watershed

watershed

skimage.morphology.watershed(image, markers, connectivity=None, offset=None, mask=None) [source]

Return a matrix labeled using the watershed segmentation algorithm

Parameters:

image: ndarray (2-D, 3-D, ...) of integers Data array where the lowest value points are labeled first. markers: ndarray of the same shape as `image` An array marking the basins with the values to be assigned in the label matrix. Zero means not a marker. This array should be of an integer type. connectivity: ndarray, optional An array with the same number of dimensions as image whose non-zero elements indicate neighbors for connection. Following the scipy convention, default is a one-connected array of the dimension of the image. offset: array_like of shape image.ndim, optional offset of the connectivity (one offset per dimension) mask: ndarray of bools or 0s and 1s, optional Array of same shape as image. Only points at which mask == True will be labeled.

Returns:

out: ndarray A labeled matrix of the same type and shape as markers

See also

skimage.segmentation.random_walker

random walker segmentation 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 [R301]_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.

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

[R301]

http://en.wikipedia.org/wiki/Watershed_%28image_processing%29

[R302]

http://cmm.ensmp.fr/~beucher/wtshed.html

Examples

The watershed algorithm is very useful to separate overlapping objects

>>> # 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)
>>> # Now we want to separate the two objects in image
>>> # Generate the markers as local 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
>>> local_maxi = peak_local_max(distance, labels=image,
...                             footprint=np.ones((3, 3)),
...                             indices=False)
>>> markers = ndi.label(local_maxi)[0]
>>> labels = watershed(-distance, markers, mask=image)

The algorithm works also for 3-D images, and can be used for example to separate overlapping spheres.