Labeled Image Functions¶

Labeled images are integer images where the values correspond to different regions. I.e., region 1 is all of the pixels which have value 1, region two is the pixels with value 2, and so on. By convention, region 0 is the background and often handled differently.

Labeling Images¶

New in version 0.6.5.

The first step is obtaining a labeled function from a binary function:

import mahotas as mh
import numpy as np
from pylab import imshow, show

regions = np.zeros((8,8), bool)

regions[:3,:3] = 1
regions[6:,6:] = 1
labeled, nr_objects = mh.label(regions)

imshow(labeled, interpolation='nearest')
show()

(Source code, png, hires.png, pdf)

This results in an image with 3 values:

background, where the original image was 0
for the first region: (0:3, 0:3);
for the second region: (6:, 6:).

There is an extra argument to label: the structuring element, which defaults to a 3x3 cross (or, 4-neighbourhood). This defines what it means for two pixels to be in the same region. You can use 8-neighbourhoods by replacing it with a square:

labeled,nr_objects = mh.label(regions, np.ones((3,3), bool))

We can now collect a few statistics on the labeled regions. For example, how big are they?

sizes = mh.labeled.labeled_size(labeled)
print('Background size', sizes[0])
print('Size of first region: {}'.format(sizes[1]))

This size is measured simply as the number of pixels in each region. We can instead measure the total weight in each area:

array = np.random.random_sample(regions.shape)
sums = mh.labeled_sum(array, labeled)
print('Sum of first region: {}'.format(sums[1]))

Filtering Regions¶

New in version 0.9.6: remove_regions & relabel were added.

Here is a slightly more complex example. The full code is in the demos directory as nuclear.py. We are going to use this image, a fluorescent microscopy image from a nuclear segmentation benchmark

This image is available as mahotas.demos.nuclear_image()

import mahotas as mh
import mahotas.demos
import numpy as np
from pylab import imshow, show

f = mh.demos.nuclear_image()
f = f[:,:,0]
imshow(f)
show()

(Source code, png, hires.png, pdf)

First we perform a bit of Gaussian filtering and thresholding:

f = mh.gaussian_filter(f, 4)
f = (f> f.mean())

(Without the Gaussian filter, the resulting thresholded image has very noisy edges. You can get the image in the demos/ directory and try it out.)

f = mh.gaussian_filter(f, 4)
f = (f> f.mean())
imshow(f)
show()

(Source code, png, hires.png, pdf)

Labeling gets us all of the nuclei:

labeled, n_nucleus  = mh.label(f)
print('Found {} nuclei.'.format(n_nucleus))

labeled, n_nucleus  = mh.label(f)
print('Found {} nuclei.'.format(n_nucleus))
imshow(labeled)
show()

(Source code, png, hires.png, pdf)

42 nuclei were found. None were missed, but, unfortunately, we also get some aggregates. In this case, we are going to assume that we wanted to perform some measurements on the real nuclei, but are willing to filter out anything that is not a complete nucleus or that is a lump on nuclei. So we measure sizes and filter:

sizes = mh.labeled.labeled_size(labeled)
too_big = np.where(sizes > 10000)
labeled = mh.labeled.remove_regions(labeled, too_big)

sizes = mh.labeled.labeled_size(labeled)
too_big = np.where(sizes > 10000)
labeled = mh.labeled.remove_regions(labeled, too_big)
imshow(labeled)
show()

(Source code, png, hires.png, pdf)

We can also remove the region touching the border:

labeled = mh.labeled.remove_bordering(labeled)

labeled = mh.labeled.remove_bordering(labeled)
imshow(labeled)
show()

(Source code, png, hires.png, pdf)

This array, labeled now has values in the range 0 to n_nucleus, but with some values missing (e.g., if region 7 was one of the ones touching the border, then 7 is not used in the labeling). We can relabel to get a cleaner version:

relabeled, n_left = mh.labeled.relabel(labeled)
print('After filtering and relabeling, there are {} nuclei left.'.format(n_left))

Now, we have 24 nuclei and relabeled goes from 0 (background) to 24.

relabeled, n_left = mh.labeled.relabel(labeled)
print('After filtering and relabeling, there are {} nuclei left.'.format(n_left))
imshow(relabeled)
show()

(Source code, png, hires.png, pdf)

In mahotas after version 1.4, we can even make many of the same operations with a single call to mh.labeled.filter_labeled:

relabeled,n_left = mh.labeled.filter_labeled(labeled, remove_bordering=True, max_size=10000)

Borders¶

A border pixel is one where there is more than one region in its neighbourhood (one of those regions can be the background).

You can retrieve border pixels with either the borders() function, which gets all the borders or the border() (note the singular) which gets only the border between a single pair of regions. As usual, what neighbour means is defined by a structuring element, defaulting to a 3x3 cross.

API Documentation¶

The mahotas.labeled submodule contains the functions mentioned above. label() is also available as mahotas.label.

mahotas.labeled.bbox(f, as_slice=False)

Bounding boxes of all objects in a labeled array.

After:

bboxes = mh.labeled.bbox(f)

bboxes[34] will contain the bounding box of (f == 34).

Parameters:

finteger ndarray
as_sliceboolean, optional: Whether to return slice objects instead of integer coordinates (default: False).

Returns:

bboxesndarray

See also

mh.bbox: the binary version of this function

mahotas.labeled.border(labeled, i, j, Bc={3x3 cross}, out={np.zeros(labeled.shape, bool)}, always_return=True)

Compute the border region between i and j regions.

A pixel is on the border if it has value i (or j) and a pixel in its neighbourhood (defined by Bc) has value j (or i).

Parameters:

labeledndarray of integer type: input labeled array
iinteger
jinteger
Bcstructure element, optional
outndarray of same shape as labeled, dtype=bool, optional: where to store the output. If None, a new array is allocated
always_returnbool, optional: if false, then, in the case where there is no pixel on the border, returns None. Otherwise (the default), it always returns an array even if it is empty.

Returns:

border_imgboolean ndarray: Pixels are True exactly where there is a border between i and j in labeled

mahotas.labeled.borders(labeled, Bc={3x3 cross}, out={np.zeros(labeled.shape, bool)})

Compute border pixels

A pixel is on a border if it has value i and a pixel in its neighbourhood (defined by Bc) has value j, with i != j.

Parameters:

labeledndarray of integer type: input labeled array
Bcstructure element, optional
outndarray of same shape as labeled, dtype=bool, optional: where to store the output. If None, a new array is allocated
mode{‘reflect’, ‘nearest’, ‘wrap’, ‘mirror’, ‘constant’ [default], ‘ignore’}: How to handle borders

Returns:

border_imgboolean ndarray: Pixels are True exactly where there is a border in labeled

mahotas.labeled.bwperim(bw, n=4)

Find the perimeter of objects in binary images.

A pixel is part of an object perimeter if its value is one and there is at least one zero-valued pixel in its neighborhood.

By default the neighborhood of a pixel is 4 nearest pixels, but if n is set to 8 the 8 nearest pixels will be considered.

Parameters:

bwndarray: A black-and-white image (any other image will be converted to black & white)
nint, optional: Connectivity. Must be 4 or 8 (default: 4)
mode{‘reflect’, ‘nearest’, ‘wrap’, ‘mirror’, ‘constant’ [default], ‘ignore’}: How to handle borders

Returns:

perimndarray: A boolean image

See also

borders: function This is a more generic function

mahotas.labeled.filter_labeled(labeled, remove_bordering=False, min_size=None, max_size=None)

Filter labeled regions based on a series of conditions

New in version 1.4.1.

Parameters:

labeledlabeled array
remove_borderingbool, optional: whether to remove regions that touch the border
min_sizeint, optional: Minimum size (in pixels) of objects to keep (default is no minimum)
max_sizeint, optional: Maximum size (in pixels) of objects to keep (default is no maximum)

Returns:

filteredlabeled array
nrint: number of new labels

mahotas.labeled.is_same_labeling(labeled0, labeled1)

Checks whether labeled0 and labeled1 represent the same labeling (i.e., whether they are the same except for a possible change of label values).

Note that the background (value 0) is treated differently. Namely

is_same_labeling(a, b) implies np.all( (a == 0) == (b == 0) )

Parameters:

labeled0ndarray of int: A labeled array
labeled1ndarray of int: A labeled array

Returns:

samebool: True if the labelings passed as argument are equivalent

See also

label: function
relabel: function

mahotas.labeled.label(array, Bc={3x3 cross}, output={new array})

Label the array, which is interpreted as a binary array

This is also called connected component labeled, where the connectivity is defined by the structuring element Bc.

See: https://en.wikipedia.org/wiki/Connected-component_labeling

Parameters:

arrayndarray: This will be interpreted as binary array
Bcndarray, optional: This is the structuring element to use
outndarray, optional: Output array. Must be a C-array, of type np.int32

Returns:

labeledndarray: Labeled result
nr_objectsint: Number of objects

mahotas.labeled.labeled_max(array, labeled, minlength=None)

Labeled minimum. mins will be an array of size labeled.max() + 1, where mins[i] is equal to np.min(array[labeled == i]).

Parameters:

arrayndarray of any type
labeledint ndarray: Label map. This is the same type as returned from mahotas.label()

Returns:

mins1-d ndarray of array.dtype

mahotas.labeled.labeled_size(labeled)

Equivalent to:

for i in range(...):
    sizes[i] = np.sum(labeled == i)

but, naturally, much faster.

Parameters:

labeledint ndarray

Returns:

sizes1-d ndarray of int

See also

mahotas.fullhistogram: function almost same function by another name (the only difference is that that function only accepts unsigned integer types).

mahotas.labeled.labeled_sum(array, labeled, minlength=None)

Labeled sum. sum will be an array of size labeled.max() + 1, where sum[i] is equal to np.sum(array[labeled == i]).

Parameters:

arrayndarray of any type
labeledint ndarray: Label map. This is the same type as returned from mahotas.label()
minlengthint, optional: Minimum size of return array. If labeled has fewer than minlength regions, 0s are added to the result. (optional)

Returns:

sums1-d ndarray of array.dtype

mahotas.labeled.perimeter(bwimage, n=4, mode='constant')

Calculate total perimeter of all objects in binary image.

Parameters:

bwimagearray: binary image
nint, optional: passed to bwperim as is
modestr, optional: passed to bwperim as is

Returns:

pfloat: total perimeter of all objects in binary image

See also

bwperim: function Finds the perimeter region

References

[1]

K. Benkrid, D. Crookes. Design and FPGA Implementation of a Perimeter Estimator. The Queen’s University of Belfast. https://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc

mahotas.labeled.relabel(labeled, inplace=False)

Relabeling ensures that relabeled is a labeled image such that every label from 1 to relabeled.max() is used (0 is reserved for the background and is passed through).

Example:

labeled,n = label(some_binary_map)
for region in range(n):
    if not good_region(labeled, region + 1):
        # This deletes the region:
        labeled[labeled == (region + 1)] = 0
relabel(labeled, inplace=True)

Parameters:

relabeledndarray of int: A labeled array
inplaceboolean, optional: Whether to perform relabeling inplace, erasing the values in labeled (default: False)

Returns:

relabeled: ndarray
nr_objsint: Number of objects

See also

label: function

mahotas.labeled.remove_bordering(labeled, rsize=1, out={np.empty_like(im)})

Remove objects that are touching the border.

Pass labeled as out to achieve in-place operation.

Parameters:

labeledndarray: Labeled array
rsizeint or tuple, optional: Minimum distance to the border (in Manhatan distance) to allow an object to survive. May be int or tuple with len == labeled.ndim.
outndarray, optional: If im is passed as out, then it operates inline.

Returns:

slabeledndarray: Subset of labeled

mahotas.labeled.remove_regions(labeled, regions, inplace=False)

removed = remove_regions(labeled, regions, inplace=False):

Removes the regions in regions. If an elementwise in operator existed, this would be equivalent to the following:

labeled[ labeled element-wise-in regions ] = 0

This function does not relabel its arguments. You can use the relabel function for that:

removed = relabel(remove_regions(labeled, regions))

Or, saving one image allocation:

removed = relabel(remove_regions(labeled, regions), inplace=True)

This is the same, but reuses the memory in the relabeling operation.

Parameters:

relabeledndarray of int: A labeled array
regionssequence of int: These regions will be removed
inplaceboolean, optional: Whether to perform removal inplace, erasing the values in labeled (default: False)

Returns:

removedndarray

See also

relabel: function After removing unecessary regions, it is often a good idea to relabel your label image.

mahotas.labeled.remove_regions_where(labeled, conditions, inplace=False)

Remove regions based on a boolean array

A region is removed if conditions[region-id] evaluates true.

This function does not relabel its arguments. You can use the relabel function for that:

removed = relabel(remove_regions_where(labeled, conditions))

Or, saving one image allocation:

removed = relabel(remove_regions(labeled, conditions), inplace=True)

This is the same, but reuses the memory in the relabeling operation.

See also

remove_regions: function Variation of this function which uses integer indexing

Labeled Image Functions¶

Labeling Images¶

Filtering Regions¶

Borders¶

API Documentation¶

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