112 lines
5 KiB
Python
112 lines
5 KiB
Python
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from .._shared.utils import deprecated
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@deprecated('skimage.segmentation.watershed', removed_version='0.19')
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def watershed(image, markers=None, connectivity=1, offset=None, mask=None,
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compactness=0, watershed_line=False):
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"""Find watershed basins in `image` flooded from given `markers`.
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Parameters
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----------
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image : ndarray (2-D, 3-D, ...) of integers
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Data array where the lowest value points are labeled first.
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markers : int, or ndarray of int, same shape as `image`, optional
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The desired number of markers, or an array marking the basins with the
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values to be assigned in the label matrix. Zero means not a marker. If
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``None`` (no markers given), the local minima of the image are used as
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markers.
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connectivity : ndarray, optional
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An array with the same number of dimensions as `image` whose
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non-zero elements indicate neighbors for connection.
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Following the scipy convention, default is a one-connected array of
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the dimension of the image.
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offset : array_like of shape image.ndim, optional
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offset of the connectivity (one offset per dimension)
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mask : ndarray of bools or 0s and 1s, optional
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Array of same shape as `image`. Only points at which mask == True
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will be labeled.
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compactness : float, optional
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Use compact watershed [3]_ with given compactness parameter.
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Higher values result in more regularly-shaped watershed basins.
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watershed_line : bool, optional
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If watershed_line is True, a one-pixel wide line separates the regions
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obtained by the watershed algorithm. The line has the label 0.
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Returns
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-------
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out: ndarray
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A labeled matrix of the same type and shape as markers
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See also
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--------
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skimage.segmentation.random_walker: random walker segmentation
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A segmentation algorithm based on anisotropic diffusion, usually
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slower than the watershed but with good results on noisy data and
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boundaries with holes.
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Notes
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-----
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This function implements a watershed algorithm [1]_ [2]_ that apportions
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pixels into marked basins. The algorithm uses a priority queue to hold
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the pixels with the metric for the priority queue being pixel value, then
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the time of entry into the queue - this settles ties in favor of the
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closest marker.
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Some ideas taken from
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Soille, "Automated Basin Delineation from Digital Elevation Models Using
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Mathematical Morphology", Signal Processing 20 (1990) 171-182
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The most important insight in the paper is that entry time onto the queue
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solves two problems: a pixel should be assigned to the neighbor with the
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largest gradient or, if there is no gradient, pixels on a plateau should
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be split between markers on opposite sides.
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This implementation converts all arguments to specific, lowest common
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denominator types, then passes these to a C algorithm.
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Markers can be determined manually, or automatically using for example
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the local minima of the gradient of the image, or the local maxima of the
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distance function to the background for separating overlapping objects
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(see example).
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References
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----------
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.. [1] https://en.wikipedia.org/wiki/Watershed_%28image_processing%29
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.. [2] http://cmm.ensmp.fr/~beucher/wtshed.html
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.. [3] Peer Neubert & Peter Protzel (2014). Compact Watershed and
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Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation
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Algorithms. ICPR 2014, pp 996-1001. :DOI:`10.1109/ICPR.2014.181`
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https://www.tu-chemnitz.de/etit/proaut/publications/cws_pSLIC_ICPR.pdf
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Examples
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--------
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The watershed algorithm is useful to separate overlapping objects.
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We first generate an initial image with two overlapping circles:
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>>> import numpy as np
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>>> x, y = np.indices((80, 80))
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>>> x1, y1, x2, y2 = 28, 28, 44, 52
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>>> r1, r2 = 16, 20
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>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
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>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
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>>> image = np.logical_or(mask_circle1, mask_circle2)
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Next, we want to separate the two circles. We generate markers at the
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maxima of the distance to the background:
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>>> from scipy import ndimage as ndi
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>>> distance = ndi.distance_transform_edt(image)
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>>> from skimage.feature import peak_local_max
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>>> local_maxi = peak_local_max(distance, labels=image,
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... footprint=np.ones((3, 3)),
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... indices=False)
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>>> markers = ndi.label(local_maxi)[0]
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Finally, we run the watershed on the image and markers:
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>>> labels = watershed(-distance, markers, mask=image) # doctest: +SKIP
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The algorithm works also for 3-D images, and can be used for example to
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separate overlapping spheres.
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"""
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from ..segmentation import watershed as _watershed
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return _watershed(image, markers, connectivity, offset, mask,
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compactness, watershed_line)
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