skimage.segmentation — skimage 0.24.0 documentation (2024)

Algorithms to partition images into meaningful regions or boundaries.

skimage.segmentation.active_contour	Active contour model.
skimage.segmentation.chan_vese	Chan-Vese segmentation algorithm.
skimage.segmentation.checkerboard_level_set	Create a checkerboard level set with binary values.
skimage.segmentation.clear_border	Clear objects connected to the label image border.
skimage.segmentation.disk_level_set	Create a disk level set with binary values.
skimage.segmentation.expand_labels	Expand labels in label image by `distance` pixels without overlapping.
skimage.segmentation.felzenszwalb	Computes Felsenszwalb's efficient graph based image segmentation.
skimage.segmentation.find_boundaries	Return bool array where boundaries between labeled regions are True.
skimage.segmentation.flood	Mask corresponding to a flood fill.
skimage.segmentation.flood_fill	Perform flood filling on an image.
skimage.segmentation.inverse_gaussian_gradient	Inverse of gradient magnitude.
skimage.segmentation.join_segmentations	Return the join of the two input segmentations.
skimage.segmentation.mark_boundaries	Return image with boundaries between labeled regions highlighted.
skimage.segmentation.morphological_chan_vese	Morphological Active Contours without Edges (MorphACWE)
skimage.segmentation.morphological_geodesic_active_contour	Morphological Geodesic Active Contours (MorphGAC).
skimage.segmentation.quickshift	Segment image using quickshift clustering in Color-(x,y) space.
skimage.segmentation.random_walker	Random walker algorithm for segmentation from markers.
skimage.segmentation.relabel_sequential	Relabel arbitrary labels to {offset, .
skimage.segmentation.slic	Segments image using k-means clustering in Color-(x,y,z) space.
skimage.segmentation.watershed	Find watershed basins in an image flooded from given markers.

skimage.segmentation.active_contour(image, snake, alpha=0.01, beta=0.1, w_line=0, w_edge=1, gamma=0.01, max_px_move=1.0, max_num_iter=2500, convergence=0.1, *, boundary_condition='periodic')[source]#

Active contour model.

Active contours by fitting snakes to features of images. Supports singleand multichannel 2D images. Snakes can be periodic (for segmentation) orhave fixed and/or free ends.The output snake has the same length as the input boundary.As the number of points is constant, make sure that the initial snakehas enough points to capture the details of the final contour.

Parameters:

image(M, N) or (M, N, 3) ndarray: Input image.
snake(K, 2) ndarray: Initial snake coordinates. For periodic boundary conditions, endpointsmust not be duplicated.
alphafloat, optional: Snake length shape parameter. Higher values makes snake contractfaster.
betafloat, optional: Snake smoothness shape parameter. Higher values makes snake smoother.
w_linefloat, optional: Controls attraction to brightness. Use negative values to attracttoward dark regions.
w_edgefloat, optional: Controls attraction to edges. Use negative values to repel snake fromedges.
gammafloat, optional: Explicit time stepping parameter.
max_px_movefloat, optional: Maximum pixel distance to move per iteration.
max_num_iterint, optional: Maximum iterations to optimize snake shape.
convergencefloat, optional: Convergence criteria.
boundary_conditionstring, optional: Boundary conditions for the contour. Can be one of ‘periodic’,‘free’, ‘fixed’, ‘free-fixed’, or ‘fixed-free’. ‘periodic’ attachesthe two ends of the snake, ‘fixed’ holds the end-points in place,and ‘free’ allows free movement of the ends. ‘fixed’ and ‘free’ canbe combined by parsing ‘fixed-free’, ‘free-fixed’. Parsing‘fixed-fixed’ or ‘free-free’ yields same behaviour as ‘fixed’ and‘free’, respectively.

Returns:

snake(K, 2) ndarray: Optimised snake, same shape as input parameter.

References

[1]

Kass, M.; Witkin, A.; Terzopoulos, D. “Snakes: Active contourmodels”. International Journal of Computer Vision 1 (4): 321(1988). DOI:10.1007/BF00133570

Examples

>>> from skimage.draw import circle_perimeter>>> from skimage.filters import gaussian

Create and smooth image:

>>> img = np.zeros((100, 100))>>> rr, cc = circle_perimeter(35, 45, 25)>>> img[rr, cc] = 1>>> img = gaussian(img, sigma=2, preserve_range=False)

Initialize spline:

>>> s = np.linspace(0, 2*np.pi, 100)>>> init = 50 * np.array([np.sin(s), np.cos(s)]).T + 50

Fit spline to image:

>>> snake = active_contour(img, init, w_edge=0, w_line=1) >>> dist = np.sqrt((45-snake[:, 0])**2 + (35-snake[:, 1])**2) >>> int(np.mean(dist)) 25

Active Contour Model

skimage.segmentation.chan_vese(image, mu=0.25, lambda1=1.0, lambda2=1.0, tol=0.001, max_num_iter=500, dt=0.5, init_level_set='checkerboard', extended_output=False)[source]#

Chan-Vese segmentation algorithm.

Active contour model by evolving a level set. Can be used tosegment objects without clearly defined boundaries.

Parameters:

image(M, N) ndarray

Grayscale image to be segmented.

mufloat, optional

‘edge length’ weight parameter. Higher mu values willproduce a ‘round’ edge, while values closer to zero willdetect smaller objects.

lambda1float, optional

‘difference from average’ weight parameter for the outputregion with value ‘True’. If it is lower than lambda2, thisregion will have a larger range of values than the other.

lambda2float, optional

‘difference from average’ weight parameter for the outputregion with value ‘False’. If it is lower than lambda1, thisregion will have a larger range of values than the other.

tolfloat, positive, optional

Level set variation tolerance between iterations. If theL2 norm difference between the level sets of successiveiterations normalized by the area of the image is below thisvalue, the algorithm will assume that the solution wasreached.

max_num_iteruint, optional

Maximum number of iterations allowed before the algorithminterrupts itself.

dtfloat, optional

A multiplication factor applied at calculations for each step,serves to accelerate the algorithm. While higher values mayspeed up the algorithm, they may also lead to convergenceproblems.

init_level_setstr or (M, N) ndarray, optional

Defines the starting level set used by the algorithm.If a string is inputted, a level set that matches the imagesize will automatically be generated. Alternatively, it ispossible to define a custom level set, which should be anarray of float values, with the same shape as ‘image’.Accepted string values are as follows.

‘checkerboard’: the starting level set is defined assin(x/5*pi)*sin(y/5*pi), where x and y are pixelcoordinates. This level set has fast convergence, but mayfail to detect implicit edges.
‘disk’: the starting level set is defined as the oppositeof the distance from the center of the image minus half ofthe minimum value between image width and image height.This is somewhat slower, but is more likely to properlydetect implicit edges.
‘small disk’: the starting level set is defined as theopposite of the distance from the center of the imageminus a quarter of the minimum value between image widthand image height.

extended_outputbool, optional

If set to True, the return value will be a tuple containingthe three return values (see below). If set to False whichis the default value, only the ‘segmentation’ array will bereturned.

Returns:

segmentation(M, N) ndarray, bool: Segmentation produced by the algorithm.
phi(M, N) ndarray of floats: Final level set computed by the algorithm.
energieslist of floats: Shows the evolution of the ‘energy’ for each step of thealgorithm. This should allow to check whether the algorithmconverged.

Notes

The Chan-Vese Algorithm is designed to segment objects withoutclearly defined boundaries. This algorithm is based on level setsthat are evolved iteratively to minimize an energy, which isdefined by weighted values corresponding to the sum of differencesintensity from the average value outside the segmented region, thesum of differences from the average value inside the segmentedregion, and a term which is dependent on the length of theboundary of the segmented region.

This algorithm was first proposed by Tony Chan and Luminita Vese,in a publication entitled “An Active Contour Model Without Edges”[1].

This implementation of the algorithm is somewhat simplified in thesense that the area factor ‘nu’ described in the original paper isnot implemented, and is only suitable for grayscale images.

Typical values for lambda1 and lambda2 are 1. If the‘background’ is very different from the segmented object in termsof distribution (for example, a uniform black image with figuresof varying intensity), then these values should be different fromeach other.

Typical values for mu are between 0 and 1, though higher valuescan be used when dealing with shapes with very ill-definedcontours.

The ‘energy’ which this algorithm tries to minimize is definedas the sum of the differences from the average within the regionsquared and weighed by the ‘lambda’ factors to which is added thelength of the contour multiplied by the ‘mu’ factor.

Supports 2D grayscale images only, and does not implement the areaterm described in the original article.

References

[1]

An Active Contour Model without Edges, Tony Chan andLuminita Vese, Scale-Space Theories in Computer Vision,1999, DOI:10.1007/3-540-48236-9_13

[2]

Chan-Vese Segmentation, Pascal Getreuer Image Processing OnLine, 2 (2012), pp. 214-224,DOI:10.5201/ipol.2012.g-cv

[3]

The Chan-Vese Algorithm - Project Report, Rami Cohen, 2011arXiv:1107.2782

Chan-Vese Segmentation

skimage.segmentation.checkerboard_level_set(image_shape, square_size=5)[source]#

Create a checkerboard level set with binary values.

Parameters:

image_shapetuple of positive integers: Shape of the image.
square_sizeint, optional: Size of the squares of the checkerboard. It defaults to 5.

Returns:

outarray with shape image_shape: Binary level set of the checkerboard.

See also

disk_level_set

Morphological Snakes

skimage.segmentation.clear_border(labels, buffer_size=0, bgval=0, mask=None, *, out=None)[source]#

Clear objects connected to the label image border.

Parameters:

labels(M[, N[, …, P]]) array of int or bool: Imaging data labels.
buffer_sizeint, optional: The width of the border examined. By default, only objectsthat touch the outside of the image are removed.
bgvalfloat or int, optional: Cleared objects are set to this value.
maskndarray of bool, same shape as image, optional.: Image data mask. Objects in labels image overlapping withFalse pixels of mask will be removed. If defined, theargument buffer_size will be ignored.
outndarray: Array of the same shape as labels, into which theoutput is placed. By default, a new array is created.

Returns:

out(M[, N[, …, P]]) array: Imaging data labels with cleared borders

Examples

>>> import numpy as np>>> from skimage.segmentation import clear_border>>> labels = np.array([[0, 0, 0, 0, 0, 0, 0, 1, 0],...  [1, 1, 0, 0, 1, 0, 0, 1, 0],...  [1, 1, 0, 1, 0, 1, 0, 0, 0],...  [0, 0, 0, 1, 1, 1, 1, 0, 0],...  [0, 1, 1, 1, 1, 1, 1, 1, 0],...  [0, 0, 0, 0, 0, 0, 0, 0, 0]])>>> clear_border(labels)array([[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]])>>> mask = np.array([[0, 0, 1, 1, 1, 1, 1, 1, 1],...  [0, 0, 1, 1, 1, 1, 1, 1, 1],...  [1, 1, 1, 1, 1, 1, 1, 1, 1],...  [1, 1, 1, 1, 1, 1, 1, 1, 1],...  [1, 1, 1, 1, 1, 1, 1, 1, 1],...  [1, 1, 1, 1, 1, 1, 1, 1, 1]]).astype(bool)>>> clear_border(labels, mask=mask)array([[0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]])

Label image regions

Colocalization metrics

Measure fluorescence intensity at the nuclear envelope

skimage.segmentation.disk_level_set(image_shape, *, center=None, radius=None)[source]#

Create a disk level set with binary values.

Parameters:

image_shapetuple of positive integers: Shape of the image
centertuple of positive integers, optional: Coordinates of the center of the disk given in (row, column). If notgiven, it defaults to the center of the image.
radiusfloat, optional: Radius of the disk. If not given, it is set to the 75% of thesmallest image dimension.

Returns:

outarray with shape image_shape: Binary level set of the disk with the given radius and center.

See also

checkerboard_level_set

skimage.segmentation.expand_labels(label_image, distance=1, spacing=1)[source]#

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 units without overflowing into neighboring regions.More specifically, each background pixel that is within Euclidean distanceof <= distance pixels of a connected component is assigned the label of thatconnected component. The spacing parameter can be used to specify the spacingrate of the distance transform used to calculate the Euclidean distance for anisotropicimages.Where multiple connected components are within distance pixels of a backgroundpixel, the label value of the closest connected component will be assigned (seeNotes for the case of multiple labels at equal distance).

Parameters:

label_imagendarray of dtype int: label image
distancefloat: Euclidean distance in pixels by which to grow the labels. Default is one.
spacingfloat, or sequence of float, optional: Spacing of elements along each dimension. If a sequence, must be of lengthequal to the input rank; if a single number, this is used for all axes. Ifnot specified, a grid spacing of unity is implied.

Returns:

enlarged_labelsndarray of dtype int: Labeled array, where all connected regions have been enlarged

See also

skimage.measure.label(), skimage.segmentation.watershed(), skimage.morphology.dilation()

Notes

Where labels are spaced more than distance pixels are apart, this isequivalent to a morphological dilation with a disc or hyperball of radius distance.However, in contrast to a morphological dilation, expand_labels willnot expand a label region into a neighboring region.

This implementation of expand_labels is derived from CellProfiler [1], whereit is known as module “IdentifySecondaryObjects (Distance-N)” [2].

There is an important edge case when a pixel has the same distance tomultiple regions, as it is not defined which region expands into thatspace. Here, the exact behavior depends on the upstream implementationof scipy.ndimage.distance_transform_edt.

References

[1]

https://cellprofiler.org

[2]

CellProfiler/CellProfiler

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 thelabel 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]])>>> expand_labels(labels2d, 1, spacing=[1, 0.5])array([[1, 1, 1, 1], [2, 2, 2, 0], [3, 3, 3, 3]])

Expand segmentation labels without overlap

skimage.segmentation.felzenszwalb(image, scale=1, sigma=0.8, min_size=20, *, channel_axis=-1)[source]#

Computes Felsenszwalb’s efficient graph based image segmentation.

Produces an oversegmentation of a multichannel (i.e. RGB) imageusing a fast, minimum spanning tree based clustering on the image grid.The parameter scale sets an observation level. Higher scale meansless and larger segments. sigma is the diameter of a Gaussian kernel,used for smoothing the image prior to segmentation.

The number of produced segments as well as their size can only becontrolled indirectly through scale. Segment size within an image canvary greatly depending on local contrast.

For RGB images, the algorithm uses the euclidean distance between pixels incolor space.

Parameters:

image(M, N[, 3]) ndarray

Input image.

scalefloat

Free parameter. Higher means larger clusters.

sigmafloat

Width (standard deviation) of Gaussian kernel used in preprocessing.

min_sizeint

Minimum component size. Enforced using postprocessing.

channel_axisint or None, optional

If None, the image is assumed to be a grayscale (single channel) image.Otherwise, this parameter indicates which axis of the array correspondsto channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

segment_mask(M, N) ndarray: Integer mask indicating segment labels.

Notes

The k parameter used in the original paper renamed to scale here.

References

[1]

Efficient graph-based image segmentation, Felzenszwalb, P.F. andHuttenlocher, D.P. International Journal of Computer Vision, 2004

Examples

>>> from skimage.segmentation import felzenszwalb>>> from skimage.data import coffee>>> img = coffee()>>> segments = felzenszwalb(img, scale=3.0, sigma=0.95, min_size=5)

Comparison of segmentation and superpixel algorithms

skimage.segmentation.find_boundaries(label_img, connectivity=1, mode='thick', background=0)[source]#

Return bool array where boundaries between labeled regions are True.

Parameters:

label_imgarray of int or bool

An array in which different regions are labeled with either differentintegers or boolean values.

connectivityint in {1, …, label_img.ndim}, optional

A pixel is considered a boundary pixel if any of its neighborshas a different label. connectivity controls which pixels areconsidered neighbors. A connectivity of 1 (default) meanspixels sharing an edge (in 2D) or a face (in 3D) will beconsidered neighbors. A connectivity of label_img.ndim meanspixels sharing a corner will be considered neighbors.

modestring in {‘thick’, ‘inner’, ‘outer’, ‘subpixel’}

How to mark the boundaries:

thick: any pixel not completely surrounded by pixels of thesame label (defined by connectivity) is marked as a boundary.This results in boundaries that are 2 pixels thick.
inner: outline the pixels just inside of objects, leavingbackground pixels untouched.
outer: outline pixels in the background around objectboundaries. When two objects touch, their boundary is alsomarked.
subpixel: return a doubled image, with pixels between theoriginal pixels marked as boundary where appropriate.

backgroundint, optional

For modes ‘inner’ and ‘outer’, a definition of a backgroundlabel is required. See mode for descriptions of these two.

Returns:

boundariesarray of bool, same shape as label_img: A bool image where True represents a boundary pixel. Formode equal to ‘subpixel’, boundaries.shape[i] is equalto 2 * label_img.shape[i] - 1 for all i (a pixel isinserted in between all other pairs of pixels).

Examples

>>> labels = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],...  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],...  [0, 0, 0, 0, 0, 5, 5, 5, 0, 0],...  [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],...  [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],...  [0, 0, 1, 1, 1, 5, 5, 5, 0, 0],...  [0, 0, 0, 0, 0, 5, 5, 5, 0, 0],...  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],...  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=np.uint8)>>> find_boundaries(labels, mode='thick').astype(np.uint8)array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0, 1, 1, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)>>> find_boundaries(labels, mode='inner').astype(np.uint8)array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1, 0, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)>>> find_boundaries(labels, mode='outer').astype(np.uint8)array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1, 0, 0, 1, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)>>> labels_small = labels[::2, ::3]>>> labels_smallarray([[0, 0, 0, 0], [0, 0, 5, 0], [0, 1, 5, 0], [0, 0, 5, 0], [0, 0, 0, 0]], dtype=uint8)>>> find_boundaries(labels_small, mode='subpixel').astype(np.uint8)array([[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]], dtype=uint8)>>> bool_image = np.array([[False, False, False, False, False],...  [False, False, False, False, False],...  [False, False, True, True, True],...  [False, False, True, True, True],...  [False, False, True, True, True]],...  dtype=bool)>>> find_boundaries(bool_image)array([[False, False, False, False, False], [False, False, True, True, True], [False, True, True, True, True], [False, True, True, False, False], [False, True, True, False, False]])

skimage.segmentation.flood(image, seed_point, *, footprint=None, connectivity=None, tolerance=None)[source]#

Mask corresponding to a flood fill.

Starting at a specific seed_point, connected points equal or withintolerance of the seed value are found.

Parameters:

imagendarray: An n-dimensional array.
seed_pointtuple or int: The point in image used as the starting point for the flood fill. Ifthe image is 1D, this point may be given as an integer.
footprintndarray, optional: The footprint (structuring element) used to determine the neighborhoodof each evaluated pixel. It must contain only 1’s and 0’s, have thesame number of dimensions as image. If not given, all adjacent pixelsare considered as part of the neighborhood (fully connected).
connectivityint, optional: A number used to determine the neighborhood of each evaluated pixel.Adjacent pixels whose squared distance from the center is less than orequal to connectivity are considered neighbors. Ignored iffootprint is not None.
tolerancefloat or int, optional: If None (default), adjacent values must be strictly equal to theinitial value of image at seed_point. This is fastest. If a valueis given, a comparison will be done at every point and if withintolerance of the initial value will also be filled (inclusive).

Returns:

maskndarray: A Boolean array with the same shape as image is returned, with Truevalues for areas connected to and equal (or within tolerance of) theseed point. All other values are False.

Notes

The conceptual analogy of this operation is the ‘paint bucket’ tool in manyraster graphics programs. This function returns just the maskrepresenting the fill.

If indices are desired rather than masks for memory reasons, the user cansimply run numpy.nonzero on the result, save the indices, and discardthis mask.

Examples

>>> from skimage.morphology import flood>>> image = np.zeros((4, 7), dtype=int)>>> image[1:3, 1:3] = 1>>> image[3, 0] = 1>>> image[1:3, 4:6] = 2>>> image[3, 6] = 3>>> imagearray([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 2, 2, 0], [0, 1, 1, 0, 2, 2, 0], [1, 0, 0, 0, 0, 0, 3]])

Fill connected ones with 5, with full connectivity (diagonals included):

>>> mask = flood(image, (1, 1))>>> image_flooded = image.copy()>>> image_flooded[mask] = 5>>> image_floodedarray([[0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 2, 2, 0], [0, 5, 5, 0, 2, 2, 0], [5, 0, 0, 0, 0, 0, 3]])

Fill connected ones with 5, excluding diagonal points (connectivity 1):

>>> mask = flood(image, (1, 1), connectivity=1)>>> image_flooded = image.copy()>>> image_flooded[mask] = 5>>> image_floodedarray([[0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 2, 2, 0], [0, 5, 5, 0, 2, 2, 0], [1, 0, 0, 0, 0, 0, 3]])

Fill with a tolerance:

>>> mask = flood(image, (0, 0), tolerance=1)>>> image_flooded = image.copy()>>> image_flooded[mask] = 5>>> image_floodedarray([[5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 5, 5, 5, 3]])

Flood Fill

skimage.segmentation.flood_fill(image, seed_point, new_value, *, footprint=None, connectivity=None, tolerance=None, in_place=False)[source]#

Perform flood filling on an image.

Starting at a specific seed_point, connected points equal or withintolerance of the seed value are found, then set to new_value.

Parameters:

imagendarray: An n-dimensional array.
seed_pointtuple or int: The point in image used as the starting point for the flood fill. Ifthe image is 1D, this point may be given as an integer.
new_valueimage type: New value to set the entire fill. This must be chosen in agreementwith the dtype of image.
footprintndarray, optional: The footprint (structuring element) used to determine the neighborhoodof each evaluated pixel. It must contain only 1’s and 0’s, have thesame number of dimensions as image. If not given, all adjacent pixelsare considered as part of the neighborhood (fully connected).
connectivityint, optional: A number used to determine the neighborhood of each evaluated pixel.Adjacent pixels whose squared distance from the center is less than orequal to connectivity are considered neighbors. Ignored iffootprint is not None.
tolerancefloat or int, optional: If None (default), adjacent values must be strictly equal to thevalue of image at seed_point to be filled. This is fastest.If a tolerance is provided, adjacent points with values within plus orminus tolerance from the seed point are filled (inclusive).
in_placebool, optional: If True, flood filling is applied to image in place. If False, theflood filled result is returned without modifying the input image(default).

Returns:

filledndarray: An array with the same shape as image is returned, with values inareas connected to and equal (or within tolerance of) the seed pointreplaced with new_value.

Notes

The conceptual analogy of this operation is the ‘paint bucket’ tool in manyraster graphics programs.

Examples

>>> from skimage.morphology import flood_fill>>> image = np.zeros((4, 7), dtype=int)>>> image[1:3, 1:3] = 1>>> image[3, 0] = 1>>> image[1:3, 4:6] = 2>>> image[3, 6] = 3>>> imagearray([[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 2, 2, 0], [0, 1, 1, 0, 2, 2, 0], [1, 0, 0, 0, 0, 0, 3]])

Fill connected ones with 5, with full connectivity (diagonals included):

>>> flood_fill(image, (1, 1), 5)array([[0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 2, 2, 0], [0, 5, 5, 0, 2, 2, 0], [5, 0, 0, 0, 0, 0, 3]])

Fill connected ones with 5, excluding diagonal points (connectivity 1):

>>> flood_fill(image, (1, 1), 5, connectivity=1)array([[0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 0, 2, 2, 0], [0, 5, 5, 0, 2, 2, 0], [1, 0, 0, 0, 0, 0, 3]])

Fill with a tolerance:

>>> flood_fill(image, (0, 0), 5, tolerance=1)array([[5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 5, 2, 2, 5], [5, 5, 5, 5, 5, 5, 3]])

Flood Fill

skimage.segmentation.inverse_gaussian_gradient(image, alpha=100.0, sigma=5.0)[source]#

Inverse of gradient magnitude.

Compute the magnitude of the gradients in the image and then inverts theresult in the range [0, 1]. Flat areas are assigned values close to 1,while areas close to borders are assigned values close to 0.

This function or a similar one defined by the user should be applied overthe image as a preprocessing step before callingmorphological_geodesic_active_contour.

Parameters:

image(M, N) or (L, M, N) array: Grayscale image or volume.
alphafloat, optional: Controls the steepness of the inversion. A larger value will make thetransition between the flat areas and border areas steeper in theresulting array.
sigmafloat, optional: Standard deviation of the Gaussian filter applied over the image.

Returns:

gimage(M, N) or (L, M, N) array: Preprocessed image (or volume) suitable formorphological_geodesic_active_contour.

Morphological Snakes

Evaluating segmentation metrics

skimage.segmentation.join_segmentations(s1, s2, return_mapping: bool = False)[source]#

Return the join of the two input segmentations.

The join J of S1 and S2 is defined as the segmentation in which twovoxels are in the same segment if and only if they are in the samesegment in both S1 and S2.

Parameters:

s1, s2numpy arrays: s1 and s2 are label fields of the same shape.
return_mappingbool, optional: If true, return mappings for joined segmentation labels to the original labels.

Returns:

jnumpy array: The join segmentation of s1 and s2.
map_j_to_s1ArrayMap, optional: Mapping from labels of the joined segmentation j to labels of s1.
map_j_to_s2ArrayMap, optional: Mapping from labels of the joined segmentation j to labels of s2.

Examples

>>> from skimage.segmentation import join_segmentations>>> s1 = np.array([[0, 0, 1, 1],...  [0, 2, 1, 1],...  [2, 2, 2, 1]])>>> s2 = np.array([[0, 1, 1, 0],...  [0, 1, 1, 0],...  [0, 1, 1, 1]])>>> join_segmentations(s1, s2)array([[0, 1, 3, 2], [0, 5, 3, 2], [4, 5, 5, 3]])>>> j, m1, m2 = join_segmentations(s1, s2, return_mapping=True)>>> m1ArrayMap(array([0, 1, 2, 3, 4, 5]), array([0, 0, 1, 1, 2, 2]))>>> np.all(m1[j] == s1)True>>> np.all(m2[j] == s2)True

Find the intersection of two segmentations

skimage.segmentation.mark_boundaries(image, label_img, color=(1, 1, 0), outline_color=None, mode='outer', background_label=0)[source]#

Return image with boundaries between labeled regions highlighted.

Parameters:

image(M, N[, 3]) array: Grayscale or RGB image.
label_img(M, N) array of int: Label array where regions are marked by different integer values.
colorlength-3 sequence, optional: RGB color of boundaries in the output image.
outline_colorlength-3 sequence, optional: RGB color surrounding boundaries in the output image. If None, nooutline is drawn.
modestring in {‘thick’, ‘inner’, ‘outer’, ‘subpixel’}, optional: The mode for finding boundaries.
background_labelint, optional: Which label to consider background (this is only useful formodes inner and outer).

Returns:

marked(M, N, 3) array of float: An image in which the boundaries between labels aresuperimposed on the original image.

See also

find_boundaries

Apply maskSLIC vs SLIC

Comparison of segmentation and superpixel algorithms

Region adjacency graph (RAG) Merging

Trainable segmentation using local features and random forests

Evaluating segmentation metrics

See also

disk_level_set, checkerboard_level_set

Notes

This is a version of the Chan-Vese algorithm that uses morphologicaloperators instead of solving a partial differential equation (PDE) for theevolution of the contour. The set of morphological operators used in thisalgorithm are proved to be infinitesimally equivalent to the Chan-Vese PDE(see [1]). However, morphological operators are do not suffer from thenumerical stability issues typically found in PDEs (it is not necessary tofind the right time step for the evolution), and are computationallyfaster.

The algorithm and its theoretical derivation are described in [1].

References

[1](1,2)

A Morphological Approach to Curvature-based Evolution of Curves andSurfaces, Pablo Márquez-Neila, Luis Baumela, Luis Álvarez. In IEEETransactions on Pattern Analysis and Machine Intelligence (PAMI),2014, DOI:10.1109/TPAMI.2013.106

Morphological Snakes

skimage.segmentation.morphological_geodesic_active_contour(gimage, num_iter, init_level_set='disk', smoothing=1, threshold='auto', balloon=0, iter_callback=<function <lambda>>)[source]#

Morphological Geodesic Active Contours (MorphGAC).

Geodesic active contours implemented with morphological operators. It canbe used to segment objects with visible but noisy, cluttered, brokenborders.

Parameters:

gimage(M, N) or (L, M, N) array: Preprocessed image or volume to be segmented. This is very rarely theoriginal image. Instead, this is usually a preprocessed version of theoriginal image that enhances and highlights the borders (or otherstructures) of the object to segment.morphological_geodesic_active_contour() will try to stop the contourevolution in areas where gimage is small. Seeinverse_gaussian_gradient() as an example function toperform this preprocessing. Note that the quality ofmorphological_geodesic_active_contour() might greatly depend on thispreprocessing.
num_iteruint: Number of num_iter to run.
init_level_setstr, (M, N) array, or (L, M, N) array: Initial level set. If an array is given, it will be binarized and usedas the initial level set. If a string is given, it defines the methodto generate a reasonable initial level set with the shape of theimage. Accepted values are ‘checkerboard’ and ‘disk’. See thedocumentation of checkerboard_level_set and disk_level_setrespectively for details about how these level sets are created.
smoothinguint, optional: Number of times the smoothing operator is applied per iteration.Reasonable values are around 1-4. Larger values lead to smoothersegmentations.
thresholdfloat, optional: Areas of the image with a value smaller than this threshold will beconsidered borders. The evolution of the contour will stop in theseareas.
balloonfloat, optional: Balloon force to guide the contour in non-informative areas of theimage, i.e., areas where the gradient of the image is too small to pushthe contour towards a border. A negative value will shrink the contour,while a positive value will expand the contour in these areas. Settingthis to zero will disable the balloon force.
iter_callbackfunction, optional: If given, this function is called once per iteration with the currentlevel set as the only argument. This is useful for debugging or forplotting intermediate results during the evolution.

Returns:

out(M, N) or (L, M, N) array: Final segmentation (i.e., the final level set)

See also

inverse_gaussian_gradient, disk_level_set, checkerboard_level_set

Notes

This is a version of the Geodesic Active Contours (GAC) algorithm that usesmorphological operators instead of solving partial differential equations(PDEs) for the evolution of the contour. The set of morphological operatorsused in this algorithm are proved to be infinitesimally equivalent to theGAC PDEs (see [1]). However, morphological operators are do not sufferfrom the numerical stability issues typically found in PDEs (e.g., it isnot necessary to find the right time step for the evolution), and arecomputationally faster.

The algorithm and its theoretical derivation are described in [1].

References

[1](1,2)

Morphological Snakes

Evaluating segmentation metrics

skimage.segmentation.quickshift(image, ratio=1.0, kernel_size=5, max_dist=10, return_tree=False, sigma=0, convert2lab=True, rng=42, *, channel_axis=-1)[source]#

Segment image using quickshift clustering in Color-(x,y) space.

Produces an oversegmentation of the image using the quickshift mode-seekingalgorithm.

Parameters:

image(M, N, C) ndarray

Input image. The axis corresponding to color channels can be specifiedvia the channel_axis argument.

ratiofloat, optional, between 0 and 1

Balances color-space proximity and image-space proximity.Higher values give more weight to color-space.

kernel_sizefloat, optional

Width of Gaussian kernel used in smoothing thesample density. Higher means fewer clusters.

max_distfloat, optional

Cut-off point for data distances.Higher means fewer clusters.

return_treebool, optional

Whether to return the full segmentation hierarchy tree and distances.

sigmafloat, optional

Width for Gaussian smoothing as preprocessing. Zero means no smoothing.

convert2labbool, optional

Whether the input should be converted to Lab colorspace prior tosegmentation. For this purpose, the input is assumed to be RGB.

rng{numpy.random.Generator, int}, optional

Pseudo-random number generator.By default, a PCG64 generator is used (see numpy.random.default_rng()).If rng is an int, it is used to seed the generator.

The PRNG is used to break ties, and is seeded with 42 by default.

channel_axisint, optional

The axis of image corresponding to color channels. Defaults to thelast axis.

Returns:

segment_mask(M, N) ndarray: Integer mask indicating segment labels.

Notes

The authors advocate to convert the image to Lab color space prior tosegmentation, though this is not strictly necessary. For this to work, theimage must be given in RGB format.

References

[1]

Quick shift and kernel methods for mode seeking,Vedaldi, A. and Soatto, S.European Conference on Computer Vision, 2008

Comparison of segmentation and superpixel algorithms

skimage.segmentation.random_walker(data, labels, beta=130, mode='cg_j', tol=0.001, copy=True, return_full_prob=False, spacing=None, *, prob_tol=0.001, channel_axis=None)[source]#

Random walker algorithm for segmentation from markers.

Random walker algorithm is implemented for gray-level or multichannelimages.

Parameters:

data(M, N[, P][, C]) ndarray

Image to be segmented in phases. Gray-level data can be two- orthree-dimensional; multichannel data can be three- or four-dimensional with channel_axis specifying the dimension containingchannels. Data spacing is assumed isotropic unless the spacingkeyword argument is used.

labels(M, N[, P]) array of ints

Array of seed markers labeled with different positive integersfor different phases. Zero-labeled pixels are unlabeled pixels.Negative labels correspond to inactive pixels that are not takeninto account (they are removed from the graph). If labels are notconsecutive integers, the labels array will be transformed so thatlabels are consecutive. In the multichannel case, labels should havethe same shape as a single channel of data, i.e. without the finaldimension denoting channels.

betafloat, optional

Penalization coefficient for the random walker motion(the greater beta, the more difficult the diffusion).

modestring, available options {‘cg’, ‘cg_j’, ‘cg_mg’, ‘bf’}

Mode for solving the linear system in the random walker algorithm.

‘bf’ (brute force): an LU factorization of the Laplacian iscomputed. This is fast for small images (<1024x1024), but very slowand memory-intensive for large images (e.g., 3-D volumes).
‘cg’ (conjugate gradient): the linear system is solved iterativelyusing the Conjugate Gradient method from scipy.sparse.linalg. This isless memory-consuming than the brute force method for large images,but it is quite slow.
‘cg_j’ (conjugate gradient with Jacobi preconditionner): theJacobi preconditionner is applied during the Conjugategradient method iterations. This may accelerate theconvergence of the ‘cg’ method.
‘cg_mg’ (conjugate gradient with multigrid preconditioner): apreconditioner is computed using a multigrid solver, then thesolution is computed with the Conjugate Gradient method. This moderequires that the pyamg module is installed.

tolfloat, optional

Tolerance to achieve when solving the linear system usingthe conjugate gradient based modes (‘cg’, ‘cg_j’ and ‘cg_mg’).

copybool, optional

If copy is False, the labels array will be overwritten withthe result of the segmentation. Use copy=False if you want tosave on memory.

return_full_probbool, optional

If True, the probability that a pixel belongs to each of thelabels will be returned, instead of only the most likelylabel.

spacingiterable of floats, optional

Spacing between voxels in each spatial dimension. If None, thenthe spacing between pixels/voxels in each dimension is assumed 1.

prob_tolfloat, optional

Tolerance on the resulting probability to be in the interval [0, 1].If the tolerance is not satisfied, a warning is displayed.

channel_axisint or None, optional

If None, the image is assumed to be a grayscale (single channel) image.Otherwise, this parameter indicates which axis of the array correspondsto channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

outputndarray

If return_full_prob is False, array of ints of same shapeand data type as labels, in which each pixel has beenlabeled according to the marker that reached the pixel firstby anisotropic diffusion.
If return_full_prob is True, array of floats of shape(nlabels, labels.shape). output[label_nb, i, j] is theprobability that label label_nb reaches the pixel (i, j)first.

See also

skimage.segmentation.watershed: A segmentation algorithm based on mathematical morphology and “flooding” of regions from markers.

Notes

Multichannel inputs are scaled with all channel data combined. Ensure allchannels are separately normalized prior to running this algorithm.

The spacing argument is specifically for anisotropic datasets, wheredata points are spaced differently in one or more spatial dimensions.Anisotropic data is commonly encountered in medical imaging.

The algorithm was first proposed in [1].

The algorithm solves the diffusion equation at infinite times forsources placed on markers of each phase in turn. A pixel is labeled withthe phase that has the greatest probability to diffuse first to the pixel.

The diffusion equation is solved by minimizing x.T L x for each phase,where L is the Laplacian of the weighted graph of the image, and x isthe probability that a marker of the given phase arrives first at a pixelby diffusion (x=1 on markers of the phase, x=0 on the other markers, andthe other coefficients are looked for). Each pixel is attributed the labelfor which it has a maximal value of x. The Laplacian L of the imageis defined as:

L_ii = d_i, the number of neighbors of pixel i (the degree of i)
L_ij = -w_ij if i and j are adjacent pixels

The weight w_ij is a decreasing function of the norm of the local gradient.This ensures that diffusion is easier between pixels of similar values.

When the Laplacian is decomposed into blocks of marked and unmarkedpixels:

L = M B.T B A

with first indices corresponding to marked pixels, and then to unmarkedpixels, minimizing x.T L x for one phase amount to solving:

A x = - B x_m

where x_m = 1 on markers of the given phase, and 0 on other markers.This linear system is solved in the algorithm using a direct method forsmall images, and an iterative method for larger images.

References

[1]

Leo Grady, Random walks for image segmentation, IEEE Trans PatternAnal Mach Intell. 2006 Nov;28(11):1768-83.DOI:10.1109/TPAMI.2006.233.

Examples

>>> rng = np.random.default_rng()>>> a = np.zeros((10, 10)) + 0.2 * rng.random((10, 10))>>> a[5:8, 5:8] += 1>>> b = np.zeros_like(a, dtype=np.int32)>>> b[3, 3] = 1 # Marker for first phase>>> b[6, 6] = 2 # Marker for second phase>>> random_walker(a, b) array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 2, 2, 2, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], dtype=int32)

Random walker segmentation

skimage.segmentation.relabel_sequential(label_field, offset=1)[source]#

Relabel arbitrary labels to {offset, … offset + number_of_labels}.

This function also returns the forward map (mapping the original labels tothe reduced labels) and the inverse map (mapping the reduced labels backto the original ones).

Parameters:

label_fieldnumpy array of int, arbitrary shape: An array of labels, which must be non-negative integers.
offsetint, optional: The return labels will start at offset, which should bestrictly positive.

Returns:

relabelednumpy array of int, same shape as label_field: The input label field with labels mapped to{offset, …, number_of_labels + offset - 1}.The data type will be the same as label_field, except whenoffset + number_of_labels causes overflow of the current data type.
forward_mapArrayMap: The map from the original label space to the returned labelspace. Can be used to re-apply the same mapping. See examplesfor usage. The output data type will be the same as relabeled.
inverse_mapArrayMap: The map from the new label space to the original space. Thiscan be used to reconstruct the original label field from therelabeled one. The output data type will be the same as label_field.

Notes

The label 0 is assumed to denote the background and is never remapped.

The forward map can be extremely big for some inputs, since itslength is given by the maximum of the label field. However, in mostsituations, label_field.max() is much smaller thanlabel_field.size, and in these cases the forward map isguaranteed to be smaller than either the input or output images.

Examples

>>> from skimage.segmentation import relabel_sequential>>> label_field = np.array([1, 1, 5, 5, 8, 99, 42])>>> relab, fw, inv = relabel_sequential(label_field)>>> relabarray([1, 1, 2, 2, 3, 5, 4])>>> print(fw)ArrayMap: 1 → 1 5 → 2 8 → 3 42 → 4 99 → 5>>> np.array(fw)array([0, 1, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5])>>> np.array(inv)array([ 0, 1, 5, 8, 42, 99])>>> (fw[label_field] == relab).all()True>>> (inv[relab] == label_field).all()True>>> relab, fw, inv = relabel_sequential(label_field, offset=5)>>> relabarray([5, 5, 6, 6, 7, 9, 8])

skimage.segmentation.slic(image, n_segments=100, compactness=10.0, max_num_iter=10, sigma=0, spacing=None, convert2lab=None, enforce_connectivity=True, min_size_factor=0.5, max_size_factor=3, slic_zero=False, start_label=1, mask=None, *, channel_axis=-1)[source]#

Segments image using k-means clustering in Color-(x,y,z) space.

Parameters:

image(M, N[, P][, C]) ndarray

Input image. Can be 2D or 3D, and grayscale or multichannel(see channel_axis parameter).Input image must either be NaN-free or the NaN’s must be masked out.

n_segmentsint, optional

The (approximate) number of labels in the segmented output image.

compactnessfloat, optional

Balances color proximity and space proximity. Higher values givemore weight to space proximity, making superpixel shapes moresquare/cubic. In SLICO mode, this is the initial compactness.This parameter depends strongly on image contrast and on theshapes of objects in the image. We recommend exploring possiblevalues on a log scale, e.g., 0.01, 0.1, 1, 10, 100, beforerefining around a chosen value.

max_num_iterint, optional

Maximum number of iterations of k-means.

sigmafloat or array-like of floats, optional

Width of Gaussian smoothing kernel for pre-processing for eachdimension of the image. The same sigma is applied to each dimension incase of a scalar value. Zero means no smoothing.Note that sigma is automatically scaled if it is scalar andif a manual voxel spacing is provided (see Notes section). Ifsigma is array-like, its size must match image’s numberof spatial dimensions.

spacingarray-like of floats, optional

The voxel spacing along each spatial dimension. By default,slic assumes uniform spacing (same voxel resolution alongeach spatial dimension).This parameter controls the weights of the distances along thespatial dimensions during k-means clustering.

convert2labbool, optional

Whether the input should be converted to Lab colorspace prior tosegmentation. The input image must be RGB. Highly recommended.This option defaults to True when channel_axis` is not None *and*``image.shape[-1] == 3.

enforce_connectivitybool, optional

Whether the generated segments are connected or not

min_size_factorfloat, optional

Proportion of the minimum segment size to be removed with respectto the supposed segment size `depth*width*height/n_segments`

max_size_factorfloat, optional

Proportion of the maximum connected segment size. A value of 3 worksin most of the cases.

slic_zerobool, optional

Run SLIC-zero, the zero-parameter mode of SLIC. [2]

start_labelint, optional

The labels’ index start. Should be 0 or 1.

Added in version 0.17: start_label was introduced in 0.17

maskndarray, optional

If provided, superpixels are computed only where mask is True,and seed points are hom*ogeneously distributed over the maskusing a k-means clustering strategy. Mask number of dimensionsmust be equal to image number of spatial dimensions.

Added in version 0.17: mask was introduced in 0.17

channel_axisint or None, optional

If None, the image is assumed to be a grayscale (single channel) image.Otherwise, this parameter indicates which axis of the array correspondsto channels.

Added in version 0.19: channel_axis was added in 0.19.

Returns:

labels2D or 3D array: Integer mask indicating segment labels.

Raises:

ValueError: If convert2lab is set to True but the last arraydimension is not of length 3.
ValueError: If start_label is not 0 or 1.
ValueError: If image contains unmasked NaN values.
ValueError: If image contains unmasked infinite values.
ValueError: If image is 2D but channel_axis is -1 (the default).

Notes

If sigma > 0, the image is smoothed using a Gaussian kernel prior tosegmentation.
If sigma is scalar and spacing is provided, the kernel width isdivided along each dimension by the spacing. For example, if sigma=1and spacing=[5, 1, 1], the effective sigma is [0.2, 1, 1]. Thisensures sensible smoothing for anisotropic images.
The image is rescaled to be in [0, 1] prior to processing (maskedvalues are ignored).
Images of shape (M, N, 3) are interpreted as 2D RGB images by default. Tointerpret them as 3D with the last dimension having length 3, usechannel_axis=None.
start_label is introduced to handle the issue [4]. Label indexingstarts at 1 by default.

References

[1]

Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi,Pascal Fua, and Sabine Süsstrunk, SLIC Superpixels Compared toState-of-the-art Superpixel Methods, TPAMI, May 2012.DOI:10.1109/TPAMI.2012.120

[2]

https://www.epfl.ch/labs/ivrl/research/slic-superpixels/#SLICO

[3]

Irving, Benjamin. “maskSLIC: regional superpixel generation withapplication to local pathology characterisation in medical images.”,2016, arXiv:1606.09518

[4]

scikit-image/scikit-image#3722

Examples

>>> from skimage.segmentation import slic>>> from skimage.data import astronaut>>> img = astronaut()>>> segments = slic(img, n_segments=100, compactness=10)

Increasing the compactness parameter yields more square regions:

>>> segments = slic(img, n_segments=100, compactness=20)

Region Boundary based Region adjacency graphs (RAGs)

Region adjacency graph (RAG) Thresholding

Normalized Cut

Drawing Region Adjacency Graphs (RAGs)

Apply maskSLIC vs SLIC

Comparison of segmentation and superpixel algorithms

Find the intersection of two segmentations

Region adjacency graph (RAG) Merging

Hierarchical Merging of Region Boundary RAGs

skimage.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 thevalues to be assigned in the label matrix. Zero means not a marker. IfNone, the (default) markers are determined as the local minima ofimage. Specifically, the computation is equivalent to applyingskimage.morphology.local_minima() onto image, followed byskimage.measure.label() onto the result (with the same givenconnectivity). Generally speaking, users are encouraged to passmarkers explicitly.
connectivityint or ndarray, optional: The neighborhood connectivity. An integer is interpreted as inscipy.ndimage.generate_binary_structure, as the maximum numberof orthogonal steps to reach a neighbor. An array is directlyinterpreted 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 == Truewill 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 regionsobtained by the watershed algorithm. The line has the label 0.Note that the method used for adding this line expects thatmarker regions are not adjacent; the watershed line may not catchborders 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 apportionspixels into marked basins. The algorithm uses a priority queue to holdthe pixels with the metric for the priority queue being pixel value, thenthe time of entry into the queue – this settles ties in favor of theclosest marker.

Some ideas are taken from [4].The most important insight in the paper is that entry time onto the queuesolves two problems: a pixel should be assigned to the neighbor with thelargest gradient or, if there is no gradient, pixels on a plateau shouldbe split between markers on opposite sides.

This implementation converts all arguments to specific, lowest commondenominator types, then passes these to a C algorithm.

Markers can be determined manually, or automatically using for examplethe local minima of the gradient of the image, or the local maxima of thedistance 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 fromdigital elevation models using mathematical morphology,” SignalProcessing, 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 themaxima 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 toseparate overlapping spheres.

Find Regular Segments Using Compact Watershed

Expand segmentation labels without overlap

Watershed segmentation

Markers for watershed transform

Comparison of segmentation and superpixel algorithms

Find the intersection of two segmentations

Evaluating segmentation metrics

Comparing edge-based and region-based segmentation

Segment human cells (in mitosis)