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import numpy as np
from scipy import ndimage as ndi
from .. import draw
def square(width, dtype=np.uint8):
"""Generates a flat, square-shaped structuring element.
Every pixel along the perimeter has a chessboard distance
no greater than radius (radius=floor(width/2)) pixels.
Parameters
----------
width : int
The width and height of the square.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
A structuring element consisting only of ones, i.e. every
pixel belongs to the neighborhood.
"""
return np.ones((width, width), dtype=dtype)
def rectangle(width, height, dtype=np.uint8):
"""Generates a flat, rectangular-shaped structuring element.
Every pixel in the rectangle generated for a given width and given height
belongs to the neighborhood.
Parameters
----------
width : int
The width of the rectangle.
height : int
The height of the rectangle.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
A structuring element consisting only of ones, i.e. every
pixel belongs to the neighborhood.
"""
return np.ones((width, height), dtype=dtype)
def diamond(radius, dtype=np.uint8):
"""Generates a flat, diamond-shaped structuring element.
A pixel is part of the neighborhood (i.e. labeled 1) if
the city block/Manhattan distance between it and the center of
the neighborhood is no greater than radius.
Parameters
----------
radius : int
The radius of the diamond-shaped structuring element.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
L = np.arange(0, radius * 2 + 1)
I, J = np.meshgrid(L, L)
return np.array(np.abs(I - radius) + np.abs(J - radius) <= radius,
dtype=dtype)
def disk(radius, dtype=np.uint8):
"""Generates a flat, disk-shaped structuring element.
A pixel is within the neighborhood if the euclidean distance between
it and the origin is no greater than radius.
Parameters
----------
radius : int
The radius of the disk-shaped structuring element.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
L = np.arange(-radius, radius + 1)
X, Y = np.meshgrid(L, L)
return np.array((X ** 2 + Y ** 2) <= radius ** 2, dtype=dtype)
def ellipse(width, height, dtype=np.uint8):
"""Generates a flat, ellipse-shaped structuring element.
Every pixel along the perimeter of ellipse satisfies
the equation ``(x/width+1)**2 + (y/height+1)**2 = 1``.
Parameters
----------
width : int
The width of the ellipse-shaped structuring element.
height : int
The height of the ellipse-shaped structuring element.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
Examples
--------
>>> from skimage.morphology import selem
>>> selem.ellipse(5, 3)
array([[0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]], dtype=uint8)
"""
selem = np.zeros((2 * height + 1, 2 * width + 1), dtype=dtype)
rows, cols = draw.ellipse(height, width, height + 1, width + 1)
selem[rows, cols] = 1
return selem
def cube(width, dtype=np.uint8):
""" Generates a cube-shaped structuring element.
This is the 3D equivalent of a square.
Every pixel along the perimeter has a chessboard distance
no greater than radius (radius=floor(width/2)) pixels.
Parameters
----------
width : int
The width, height and depth of the cube.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
A structuring element consisting only of ones, i.e. every
pixel belongs to the neighborhood.
"""
return np.ones((width, width, width), dtype=dtype)
def octahedron(radius, dtype=np.uint8):
"""Generates a octahedron-shaped structuring element.
This is the 3D equivalent of a diamond.
A pixel is part of the neighborhood (i.e. labeled 1) if
the city block/Manhattan distance between it and the center of
the neighborhood is no greater than radius.
Parameters
----------
radius : int
The radius of the octahedron-shaped structuring element.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
# note that in contrast to diamond(), this method allows non-integer radii
n = 2 * radius + 1
Z, Y, X = np.mgrid[-radius:radius:n * 1j,
-radius:radius:n * 1j,
-radius:radius:n * 1j]
s = np.abs(X) + np.abs(Y) + np.abs(Z)
return np.array(s <= radius, dtype=dtype)
def ball(radius, dtype=np.uint8):
"""Generates a ball-shaped structuring element.
This is the 3D equivalent of a disk.
A pixel is within the neighborhood if the euclidean distance between
it and the origin is no greater than radius.
Parameters
----------
radius : int
The radius of the ball-shaped structuring element.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
n = 2 * radius + 1
Z, Y, X = np.mgrid[-radius:radius:n * 1j,
-radius:radius:n * 1j,
-radius:radius:n * 1j]
s = X ** 2 + Y ** 2 + Z ** 2
return np.array(s <= radius * radius, dtype=dtype)
def octagon(m, n, dtype=np.uint8):
"""Generates an octagon shaped structuring element.
For a given size of (m) horizontal and vertical sides
and a given (n) height or width of slanted sides octagon is generated.
The slanted sides are 45 or 135 degrees to the horizontal axis
and hence the widths and heights are equal.
Parameters
----------
m : int
The size of the horizontal and vertical sides.
n : int
The height or width of the slanted sides.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
from . import convex_hull_image
selem = np.zeros((m + 2 * n, m + 2 * n))
selem[0, n] = 1
selem[n, 0] = 1
selem[0, m + n - 1] = 1
selem[m + n - 1, 0] = 1
selem[-1, n] = 1
selem[n, -1] = 1
selem[-1, m + n - 1] = 1
selem[m + n - 1, -1] = 1
selem = convex_hull_image(selem).astype(dtype)
return selem
def star(a, dtype=np.uint8):
"""Generates a star shaped structuring element.
Start has 8 vertices and is an overlap of square of size `2*a + 1`
with its 45 degree rotated version.
The slanted sides are 45 or 135 degrees to the horizontal axis.
Parameters
----------
a : int
Parameter deciding the size of the star structural element. The side
of the square array returned is `2*a + 1 + 2*floor(a / 2)`.
Other Parameters
----------------
dtype : data-type
The data type of the structuring element.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
from . import convex_hull_image
if a == 1:
bfilter = np.zeros((3, 3), dtype)
bfilter[:] = 1
return bfilter
m = 2 * a + 1
n = a // 2
selem_square = np.zeros((m + 2 * n, m + 2 * n))
selem_square[n: m + n, n: m + n] = 1
c = (m + 2 * n - 1) // 2
selem_rotated = np.zeros((m + 2 * n, m + 2 * n))
selem_rotated[0, c] = selem_rotated[-1, c] = 1
selem_rotated[c, 0] = selem_rotated[c, -1] = 1
selem_rotated = convex_hull_image(selem_rotated).astype(int)
selem = selem_square + selem_rotated
selem[selem > 0] = 1
return selem.astype(dtype)
def _default_selem(ndim):
"""Generates a cross-shaped structuring element (connectivity=1).
This is the default structuring element (selem) if no selem was specified.
Parameters
----------
ndim : int
Number of dimensions of the image.
Returns
-------
selem : ndarray
The structuring element where elements of the neighborhood
are 1 and 0 otherwise.
"""
return ndi.morphology.generate_binary_structure(ndim, 1)