morphology
¶skimage.morphology.binary_erosion (image[, …]) 
Return fast binary morphological erosion of an image. 
skimage.morphology.binary_dilation (image[, …]) 
Return fast binary morphological dilation of an image. 
skimage.morphology.binary_opening (image[, …]) 
Return fast binary morphological opening of an image. 
skimage.morphology.binary_closing (image[, …]) 
Return fast binary morphological closing of an image. 
skimage.morphology.erosion (image[, selem, …]) 
Return greyscale morphological erosion of an image. 
skimage.morphology.dilation (image[, selem, …]) 
Return greyscale morphological dilation of an image. 
skimage.morphology.opening (image[, selem, out]) 
Return greyscale morphological opening of an image. 
skimage.morphology.closing (image[, selem, out]) 
Return greyscale morphological closing of an image. 
skimage.morphology.white_tophat (image[, …]) 
Return white top hat of an image. 
skimage.morphology.black_tophat (image[, …]) 
Return black top hat of an image. 
skimage.morphology.square (width[, dtype]) 
Generates a flat, squareshaped structuring element. 
skimage.morphology.rectangle (width, height) 
Generates a flat, rectangularshaped structuring element. 
skimage.morphology.diamond (radius[, dtype]) 
Generates a flat, diamondshaped structuring element. 
skimage.morphology.disk (radius[, dtype]) 
Generates a flat, diskshaped structuring element. 
skimage.morphology.cube (width[, dtype]) 
Generates a cubeshaped structuring element. 
skimage.morphology.octahedron (radius[, dtype]) 
Generates a octahedronshaped structuring element. 
skimage.morphology.ball (radius[, dtype]) 
Generates a ballshaped structuring element. 
skimage.morphology.octagon (m, n[, dtype]) 
Generates an octagon shaped structuring element. 
skimage.morphology.star (a[, dtype]) 
Generates a star shaped structuring element. 
skimage.morphology.label (input[, neighbors, …]) 
Label connected regions of an integer array. 
skimage.morphology.watershed (image, markers) 
Find watershed basins in image flooded from given markers. 
skimage.morphology.skeletonize (image) 
Return the skeleton of a binary image. 
skimage.morphology.skeletonize_3d (img) 
Compute the skeleton of a binary image. 
skimage.morphology.thin (image[, max_iter]) 
Perform morphological thinning of a binary image. 
skimage.morphology.medial_axis (image[, …]) 
Compute the medial axis transform of a binary image 
skimage.morphology.convex_hull_image (image) 
Compute the convex hull image of a binary image. 
skimage.morphology.convex_hull_object (image) 
Compute the convex hull image of individual objects in a binary image. 
skimage.morphology.reconstruction (seed, mask) 
Perform a morphological reconstruction of an image. 
skimage.morphology.remove_small_objects (ar) 
Remove objects smaller than the specified size. 
skimage.morphology.remove_small_holes (ar[, …]) 
Remove contiguous holes smaller than the specified size. 
skimage.morphology.h_minima (image, h[, selem]) 
Determine all minima of the image with depth >= h. 
skimage.morphology.h_maxima (image, h[, selem]) 
Determine all maxima of the image with height >= h. 
skimage.morphology.local_maxima (image[, …]) 
Find local maxima of ndimensional array. 
skimage.morphology.local_minima (image[, …]) 
Find local minima of ndimensional array. 
skimage.morphology.max_tree (image[, …]) 
Build the max tree from an image. 
skimage.morphology.area_opening (image[, …]) 
Perform an area opening of the image. 
skimage.morphology.area_closing (image[, …]) 
Perform an area closing of the image. 
skimage.morphology.diameter_opening (image[, …]) 
Perform a diameter opening of the image. 
skimage.morphology.diameter_closing (image[, …]) 
Perform a diameter closing of the image. 
skimage.morphology.max_tree_local_maxima (image) 
Determine all local maxima of the image. 
skimage.morphology.
binary_erosion
(image, selem=None, out=None)[source]¶Return fast binary morphological erosion of an image.
This function returns the same result as greyscale erosion but performs faster for binary images.
Morphological erosion sets a pixel at (i,j)
to the minimum over all
pixels in the neighborhood centered at (i,j)
. Erosion shrinks bright
regions and enlarges dark regions.
Parameters: 


Returns: 

skimage.morphology.
binary_dilation
(image, selem=None, out=None)[source]¶Return fast binary morphological dilation of an image.
This function returns the same result as greyscale dilation but performs faster for binary images.
Morphological dilation sets a pixel at (i,j)
to the maximum over all
pixels in the neighborhood centered at (i,j)
. Dilation enlarges bright
regions and shrinks dark regions.
Parameters: 


Returns: 

skimage.morphology.
binary_opening
(image, selem=None, out=None)[source]¶Return fast binary morphological opening of an image.
This function returns the same result as greyscale opening but performs faster for binary images.
The morphological opening on an image is defined as an erosion followed by a dilation. Opening can remove small bright spots (i.e. “salt”) and connect small dark cracks. This tends to “open” up (dark) gaps between (bright) features.
Parameters: 


Returns: 

skimage.morphology.
binary_closing
(image, selem=None, out=None)[source]¶Return fast binary morphological closing of an image.
This function returns the same result as greyscale closing but performs faster for binary images.
The morphological closing on an image is defined as a dilation followed by an erosion. Closing can remove small dark spots (i.e. “pepper”) and connect small bright cracks. This tends to “close” up (dark) gaps between (bright) features.
Parameters: 


Returns: 

skimage.morphology.
erosion
(image, selem=None, out=None, shift_x=False, shift_y=False)[source]¶Return greyscale morphological erosion of an image.
Morphological erosion sets a pixel at (i,j) to the minimum over all pixels in the neighborhood centered at (i,j). Erosion shrinks bright regions and enlarges dark regions.
Parameters: 


Returns: 

Notes
For uint8
(and uint16
up to a certain bitdepth) data, the
lower algorithm complexity makes the skimage.filters.rank.minimum
function more efficient for larger images and structuring elements.
Examples
>>> # Erosion shrinks bright regions
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_square = np.array([[0, 0, 0, 0, 0],
... [0, 1, 1, 1, 0],
... [0, 1, 1, 1, 0],
... [0, 1, 1, 1, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> erosion(bright_square, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.erosion
¶skimage.morphology.
dilation
(image, selem=None, out=None, shift_x=False, shift_y=False)[source]¶Return greyscale morphological dilation of an image.
Morphological dilation sets a pixel at (i,j) to the maximum over all pixels in the neighborhood centered at (i,j). Dilation enlarges bright regions and shrinks dark regions.
Parameters: 


Returns: 

Notes
For uint8 (and uint16 up to a certain bitdepth) data, the lower algorithm complexity makes the skimage.filters.rank.maximum function more efficient for larger images and structuring elements.
Examples
>>> # Dilation enlarges bright regions
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_pixel = np.array([[0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0],
... [0, 0, 1, 0, 0],
... [0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> dilation(bright_pixel, square(3))
array([[0, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.
opening
(image, selem=None, out=None)[source]¶Return greyscale morphological opening of an image.
The morphological opening on an image is defined as an erosion followed by a dilation. Opening can remove small bright spots (i.e. “salt”) and connect small dark cracks. This tends to “open” up (dark) gaps between (bright) features.
Parameters: 


Returns: 

Examples
>>> # Open up gap between two bright regions (but also shrink regions)
>>> import numpy as np
>>> from skimage.morphology import square
>>> bad_connection = np.array([[1, 0, 0, 0, 1],
... [1, 1, 0, 1, 1],
... [1, 1, 1, 1, 1],
... [1, 1, 0, 1, 1],
... [1, 0, 0, 0, 1]], dtype=np.uint8)
>>> opening(bad_connection, square(3))
array([[0, 0, 0, 0, 0],
[1, 1, 0, 1, 1],
[1, 1, 0, 1, 1],
[1, 1, 0, 1, 1],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.opening
¶skimage.morphology.
closing
(image, selem=None, out=None)[source]¶Return greyscale morphological closing of an image.
The morphological closing on an image is defined as a dilation followed by an erosion. Closing can remove small dark spots (i.e. “pepper”) and connect small bright cracks. This tends to “close” up (dark) gaps between (bright) features.
Parameters: 


Returns: 

Examples
>>> # Close a gap between two bright lines
>>> import numpy as np
>>> from skimage.morphology import square
>>> broken_line = np.array([[0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0],
... [1, 1, 0, 1, 1],
... [0, 0, 0, 0, 0],
... [0, 0, 0, 0, 0]], dtype=np.uint8)
>>> closing(broken_line, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[1, 1, 1, 1, 1],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.
white_tophat
(image, selem=None, out=None)[source]¶Return white top hat of an image.
The white top hat of an image is defined as the image minus its morphological opening. This operation returns the bright spots of the image that are smaller than the structuring element.
Parameters: 


Returns: 

Examples
>>> # Subtract grey background from bright peak
>>> import numpy as np
>>> from skimage.morphology import square
>>> bright_on_grey = np.array([[2, 3, 3, 3, 2],
... [3, 4, 5, 4, 3],
... [3, 5, 9, 5, 3],
... [3, 4, 5, 4, 3],
... [2, 3, 3, 3, 2]], dtype=np.uint8)
>>> white_tophat(bright_on_grey, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 5, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.white_tophat
¶skimage.morphology.
black_tophat
(image, selem=None, out=None)[source]¶Return black top hat of an image.
The black top hat of an image is defined as its morphological closing minus the original image. This operation returns the dark spots of the image that are smaller than the structuring element. Note that dark spots in the original image are bright spots after the black top hat.
Parameters: 


Returns: 

Examples
>>> # Change dark peak to bright peak and subtract background
>>> import numpy as np
>>> from skimage.morphology import square
>>> dark_on_grey = np.array([[7, 6, 6, 6, 7],
... [6, 5, 4, 5, 6],
... [6, 4, 0, 4, 6],
... [6, 5, 4, 5, 6],
... [7, 6, 6, 6, 7]], dtype=np.uint8)
>>> black_tophat(dark_on_grey, square(3))
array([[0, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 1, 5, 1, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.black_tophat
¶skimage.morphology.
square
(width, dtype=<class 'numpy.uint8'>)[source]¶Generates a flat, squareshaped structuring element.
Every pixel along the perimeter has a chessboard distance no greater than radius (radius=floor(width/2)) pixels.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
rectangle
(width, height, dtype=<class 'numpy.uint8'>)[source]¶Generates a flat, rectangularshaped structuring element.
Every pixel in the rectangle generated for a given width and given height belongs to the neighborhood.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
diamond
(radius, dtype=<class 'numpy.uint8'>)[source]¶Generates a flat, diamondshaped structuring element.
A pixel is part of the neighborhood (i.e. labeled 1) if the city block/Manhattan distance between it and the center of the neighborhood is no greater than radius.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
disk
(radius, dtype=<class 'numpy.uint8'>)[source]¶Generates a flat, diskshaped structuring element.
A pixel is within the neighborhood if the euclidean distance between it and the origin is no greater than radius.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
cube
(width, dtype=<class 'numpy.uint8'>)[source]¶Generates a cubeshaped structuring element.
This is the 3D equivalent of a square. Every pixel along the perimeter has a chessboard distance no greater than radius (radius=floor(width/2)) pixels.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
octahedron
(radius, dtype=<class 'numpy.uint8'>)[source]¶Generates a octahedronshaped structuring element.
This is the 3D equivalent of a diamond. A pixel is part of the neighborhood (i.e. labeled 1) if the city block/Manhattan distance between it and the center of the neighborhood is no greater than radius.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
ball
(radius, dtype=<class 'numpy.uint8'>)[source]¶Generates a ballshaped structuring element.
This is the 3D equivalent of a disk. A pixel is within the neighborhood if the euclidean distance between it and the origin is no greater than radius.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
octagon
(m, n, dtype=<class 'numpy.uint8'>)[source]¶Generates an octagon shaped structuring element.
For a given size of (m) horizontal and vertical sides and a given (n) height or width of slanted sides octagon is generated. The slanted sides are 45 or 135 degrees to the horizontal axis and hence the widths and heights are equal.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
star
(a, dtype=<class 'numpy.uint8'>)[source]¶Generates a star shaped structuring element.
Start has 8 vertices and is an overlap of square of size 2*a + 1 with its 45 degree rotated version. The slanted sides are 45 or 135 degrees to the horizontal axis.
Parameters: 


Returns: 

Other Parameters:  

skimage.morphology.
label
(input, neighbors=None, background=None, return_num=False, connectivity=None)[source]¶Label connected regions of an integer array.
Two pixels are connected when they are neighbors and have the same value. In 2D, they can be neighbors either in a 1 or 2connected sense. The value refers to the maximum number of orthogonal hops to consider a pixel/voxel a neighbor:
1connectivity 2connectivity diagonal connection closeup
[ ] [ ] [ ] [ ] [ ]
 \  /  < hop 2
[ ][x][ ] [ ][x][ ] [x][ ]
 /  \ hop 1
[ ] [ ] [ ] [ ]
Parameters: 


Returns: 

See also
regionprops
References
[1]  Christophe Fiorio and Jens Gustedt, “Two linear time UnionFind strategies for image processing”, Theoretical Computer Science 154 (1996), pp. 165181. 
[2]  Kensheng Wu, Ekow Otoo and Arie Shoshani, “Optimizing connected component labeling algorithms”, Paper LBNL56864, 2005, Lawrence Berkeley National Laboratory (University of California), http://repositories.cdlib.org/lbnl/LBNL56864 
Examples
>>> import numpy as np
>>> x = np.eye(3).astype(int)
>>> print(x)
[[1 0 0]
[0 1 0]
[0 0 1]]
>>> print(label(x, connectivity=1))
[[1 0 0]
[0 2 0]
[0 0 3]]
>>> print(label(x, connectivity=2))
[[1 0 0]
[0 1 0]
[0 0 1]]
>>> print(label(x, background=1))
[[1 2 2]
[2 1 2]
[2 2 1]]
>>> x = np.array([[1, 0, 0],
... [1, 1, 5],
... [0, 0, 0]])
>>> print(label(x))
[[1 0 0]
[1 1 2]
[0 0 0]]
skimage.morphology.
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: 


Returns: 

See also
skimage.segmentation.random_walker
Notes
This function implements a watershed algorithm [1] [2] 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) 171182
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]  (1, 2) https://en.wikipedia.org/wiki/Watershed_%28image_processing%29 
[2]  (1, 2) http://cmm.ensmp.fr/~beucher/wtshed.html 
[3]  (1, 2) Peer Neubert & Peter Protzel (2014). Compact Watershed and Preemptive SLIC: On Improving Tradeoffs of Superpixel Segmentation Algorithms. ICPR 2014, pp 9961001. DOI:10.1109/ICPR.2014.181 https://www.tuchemnitz.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
>>> 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 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 3D images, and can be used for example to separate overlapping spheres.
skimage.morphology.
skeletonize
(image)[source]¶Return the skeleton of a binary image.
Thinning is used to reduce each connected component in a binary image to a singlepixel wide skeleton.
Parameters: 


Returns: 

See also
Notes
The algorithm [Zha84] works by making successive passes of the image, removing pixels on object borders. This continues until no more pixels can be removed. The image is correlated with a mask that assigns each pixel a number in the range [0…255] corresponding to each possible pattern of its 8 neighbouring pixels. A look up table is then used to assign the pixels a value of 0, 1, 2 or 3, which are selectively removed during the iterations.
Note that this algorithm will give different results than a medial axis transform, which is also often referred to as “skeletonization”.
References
[Zha84]  (1, 2) A fast parallel algorithm for thinning digital patterns, T. Y. Zhang and C. Y. Suen, Communications of the ACM, March 1984, Volume 27, Number 3. 
Examples
>>> X, Y = np.ogrid[0:9, 0:9]
>>> ellipse = (1./3 * (X  4)**2 + (Y  4)**2 < 3**2).astype(np.uint8)
>>> ellipse
array([[0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0, 0]], dtype=uint8)
>>> skel = skeletonize(ellipse)
>>> skel.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, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 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)
skimage.morphology.
skeletonize_3d
(img)[source]¶Compute the skeleton of a binary image.
Thinning is used to reduce each connected component in a binary image to a singlepixel wide skeleton.
Parameters: 


Returns: 

See also
Notes
The method of [Lee94] uses an octree data structure to examine a 3x3x3 neighborhood of a pixel. The algorithm proceeds by iteratively sweeping over the image, and removing pixels at each iteration until the image stops changing. Each iteration consists of two steps: first, a list of candidates for removal is assembled; then pixels from this list are rechecked sequentially, to better preserve connectivity of the image.
The algorithm this function implements is different from the algorithms used by either skeletonize or medial_axis, thus for 2D images the results produced by this function are generally different.
References
[Lee94]  (1, 2) T.C. Lee, R.L. Kashyap and C.N. Chu, Building skeleton models via 3D medial surface/axis thinning algorithms. Computer Vision, Graphics, and Image Processing, 56(6):462478, 1994. 
skimage.morphology.skeletonize_3d
¶skimage.morphology.
thin
(image, max_iter=None)[source]¶Perform morphological thinning of a binary image.
Parameters: 


Returns: 

See also
Notes
This algorithm [1] works by making multiple passes over the image, removing pixels matching a set of criteria designed to thin connected regions while preserving eightconnected components and 2 x 2 squares [2]. In each of the two subiterations the algorithm correlates the intermediate skeleton image with a neighborhood mask, then looks up each neighborhood in a lookup table indicating whether the central pixel should be deleted in that subiteration.
References
[1]  (1, 2) Z. Guo and R. W. Hall, “Parallel thinning with twosubiteration algorithms,” Comm. ACM, vol. 32, no. 3, pp. 359373, 1989. DOI:10.1145/62065.62074 
[2]  (1, 2) Lam, L., SeongWhan Lee, and Ching Y. Suen, “Thinning MethodologiesA Comprehensive Survey,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 14, No. 9, p. 879, 1992. DOI:10.1109/34.161346 
Examples
>>> square = np.zeros((7, 7), dtype=np.uint8)
>>> square[1:1, 2:2] = 1
>>> square[0, 1] = 1
>>> square
array([[0, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> skel = thin(square)
>>> skel.astype(np.uint8)
array([[0, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.thin
¶skimage.morphology.
medial_axis
(image, mask=None, return_distance=False)[source]¶Compute the medial axis transform of a binary image
Parameters: 


Returns: 

See also
Notes
This algorithm computes the medial axis transform of an image as the ridges of its distance transform.
Examples
>>> square = np.zeros((7, 7), dtype=np.uint8)
>>> square[1:1, 2:2] = 1
>>> square
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> medial_axis(square).astype(np.uint8)
array([[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
skimage.morphology.medial_axis
¶skimage.morphology.
convex_hull_image
(image, offset_coordinates=True, tolerance=1e10)[source]¶Compute the convex hull image of a binary image.
The convex hull is the set of pixels included in the smallest convex polygon that surround all white pixels in the input image.
Parameters: 


Returns: 

References
[1]  https://blogs.mathworks.com/steve/2011/10/04/binaryimageconvexhullalgorithmnotes/ 
skimage.morphology.
convex_hull_object
(image, neighbors=8)[source]¶Compute the convex hull image of individual objects in a binary image.
The convex hull is the set of pixels included in the smallest convex polygon that surround all white pixels in the input image.
Parameters: 


Returns: 

Notes
This function uses skimage.morphology.label to define unique objects, finds the convex hull of each using convex_hull_image, and combines these regions with logical OR. Be aware the convex hulls of unconnected objects may overlap in the result. If this is suspected, consider using convex_hull_image separately on each object.
skimage.morphology.
reconstruction
(seed, mask, method='dilation', selem=None, offset=None)[source]¶Perform a morphological reconstruction of an image.
Morphological reconstruction by dilation is similar to basic morphological dilation: highintensity values will replace nearby lowintensity values. The basic dilation operator, however, uses a structuring element to determine how far a value in the input image can spread. In contrast, reconstruction uses two images: a “seed” image, which specifies the values that spread, and a “mask” image, which gives the maximum allowed value at each pixel. The mask image, like the structuring element, limits the spread of highintensity values. Reconstruction by erosion is simply the inverse: lowintensity values spread from the seed image and are limited by the mask image, which represents the minimum allowed value.
Alternatively, you can think of reconstruction as a way to isolate the connected regions of an image. For dilation, reconstruction connects regions marked by local maxima in the seed image: neighboring pixels lessthanorequalto those seeds are connected to the seeded region. Local maxima with values larger than the seed image will get truncated to the seed value.
Parameters: 


Returns: 

Notes
The algorithm is taken from [1]. Applications for greyscale reconstruction are discussed in [2] and [3].
References
[1]  (1, 2) Robinson, “Efficient morphological reconstruction: a downhill filter”, Pattern Recognition Letters 25 (2004) 17591767. 
[2]  (1, 2) Vincent, L., “Morphological Grayscale Reconstruction in Image Analysis: Applications and Efficient Algorithms”, IEEE Transactions on Image Processing (1993) 
[3]  (1, 2) Soille, P., “Morphological Image Analysis: Principles and Applications”, Chapter 6, 2nd edition (2003), ISBN 3540429883. 
Examples
>>> import numpy as np
>>> from skimage.morphology import reconstruction
First, we create a sinusoidal mask image with peaks at middle and ends.
>>> x = np.linspace(0, 4 * np.pi)
>>> y_mask = np.cos(x)
Then, we create a seed image initialized to the minimum mask value (for reconstruction by dilation, minintensity values don’t spread) and add “seeds” to the left and right peak, but at a fraction of peak value (1).
>>> y_seed = y_mask.min() * np.ones_like(x)
>>> y_seed[0] = 0.5
>>> y_seed[1] = 0
>>> y_rec = reconstruction(y_seed, y_mask)
The reconstructed image (or curve, in this case) is exactly the same as the mask image, except that the peaks are truncated to 0.5 and 0. The middle peak disappears completely: Since there were no seed values in this peak region, its reconstructed value is truncated to the surrounding value (1).
As a more practical example, we try to extract the bright features of an image by subtracting a background image created by reconstruction.
>>> y, x = np.mgrid[:20:0.5, :20:0.5]
>>> bumps = np.sin(x) + np.sin(y)
To create the background image, set the mask image to the original image, and the seed image to the original image with an intensity offset, h.
>>> h = 0.3
>>> seed = bumps  h
>>> background = reconstruction(seed, bumps)
The resulting reconstructed image looks exactly like the original image, but with the peaks of the bumps cut off. Subtracting this reconstructed image from the original image leaves just the peaks of the bumps
>>> hdome = bumps  background
This operation is known as the hdome of the image and leaves features of height h in the subtracted image.
skimage.morphology.
remove_small_objects
(ar, min_size=64, connectivity=1, in_place=False)[source]¶Remove objects smaller than the specified size.
Expects ar to be an array with labeled objects, and removes objects smaller than min_size. If ar is bool, the image is first labeled. This leads to potentially different behavior for bool and 0and1 arrays.
Parameters: 


Returns: 

Raises: 

Examples
>>> from skimage import morphology
>>> a = np.array([[0, 0, 0, 1, 0],
... [1, 1, 1, 0, 0],
... [1, 1, 1, 0, 1]], bool)
>>> b = morphology.remove_small_objects(a, 6)
>>> b
array([[False, False, False, False, False],
[ True, True, True, False, False],
[ True, True, True, False, False]], dtype=bool)
>>> c = morphology.remove_small_objects(a, 7, connectivity=2)
>>> c
array([[False, False, False, True, False],
[ True, True, True, False, False],
[ True, True, True, False, False]], dtype=bool)
>>> d = morphology.remove_small_objects(a, 6, in_place=True)
>>> d is a
True
skimage.morphology.remove_small_objects
¶skimage.morphology.
remove_small_holes
(ar, area_threshold=64, connectivity=1, in_place=False, min_size=None)[source]¶Remove contiguous holes smaller than the specified size.
Parameters: 


Returns: 

Raises: 

Notes
If the array type is int, it is assumed that it contains alreadylabeled objects. The labels are not kept in the output image (this function always outputs a bool image). It is suggested that labeling is completed after using this function.
Examples
>>> from skimage import morphology
>>> a = np.array([[1, 1, 1, 1, 1, 0],
... [1, 1, 1, 0, 1, 0],
... [1, 0, 0, 1, 1, 0],
... [1, 1, 1, 1, 1, 0]], bool)
>>> b = morphology.remove_small_holes(a, 2)
>>> b
array([[ True, True, True, True, True, False],
[ True, True, True, True, True, False],
[ True, False, False, True, True, False],
[ True, True, True, True, True, False]], dtype=bool)
>>> c = morphology.remove_small_holes(a, 2, connectivity=2)
>>> c
array([[ True, True, True, True, True, False],
[ True, True, True, False, True, False],
[ True, False, False, True, True, False],
[ True, True, True, True, True, False]], dtype=bool)
>>> d = morphology.remove_small_holes(a, 2, in_place=True)
>>> d is a
True
skimage.morphology.
h_minima
(image, h, selem=None)[source]¶Determine all minima of the image with depth >= h.
The local minima are defined as connected sets of pixels with equal grey level strictly smaller than the grey levels of all pixels in direct neighborhood of the set.
A local minimum M of depth h is a local minimum for which there is at least one path joining M with a deeper minimum on which the maximal value is f(M) + h (i.e. the values along the path are not increasing by more than h with respect to the minimum’s value) and no path for which the maximal value is smaller.
Parameters: 


Returns: 

See also
skimage.morphology.extrema.h_maxima
, skimage.morphology.extrema.local_maxima
, skimage.morphology.extrema.local_minima
References
[1]  Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. 
Examples
>>> import numpy as np
>>> from skimage.morphology import extrema
We create an image (quadratic function with a minimum in the center and 4 additional constant maxima. The depth of the minima are: 1, 21, 41, 61, 81, 101
>>> w = 10
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 180 + 0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:4,2:4] = 160; f[2:4,7:9] = 140; f[7:9,2:4] = 120; f[7:9,7:9] = 100
>>> f = f.astype(np.int)
We can calculate all minima with a depth of at least 40:
>>> minima = extrema.h_minima(f, 40)
The resulting image will contain 4 local minima.
skimage.morphology.
h_maxima
(image, h, selem=None)[source]¶Determine all maxima of the image with height >= h.
The local maxima are defined as connected sets of pixels with equal grey level strictly greater than the grey level of all pixels in direct neighborhood of the set.
A local maximum M of height h is a local maximum for which there is at least one path joining M with a higher maximum on which the minimal value is f(M)  h (i.e. the values along the path are not decreasing by more than h with respect to the maximum’s value) and no path for which the minimal value is greater.
Parameters: 


Returns: 

See also
skimage.morphology.extrema.h_minima
, skimage.morphology.extrema.local_maxima
, skimage.morphology.extrema.local_minima
References
[1]  Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. 
Examples
>>> import numpy as np
>>> from skimage.morphology import extrema
We create an image (quadratic function with a maximum in the center and 4 additional constant maxima. The heights of the maxima are: 1, 21, 41, 61, 81, 101
>>> w = 10
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 20  0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:4,2:4] = 40; f[2:4,7:9] = 60; f[7:9,2:4] = 80; f[7:9,7:9] = 100
>>> f = f.astype(np.int)
We can calculate all maxima with a height of at least 40:
>>> maxima = extrema.h_maxima(f, 40)
The resulting image will contain 4 local maxima.
skimage.morphology.h_maxima
¶skimage.morphology.
local_maxima
(image, selem=None, connectivity=None, indices=False, allow_borders=True)[source]¶Find local maxima of ndimensional array.
The local maxima are defined as connected sets of pixels with equal gray level (plateaus) strictly greater than the gray levels of all pixels in the neighborhood.
Parameters: 


Returns: 

Warns: 

Notes
This function operates on the following ideas:
For each candidate:
Examples
>>> from skimage.morphology import local_maxima
>>> 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
>>> image
array([[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]])
Find local maxima by comparing to all neighboring pixels (maximal connectivity):
>>> local_maxima(image)
array([[False, False, False, False, False, False, False],
[False, True, True, False, False, False, False],
[False, True, True, False, False, False, False],
[ True, False, False, False, False, False, True]], dtype=bool)
>>> local_maxima(image, indices=True)
(array([1, 1, 2, 2, 3, 3]), array([1, 2, 1, 2, 0, 6]))
Find local maxima without comparing to diagonal pixels (connectivity 1):
>>> local_maxima(image, connectivity=1)
array([[False, False, False, False, False, False, False],
[False, True, True, False, True, True, False],
[False, True, True, False, True, True, False],
[ True, False, False, False, False, False, True]], dtype=bool)
and exclude maxima that border the image edge:
>>> local_maxima(image, connectivity=1, allow_borders=False)
array([[False, False, False, False, False, False, False],
[False, True, True, False, True, True, False],
[False, True, True, False, True, True, False],
[False, False, False, False, False, False, False]], dtype=bool)
skimage.morphology.local_maxima
¶skimage.morphology.
local_minima
(image, selem=None, connectivity=None, indices=False, allow_borders=True)[source]¶Find local minima of ndimensional array.
The local minima are defined as connected sets of pixels with equal gray level (plateaus) strictly smaller than the gray levels of all pixels in the neighborhood.
Parameters: 


Returns: 

Notes
This function operates on the following ideas:
For each candidate:
Examples
>>> from skimage.morphology import local_minima
>>> 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
>>> image
array([[ 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]])
Find local minima by comparing to all neighboring pixels (maximal connectivity):
>>> local_minima(image)
array([[False, False, False, False, False, False, False],
[False, True, True, False, False, False, False],
[False, True, True, False, False, False, False],
[ True, False, False, False, False, False, True]], dtype=bool)
>>> local_minima(image, indices=True)
(array([1, 1, 2, 2, 3, 3]), array([1, 2, 1, 2, 0, 6]))
Find local minima without comparing to diagonal pixels (connectivity 1):
>>> local_minima(image, connectivity=1)
array([[False, False, False, False, False, False, False],
[False, True, True, False, True, True, False],
[False, True, True, False, True, True, False],
[ True, False, False, False, False, False, True]], dtype=bool)
and exclude minima that border the image edge:
>>> local_minima(image, connectivity=1, allow_borders=False)
array([[False, False, False, False, False, False, False],
[False, True, True, False, True, True, False],
[False, True, True, False, True, True, False],
[False, False, False, False, False, False, False]], dtype=bool)
skimage.morphology.
max_tree
(image, connectivity=1)[source]¶Build the max tree from an image.
Component trees represent the hierarchical structure of the connected components resulting from sequential thresholding operations applied to an image. A connected component at one level is parent of a component at a higher level if the latter is included in the first. A maxtree is an efficient representation of a component tree. A connected component at one level is represented by one reference pixel at this level, which is parent to all other pixels at that level and to the reference pixel at the level above. The maxtree is the basis for many morphological operators, namely connected operators.
Parameters: 


Returns: 

References
[1]  Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive Connected Operators for Image and Sequence Processing. IEEE Transactions on Image Processing, 7(4), 555570. DOI:10.1109/83.663500 
[2]  Berger, C., Geraud, T., Levillain, R., Widynski, N., Baillard, A., Bertin, E. (2007). Effective Component Tree Computation with Application to Pattern Recognition in Astronomical Imaging. In International Conference on Image Processing (ICIP) (pp. 4144). DOI:10.1109/ICIP.2007.4379949 
[3]  Najman, L., & Couprie, M. (2006). Building the component tree in quasilinear time. IEEE Transactions on Image Processing, 15(11), 35313539. DOI:10.1109/TIP.2006.877518 
[4]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create a small sample image (Figure 1 from [4]) and build the maxtree.
>>> image = np.array([[15, 13, 16], [12, 12, 10], [16, 12, 14]])
>>> P, S = max_tree(image, connectivity=2)
skimage.morphology.max_tree
¶skimage.morphology.
area_opening
(image, area_threshold=64, connectivity=1, parent=None, tree_traverser=None)[source]¶Perform an area opening of the image.
Area opening removes all bright structures of an image with a surface smaller than area_threshold. The output image is thus the largest image smaller than the input for which all local maxima have at least a surface of area_threshold pixels.
Area openings are similar to morphological openings, but they do not use a fixed structuring element, but rather a deformable one, with surface = area_threshold. Consequently, the area_opening with area_threshold=1 is the identity.
In the binary case, area openings are equivalent to remove_small_objects; this operator is thus extended to graylevel images.
Technically, this operator is based on the maxtree representation of the image.
Parameters: 


Returns: 

See also
skimage.morphology.area_closing
, skimage.morphology.diameter_opening
, skimage.morphology.diameter_closing
, skimage.morphology.max_tree
, skimage.morphology.remove_small_objects
, skimage.morphology.remove_small_holes
References
[1]  Vincent L., Proc. “Grayscale area openings and closings, their efficient implementation and applications”, EURASIP Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, pp.2227, May 1993. 
[2]  Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. DOI:10.1007/9783662050880 
[3]  Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive Connected Operators for Image and Sequence Processing. IEEE Transactions on Image Processing, 7(4), 555570. DOI:10.1109/83.663500 
[4]  Najman, L., & Couprie, M. (2006). Building the component tree in quasilinear time. IEEE Transactions on Image Processing, 15(11), 35313539. DOI:10.1109/TIP.2006.877518 
[5]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create an image (quadratic function with a maximum in the center and 4 additional local maxima.
>>> w = 12
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 20  0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:3,1:5] = 40; f[2:4,9:11] = 60; f[9:11,2:4] = 80
>>> f[9:10,9:11] = 100; f[10,10] = 100
>>> f = f.astype(np.int)
We can calculate the area opening:
>>> open = area_opening(f, 8, connectivity=1)
The peaks with a surface smaller than 8 are removed.
skimage.morphology.
area_closing
(image, area_threshold=64, connectivity=1, parent=None, tree_traverser=None)[source]¶Perform an area closing of the image.
Area closing removes all dark structures of an image with a surface smaller than area_threshold. The output image is larger than or equal to the input image for every pixel and all local minima have at least a surface of area_threshold pixels.
Area closings are similar to morphological closings, but they do not use a fixed structuring element, but rather a deformable one, with surface = area_threshold.
In the binary case, area closings are equivalent to remove_small_holes; this operator is thus extended to graylevel images.
Technically, this operator is based on the maxtree representation of the image.
Parameters: 


Returns: 

See also
skimage.morphology.area_opening
, skimage.morphology.diameter_opening
, skimage.morphology.diameter_closing
, skimage.morphology.max_tree
, skimage.morphology.remove_small_objects
, skimage.morphology.remove_small_holes
References
[1]  Vincent L., Proc. “Grayscale area openings and closings, their efficient implementation and applications”, EURASIP Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, pp.2227, May 1993. 
[2]  Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. DOI:10.1007/9783662050880 
[3]  Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive Connected Operators for Image and Sequence Processing. IEEE Transactions on Image Processing, 7(4), 555570. DOI:10.1109/83.663500 
[4]  Najman, L., & Couprie, M. (2006). Building the component tree in quasilinear time. IEEE Transactions on Image Processing, 15(11), 35313539. DOI:10.1109/TIP.2006.877518 
[5]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create an image (quadratic function with a minimum in the center and 4 additional local minima.
>>> w = 12
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 180 + 0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:3,1:5] = 160; f[2:4,9:11] = 140; f[9:11,2:4] = 120
>>> f[9:10,9:11] = 100; f[10,10] = 100
>>> f = f.astype(np.int)
We can calculate the area closing:
>>> closed = area_closing(f, 8, connectivity=1)
All small minima are removed, and the remaining minima have at least a size of 8.
skimage.morphology.
diameter_opening
(image, diameter_threshold=8, connectivity=1, parent=None, tree_traverser=None)[source]¶Perform a diameter opening of the image.
Diameter opening removes all bright structures of an image with maximal extension smaller than diameter_threshold. The maximal extension is defined as the maximal extension of the bounding box. The operator is also called Bounding Box Opening. In practice, the result is similar to a morphological opening, but long and thin structures are not removed.
Technically, this operator is based on the maxtree representation of the image.
Parameters: 


Returns: 

See also
skimage.morphology.area_opening
, skimage.morphology.area_closing
, skimage.morphology.diameter_closing
, skimage.morphology.max_tree
References
[1]  Walter, T., & Klein, J.C. (2002). Automatic Detection of Microaneurysms in Color Fundus Images of the Human Retina by Means of the Bounding Box Closing. In A. Colosimo, P. Sirabella, A. Giuliani (Eds.), Medical Data Analysis. Lecture Notes in Computer Science, vol 2526, pp. 210220. Springer Berlin Heidelberg. DOI:10.1007/3540361049_23 
[2]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create an image (quadratic function with a maximum in the center and 4 additional local maxima.
>>> w = 12
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 20  0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:3,1:5] = 40; f[2:4,9:11] = 60; f[9:11,2:4] = 80
>>> f[9:10,9:11] = 100; f[10,10] = 100
>>> f = f.astype(np.int)
We can calculate the diameter opening:
>>> open = diameter_opening(f, 3, connectivity=1)
The peaks with a maximal extension of 2 or less are removed. The remaining peaks have all a maximal extension of at least 3.
skimage.morphology.
diameter_closing
(image, diameter_threshold=8, connectivity=1, parent=None, tree_traverser=None)[source]¶Perform a diameter closing of the image.
Diameter closing removes all dark structures of an image with maximal extension smaller than diameter_threshold. The maximal extension is defined as the maximal extension of the bounding box. The operator is also called Bounding Box Closing. In practice, the result is similar to a morphological closing, but long and thin structures are not removed.
Technically, this operator is based on the maxtree representation of the image.
Parameters: 


Returns: 

See also
skimage.morphology.area_opening
, skimage.morphology.area_closing
, skimage.morphology.diameter_opening
, skimage.morphology.max_tree
References
[1]  Walter, T., & Klein, J.C. (2002). Automatic Detection of Microaneurysms in Color Fundus Images of the Human Retina by Means of the Bounding Box Closing. In A. Colosimo, P. Sirabella, A. Giuliani (Eds.), Medical Data Analysis. Lecture Notes in Computer Science, vol 2526, pp. 210220. Springer Berlin Heidelberg. DOI:10.1007/3540361049_23 
[2]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create an image (quadratic function with a minimum in the center and 4 additional local minima.
>>> w = 12
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 180 + 0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:3,1:5] = 160; f[2:4,9:11] = 140; f[9:11,2:4] = 120
>>> f[9:10,9:11] = 100; f[10,10] = 100
>>> f = f.astype(np.int)
We can calculate the diameter closing:
>>> closed = diameter_closing(f, 3, connectivity=1)
All small minima with a maximal extension of 2 or less are removed. The remaining minima have all a maximal extension of at least 3.
skimage.morphology.diameter_closing
¶skimage.morphology.
max_tree_local_maxima
(image, connectivity=1, parent=None, tree_traverser=None)[source]¶Determine all local maxima of the image.
The local maxima are defined as connected sets of pixels with equal gray level strictly greater than the gray levels of all pixels in direct neighborhood of the set. The function labels the local maxima.
Technically, the implementation is based on the maxtree representation of an image. The function is very efficient if the maxtree representation has already been computed. Otherwise, it is preferable to use the function local_maxima.
Parameters: 


Returns: 

References
[1]  Vincent L., Proc. “Grayscale area openings and closings, their efficient implementation and applications”, EURASIP Workshop on Mathematical Morphology and its Applications to Signal Processing, Barcelona, Spain, pp.2227, May 1993. 
[2]  Soille, P., “Morphological Image Analysis: Principles and Applications” (Chapter 6), 2nd edition (2003), ISBN 3540429883. DOI:10.1007/9783662050880 
[3]  Salembier, P., Oliveras, A., & Garrido, L. (1998). Antiextensive Connected Operators for Image and Sequence Processing. IEEE Transactions on Image Processing, 7(4), 555570. DOI:10.1109/83.663500 
[4]  Najman, L., & Couprie, M. (2006). Building the component tree in quasilinear time. IEEE Transactions on Image Processing, 15(11), 35313539. DOI:10.1109/TIP.2006.877518 
[5]  Carlinet, E., & Geraud, T. (2014). A Comparative Review of Component Tree Computation Algorithms. IEEE Transactions on Image Processing, 23(9), 38853895. DOI:10.1109/TIP.2014.2336551 
Examples
We create an image (quadratic function with a maximum in the center and 4 additional constant maxima.
>>> w = 10
>>> x, y = np.mgrid[0:w,0:w]
>>> f = 20  0.2*((x  w/2)**2 + (yw/2)**2)
>>> f[2:4,2:4] = 40; f[2:4,7:9] = 60; f[7:9,2:4] = 80; f[7:9,7:9] = 100
>>> f = f.astype(np.int)
We can calculate all local maxima:
>>> maxima = max_tree_local_maxima(f)
The resulting image contains the labeled local maxima.