"""watershed.py - watershed algorithm
This module implements a watershed algorithm that apportions pixels into
marked basins. The algorithm uses a priority queue to hold the pixels
with the metric for the priority queue being pixel value, then the time
of entry into the queue - this settles ties in favor of the closest marker.
Some ideas taken from
Soille, "Automated Basin Delineation from Digital Elevation Models Using
Mathematical Morphology", Signal Processing 20 (1990) 171-182.
The most important insight in the paper is that entry time onto the queue
solves two problems: a pixel should be assigned to the neighbor with the
largest gradient or, if there is no gradient, pixels on a plateau should
be split between markers on opposite sides.
"""
import numpy as np
from scipy import ndimage as ndi
from . import _watershed_cy
from ..morphology.extrema import local_minima
from ..morphology._util import _validate_connectivity, _offsets_to_raveled_neighbors
from ..util import crop, regular_seeds
def _validate_inputs(image, markers, mask, connectivity):
"""Ensure that all inputs to watershed have matching shapes and types.
Parameters
----------
image : array
The input image.
markers : int or array of int
The marker image.
mask : array, or None
A boolean mask, True where we want to compute the watershed.
connectivity : int in {1, ..., image.ndim}
The connectivity of the neighborhood of a pixel.
Returns
-------
image, markers, mask : arrays
The validated and formatted arrays. Image will have dtype float64,
markers int32, and mask int8. If ``None`` was given for the mask,
it is a volume of all 1s.
Raises
------
ValueError
If the shapes of the given arrays don't match.
"""
n_pixels = image.size
if mask is None:
# Use a complete `True` mask if none is provided
mask = np.ones(image.shape, bool)
else:
mask = np.asanyarray(mask, dtype=bool)
n_pixels = np.sum(mask)
if mask.shape != image.shape:
message = (
f'`mask` (shape {mask.shape}) must have same shape '
f'as `image` (shape {image.shape})'
)
raise ValueError(message)
if markers is None:
markers_bool = local_minima(image, connectivity=connectivity) * mask
footprint = ndi.generate_binary_structure(markers_bool.ndim, connectivity)
markers = ndi.label(markers_bool, structure=footprint)[0]
elif not isinstance(markers, (np.ndarray, list, tuple)):
# not array-like, assume int
# given int, assume that number of markers *within mask*.
markers = regular_seeds(image.shape, int(markers / (n_pixels / image.size)))
markers *= mask
else:
markers = np.asanyarray(markers) * mask
if markers.shape != image.shape:
message = (
f'`markers` (shape {markers.shape}) must have same '
f'shape as `image` (shape {image.shape})'
)
raise ValueError(message)
return (image.astype(np.float64), markers, mask.astype(np.int8))
[文档]
def watershed(
image,
markers=None,
connectivity=1,
offset=None,
mask=None,
compactness=0,
watershed_line=False,
):
"""Find watershed basins in an image flooded from given markers.
Parameters
----------
image : (M, N[, ...]) ndarray
Data array where the lowest value points are labeled first.
markers : int, or (M, N[, ...]) ndarray of int, optional
The desired number of basins, or an array marking the basins with the
values to be assigned in the label matrix. Zero means not a marker. If
None, the (default) markers are determined as the local minima of
`image`. Specifically, the computation is equivalent to applying
:func:`skimage.morphology.local_minima` onto `image`, followed by
:func:`skimage.measure.label` onto the result (with the same given
`connectivity`). Generally speaking, users are encouraged to pass
markers explicitly.
connectivity : int or ndarray, optional
The neighborhood connectivity. An integer is interpreted as in
``scipy.ndimage.generate_binary_structure``, as the maximum number
of orthogonal steps to reach a neighbor. An array is directly
interpreted as a footprint (structuring element). Default value is 1.
In 2D, 1 gives a 4-neighborhood while 2 gives an 8-neighborhood.
offset : array_like of shape image.ndim, optional
The coordinates of the center of the footprint.
mask : (M, N[, ...]) ndarray of bools or 0's and 1's, optional
Array of same shape as `image`. Only points at which mask == True
will be labeled.
compactness : float, optional
Use compact watershed [1]_ with given compactness parameter.
Higher values result in more regularly-shaped watershed basins.
watershed_line : bool, optional
If True, a one-pixel wide line separates the regions
obtained by the watershed algorithm. The line has the label 0.
Note that the method used for adding this line expects that
marker regions are not adjacent; the watershed line may not catch
borders between adjacent marker regions.
Returns
-------
out : ndarray
A labeled matrix of the same type and shape as `markers`.
See Also
--------
skimage.segmentation.random_walker
A segmentation algorithm based on anisotropic diffusion, usually
slower than the watershed but with good results on noisy data and
boundaries with holes.
Notes
-----
This function implements a watershed algorithm [2]_ [3]_ that apportions
pixels into marked basins. The algorithm uses a priority queue to hold
the pixels with the metric for the priority queue being pixel value, then
the time of entry into the queue -- this settles ties in favor of the
closest marker.
Some ideas are taken from [4]_.
The most important insight in the paper is that entry time onto the queue
solves two problems: a pixel should be assigned to the neighbor with the
largest gradient or, if there is no gradient, pixels on a plateau should
be split between markers on opposite sides.
This implementation converts all arguments to specific, lowest common
denominator types, then passes these to a C algorithm.
Markers can be determined manually, or automatically using for example
the local minima of the gradient of the image, or the local maxima of the
distance function to the background for separating overlapping objects
(see example).
References
----------
.. [1] P. Neubert and P. Protzel, "Compact Watershed and Preemptive SLIC:
On Improving Trade-offs of Superpixel Segmentation Algorithms,"
2014 22nd International Conference on Pattern Recognition,
Stockholm, Sweden, 2014, pp. 996-1001, :DOI:`10.1109/ICPR.2014.181`
https://www.tu-chemnitz.de/etit/proaut/publications/cws_pSLIC_ICPR.pdf
.. [2] https://en.wikipedia.org/wiki/Watershed_%28image_processing%29
.. [3] http://cmm.ensmp.fr/~beucher/wtshed.html
.. [4] P. J. Soille and M. M. Ansoult, "Automated basin delineation from
digital elevation models using mathematical morphology," Signal
Processing, 20(2):171-182, :DOI:`10.1016/0165-1684(90)90127-K`
Examples
--------
The watershed algorithm is useful to separate overlapping objects.
We first generate an initial image with two overlapping circles:
>>> x, y = np.indices((80, 80))
>>> x1, y1, x2, y2 = 28, 28, 44, 52
>>> r1, r2 = 16, 20
>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
>>> image = np.logical_or(mask_circle1, mask_circle2)
Next, we want to separate the two circles. We generate markers at the
maxima of the distance to the background:
>>> from scipy import ndimage as ndi
>>> distance = ndi.distance_transform_edt(image)
>>> from skimage.feature import peak_local_max
>>> max_coords = peak_local_max(distance, labels=image,
... footprint=np.ones((3, 3)))
>>> local_maxima = np.zeros_like(image, dtype=bool)
>>> local_maxima[tuple(max_coords.T)] = True
>>> markers = ndi.label(local_maxima)[0]
Finally, we run the watershed on the image and markers:
>>> labels = watershed(-distance, markers, mask=image)
The algorithm works also for 3D images, and can be used for example to
separate overlapping spheres.
"""
image, markers, mask = _validate_inputs(image, markers, mask, connectivity)
connectivity, offset = _validate_connectivity(image.ndim, connectivity, offset)
# pad the image, markers, and mask so that we can use the mask to
# keep from running off the edges
pad_width = [(p, p) for p in offset]
image = np.pad(image, pad_width, mode='constant')
mask = np.pad(mask, pad_width, mode='constant').ravel()
output = np.pad(markers, pad_width, mode='constant')
flat_neighborhood = _offsets_to_raveled_neighbors(
image.shape, connectivity, center=offset
)
marker_locations = np.flatnonzero(output)
image_strides = np.array(image.strides, dtype=np.intp) // image.itemsize
_watershed_cy.watershed_raveled(
image.ravel(),
marker_locations,
flat_neighborhood,
mask,
image_strides,
compactness,
output.ravel(),
watershed_line,
)
output = crop(output, pad_width, copy=True)
return output
