skimage2.segmentation.watershed#

skimage2.segmentation.watershed(image, markers=None, connectivity=1, offset=None, mask=None, compactness=0, watershed_line=False)[source]#

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.

markersint, 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 skimage.morphology.local_minima() onto image, followed by skimage.measure.label() onto the result (with the same given connectivity). Generally speaking, users are encouraged to pass markers explicitly.

connectivityint 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.

offsetarray_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.

compactnessfloat, optional

Use compact watershed [1] with given compactness parameter. Higher values result in more regularly-shaped watershed basins.

watershed_linebool, 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:
outndarray

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

[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 _skimage2.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.