359 lines
9.5 KiB
Python
359 lines
9.5 KiB
Python
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)
|