490 lines
16 KiB
Python
490 lines
16 KiB
Python
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"""
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Grayscale morphological operations
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"""
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import functools
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import numpy as np
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from scipy import ndimage as ndi
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from .misc import default_selem
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from ..util import crop
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__all__ = ['erosion', 'dilation', 'opening', 'closing', 'white_tophat',
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'black_tophat']
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def _shift_selem(selem, shift_x, shift_y):
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"""Shift the binary image `selem` in the left and/or up.
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This only affects 2D structuring elements with even number of rows
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or columns.
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Parameters
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----------
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selem : 2D array, shape (M, N)
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The input structuring element.
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shift_x, shift_y : bool
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Whether to move `selem` along each axis.
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Returns
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-------
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out : 2D array, shape (M + int(shift_x), N + int(shift_y))
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The shifted structuring element.
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"""
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if selem.ndim != 2:
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# do nothing for 1D or 3D or higher structuring elements
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return selem
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m, n = selem.shape
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if m % 2 == 0:
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extra_row = np.zeros((1, n), selem.dtype)
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if shift_x:
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selem = np.vstack((selem, extra_row))
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else:
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selem = np.vstack((extra_row, selem))
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m += 1
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if n % 2 == 0:
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extra_col = np.zeros((m, 1), selem.dtype)
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if shift_y:
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selem = np.hstack((selem, extra_col))
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else:
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selem = np.hstack((extra_col, selem))
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return selem
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def _invert_selem(selem):
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"""Change the order of the values in `selem`.
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This is a patch for the *weird* footprint inversion in
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`ndi.grey_morphology` [1]_.
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Parameters
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----------
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selem : array
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The input structuring element.
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Returns
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-------
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inverted : array, same shape and type as `selem`
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The structuring element, in opposite order.
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Examples
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--------
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>>> selem = np.array([[0, 0, 0], [0, 1, 1], [0, 1, 1]], np.uint8)
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>>> _invert_selem(selem)
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array([[1, 1, 0],
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[1, 1, 0],
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[0, 0, 0]], dtype=uint8)
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References
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----------
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.. [1] https://github.com/scipy/scipy/blob/ec20ababa400e39ac3ffc9148c01ef86d5349332/scipy/ndimage/morphology.py#L1285
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"""
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inverted = selem[(slice(None, None, -1),) * selem.ndim]
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return inverted
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def pad_for_eccentric_selems(func):
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"""Pad input images for certain morphological operations.
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Parameters
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----------
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func : callable
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A morphological function, either opening or closing, that
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supports eccentric structuring elements. Its parameters must
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include at least `image`, `selem`, and `out`.
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Returns
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-------
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func_out : callable
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The same function, but correctly padding the input image before
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applying the input function.
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See Also
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--------
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opening, closing.
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"""
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@functools.wraps(func)
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def func_out(image, selem, out=None, *args, **kwargs):
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pad_widths = []
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padding = False
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if out is None:
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out = np.empty_like(image)
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for axis_len in selem.shape:
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if axis_len % 2 == 0:
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axis_pad_width = axis_len - 1
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padding = True
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else:
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axis_pad_width = 0
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pad_widths.append((axis_pad_width,) * 2)
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if padding:
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image = np.pad(image, pad_widths, mode='edge')
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out_temp = np.empty_like(image)
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else:
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out_temp = out
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out_temp = func(image, selem, out=out_temp, *args, **kwargs)
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if padding:
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out[:] = crop(out_temp, pad_widths)
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else:
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out = out_temp
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return out
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return func_out
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@default_selem
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def erosion(image, selem=None, out=None, shift_x=False, shift_y=False):
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"""Return greyscale morphological erosion of an image.
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Morphological erosion sets a pixel at (i,j) to the minimum over all pixels
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in the neighborhood centered at (i,j). Erosion shrinks bright regions and
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enlarges dark regions.
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Parameters
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----------
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image : ndarray
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Image array.
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selem : ndarray, optional
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The neighborhood expressed as an array of 1's and 0's.
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If None, use cross-shaped structuring element (connectivity=1).
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out : ndarrays, optional
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The array to store the result of the morphology. If None is
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passed, a new array will be allocated.
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shift_x, shift_y : bool, optional
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shift structuring element about center point. This only affects
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eccentric structuring elements (i.e. selem with even numbered sides).
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Returns
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-------
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eroded : array, same shape as `image`
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The result of the morphological erosion.
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Notes
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-----
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For ``uint8`` (and ``uint16`` up to a certain bit-depth) data, the
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lower algorithm complexity makes the `skimage.filters.rank.minimum`
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function more efficient for larger images and structuring elements.
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Examples
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--------
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>>> # Erosion shrinks bright regions
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>>> import numpy as np
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>>> from skimage.morphology import square
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>>> bright_square = np.array([[0, 0, 0, 0, 0],
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... [0, 1, 1, 1, 0],
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... [0, 1, 1, 1, 0],
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... [0, 1, 1, 1, 0],
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... [0, 0, 0, 0, 0]], dtype=np.uint8)
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>>> erosion(bright_square, square(3))
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array([[0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0],
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[0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0]], dtype=uint8)
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"""
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selem = np.array(selem)
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selem = _shift_selem(selem, shift_x, shift_y)
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if out is None:
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out = np.empty_like(image)
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ndi.grey_erosion(image, footprint=selem, output=out)
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return out
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@default_selem
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def dilation(image, selem=None, out=None, shift_x=False, shift_y=False):
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"""Return greyscale morphological dilation of an image.
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Morphological dilation sets a pixel at (i,j) to the maximum over all pixels
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in the neighborhood centered at (i,j). Dilation enlarges bright regions
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and shrinks dark regions.
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Parameters
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----------
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image : ndarray
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Image array.
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selem : ndarray, optional
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The neighborhood expressed as a 2-D array of 1's and 0's.
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If None, use cross-shaped structuring element (connectivity=1).
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out : ndarray, optional
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The array to store the result of the morphology. If None, is
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passed, a new array will be allocated.
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shift_x, shift_y : bool, optional
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shift structuring element about center point. This only affects
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eccentric structuring elements (i.e. selem with even numbered sides).
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Returns
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-------
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dilated : uint8 array, same shape and type as `image`
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The result of the morphological dilation.
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Notes
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-----
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For `uint8` (and `uint16` up to a certain bit-depth) data, the lower
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algorithm complexity makes the `skimage.filters.rank.maximum` function more
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efficient for larger images and structuring elements.
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Examples
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--------
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>>> # Dilation enlarges bright regions
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>>> import numpy as np
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>>> from skimage.morphology import square
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>>> bright_pixel = np.array([[0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 0],
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... [0, 0, 1, 0, 0],
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... [0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 0]], dtype=np.uint8)
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>>> dilation(bright_pixel, square(3))
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array([[0, 0, 0, 0, 0],
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[0, 1, 1, 1, 0],
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[0, 1, 1, 1, 0],
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[0, 1, 1, 1, 0],
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[0, 0, 0, 0, 0]], dtype=uint8)
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"""
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selem = np.array(selem)
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selem = _shift_selem(selem, shift_x, shift_y)
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# Inside ndimage.grey_dilation, the structuring element is inverted,
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# eg. `selem = selem[::-1, ::-1]` for 2D [1]_, for reasons unknown to
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# this author (@jni). To "patch" this behaviour, we invert our own
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# selem before passing it to `ndi.grey_dilation`.
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# [1] https://github.com/scipy/scipy/blob/ec20ababa400e39ac3ffc9148c01ef86d5349332/scipy/ndimage/morphology.py#L1285
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selem = _invert_selem(selem)
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if out is None:
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out = np.empty_like(image)
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ndi.grey_dilation(image, footprint=selem, output=out)
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return out
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@default_selem
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@pad_for_eccentric_selems
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def opening(image, selem=None, out=None):
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"""Return greyscale morphological opening of an image.
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The morphological opening on an image is defined as an erosion followed by
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a dilation. Opening can remove small bright spots (i.e. "salt") and connect
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small dark cracks. This tends to "open" up (dark) gaps between (bright)
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features.
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Parameters
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----------
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image : ndarray
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Image array.
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selem : ndarray, optional
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The neighborhood expressed as an array of 1's and 0's.
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If None, use cross-shaped structuring element (connectivity=1).
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out : ndarray, optional
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The array to store the result of the morphology. If None
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is passed, a new array will be allocated.
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Returns
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-------
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opening : array, same shape and type as `image`
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The result of the morphological opening.
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Examples
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--------
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>>> # Open up gap between two bright regions (but also shrink regions)
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>>> import numpy as np
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>>> from skimage.morphology import square
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>>> bad_connection = np.array([[1, 0, 0, 0, 1],
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... [1, 1, 0, 1, 1],
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... [1, 1, 1, 1, 1],
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... [1, 1, 0, 1, 1],
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... [1, 0, 0, 0, 1]], dtype=np.uint8)
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>>> opening(bad_connection, square(3))
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array([[0, 0, 0, 0, 0],
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[1, 1, 0, 1, 1],
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[1, 1, 0, 1, 1],
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[1, 1, 0, 1, 1],
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[0, 0, 0, 0, 0]], dtype=uint8)
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"""
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eroded = erosion(image, selem)
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# note: shift_x, shift_y do nothing if selem side length is odd
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out = dilation(eroded, selem, out=out, shift_x=True, shift_y=True)
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return out
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@default_selem
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@pad_for_eccentric_selems
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def closing(image, selem=None, out=None):
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"""Return greyscale morphological closing of an image.
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The morphological closing on an image is defined as a dilation followed by
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an erosion. Closing can remove small dark spots (i.e. "pepper") and connect
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small bright cracks. This tends to "close" up (dark) gaps between (bright)
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features.
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Parameters
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----------
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image : ndarray
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Image array.
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selem : ndarray, optional
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The neighborhood expressed as an array of 1's and 0's.
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If None, use cross-shaped structuring element (connectivity=1).
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out : ndarray, optional
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The array to store the result of the morphology. If None,
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is passed, a new array will be allocated.
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Returns
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-------
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closing : array, same shape and type as `image`
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The result of the morphological closing.
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Examples
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--------
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>>> # Close a gap between two bright lines
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>>> import numpy as np
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>>> from skimage.morphology import square
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>>> broken_line = np.array([[0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 0],
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... [1, 1, 0, 1, 1],
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... [0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 0]], dtype=np.uint8)
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>>> closing(broken_line, square(3))
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array([[0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0],
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[1, 1, 1, 1, 1],
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[0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0]], dtype=uint8)
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"""
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dilated = dilation(image, selem)
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# note: shift_x, shift_y do nothing if selem side length is odd
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out = erosion(dilated, selem, out=out, shift_x=True, shift_y=True)
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return out
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@default_selem
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def white_tophat(image, selem=None, out=None):
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"""Return white top hat of an image.
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The white top hat of an image is defined as the image minus its
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morphological opening. This operation returns the bright spots of the image
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that are smaller than the structuring element.
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Parameters
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----------
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image : ndarray
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Image array.
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selem : ndarray, optional
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The neighborhood expressed as an array of 1's and 0's.
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If None, use cross-shaped structuring element (connectivity=1).
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out : ndarray, optional
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The array to store the result of the morphology. If None
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is passed, a new array will be allocated.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array, same shape and type as `image`
|
||
|
|
The result of the morphological white top hat.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
black_tophat
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] https://en.wikipedia.org/wiki/Top-hat_transform
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> # Subtract grey background from bright peak
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from skimage.morphology import square
|
||
|
|
>>> bright_on_grey = 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]], dtype=np.uint8)
|
||
|
|
>>> white_tophat(bright_on_grey, square(3))
|
||
|
|
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]], dtype=uint8)
|
||
|
|
|
||
|
|
"""
|
||
|
|
selem = np.array(selem)
|
||
|
|
if out is image:
|
||
|
|
opened = opening(image, selem)
|
||
|
|
if np.issubdtype(opened.dtype, np.bool_):
|
||
|
|
np.logical_xor(out, opened, out=out)
|
||
|
|
else:
|
||
|
|
out -= opened
|
||
|
|
return out
|
||
|
|
elif out is None:
|
||
|
|
out = np.empty_like(image)
|
||
|
|
# work-around for NumPy deprecation warning for arithmetic
|
||
|
|
# operations on bool arrays
|
||
|
|
if isinstance(image, np.ndarray) and image.dtype == np.bool:
|
||
|
|
image_ = image.view(dtype=np.uint8)
|
||
|
|
else:
|
||
|
|
image_ = image
|
||
|
|
if isinstance(out, np.ndarray) and out.dtype == np.bool:
|
||
|
|
out_ = out.view(dtype=np.uint8)
|
||
|
|
else:
|
||
|
|
out_ = out
|
||
|
|
out_ = ndi.white_tophat(image_, footprint=selem, output=out_)
|
||
|
|
return out
|
||
|
|
|
||
|
|
|
||
|
|
@default_selem
|
||
|
|
def black_tophat(image, selem=None, out=None):
|
||
|
|
"""Return black top hat of an image.
|
||
|
|
|
||
|
|
The black top hat of an image is defined as its morphological closing minus
|
||
|
|
the original image. This operation returns the dark spots of the image that
|
||
|
|
are smaller than the structuring element. Note that dark spots in the
|
||
|
|
original image are bright spots after the black top hat.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
image : ndarray
|
||
|
|
Image array.
|
||
|
|
selem : ndarray, optional
|
||
|
|
The neighborhood expressed as a 2-D array of 1's and 0's.
|
||
|
|
If None, use cross-shaped structuring element (connectivity=1).
|
||
|
|
out : ndarray, optional
|
||
|
|
The array to store the result of the morphology. If None
|
||
|
|
is passed, a new array will be allocated.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
out : array, same shape and type as `image`
|
||
|
|
The result of the morphological black top hat.
|
||
|
|
|
||
|
|
See also
|
||
|
|
--------
|
||
|
|
white_tophat
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] https://en.wikipedia.org/wiki/Top-hat_transform
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> # Change dark peak to bright peak and subtract background
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from skimage.morphology import square
|
||
|
|
>>> dark_on_grey = 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]], dtype=np.uint8)
|
||
|
|
>>> black_tophat(dark_on_grey, square(3))
|
||
|
|
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]], dtype=uint8)
|
||
|
|
|
||
|
|
"""
|
||
|
|
if out is image:
|
||
|
|
original = image.copy()
|
||
|
|
else:
|
||
|
|
original = image
|
||
|
|
out = closing(image, selem, out=out)
|
||
|
|
if np.issubdtype(out.dtype, np.bool_):
|
||
|
|
np.logical_xor(out, original, out=out)
|
||
|
|
else:
|
||
|
|
out -= original
|
||
|
|
return out
|