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# Module: segmentation¶

 skimage.segmentation.active_contour(image, snake) Active contour model. skimage.segmentation.clear_border(labels[, …]) Clear objects connected to the label image border. skimage.segmentation.felzenszwalb(image[, …]) Computes Felsenszwalb’s efficient graph based image segmentation. skimage.segmentation.find_boundaries(label_img) Return bool array where boundaries between labeled regions are True. skimage.segmentation.join_segmentations(s1, s2) Return the join of the two input segmentations. skimage.segmentation.mark_boundaries(image, …) Return image with boundaries between labeled regions highlighted. skimage.segmentation.quickshift(image[, …]) Segments image using quickshift clustering in Color-(x,y) space. skimage.segmentation.random_walker(data, labels) Random walker algorithm for segmentation from markers. skimage.segmentation.relabel_from_one(…) Deprecated function. Use relabel_sequential instead. skimage.segmentation.relabel_sequential(…) Relabel arbitrary labels to {offset, … skimage.segmentation.slic(image[, …]) Segments image using k-means clustering in Color-(x,y,z) space. skimage.segmentation.watershed(image, markers) Find watershed basins in image flooded from given markers. skimage.segmentation.active_contour_model skimage.segmentation.boundaries skimage.segmentation.random_walker_segmentation Random walker segmentation algorithm skimage.segmentation.slic_superpixels

## active_contour¶

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

Active contour model.

Active contours by fitting snakes to features of images. Supports single and multichannel 2D images. Snakes can be periodic (for segmentation) or have 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 snake has enough points to capture the details of the final contour.

Parameters: image : (N, M) or (N, M, 3) ndarray Input image. snake : (N, 2) ndarray Initialisation coordinates of snake. For periodic snakes, it should not include duplicate endpoints. alpha : float, optional Snake length shape parameter. Higher values makes snake contract faster. beta : float, optional Snake smoothness shape parameter. Higher values makes snake smoother. w_line : float, optional Controls attraction to brightness. Use negative values to attract to dark regions. w_edge : float, optional Controls attraction to edges. Use negative values to repel snake from edges. gamma : float, optional Explicit time stepping parameter. bc : {‘periodic’, ‘free’, ‘fixed’}, optional Boundary conditions for worm. ‘periodic’ attaches the two ends of the snake, ‘fixed’ holds the end-points in place, and’free’ allows free movement of the ends. ‘fixed’ and ‘free’ can be combined by parsing ‘fixed-free’, ‘free-fixed’. Parsing ‘fixed-fixed’ or ‘free-free’ yields same behaviour as ‘fixed’ and ‘free’, respectively. max_px_move : float, optional Maximum pixel distance to move per iteration. max_iterations : int, optional Maximum iterations to optimize snake shape. convergence: float, optional Convergence criteria. snake : (N, 2) ndarray Optimised snake, same shape as input parameter.

References

 [R449] Kass, M.; Witkin, A.; Terzopoulos, D. “Snakes: Active contour models”. International Journal of Computer Vision 1 (4): 321 (1988).

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, 2)


Initiliaze spline:

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


## clear_border¶

skimage.segmentation.clear_border(labels, buffer_size=0, bgval=0, in_place=False)[source]

Clear objects connected to the label image border.

Parameters: labels : (M[, N[, …, P]]) array of int or bool Imaging data labels. buffer_size : int, optional The width of the border examined. By default, only objects that touch the outside of the image are removed. bgval : float or int, optional Cleared objects are set to this value. in_place : bool, optional Whether or not to manipulate the labels array in-place. 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],
...                    [0, 0, 0, 0, 1, 0, 0, 0, 0],
...                    [1, 0, 0, 1, 0, 1, 0, 0, 0],
...                    [0, 0, 1, 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, 1, 1, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]])


## felzenszwalb¶

skimage.segmentation.felzenszwalb(image, scale=1, sigma=0.8, min_size=20, multichannel=True)[source]

Computes Felsenszwalb’s efficient graph based image segmentation.

Produces an oversegmentation of a multichannel (i.e. RGB) image using a fast, minimum spanning tree based clustering on the image grid. The parameter scale sets an observation level. Higher scale means less 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 be controlled indirectly through scale. Segment size within an image can vary greatly depending on local contrast.

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

Parameters: image : (width, height, 3) or (width, height) ndarray Input image. scale : float Free parameter. Higher means larger clusters. sigma : float Width of Gaussian kernel used in preprocessing. min_size : int Minimum component size. Enforced using postprocessing. multichannel : bool, optional (default: True) Whether the last axis of the image is to be interpreted as multiple channels. A value of False, for a 3D image, is not currently supported. segment_mask : (width, height) ndarray Integer mask indicating segment labels.

References

 [R450] Efficient graph-based image segmentation, Felzenszwalb, P.F. and Huttenlocher, 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)


## find_boundaries¶

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_img : array of int or bool An array in which different regions are labeled with either different integers or boolean values. connectivity: int in {1, …, label_img.ndim}, optional A pixel is considered a boundary pixel if any of its neighbors has a different label. connectivity controls which pixels are considered neighbors. A connectivity of 1 (default) means pixels sharing an edge (in 2D) or a face (in 3D) will be considered neighbors. A connectivity of label_img.ndim means pixels sharing a corner will be considered neighbors. mode: string in {‘thick’, ‘inner’, ‘outer’, ‘subpixel’} How to mark the boundaries: thick: any pixel not completely surrounded by pixels of the same 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, leaving background pixels untouched. outer: outline pixels in the background around object boundaries. When two objects touch, their boundary is also marked. subpixel: return a doubled image, with pixels between the original pixels marked as boundary where appropriate. background: int, optional For modes ‘inner’ and ‘outer’, a definition of a background label is required. See mode for descriptions of these two. boundaries : array of bool, same shape as label_img A bool image where True represents a boundary pixel. For mode equal to ‘subpixel’, boundaries.shape[i] is equal to 2 * label_img.shape[i] - 1 for all i (a pixel is inserted 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_small
array([[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=np.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]], dtype=bool)


## join_segmentations¶

skimage.segmentation.join_segmentations(s1, s2)[source]

Return the join of the two input segmentations.

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

Parameters: s1, s2 : numpy arrays s1 and s2 are label fields of the same shape. j : numpy array The join segmentation of s1 and 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]])


## mark_boundaries¶

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. color : length-3 sequence, optional RGB color of boundaries in the output image. outline_color : length-3 sequence, optional RGB color surrounding boundaries in the output image. If None, no outline is drawn. mode : string in {‘thick’, ‘inner’, ‘outer’, ‘subpixel’}, optional The mode for finding boundaries. background_label : int, optional Which label to consider background (this is only useful for modes inner and outer). marked : (M, N, 3) array of float An image in which the boundaries between labels are superimposed on the original image.

## quickshift¶

skimage.segmentation.quickshift(image, ratio=1.0, kernel_size=5, max_dist=10, return_tree=False, sigma=0, convert2lab=True, random_seed=42)[source]

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

Produces an oversegmentation of the image using the quickshift mode-seeking algorithm.

Parameters: image : (width, height, channels) ndarray Input image. ratio : float, optional, between 0 and 1 Balances color-space proximity and image-space proximity. Higher values give more weight to color-space. kernel_size : float, optional Width of Gaussian kernel used in smoothing the sample density. Higher means fewer clusters. max_dist : float, optional Cut-off point for data distances. Higher means fewer clusters. return_tree : bool, optional Whether to return the full segmentation hierarchy tree and distances. sigma : float, optional Width for Gaussian smoothing as preprocessing. Zero means no smoothing. convert2lab : bool, optional Whether the input should be converted to Lab colorspace prior to segmentation. For this purpose, the input is assumed to be RGB. random_seed : int, optional Random seed used for breaking ties. segment_mask : (width, height) ndarray Integer mask indicating segment labels.

Notes

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

References

 [R451] Quick shift and kernel methods for mode seeking, Vedaldi, A. and Soatto, S. European Conference on Computer Vision, 2008

## random_walker¶

skimage.segmentation.random_walker(data, labels, beta=130, mode='bf', tol=0.001, copy=True, multichannel=False, return_full_prob=False, spacing=None)[source]

Random walker algorithm for segmentation from markers.

Random walker algorithm is implemented for gray-level or multichannel images.

Parameters: data : array_like Image to be segmented in phases. Gray-level data can be two- or three-dimensional; multichannel data can be three- or four- dimensional (multichannel=True) with the highest dimension denoting channels. Data spacing is assumed isotropic unless the spacing keyword argument is used. labels : array of ints, of same shape as data without channels dimension Array of seed markers labeled with different positive integers for different phases. Zero-labeled pixels are unlabeled pixels. Negative labels correspond to inactive pixels that are not taken into account (they are removed from the graph). If labels are not consecutive integers, the labels array will be transformed so that labels are consecutive. In the multichannel case, labels should have the same shape as a single channel of data, i.e. without the final dimension denoting channels. beta : float Penalization coefficient for the random walker motion (the greater beta, the more difficult the diffusion). mode : string, available options {‘cg_mg’, ‘cg’, ‘bf’} Mode for solving the linear system in the random walker algorithm. If no preference given, automatically attempt to use the fastest option available (‘cg_mg’ from pyamg >> ‘cg’ with UMFPACK > ‘bf’). ‘bf’ (brute force): an LU factorization of the Laplacian is computed. This is fast for small images (<1024x1024), but very slow and memory-intensive for large images (e.g., 3-D volumes). ‘cg’ (conjugate gradient): the linear system is solved iteratively using the Conjugate Gradient method from scipy.sparse.linalg. This is less memory-consuming than the brute force method for large images, but it is quite slow. ‘cg_mg’ (conjugate gradient with multigrid preconditioner): a preconditioner is computed using a multigrid solver, then the solution is computed with the Conjugate Gradient method. This mode requires that the pyamg module (http://pyamg.org/) is installed. For images of size > 512x512, this is the recommended (fastest) mode. tol : float tolerance to achieve when solving the linear system, in cg’ and ‘cg_mg’ modes. copy : bool If copy is False, the labels array will be overwritten with the result of the segmentation. Use copy=False if you want to save on memory. multichannel : bool, default False If True, input data is parsed as multichannel data (see ‘data’ above for proper input format in this case) return_full_prob : bool, default False If True, the probability that a pixel belongs to each of the labels will be returned, instead of only the most likely label. spacing : iterable of floats Spacing between voxels in each spatial dimension. If None, then the spacing between pixels/voxels in each dimension is assumed 1. output : ndarray If return_full_prob is False, array of ints of same shape as data, in which each pixel has been labeled according to the marker that reached the pixel first by anisotropic diffusion. If return_full_prob is True, array of floats of shape (nlabels, data.shape). output[label_nb, i, j] is the probability that label label_nb reaches the pixel (i, j) first.

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

Notes

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

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

The algorithm was first proposed in Random walks for image segmentation, Leo Grady, IEEE Trans Pattern Anal Mach Intell. 2006 Nov;28(11):1768-83.

The algorithm solves the diffusion equation at infinite times for sources placed on markers of each phase in turn. A pixel is labeled with the 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 is the probability that a marker of the given phase arrives first at a pixel by diffusion (x=1 on markers of the phase, x=0 on the other markers, and the other coefficients are looked for). Each pixel is attributed the label for which it has a maximal value of x. The Laplacian L of the image is 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 unmarked pixels:

L = M B.T
B A


with first indices corresponding to marked pixels, and then to unmarked pixels, 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 for small images, and an iterative method for larger images.

Examples

>>> np.random.seed(0)
>>> a = np.zeros((10, 10)) + 0.2 * np.random.rand(10, 10)
>>> a[5:8, 5:8] += 1
>>> b = np.zeros_like(a)
>>> 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)


## relabel_from_one¶

skimage.segmentation.relabel_from_one(label_field)[source]

Deprecated function. Use relabel_sequential instead.

Convert labels in an arbitrary label field to {1, … number_of_labels}.

This function is deprecated, see relabel_sequential for more.

## relabel_sequential¶

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 to the reduced labels) and the inverse map (mapping the reduced labels back to the original ones).

Parameters: label_field : numpy array of int, arbitrary shape An array of labels. offset : int, optional The return labels will start at offset, which should be strictly positive. relabeled : numpy array of int, same shape as label_field The input label field with labels mapped to {offset, …, number_of_labels + offset - 1}. forward_map : numpy array of int, shape (label_field.max() + 1,) The map from the original label space to the returned label space. Can be used to re-apply the same mapping. See examples for usage. inverse_map : 1D numpy array of int, of length offset + number of labels The map from the new label space to the original space. This can be used to reconstruct the original label field from the relabeled one.

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 its length is given by the maximum of the label field. However, in most situations, label_field.max() is much smaller than label_field.size, and in these cases the forward map is guaranteed 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)
>>> relab
array([1, 1, 2, 2, 3, 5, 4])
>>> 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])
>>> 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)
>>> relab
array([5, 5, 6, 6, 7, 9, 8])


## slic¶

skimage.segmentation.slic(image, n_segments=100, compactness=10.0, max_iter=10, sigma=0, spacing=None, multichannel=True, convert2lab=None, enforce_connectivity=True, min_size_factor=0.5, max_size_factor=3, slic_zero=False)[source]

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

Parameters: image : 2D, 3D or 4D ndarray Input image, which can be 2D or 3D, and grayscale or multichannel (see multichannel parameter). n_segments : int, optional The (approximate) number of labels in the segmented output image. compactness : float, optional Balances color proximity and space proximity. Higher values give more weight to space proximity, making superpixel shapes more square/cubic. In SLICO mode, this is the initial compactness. This parameter depends strongly on image contrast and on the shapes of objects in the image. We recommend exploring possible values on a log scale, e.g., 0.01, 0.1, 1, 10, 100, before refining around a chosen value. max_iter : int, optional Maximum number of iterations of k-means. sigma : float or (3,) array-like of floats, optional Width of Gaussian smoothing kernel for pre-processing for each dimension of the image. The same sigma is applied to each dimension in case of a scalar value. Zero means no smoothing. Note, that sigma is automatically scaled if it is scalar and a manual voxel spacing is provided (see Notes section). spacing : (3,) array-like of floats, optional The voxel spacing along each image dimension. By default, slic assumes uniform spacing (same voxel resolution along z, y and x). This parameter controls the weights of the distances along z, y, and x during k-means clustering. multichannel : bool, optional Whether the last axis of the image is to be interpreted as multiple channels or another spatial dimension. convert2lab : bool, optional Whether the input should be converted to Lab colorspace prior to segmentation. The input image must be RGB. Highly recommended. This option defaults to True when multichannel=True and image.shape[-1] == 3. enforce_connectivity: bool, optional Whether the generated segments are connected or not min_size_factor: float, optional Proportion of the minimum segment size to be removed with respect to the supposed segment size depth*width*height/n_segments max_size_factor: float, optional Proportion of the maximum connected segment size. A value of 3 works in most of the cases. slic_zero: bool, optional Run SLIC-zero, the zero-parameter mode of SLIC. [R453] labels : 2D or 3D array Integer mask indicating segment labels. ValueError If convert2lab is set to True but the last array dimension is not of length 3.

Notes

• If sigma > 0, the image is smoothed using a Gaussian kernel prior to segmentation.
• If sigma is scalar and spacing is provided, the kernel width is divided along each dimension by the spacing. For example, if sigma=1 and spacing=[5, 1, 1], the effective sigma is [0.2, 1, 1]. This ensures sensible smoothing for anisotropic images.
• The image is rescaled to be in [0, 1] prior to processing.
• Images of shape (M, N, 3) are interpreted as 2D RGB images by default. To interpret them as 3D with the last dimension having length 3, use multichannel=False.

References

 [R452] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süsstrunk, SLIC Superpixels Compared to State-of-the-art Superpixel Methods, TPAMI, May 2012.

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)


## watershed¶

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

Find watershed basins in image flooded from given markers.

Parameters: image: ndarray (2-D, 3-D, …) of integers Data array where the lowest value points are labeled first. markers: int, or ndarray of int, same shape as image The desired number of markers, or an array marking the basins with the values to be assigned in the label matrix. Zero means not a marker. 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. compactness : float, optional Use compact watershed [R456] with given compactness parameter. Higher values result in more regularly-shaped watershed basins. watershed_line : bool, optional If watershed_line is True, a one-pixel wide line separates the regions obtained by the watershed algorithm. The line has the label 0. out: ndarray A labeled matrix of the same type and shape as markers

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 [R454] [R455] 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

 [R455] (1, 2) http://cmm.ensmp.fr/~beucher/wtshed.html
 [R456] (1, 2) Peer Neubert & Peter Protzel (2014). Compact Watershed and Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation Algorithms. ICPR 2014, pp 996-1001. DOI:10.1109/ICPR.2014.181 https://www.tu-chemnitz.de/etit/proaut/forschung/rsrc/cws_pSLIC_ICPR.pdf

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


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
>>> local_maxi = peak_local_max(distance, labels=image,
...                             footprint=np.ones((3, 3)),
...                             indices=False)
>>> markers = ndi.label(local_maxi)[0]


Finally, we run the watershed on the image and markers:

>>> labels = watershed(-distance, markers, mask=image)


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