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