # Opening can also smooth corners
>>> ndimage.binary_opening(a).astype(int)
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 1, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]])
>>> # Opening is the dilation of the erosion of the input
>>> ndimage.binary_erosion(a).astype(int)
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]])
>>> ndimage.binary_dilation(ndimage.binary_erosion(a)).astype(int)
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 1, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]])
"""
input = numpy.asarray(input)
if structure is None:
rank = input.ndim
structure = generate_binary_structure(rank, 1)
tmp = binary_erosion(input, structure, iterations, mask, None,
border_value, origin, brute_force)
return binary_dilation(tmp, structure, iterations, mask, output,
border_value, origin, brute_force)
def binary_closing(input, structure=None, iterations=1, output=None,
origin=0, mask=None, border_value=0, brute_force=False):
"""
Multidimensional binary closing with the given structuring element.
The *closing* of an input image by a structuring element is the
*erosion* of the *dilation* of the image by the structuring element.
Parameters
----------
input : array_like
Binary array_like to be closed. Non-zero (True) elements form
the subset to be closed.
structure : array_like, optional
Structuring element used for the closing. Non-zero elements are
considered True. If no structuring element is provided an element
is generated with a square connectivity equal to one (i.e., only
nearest neighbors are connected to the center, diagonally-connected
elements are not considered neighbors).
iterations : int, optional
The dilation step of the closing, then the erosion step are each
repeated `iterations` times (one, by default). If iterations is
less than 1, each operations is repeated until the result does
not change anymore. Only an integer of iterations is accepted.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
origin : int or tuple of ints, optional
Placement of the filter, by default 0.
mask : array_like, optional
If a mask is given, only those elements with a True value at
the corresponding mask element are modified at each iteration.
.. versionadded:: 1.1.0
border_value : int (cast to 0 or 1), optional
Value at the border in the output array.
.. versionadded:: 1.1.0
brute_force : boolean, optional
Memory condition: if False, only the pixels whose value was changed in
the last iteration are tracked as candidates to be updated in the
current iteration; if true al pixels are considered as candidates for
update, regardless of what happened in the previous iteration.
False by default.
.. versionadded:: 1.1.0
Returns
-------
binary_closing : ndarray of bools
Closing of the input by the structuring element.
See Also
--------
grey_closing, binary_opening, binary_dilation, binary_erosion,
generate_binary_structure
Notes
-----
*Closing* [1]_ is a mathematical morphology operation [2]_ that
consists in the succession of a dilation and an erosion of the
input with the same structuring element. Closing therefore fills
holes smaller than the structuring element.
Together with *opening* (`binary_opening`), closing can be used for
noise removal.
References
----------
.. [1] https://en.wikipedia.org/wiki/Closing_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((5,5), dtype=int)
>>> a[1:-1, 1:-1] = 1; a[2,2] = 0
>>> a
array([[0, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 0, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]])
>>> # Closing removes small holes
>>> ndimage.binary_closing(a).astype(int)
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]])
>>> # Closing is the erosion of the dilation of the input
>>> ndimage.binary_dilation(a).astype(int)
array([[0, 1, 1, 1, 0],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 1, 1, 1, 1],
[0, 1, 1, 1, 0]])
>>> ndimage.binary_erosion(ndimage.binary_dilation(a)).astype(int)
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]])
>>> a = np.zeros((7,7), dtype=int)
>>> a[1:6, 2:5] = 1; a[1:3,3] = 0
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 1, 0, 0],
[0, 0, 1, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> # In addition to removing holes, closing can also
>>> # coarsen boundaries with fine hollows.
>>> ndimage.binary_closing(a).astype(int)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.binary_closing(a, structure=np.ones((2,2))).astype(int)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
"""
input = numpy.asarray(input)
if structure is None:
rank = input.ndim
structure = generate_binary_structure(rank, 1)
tmp = binary_dilation(input, structure, iterations, mask, None,
border_value, origin, brute_force)
return binary_erosion(tmp, structure, iterations, mask, output,
border_value, origin, brute_force)
def binary_hit_or_miss(input, structure1=None, structure2=None,
output=None, origin1=0, origin2=None):
"""
Multidimensional binary hit-or-miss transform.
The hit-or-miss transform finds the locations of a given pattern
inside the input image.
Parameters
----------
input : array_like (cast to booleans)
Binary image where a pattern is to be detected.
structure1 : array_like (cast to booleans), optional
Part of the structuring element to be fitted to the foreground
(non-zero elements) of `input`. If no value is provided, a
structure of square connectivity 1 is chosen.
structure2 : array_like (cast to booleans), optional
Second part of the structuring element that has to miss completely
the foreground. If no value is provided, the complementary of
`structure1` is taken.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
origin1 : int or tuple of ints, optional
Placement of the first part of the structuring element `structure1`,
by default 0 for a centered structure.
origin2 : int or tuple of ints, optional
Placement of the second part of the structuring element `structure2`,
by default 0 for a centered structure. If a value is provided for
`origin1` and not for `origin2`, then `origin2` is set to `origin1`.
Returns
-------
binary_hit_or_miss : ndarray
Hit-or-miss transform of `input` with the given structuring
element (`structure1`, `structure2`).
See Also
--------
binary_erosion
References
----------
.. [1] https://en.wikipedia.org/wiki/Hit-or-miss_transform
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[1, 1] = 1; a[2:4, 2:4] = 1; a[4:6, 4:6] = 1
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 0, 0, 0],
[0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> structure1 = np.array([[1, 0, 0], [0, 1, 1], [0, 1, 1]])
>>> structure1
array([[1, 0, 0],
[0, 1, 1],
[0, 1, 1]])
>>> # Find the matches of structure1 in the array a
>>> ndimage.binary_hit_or_miss(a, structure1=structure1).astype(int)
array([[0, 0, 0, 0, 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, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> # Change the origin of the filter
>>> # origin1=1 is equivalent to origin1=(1,1) here
>>> ndimage.binary_hit_or_miss(a, structure1=structure1,\\
... origin1=1).astype(int)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 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, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0]])
"""
input = numpy.asarray(input)
if structure1 is None:
structure1 = generate_binary_structure(input.ndim, 1)
if structure2 is None:
structure2 = numpy.logical_not(structure1)
origin1 = _ni_support._normalize_sequence(origin1, input.ndim)
if origin2 is None:
origin2 = origin1
else:
origin2 = _ni_support._normalize_sequence(origin2, input.ndim)
tmp1 = _binary_erosion(input, structure1, 1, None, None, 0, origin1,
0, False)
inplace = isinstance(output, numpy.ndarray)
result = _binary_erosion(input, structure2, 1, None, output, 0,
origin2, 1, False)
if inplace:
numpy.logical_not(output, output)
numpy.logical_and(tmp1, output, output)
else:
numpy.logical_not(result, result)
return numpy.logical_and(tmp1, result)
def binary_propagation(input, structure=None, mask=None,
output=None, border_value=0, origin=0):
"""
Multidimensional binary propagation with the given structuring element.
Parameters
----------
input : array_like
Binary image to be propagated inside `mask`.
structure : array_like, optional
Structuring element used in the successive dilations. The output
may depend on the structuring element, especially if `mask` has
several connex components. If no structuring element is
provided, an element is generated with a squared connectivity equal
to one.
mask : array_like, optional
Binary mask defining the region into which `input` is allowed to
propagate.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
border_value : int (cast to 0 or 1), optional
Value at the border in the output array.
origin : int or tuple of ints, optional
Placement of the filter, by default 0.
Returns
-------
binary_propagation : ndarray
Binary propagation of `input` inside `mask`.
Notes
-----
This function is functionally equivalent to calling binary_dilation
with the number of iterations less than one: iterative dilation until
the result does not change anymore.
The succession of an erosion and propagation inside the original image
can be used instead of an *opening* for deleting small objects while
keeping the contours of larger objects untouched.
References
----------
.. [1] http://cmm.ensmp.fr/~serra/cours/pdf/en/ch6en.pdf, slide 15.
.. [2] I.T. Young, J.J. Gerbrands, and L.J. van Vliet, "Fundamentals of
image processing", 1998
ftp://qiftp.tudelft.nl/DIPimage/docs/FIP2.3.pdf
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> input = np.zeros((8, 8), dtype=int)
>>> input[2, 2] = 1
>>> mask = np.zeros((8, 8), dtype=int)
>>> mask[1:4, 1:4] = mask[4, 4] = mask[6:8, 6:8] = 1
>>> input
array([[0, 0, 0, 0, 0, 0, 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, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0]])
>>> mask
array([[0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 1],
[0, 0, 0, 0, 0, 0, 1, 1]])
>>> ndimage.binary_propagation(input, mask=mask).astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.binary_propagation(input, mask=mask,\\
... structure=np.ones((3,3))).astype(int)
array([[0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0]])
>>> # Comparison between opening and erosion+propagation
>>> a = np.zeros((6,6), dtype=int)
>>> a[2:5, 2:5] = 1; a[0, 0] = 1; a[5, 5] = 1
>>> a
array([[1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1]])
>>> ndimage.binary_opening(a).astype(int)
array([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0]])
>>> b = ndimage.binary_erosion(a)
>>> b.astype(int)
array([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 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, 0, 0]])
>>> ndimage.binary_propagation(b, mask=a).astype(int)
array([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0]])
"""
return binary_dilation(input, structure, -1, mask, output,
border_value, origin)
def binary_fill_holes(input, structure=None, output=None, origin=0):
"""
Fill the holes in binary objects.
Parameters
----------
input : array_like
N-D binary array with holes to be filled
structure : array_like, optional
Structuring element used in the computation; large-size elements
make computations faster but may miss holes separated from the
background by thin regions. The default element (with a square
connectivity equal to one) yields the intuitive result where all
holes in the input have been filled.
output : ndarray, optional
Array of the same shape as input, into which the output is placed.
By default, a new array is created.
origin : int, tuple of ints, optional
Position of the structuring element.
Returns
-------
out : ndarray
Transformation of the initial image `input` where holes have been
filled.
See Also
--------
binary_dilation, binary_propagation, label
Notes
-----
The algorithm used in this function consists in invading the complementary
of the shapes in `input` from the outer boundary of the image,
using binary dilations. Holes are not connected to the boundary and are
therefore not invaded. The result is the complementary subset of the
invaded region.
References
----------
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((5, 5), dtype=int)
>>> a[1:4, 1:4] = 1
>>> a[2,2] = 0
>>> a
array([[0, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 0, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]])
>>> ndimage.binary_fill_holes(a).astype(int)
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]])
>>> # Too big structuring element
>>> ndimage.binary_fill_holes(a, structure=np.ones((5,5))).astype(int)
array([[0, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 0, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]])
"""
mask = numpy.logical_not(input)
tmp = numpy.zeros(mask.shape, bool)
inplace = isinstance(output, numpy.ndarray)
if inplace:
binary_dilation(tmp, structure, -1, mask, output, 1, origin)
numpy.logical_not(output, output)
else:
output = binary_dilation(tmp, structure, -1, mask, None, 1,
origin)
numpy.logical_not(output, output)
return output
def grey_erosion(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Calculate a greyscale erosion, using either a structuring element,
or a footprint corresponding to a flat structuring element.
Grayscale erosion is a mathematical morphology operation. For the
simple case of a full and flat structuring element, it can be viewed
as a minimum filter over a sliding window.
Parameters
----------
input : array_like
Array over which the grayscale erosion is to be computed.
size : tuple of ints
Shape of a flat and full structuring element used for the grayscale
erosion. Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the grayscale erosion. Non-zero values give the set of
neighbors of the center over which the minimum is chosen.
structure : array of ints, optional
Structuring element used for the grayscale erosion. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the erosion may be provided.
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
output : ndarray
Grayscale erosion of `input`.
See Also
--------
binary_erosion, grey_dilation, grey_opening, grey_closing
generate_binary_structure, minimum_filter
Notes
-----
The grayscale erosion of an image input by a structuring element s defined
over a domain E is given by:
(input+s)(x) = min {input(y) - s(x-y), for y in E}
In particular, for structuring elements defined as
s(y) = 0 for y in E, the grayscale erosion computes the minimum of the
input image inside a sliding window defined by E.
Grayscale erosion [1]_ is a *mathematical morphology* operation [2]_.
References
----------
.. [1] https://en.wikipedia.org/wiki/Erosion_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[1:6, 1:6] = 3
>>> a[4,4] = 2; a[2,3] = 1
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 3, 3, 3, 3, 3, 0],
[0, 3, 3, 1, 3, 3, 0],
[0, 3, 3, 3, 3, 3, 0],
[0, 3, 3, 3, 2, 3, 0],
[0, 3, 3, 3, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.grey_erosion(a, size=(3,3))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 3, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> footprint = ndimage.generate_binary_structure(2, 1)
>>> footprint
array([[False, True, False],
[ True, True, True],
[False, True, False]], dtype=bool)
>>> # Diagonally-connected elements are not considered neighbors
>>> ndimage.grey_erosion(a, footprint=footprint)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 3, 1, 2, 0, 0],
[0, 0, 3, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
"""
if size is None and footprint is None and structure is None:
raise ValueError("size, footprint, or structure must be specified")
return _filters._min_or_max_filter(input, size, footprint, structure,
output, mode, cval, origin, 1)
def grey_dilation(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Calculate a greyscale dilation, using either a structuring element,
or a footprint corresponding to a flat structuring element.
Grayscale dilation is a mathematical morphology operation. For the
simple case of a full and flat structuring element, it can be viewed
as a maximum filter over a sliding window.
Parameters
----------
input : array_like
Array over which the grayscale dilation is to be computed.
size : tuple of ints
Shape of a flat and full structuring element used for the grayscale
dilation. Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the grayscale dilation. Non-zero values give the set of
neighbors of the center over which the maximum is chosen.
structure : array of ints, optional
Structuring element used for the grayscale dilation. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the dilation may be provided.
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
grey_dilation : ndarray
Grayscale dilation of `input`.
See Also
--------
binary_dilation, grey_erosion, grey_closing, grey_opening
generate_binary_structure, maximum_filter
Notes
-----
The grayscale dilation of an image input by a structuring element s defined
over a domain E is given by:
(input+s)(x) = max {input(y) + s(x-y), for y in E}
In particular, for structuring elements defined as
s(y) = 0 for y in E, the grayscale dilation computes the maximum of the
input image inside a sliding window defined by E.
Grayscale dilation [1]_ is a *mathematical morphology* operation [2]_.
References
----------
.. [1] https://en.wikipedia.org/wiki/Dilation_%28morphology%29
.. [2] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[2:5, 2:5] = 1
>>> a[4,4] = 2; a[2,3] = 3
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 3, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.grey_dilation(a, size=(3,3))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 3, 3, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.grey_dilation(a, footprint=np.ones((3,3)))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 3, 3, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> s = ndimage.generate_binary_structure(2,1)
>>> s
array([[False, True, False],
[ True, True, True],
[False, True, False]], dtype=bool)
>>> ndimage.grey_dilation(a, footprint=s)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 3, 1, 0, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 1, 3, 2, 1, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 0, 1, 1, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.grey_dilation(a, size=(3,3), structure=np.ones((3,3)))
array([[1, 1, 1, 1, 1, 1, 1],
[1, 2, 4, 4, 4, 2, 1],
[1, 2, 4, 4, 4, 2, 1],
[1, 2, 4, 4, 4, 3, 1],
[1, 2, 2, 3, 3, 3, 1],
[1, 2, 2, 3, 3, 3, 1],
[1, 1, 1, 1, 1, 1, 1]])
"""
if size is None and footprint is None and structure is None:
raise ValueError("size, footprint, or structure must be specified")
if structure is not None:
structure = numpy.asarray(structure)
structure = structure[tuple([slice(None, None, -1)] *
structure.ndim)]
if footprint is not None:
footprint = numpy.asarray(footprint)
footprint = footprint[tuple([slice(None, None, -1)] *
footprint.ndim)]
input = numpy.asarray(input)
origin = _ni_support._normalize_sequence(origin, input.ndim)
for ii in range(len(origin)):
origin[ii] = -origin[ii]
if footprint is not None:
sz = footprint.shape[ii]
elif structure is not None:
sz = structure.shape[ii]
elif numpy.isscalar(size):
sz = size
else:
sz = size[ii]
if not sz & 1:
origin[ii] -= 1
return _filters._min_or_max_filter(input, size, footprint, structure,
output, mode, cval, origin, 0)
def grey_opening(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Multidimensional grayscale opening.
A grayscale opening consists in the succession of a grayscale erosion,
and a grayscale dilation.
Parameters
----------
input : array_like
Array over which the grayscale opening is to be computed.
size : tuple of ints
Shape of a flat and full structuring element used for the grayscale
opening. Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the grayscale opening.
structure : array of ints, optional
Structuring element used for the grayscale opening. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the opening may be provided.
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
grey_opening : ndarray
Result of the grayscale opening of `input` with `structure`.
See Also
--------
binary_opening, grey_dilation, grey_erosion, grey_closing
generate_binary_structure
Notes
-----
The action of a grayscale opening with a flat structuring element amounts
to smoothen high local maxima, whereas binary opening erases small objects.
References
----------
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.arange(36).reshape((6,6))
>>> a[3, 3] = 50
>>> a
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 50, 22, 23],
[24, 25, 26, 27, 28, 29],
[30, 31, 32, 33, 34, 35]])
>>> ndimage.grey_opening(a, size=(3,3))
array([[ 0, 1, 2, 3, 4, 4],
[ 6, 7, 8, 9, 10, 10],
[12, 13, 14, 15, 16, 16],
[18, 19, 20, 22, 22, 22],
[24, 25, 26, 27, 28, 28],
[24, 25, 26, 27, 28, 28]])
>>> # Note that the local maximum a[3,3] has disappeared
"""
if (size is not None) and (footprint is not None):
warnings.warn("ignoring size because footprint is set",
UserWarning, stacklevel=2)
tmp = grey_erosion(input, size, footprint, structure, None, mode,
cval, origin)
return grey_dilation(tmp, size, footprint, structure, output, mode,
cval, origin)
def grey_closing(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Multidimensional grayscale closing.
A grayscale closing consists in the succession of a grayscale dilation,
and a grayscale erosion.
Parameters
----------
input : array_like
Array over which the grayscale closing is to be computed.
size : tuple of ints
Shape of a flat and full structuring element used for the grayscale
closing. Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the grayscale closing.
structure : array of ints, optional
Structuring element used for the grayscale closing. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the closing may be provided.
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
grey_closing : ndarray
Result of the grayscale closing of `input` with `structure`.
See Also
--------
binary_closing, grey_dilation, grey_erosion, grey_opening,
generate_binary_structure
Notes
-----
The action of a grayscale closing with a flat structuring element amounts
to smoothen deep local minima, whereas binary closing fills small holes.
References
----------
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.arange(36).reshape((6,6))
>>> a[3,3] = 0
>>> a
array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 0, 22, 23],
[24, 25, 26, 27, 28, 29],
[30, 31, 32, 33, 34, 35]])
>>> ndimage.grey_closing(a, size=(3,3))
array([[ 7, 7, 8, 9, 10, 11],
[ 7, 7, 8, 9, 10, 11],
[13, 13, 14, 15, 16, 17],
[19, 19, 20, 20, 22, 23],
[25, 25, 26, 27, 28, 29],
[31, 31, 32, 33, 34, 35]])
>>> # Note that the local minimum a[3,3] has disappeared
"""
if (size is not None) and (footprint is not None):
warnings.warn("ignoring size because footprint is set",
UserWarning, stacklevel=2)
tmp = grey_dilation(input, size, footprint, structure, None, mode,
cval, origin)
return grey_erosion(tmp, size, footprint, structure, output, mode,
cval, origin)
def morphological_gradient(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Multidimensional morphological gradient.
The morphological gradient is calculated as the difference between a
dilation and an erosion of the input with a given structuring element.
Parameters
----------
input : array_like
Array over which to compute the morphlogical gradient.
size : tuple of ints
Shape of a flat and full structuring element used for the mathematical
morphology operations. Optional if `footprint` or `structure` is
provided. A larger `size` yields a more blurred gradient.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the morphology operations. Larger footprints
give a more blurred morphological gradient.
structure : array of ints, optional
Structuring element used for the morphology operations.
`structure` may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the morphological gradient
may be provided.
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
morphological_gradient : ndarray
Morphological gradient of `input`.
See Also
--------
grey_dilation, grey_erosion, gaussian_gradient_magnitude
Notes
-----
For a flat structuring element, the morphological gradient
computed at a given point corresponds to the maximal difference
between elements of the input among the elements covered by the
structuring element centered on the point.
References
----------
.. [1] https://en.wikipedia.org/wiki/Mathematical_morphology
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[2:5, 2:5] = 1
>>> ndimage.morphological_gradient(a, size=(3,3))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 0, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> # The morphological gradient is computed as the difference
>>> # between a dilation and an erosion
>>> ndimage.grey_dilation(a, size=(3,3)) -\\
... ndimage.grey_erosion(a, size=(3,3))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 0, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> a = np.zeros((7,7), dtype=int)
>>> a[2:5, 2:5] = 1
>>> a[4,4] = 2; a[2,3] = 3
>>> a
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 3, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
>>> ndimage.morphological_gradient(a, size=(3,3))
array([[0, 0, 0, 0, 0, 0, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 3, 3, 1, 0],
[0, 1, 3, 2, 3, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 1, 1, 2, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0]])
"""
tmp = grey_dilation(input, size, footprint, structure, None, mode,
cval, origin)
if isinstance(output, numpy.ndarray):
grey_erosion(input, size, footprint, structure, output, mode,
cval, origin)
return numpy.subtract(tmp, output, output)
else:
return (tmp - grey_erosion(input, size, footprint, structure,
None, mode, cval, origin))
def morphological_laplace(input, size=None, footprint=None,
structure=None, output=None,
mode="reflect", cval=0.0, origin=0):
"""
Multidimensional morphological laplace.
Parameters
----------
input : array_like
Input.
size : int or sequence of ints, optional
See `structure`.
footprint : bool or ndarray, optional
See `structure`.
structure : structure, optional
Either `size`, `footprint`, or the `structure` must be provided.
output : ndarray, optional
An output array can optionally be provided.
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
The mode parameter determines how the array borders are handled.
For 'constant' mode, values beyond borders are set to be `cval`.
Default is 'reflect'.
cval : scalar, optional
Value to fill past edges of input if mode is 'constant'.
Default is 0.0
origin : origin, optional
The origin parameter controls the placement of the filter.
Returns
-------
morphological_laplace : ndarray
Output
"""
tmp1 = grey_dilation(input, size, footprint, structure, None, mode,
cval, origin)
if isinstance(output, numpy.ndarray):
grey_erosion(input, size, footprint, structure, output, mode,
cval, origin)
numpy.add(tmp1, output, output)
numpy.subtract(output, input, output)
return numpy.subtract(output, input, output)
else:
tmp2 = grey_erosion(input, size, footprint, structure, None, mode,
cval, origin)
numpy.add(tmp1, tmp2, tmp2)
numpy.subtract(tmp2, input, tmp2)
numpy.subtract(tmp2, input, tmp2)
return tmp2
def white_tophat(input, size=None, footprint=None, structure=None,
output=None, mode="reflect", cval=0.0, origin=0):
"""
Multidimensional white tophat filter.
Parameters
----------
input : array_like
Input.
size : tuple of ints
Shape of a flat and full structuring element used for the filter.
Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of elements of a flat structuring element
used for the white tophat filter.
structure : array of ints, optional
Structuring element used for the filter. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the filter may be provided.
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'.
Default is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default is 0.
Returns
-------
output : ndarray
Result of the filter of `input` with `structure`.
See Also
--------
black_tophat
Examples
--------
Subtract gray background from a bright peak.
>>> from scipy.ndimage import generate_binary_structure, white_tophat
>>> import numpy as np
>>> square = generate_binary_structure(rank=2, connectivity=3)
>>> 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]])
>>> white_tophat(input=bright_on_gray, structure=square)
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]])
"""
if (size is not None) and (footprint is not None):
warnings.warn("ignoring size because footprint is set",
UserWarning, stacklevel=2)
tmp = grey_erosion(input, size, footprint, structure, None, mode,
cval, origin)
tmp = grey_dilation(tmp, size, footprint, structure, output, mode,
cval, origin)
if tmp is None:
tmp = output
if input.dtype == numpy.bool_ and tmp.dtype == numpy.bool_:
numpy.bitwise_xor(input, tmp, out=tmp)
else:
numpy.subtract(input, tmp, out=tmp)
return tmp
def black_tophat(input, size=None, footprint=None,
structure=None, output=None, mode="reflect",
cval=0.0, origin=0):
"""
Multidimensional black tophat filter.
Parameters
----------
input : array_like
Input.
size : tuple of ints, optional
Shape of a flat and full structuring element used for the filter.
Optional if `footprint` or `structure` is provided.
footprint : array of ints, optional
Positions of non-infinite elements of a flat structuring element
used for the black tophat filter.
structure : array of ints, optional
Structuring element used for the filter. `structure`
may be a non-flat structuring element.
output : array, optional
An array used for storing the output of the filter may be provided.
mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `mode` parameter determines how the array borders are
handled, where `cval` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
origin : scalar, optional
The `origin` parameter controls the placement of the filter.
Default 0
Returns
-------
black_tophat : ndarray
Result of the filter of `input` with `structure`.
See Also
--------
white_tophat, grey_opening, grey_closing
Examples
--------
Change dark peak to bright peak and subtract background.
>>> from scipy.ndimage import generate_binary_structure, black_tophat
>>> import numpy as np
>>> square = generate_binary_structure(rank=2, connectivity=3)
>>> 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]])
>>> black_tophat(input=dark_on_gray, structure=square)
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]])
"""
if (size is not None) and (footprint is not None):
warnings.warn("ignoring size because footprint is set",
UserWarning, stacklevel=2)
tmp = grey_dilation(input, size, footprint, structure, None, mode,
cval, origin)
tmp = grey_erosion(tmp, size, footprint, structure, output, mode,
cval, origin)
if tmp is None:
tmp = output
if input.dtype == numpy.bool_ and tmp.dtype == numpy.bool_:
numpy.bitwise_xor(tmp, input, out=tmp)
else:
numpy.subtract(tmp, input, out=tmp)
return tmp
def distance_transform_bf(input, metric="euclidean", sampling=None,
return_distances=True, return_indices=False,
distances=None, indices=None):
"""
Distance transform function by a brute force algorithm.
This function calculates the distance transform of the `input`, by
replacing each foreground (non-zero) element, with its
shortest distance to the background (any zero-valued element).
In addition to the distance transform, the feature transform can
be calculated. In this case the index of the closest background
element to each foreground element is returned in a separate array.
Parameters
----------
input : array_like
Input
metric : {'euclidean', 'taxicab', 'chessboard'}, optional
'cityblock' and 'manhattan' are also valid, and map to 'taxicab'.
The default is 'euclidean'.
sampling : float, or sequence of float, optional
This parameter is only used when `metric` is 'euclidean'.
Spacing of elements along each dimension. If a sequence, must be of
length equal to the input rank; if a single number, this is used for
all axes. If not specified, a grid spacing of unity is implied.
return_distances : bool, optional
Whether to calculate the distance transform.
Default is True.
return_indices : bool, optional
Whether to calculate the feature transform.
Default is False.
distances : ndarray, optional
An output array to store the calculated distance transform, instead of
returning it.
`return_distances` must be True.
It must be the same shape as `input`, and of type float64 if `metric`
is 'euclidean', uint32 otherwise.
indices : int32 ndarray, optional
An output array to store the calculated feature transform, instead of
returning it.
`return_indicies` must be True.
Its shape must be `(input.ndim,) + input.shape`.
Returns
-------
distances : ndarray, optional
The calculated distance transform. Returned only when
`return_distances` is True and `distances` is not supplied.
It will have the same shape as the input array.
indices : int32 ndarray, optional
The calculated feature transform. It has an input-shaped array for each
dimension of the input. See distance_transform_edt documentation for an
example.
Returned only when `return_indices` is True and `indices` is not
supplied.
See Also
--------
distance_transform_cdt : Faster distance transform for taxicab and
chessboard metrics
distance_transform_edt : Faster distance transform for euclidean metric
Notes
-----
This function employs a slow brute force algorithm. See also the
function `distance_transform_cdt` for more efficient taxicab [1]_ and
chessboard algorithms [2]_.
References
----------
.. [1] Taxicab distance. Wikipedia, 2023.
https://en.wikipedia.org/wiki/Taxicab_geometry
.. [2] Chessboard distance. Wikipedia, 2023.
https://en.wikipedia.org/wiki/Chebyshev_distance
Examples
--------
Import the necessary modules.
>>> import numpy as np
>>> from scipy.ndimage import distance_transform_bf
>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.axes_grid1 import ImageGrid
First, we create a toy binary image.
>>> def add_circle(center_x, center_y, radius, image, fillvalue=1):
... # fill circular area with 1
... xx, yy = np.mgrid[:image.shape[0], :image.shape[1]]
... circle = (xx - center_x) ** 2 + (yy - center_y) ** 2
... circle_shape = np.sqrt(circle) < radius
... image[circle_shape] = fillvalue
... return image
>>> image = np.zeros((100, 100), dtype=np.uint8)
>>> image[35:65, 20:80] = 1
>>> image = add_circle(28, 65, 10, image)
>>> image = add_circle(37, 30, 10, image)
>>> image = add_circle(70, 45, 20, image)
>>> image = add_circle(45, 80, 10, image)
Next, we set up the figure.
>>> fig = plt.figure(figsize=(8, 8)) # set up the figure structure
>>> grid = ImageGrid(fig, 111, nrows_ncols=(2, 2), axes_pad=(0.4, 0.3),
... label_mode="1", share_all=True,
... cbar_location="right", cbar_mode="each",
... cbar_size="7%", cbar_pad="2%")
>>> for ax in grid:
... ax.axis('off') # remove axes from images
The top left image is the original binary image.
>>> binary_image = grid[0].imshow(image, cmap='gray')
>>> cbar_binary_image = grid.cbar_axes[0].colorbar(binary_image)
>>> cbar_binary_image.set_ticks([0, 1])
>>> grid[0].set_title("Binary image: foreground in white")
The distance transform calculates the distance between foreground pixels
and the image background according to a distance metric. Available metrics
in `distance_transform_bf` are: ``euclidean`` (default), ``taxicab``
and ``chessboard``. The top right image contains the distance transform
based on the ``euclidean`` metric.
>>> distance_transform_euclidean = distance_transform_bf(image)
>>> euclidean_transform = grid[1].imshow(distance_transform_euclidean,
... cmap='gray')
>>> cbar_euclidean = grid.cbar_axes[1].colorbar(euclidean_transform)
>>> colorbar_ticks = [0, 10, 20]
>>> cbar_euclidean.set_ticks(colorbar_ticks)
>>> grid[1].set_title("Euclidean distance")
The lower left image contains the distance transform using the ``taxicab``
metric.
>>> distance_transform_taxicab = distance_transform_bf(image,
... metric='taxicab')
>>> taxicab_transformation = grid[2].imshow(distance_transform_taxicab,
... cmap='gray')
>>> cbar_taxicab = grid.cbar_axes[2].colorbar(taxicab_transformation)
>>> cbar_taxicab.set_ticks(colorbar_ticks)
>>> grid[2].set_title("Taxicab distance")
Finally, the lower right image contains the distance transform using the
``chessboard`` metric.
>>> distance_transform_cb = distance_transform_bf(image,
... metric='chessboard')
>>> chessboard_transformation = grid[3].imshow(distance_transform_cb,
... cmap='gray')
>>> cbar_taxicab = grid.cbar_axes[3].colorbar(chessboard_transformation)
>>> cbar_taxicab.set_ticks(colorbar_ticks)
>>> grid[3].set_title("Chessboard distance")
>>> plt.show()
"""
ft_inplace = isinstance(indices, numpy.ndarray)
dt_inplace = isinstance(distances, numpy.ndarray)
_distance_tranform_arg_check(
dt_inplace, ft_inplace, return_distances, return_indices
)
tmp1 = numpy.asarray(input) != 0
struct = generate_binary_structure(tmp1.ndim, tmp1.ndim)
tmp2 = binary_dilation(tmp1, struct)
tmp2 = numpy.logical_xor(tmp1, tmp2)
tmp1 = tmp1.astype(numpy.int8) - tmp2.astype(numpy.int8)
metric = metric.lower()
if metric == 'euclidean':
metric = 1
elif metric in ['taxicab', 'cityblock', 'manhattan']:
metric = 2
elif metric == 'chessboard':
metric = 3
else:
raise RuntimeError('distance metric not supported')
if sampling is not None:
sampling = _ni_support._normalize_sequence(sampling, tmp1.ndim)
sampling = numpy.asarray(sampling, dtype=numpy.float64)
if not sampling.flags.contiguous:
sampling = sampling.copy()
if return_indices:
ft = numpy.zeros(tmp1.shape, dtype=numpy.int32)
else:
ft = None
if return_distances:
if distances is None:
if metric == 1:
dt = numpy.zeros(tmp1.shape, dtype=numpy.float64)
else:
dt = numpy.zeros(tmp1.shape, dtype=numpy.uint32)
else:
if distances.shape != tmp1.shape:
raise RuntimeError('distances array has wrong shape')
if metric == 1:
if distances.dtype.type != numpy.float64:
raise RuntimeError('distances array must be float64')
else:
if distances.dtype.type != numpy.uint32:
raise RuntimeError('distances array must be uint32')
dt = distances
else:
dt = None
_nd_image.distance_transform_bf(tmp1, metric, sampling, dt, ft)
if return_indices:
if isinstance(indices, numpy.ndarray):
if indices.dtype.type != numpy.int32:
raise RuntimeError('indices array must be int32')
if indices.shape != (tmp1.ndim,) + tmp1.shape:
raise RuntimeError('indices array has wrong shape')
tmp2 = indices
else:
tmp2 = numpy.indices(tmp1.shape, dtype=numpy.int32)
ft = numpy.ravel(ft)
for ii in range(tmp2.shape[0]):
rtmp = numpy.ravel(tmp2[ii, ...])[ft]
rtmp.shape = tmp1.shape
tmp2[ii, ...] = rtmp
ft = tmp2
# construct and return the result
result = []
if return_distances and not dt_inplace:
result.append(dt)
if return_indices and not ft_inplace:
result.append(ft)
if len(result) == 2:
return tuple(result)
elif len(result) == 1:
return result[0]
else:
return None
def distance_transform_cdt(input, metric='chessboard', return_distances=True,
return_indices=False, distances=None, indices=None):
"""
Distance transform for chamfer type of transforms.
This function calculates the distance transform of the `input`, by
replacing each foreground (non-zero) element, with its
shortest distance to the background (any zero-valued element).
In addition to the distance transform, the feature transform can
be calculated. In this case the index of the closest background
element to each foreground element is returned in a separate array.
Parameters
----------
input : array_like
Input. Values of 0 are treated as background.
metric : {'chessboard', 'taxicab'} or array_like, optional
The `metric` determines the type of chamfering that is done. If the
`metric` is equal to 'taxicab' a structure is generated using
`generate_binary_structure` with a squared distance equal to 1. If
the `metric` is equal to 'chessboard', a `metric` is generated
using `generate_binary_structure` with a squared distance equal to
the dimensionality of the array. These choices correspond to the
common interpretations of the 'taxicab' and the 'chessboard'
distance metrics in two dimensions.
A custom metric may be provided, in the form of a matrix where
each dimension has a length of three.
'cityblock' and 'manhattan' are also valid, and map to 'taxicab'.
The default is 'chessboard'.
return_distances : bool, optional
Whether to calculate the distance transform.
Default is True.
return_indices : bool, optional
Whether to calculate the feature transform.
Default is False.
distances : int32 ndarray, optional
An output array to store the calculated distance transform, instead of
returning it.
`return_distances` must be True.
It must be the same shape as `input`.
indices : int32 ndarray, optional
An output array to store the calculated feature transform, instead of
returning it.
`return_indicies` must be True.
Its shape must be `(input.ndim,) + input.shape`.
Returns
-------
distances : int32 ndarray, optional
The calculated distance transform. Returned only when
`return_distances` is True, and `distances` is not supplied.
It will have the same shape as the input array.
indices : int32 ndarray, optional
The calculated feature transform. It has an input-shaped array for each
dimension of the input. See distance_transform_edt documentation for an
example.
Returned only when `return_indices` is True, and `indices` is not
supplied.
See Also
--------
distance_transform_edt : Fast distance transform for euclidean metric
distance_transform_bf : Distance transform for different metrics using
a slower brute force algorithm
Examples
--------
Import the necessary modules.
>>> import numpy as np
>>> from scipy.ndimage import distance_transform_cdt
>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.axes_grid1 import ImageGrid
First, we create a toy binary image.
>>> def add_circle(center_x, center_y, radius, image, fillvalue=1):
... # fill circular area with 1
... xx, yy = np.mgrid[:image.shape[0], :image.shape[1]]
... circle = (xx - center_x) ** 2 + (yy - center_y) ** 2
... circle_shape = np.sqrt(circle) < radius
... image[circle_shape] = fillvalue
... return image
>>> image = np.zeros((100, 100), dtype=np.uint8)
>>> image[35:65, 20:80] = 1
>>> image = add_circle(28, 65, 10, image)
>>> image = add_circle(37, 30, 10, image)
>>> image = add_circle(70, 45, 20, image)
>>> image = add_circle(45, 80, 10, image)
Next, we set up the figure.
>>> fig = plt.figure(figsize=(5, 15))
>>> grid = ImageGrid(fig, 111, nrows_ncols=(3, 1), axes_pad=(0.5, 0.3),
... label_mode="1", share_all=True,
... cbar_location="right", cbar_mode="each",
... cbar_size="7%", cbar_pad="2%")
>>> for ax in grid:
... ax.axis('off')
>>> top, middle, bottom = grid
>>> colorbar_ticks = [0, 10, 20]
The top image contains the original binary image.
>>> binary_image = top.imshow(image, cmap='gray')
>>> cbar_binary_image = top.cax.colorbar(binary_image)
>>> cbar_binary_image.set_ticks([0, 1])
>>> top.set_title("Binary image: foreground in white")
The middle image contains the distance transform using the ``taxicab``
metric.
>>> distance_taxicab = distance_transform_cdt(image, metric="taxicab")
>>> taxicab_transform = middle.imshow(distance_taxicab, cmap='gray')
>>> cbar_taxicab = middle.cax.colorbar(taxicab_transform)
>>> cbar_taxicab.set_ticks(colorbar_ticks)
>>> middle.set_title("Taxicab metric")
The bottom image contains the distance transform using the ``chessboard``
metric.
>>> distance_chessboard = distance_transform_cdt(image,
... metric="chessboard")
>>> chessboard_transform = bottom.imshow(distance_chessboard, cmap='gray')
>>> cbar_chessboard = bottom.cax.colorbar(chessboard_transform)
>>> cbar_chessboard.set_ticks(colorbar_ticks)
>>> bottom.set_title("Chessboard metric")
>>> plt.tight_layout()
>>> plt.show()
"""
ft_inplace = isinstance(indices, numpy.ndarray)
dt_inplace = isinstance(distances, numpy.ndarray)
_distance_tranform_arg_check(
dt_inplace, ft_inplace, return_distances, return_indices
)
input = numpy.asarray(input)
if isinstance(metric, str):
if metric in ['taxicab', 'cityblock', 'manhattan']:
rank = input.ndim
metric = generate_binary_structure(rank, 1)
elif metric == 'chessboard':
rank = input.ndim
metric = generate_binary_structure(rank, rank)
else:
raise ValueError('invalid metric provided')
else:
try:
metric = numpy.asarray(metric)
except Exception as e:
raise ValueError('invalid metric provided') from e
for s in metric.shape:
if s != 3:
raise ValueError('metric sizes must be equal to 3')
if not metric.flags.contiguous:
metric = metric.copy()
if dt_inplace:
if distances.dtype.type != numpy.int32:
raise ValueError('distances must be of int32 type')
if distances.shape != input.shape:
raise ValueError('distances has wrong shape')
dt = distances
dt[...] = numpy.where(input, -1, 0).astype(numpy.int32)
else:
dt = numpy.where(input, -1, 0).astype(numpy.int32)
rank = dt.ndim
if return_indices:
sz = numpy.prod(dt.shape, axis=0)
ft = numpy.arange(sz, dtype=numpy.int32)
ft.shape = dt.shape
else:
ft = None
_nd_image.distance_transform_op(metric, dt, ft)
dt = dt[tuple([slice(None, None, -1)] * rank)]
if return_indices:
ft = ft[tuple([slice(None, None, -1)] * rank)]
_nd_image.distance_transform_op(metric, dt, ft)
dt = dt[tuple([slice(None, None, -1)] * rank)]
if return_indices:
ft = ft[tuple([slice(None, None, -1)] * rank)]
ft = numpy.ravel(ft)
if ft_inplace:
if indices.dtype.type != numpy.int32:
raise ValueError('indices array must be int32')
if indices.shape != (dt.ndim,) + dt.shape:
raise ValueError('indices array has wrong shape')
tmp = indices
else:
tmp = numpy.indices(dt.shape, dtype=numpy.int32)
for ii in range(tmp.shape[0]):
rtmp = numpy.ravel(tmp[ii, ...])[ft]
rtmp.shape = dt.shape
tmp[ii, ...] = rtmp
ft = tmp
# construct and return the result
result = []
if return_distances and not dt_inplace:
result.append(dt)
if return_indices and not ft_inplace:
result.append(ft)
if len(result) == 2:
return tuple(result)
elif len(result) == 1:
return result[0]
else:
return None
def distance_transform_edt(input, sampling=None, return_distances=True,
return_indices=False, distances=None, indices=None):
"""
Exact Euclidean distance transform.
This function calculates the distance transform of the `input`, by
replacing each foreground (non-zero) element, with its
shortest distance to the background (any zero-valued element).
In addition to the distance transform, the feature transform can
be calculated. In this case the index of the closest background
element to each foreground element is returned in a separate array.
Parameters
----------
input : array_like
Input data to transform. Can be any type but will be converted
into binary: 1 wherever input equates to True, 0 elsewhere.
sampling : float, or sequence of float, optional
Spacing of elements along each dimension. If a sequence, must be of
length equal to the input rank; if a single number, this is used for
all axes. If not specified, a grid spacing of unity is implied.
return_distances : bool, optional
Whether to calculate the distance transform.
Default is True.
return_indices : bool, optional
Whether to calculate the feature transform.
Default is False.
distances : float64 ndarray, optional
An output array to store the calculated distance transform, instead of
returning it.
`return_distances` must be True.
It must be the same shape as `input`.
indices : int32 ndarray, optional
An output array to store the calculated feature transform, instead of
returning it.
`return_indicies` must be True.
Its shape must be `(input.ndim,) + input.shape`.
Returns
-------
distances : float64 ndarray, optional
The calculated distance transform. Returned only when
`return_distances` is True and `distances` is not supplied.
It will have the same shape as the input array.
indices : int32 ndarray, optional
The calculated feature transform. It has an input-shaped array for each
dimension of the input. See example below.
Returned only when `return_indices` is True and `indices` is not
supplied.
Notes
-----
The Euclidean distance transform gives values of the Euclidean
distance::
n
y_i = sqrt(sum (x[i]-b[i])**2)
i
where b[i] is the background point (value 0) with the smallest
Euclidean distance to input points x[i], and n is the
number of dimensions.
Examples
--------
>>> from scipy import ndimage
>>> import numpy as np
>>> a = np.array(([0,1,1,1,1],
... [0,0,1,1,1],
... [0,1,1,1,1],
... [0,1,1,1,0],
... [0,1,1,0,0]))
>>> ndimage.distance_transform_edt(a)
array([[ 0. , 1. , 1.4142, 2.2361, 3. ],
[ 0. , 0. , 1. , 2. , 2. ],
[ 0. , 1. , 1.4142, 1.4142, 1. ],
[ 0. , 1. , 1.4142, 1. , 0. ],
[ 0. , 1. , 1. , 0. , 0. ]])
With a sampling of 2 units along x, 1 along y:
>>> ndimage.distance_transform_edt(a, sampling=[2,1])
array([[ 0. , 1. , 2. , 2.8284, 3.6056],
[ 0. , 0. , 1. , 2. , 3. ],
[ 0. , 1. , 2. , 2.2361, 2. ],
[ 0. , 1. , 2. , 1. , 0. ],
[ 0. , 1. , 1. , 0. , 0. ]])
Asking for indices as well:
>>> edt, inds = ndimage.distance_transform_edt(a, return_indices=True)
>>> inds
array([[[0, 0, 1, 1, 3],
[1, 1, 1, 1, 3],
[2, 2, 1, 3, 3],
[3, 3, 4, 4, 3],
[4, 4, 4, 4, 4]],
[[0, 0, 1, 1, 4],
[0, 1, 1, 1, 4],
[0, 0, 1, 4, 4],
[0, 0, 3, 3, 4],
[0, 0, 3, 3, 4]]])
With arrays provided for inplace outputs:
>>> indices = np.zeros(((np.ndim(a),) + a.shape), dtype=np.int32)
>>> ndimage.distance_transform_edt(a, return_indices=True, indices=indices)
array([[ 0. , 1. , 1.4142, 2.2361, 3. ],
[ 0. , 0. , 1. , 2. , 2. ],
[ 0. , 1. , 1.4142, 1.4142, 1. ],
[ 0. , 1. , 1.4142, 1. , 0. ],
[ 0. , 1. , 1. , 0. , 0. ]])
>>> indices
array([[[0, 0, 1, 1, 3],
[1, 1, 1, 1, 3],
[2, 2, 1, 3, 3],
[3, 3, 4, 4, 3],
[4, 4, 4, 4, 4]],
[[0, 0, 1, 1, 4],
[0, 1, 1, 1, 4],
[0, 0, 1, 4, 4],
[0, 0, 3, 3, 4],
[0, 0, 3, 3, 4]]])
"""
ft_inplace = isinstance(indices, numpy.ndarray)
dt_inplace = isinstance(distances, numpy.ndarray)
_distance_tranform_arg_check(
dt_inplace, ft_inplace, return_distances, return_indices
)
# calculate the feature transform
input = numpy.atleast_1d(numpy.where(input, 1, 0).astype(numpy.int8))
if sampling is not None:
sampling = _ni_support._normalize_sequence(sampling, input.ndim)
sampling = numpy.asarray(sampling, dtype=numpy.float64)
if not sampling.flags.contiguous:
sampling = sampling.copy()
if ft_inplace:
ft = indices
if ft.shape != (input.ndim,) + input.shape:
raise RuntimeError('indices array has wrong shape')
if ft.dtype.type != numpy.int32:
raise RuntimeError('indices array must be int32')
else:
ft = numpy.zeros((input.ndim,) + input.shape, dtype=numpy.int32)
_nd_image.euclidean_feature_transform(input, sampling, ft)
# if requested, calculate the distance transform
if return_distances:
dt = ft - numpy.indices(input.shape, dtype=ft.dtype)
dt = dt.astype(numpy.float64)
if sampling is not None:
for ii in range(len(sampling)):
dt[ii, ...] *= sampling[ii]
numpy.multiply(dt, dt, dt)
if dt_inplace:
dt = numpy.add.reduce(dt, axis=0)
if distances.shape != dt.shape:
raise RuntimeError('distances array has wrong shape')
if distances.dtype.type != numpy.float64:
raise RuntimeError('distances array must be float64')
numpy.sqrt(dt, distances)
else:
dt = numpy.add.reduce(dt, axis=0)
dt = numpy.sqrt(dt)
# construct and return the result
result = []
if return_distances and not dt_inplace:
result.append(dt)
if return_indices and not ft_inplace:
result.append(ft)
if len(result) == 2:
return tuple(result)
elif len(result) == 1:
return result[0]
else:
return None
def _distance_tranform_arg_check(distances_out, indices_out,
return_distances, return_indices):
"""Raise a RuntimeError if the arguments are invalid"""
error_msgs = []
if (not return_distances) and (not return_indices):
error_msgs.append(
'at least one of return_distances/return_indices must be True')
if distances_out and not return_distances:
error_msgs.append(
'return_distances must be True if distances is supplied'
)
if indices_out and not return_indices:
error_msgs.append('return_indices must be True if indices is supplied')
if error_msgs:
raise RuntimeError(', '.join(error_msgs))