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_expand_labels.py
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_expand_labels.py
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"""
expand_labels is derived from code that was
originally part of CellProfiler, code licensed under BSD license.
Website: http://www.cellprofiler.org
Copyright (c) 2020 Broad Institute
All rights reserved.
Original authors: CellProfiler team
"""
import numpy as np
from scipy.ndimage import distance_transform_edt
def expand_labels(label_image, distance=1):
"""Expand labels in label image by ``distance`` pixels without overlapping.
Given a label image, ``expand_labels`` grows label regions (connected components)
outwards by up to ``distance`` pixels without overflowing into neighboring regions.
More specifically, each background pixel that is within Euclidean distance
of <= ``distance`` pixels of a connected component is assigned the label of that
connected component.
Where multiple connected components are within ``distance`` pixels of a background
pixel, the label value of the closest connected component will be assigned (see
Notes for the case of multiple labels at equal distance).
Parameters
----------
label_image : ndarray of dtype int
label image
distance : float
Euclidean distance in pixels by which to grow the labels. Default is one.
Returns
-------
enlarged_labels : ndarray of dtype int
Labeled array, where all connected regions have been enlarged
Notes
-----
Where labels are spaced more than ``distance`` pixels are apart, this is
equivalent to a morphological dilation with a disc or hyperball of radius ``distance``.
However, in contrast to a morphological dilation, ``expand_labels`` will
not expand a label region into a neighboring region.
This implementation of ``expand_labels`` is derived from CellProfiler [1]_, where
it is known as module "IdentifySecondaryObjects (Distance-N)" [2]_.
There is an important edge case when a pixel has the same distance to
multiple regions, as it is not defined which region expands into that
space. Here, the exact behavior depends on the upstream implementation
of ``scipy.ndimage.distance_transform_edt``.
See Also
--------
:func:`skimage.measure.label`, :func:`skimage.segmentation.watershed`, :func:`skimage.morphology.dilation`
References
----------
.. [1] https://cellprofiler.org
.. [2] https://github.com/CellProfiler/CellProfiler/blob/082930ea95add7b72243a4fa3d39ae5145995e9c/cellprofiler/modules/identifysecondaryobjects.py#L559
Examples
--------
>>> labels = np.array([0, 1, 0, 0, 0, 0, 2])
>>> expand_labels(labels, distance=1)
array([1, 1, 1, 0, 0, 2, 2])
Labels will not overwrite each other:
>>> expand_labels(labels, distance=3)
array([1, 1, 1, 1, 2, 2, 2])
In case of ties, behavior is undefined, but currently resolves to the
label closest to ``(0,) * ndim`` in lexicographical order.
>>> labels_tied = np.array([0, 1, 0, 2, 0])
>>> expand_labels(labels_tied, 1)
array([1, 1, 1, 2, 2])
>>> labels2d = np.array(
... [[0, 1, 0, 0],
... [2, 0, 0, 0],
... [0, 3, 0, 0]]
... )
>>> expand_labels(labels2d, 1)
array([[2, 1, 1, 0],
[2, 2, 0, 0],
[2, 3, 3, 0]])
"""
distances, nearest_label_coords = distance_transform_edt(
label_image == 0, return_indices=True
)
labels_out = np.zeros_like(label_image)
dilate_mask = distances <= distance
# build the coordinates to find nearest labels,
# in contrast to [1] this implementation supports label arrays
# of any dimension
masked_nearest_label_coords = [
dimension_indices[dilate_mask]
for dimension_indices in nearest_label_coords
]
nearest_labels = label_image[tuple(masked_nearest_label_coords)]
labels_out[dilate_mask] = nearest_labels
return labels_out