footprints.py

import numpy as np
from scipy import ndimage as ndi

from .. import draw
from .._shared.utils import deprecate_kwarg


def square(width, dtype=np.uint8):
    """Generates a flat, square-shaped footprint.

    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 footprint.

    Returns
    -------
    footprint : ndarray
        A footprint consisting only of ones, i.e. every pixel belongs to the
        neighborhood.

    """
    return np.ones((width, width), dtype=dtype)


@deprecate_kwarg({'height': 'ncols', 'width': 'nrows'},
                 deprecated_version='0.18.0',
                 removed_version='0.20.0')
def rectangle(nrows, ncols, dtype=np.uint8):
    """Generates a flat, rectangular-shaped footprint.

    Every pixel in the rectangle generated for a given width and given height
    belongs to the neighborhood.

    Parameters
    ----------
    nrows : int
        The number of rows of the rectangle.
    ncols : int
        The number of columns of the rectangle.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        A footprint consisting only of ones, i.e. every pixel belongs to the
        neighborhood.

    Notes
    -----
    - The use of ``width`` and ``height`` has been deprecated in
      version 0.18.0. Use ``nrows`` and ``ncols`` instead.
    """

    return np.ones((nrows, ncols), dtype=dtype)


def diamond(radius, dtype=np.uint8):
    """Generates a flat, diamond-shaped footprint.

    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 footprint.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        The footprint 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 footprint.

    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 footprint.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        The footprint 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 footprint.

    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 footprint.
    height : int
        The height of the ellipse-shaped footprint.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        The footprint where elements of the neighborhood are 1 and 0 otherwise.

    Examples
    --------
    >>> from skimage.morphology import footprints
    >>> footprints.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)

    """
    footprint = np.zeros((2 * height + 1, 2 * width + 1), dtype=dtype)
    rows, cols = draw.ellipse(height, width, height + 1, width + 1)
    footprint[rows, cols] = 1
    return footprint


def cube(width, dtype=np.uint8):
    """ Generates a cube-shaped footprint.

    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 footprint.

    Returns
    -------
    footprint : ndarray
        A footprint 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 footprint.

    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 footprint.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        The footprint 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 footprint.

    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 footprint.

    Other Parameters
    ----------------
    dtype : data-type
        The data type of the footprint.

    Returns
    -------
    footprint : ndarray
        The footprint 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 footprint.

    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 footprint.

    Returns
    -------
    footprint : ndarray
        The footprint where elements of the neighborhood are 1 and 0 otherwise.

    """
    from . import convex_hull_image
    footprint = np.zeros((m + 2 * n, m + 2 * n))
    footprint[0, n] = 1
    footprint[n, 0] = 1
    footprint[0, m + n - 1] = 1
    footprint[m + n - 1, 0] = 1
    footprint[-1, n] = 1
    footprint[n, -1] = 1
    footprint[-1, m + n - 1] = 1
    footprint[m + n - 1, -1] = 1
    footprint = convex_hull_image(footprint).astype(dtype)
    return footprint


def star(a, dtype=np.uint8):
    """Generates a star shaped footprint.

    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 footprint.

    Returns
    -------
    footprint : ndarray
        The footprint 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
    footprint_square = np.zeros((m + 2 * n, m + 2 * n))
    footprint_square[n: m + n, n: m + n] = 1

    c = (m + 2 * n - 1) // 2
    footprint_rotated = np.zeros((m + 2 * n, m + 2 * n))
    footprint_rotated[0, c] = footprint_rotated[-1, c] = 1
    footprint_rotated[c, 0] = footprint_rotated[c, -1] = 1
    footprint_rotated = convex_hull_image(footprint_rotated).astype(int)

    footprint = footprint_square + footprint_rotated
    footprint[footprint > 0] = 1

    return footprint.astype(dtype)


def _default_footprint(ndim):
    """Generates a cross-shaped footprint (connectivity=1).

    This is the default footprint (footprint) if no footprint was
    specified.

    Parameters
    ----------
    ndim : int
        Number of dimensions of the image.

    Returns
    -------
    footprint : ndarray
        The footprint where elements of the neighborhood are 1 and 0 otherwise.

    """
    return ndi.generate_binary_structure(ndim, 1)