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import numpy as np
from scipy import ndimage as ndi
from ..morphology import dilation, erosion, square
from ..util import img_as_float, view_as_windows
from ..color import gray2rgb
def _find_boundaries_subpixel(label_img):
"""See ``find_boundaries(..., mode='subpixel')``.
Notes
-----
This function puts in an empty row and column between each *actual*
row and column of the image, for a corresponding shape of $2s - 1$
for every image dimension of size $s$. These "interstitial" rows
and columns are filled as ``True`` if they separate two labels in
`label_img`, ``False`` otherwise.
I used ``view_as_windows`` to get the neighborhood of each pixel.
Then I check whether there are two labels or more in that
neighborhood.
"""
ndim = label_img.ndim
max_label = np.iinfo(label_img.dtype).max
label_img_expanded = np.zeros([(2 * s - 1) for s in label_img.shape],
label_img.dtype)
pixels = (slice(None, None, 2), ) * ndim
label_img_expanded[pixels] = label_img
edges = np.ones(label_img_expanded.shape, dtype=bool)
edges[pixels] = False
label_img_expanded[edges] = max_label
windows = view_as_windows(np.pad(label_img_expanded, 1,
mode='constant', constant_values=0),
(3,) * ndim)
boundaries = np.zeros_like(edges)
for index in np.ndindex(label_img_expanded.shape):
if edges[index]:
values = np.unique(windows[index].ravel())
if len(values) > 2: # single value and max_label
boundaries[index] = True
return boundaries
def find_boundaries(label_img, connectivity=1, mode='thick', background=0):
"""Return bool array where boundaries between labeled regions are True.
Parameters
----------
label_img : array of int or bool
An array in which different regions are labeled with either different
integers or boolean values.
connectivity: int in {1, ..., `label_img.ndim`}, optional
A pixel is considered a boundary pixel if any of its neighbors
has a different label. `connectivity` controls which pixels are
considered neighbors. A connectivity of 1 (default) means
pixels sharing an edge (in 2D) or a face (in 3D) will be
considered neighbors. A connectivity of `label_img.ndim` means
pixels sharing a corner will be considered neighbors.
mode: string in {'thick', 'inner', 'outer', 'subpixel'}
How to mark the boundaries:
- thick: any pixel not completely surrounded by pixels of the
same label (defined by `connectivity`) is marked as a boundary.
This results in boundaries that are 2 pixels thick.
- inner: outline the pixels *just inside* of objects, leaving
background pixels untouched.
- outer: outline pixels in the background around object
boundaries. When two objects touch, their boundary is also
marked.
- subpixel: return a doubled image, with pixels *between* the
original pixels marked as boundary where appropriate.
background: int, optional
For modes 'inner' and 'outer', a definition of a background
label is required. See `mode` for descriptions of these two.
Returns
-------
boundaries : array of bool, same shape as `label_img`
A bool image where ``True`` represents a boundary pixel. For
`mode` equal to 'subpixel', ``boundaries.shape[i]`` is equal
to ``2 * label_img.shape[i] - 1`` for all ``i`` (a pixel is
inserted in between all other pairs of pixels).
Examples
--------
>>> labels = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 5, 5, 5, 0, 0],
... [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],
... [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],
... [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],
... [0, 0, 0, 0, 0, 5, 5, 5, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=np.uint8)
>>> find_boundaries(labels, mode='thick').astype(np.uint8)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0, 1, 1, 0],
[0, 1, 1, 0, 1, 1, 0, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> find_boundaries(labels, mode='inner').astype(np.uint8)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 1, 0, 0],
[0, 0, 1, 0, 1, 1, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> find_boundaries(labels, mode='outer').astype(np.uint8)
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 0],
[0, 0, 1, 1, 1, 1, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> labels_small = labels[::2, ::3]
>>> labels_small
array([[0, 0, 0, 0],
[0, 0, 5, 0],
[0, 1, 5, 0],
[0, 0, 5, 0],
[0, 0, 0, 0]], dtype=uint8)
>>> find_boundaries(labels_small, mode='subpixel').astype(np.uint8)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 0],
[0, 0, 0, 1, 0, 1, 0],
[0, 1, 1, 1, 0, 1, 0],
[0, 1, 0, 1, 0, 1, 0],
[0, 1, 1, 1, 0, 1, 0],
[0, 0, 0, 1, 0, 1, 0],
[0, 0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> bool_image = np.array([[False, False, False, False, False],
... [False, False, False, False, False],
... [False, False, True, True, True],
... [False, False, True, True, True],
... [False, False, True, True, True]], dtype=np.bool)
>>> find_boundaries(bool_image)
array([[False, False, False, False, False],
[False, False, True, True, True],
[False, True, True, True, True],
[False, True, True, False, False],
[False, True, True, False, False]], dtype=bool)
"""
if label_img.dtype == 'bool':
label_img = label_img.astype(np.uint8)
ndim = label_img.ndim
selem = ndi.generate_binary_structure(ndim, connectivity)
if mode != 'subpixel':
boundaries = dilation(label_img, selem) != erosion(label_img, selem)
if mode == 'inner':
foreground_image = (label_img != background)
boundaries &= foreground_image
elif mode == 'outer':
max_label = np.iinfo(label_img.dtype).max
background_image = (label_img == background)
selem = ndi.generate_binary_structure(ndim, ndim)
inverted_background = np.array(label_img, copy=True)
inverted_background[background_image] = max_label
adjacent_objects = ((dilation(label_img, selem) !=
erosion(inverted_background, selem)) &
~background_image)
boundaries &= (background_image | adjacent_objects)
return boundaries
else:
boundaries = _find_boundaries_subpixel(label_img)
return boundaries
def mark_boundaries(image, label_img, color=(1, 1, 0),
outline_color=None, mode='outer', background_label=0):
"""Return image with boundaries between labeled regions highlighted.
Parameters
----------
image : (M, N[, 3]) array
Grayscale or RGB image.
label_img : (M, N) array of int
Label array where regions are marked by different integer values.
color : length-3 sequence, optional
RGB color of boundaries in the output image.
outline_color : length-3 sequence, optional
RGB color surrounding boundaries in the output image. If None, no
outline is drawn.
mode : string in {'thick', 'inner', 'outer', 'subpixel'}, optional
The mode for finding boundaries.
background_label : int, optional
Which label to consider background (this is only useful for
modes ``inner`` and ``outer``).
Returns
-------
marked : (M, N, 3) array of float
An image in which the boundaries between labels are
superimposed on the original image.
See Also
--------
find_boundaries
"""
marked = img_as_float(image, force_copy=True)
if marked.ndim == 2:
marked = gray2rgb(marked)
if mode == 'subpixel':
# Here, we want to interpose an extra line of pixels between
# each original line - except for the last axis which holds
# the RGB information. ``ndi.zoom`` then performs the (cubic)
# interpolation, filling in the values of the interposed pixels
marked = ndi.zoom(marked, [2 - 1/s for s in marked.shape[:-1]] + [1],
mode='reflect')
boundaries = find_boundaries(label_img, mode=mode,
background=background_label)
if outline_color is not None:
outlines = dilation(boundaries, square(3))
marked[outlines] = outline_color
marked[boundaries] = color
return marked