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
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 = mahotas.label(regions)

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

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

This results in an image with 3 values:

0. background, where the original image was 0
1. for the first region: (0:3, 0:3);
2. 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).

New in version 0.7: labeled_size and labeled_sum were added in version 0.7

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

sizes = mahotas.labeled_size(labeled)
print 'Background size', sizes[0]
print 'Size of first region', 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 = mahotas.labeled_sum(array, labeled)
print 'Sum of first region', sums[1]

Filtering Regions

New in version 0.9.6: remove_regions & relabel were only added in version 0.9.6

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

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

First we perform a bit of Gaussian filtering and thresholding:

f = mahotas.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.)

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

Labeling gets us all of the nuclei:

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

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

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

We can also remove the region touching the border:

labeled = mahotas.labeled.remove_bordering(labeled)

(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 = mahotas.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.

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

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.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 :

labeled : ndarray of integer type

input labeled array

Bc : structure element, optional

out : ndarray 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_img : boolean ndarray

Pixels are True exactly where there is a border in labeled

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 :

labeled : ndarray of integer type

input labeled array

i : integer

j : integer

Bc : structure element, optional

out : ndarray of same shape as labeled, dtype=bool, optional

where to store the output. If None, a new array is allocated

always_return : bool, 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_img : boolean ndarray

Pixels are True exactly where there is a border between i and j 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 :

bw : ndarray

A black-and-white image (any other image will be converted to black & white)

n : int, optional

Connectivity. Must be 4 or 8 (default: 4)

mode : {‘reflect’, ‘nearest’, ‘wrap’, ‘mirror’, ‘constant’ [default], ‘ignore’}

How to handle borders

Returns :

perim : ndarray

A boolean image

See also

borders

function This is a more generic 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: http://en.wikipedia.org/wiki/Connected-component_labeling

Parameters :

array : ndarray

This will be interpreted as binary array

Bc : ndarray, optional

This is the structuring element to use

out : ndarray, optional

Output array. Must be a C-array, of type np.int32

Returns :

labeled : ndarray

Labeled result

nr_objects : int

Number of objects

mahotas.labeled.labeled_sum(array, labeled)

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

Parameters :

array : ndarray of any type

labeled : int ndarray

Label map. This is the same type as returned from mahotas.label()

Returns :

sums : 1-d ndarray of array.dtype

mahotas.labeled.labeled_max(array, labeled)

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

Parameters :

array : ndarray of any type

labeled : int ndarray

Label map. This is the same type as returned from mahotas.label()

Returns :

mins : 1-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 :labeled : int ndarray Returns :sizes : 1-d ndarray of int

See also

mahotas.fullhistogram

almost same function by another name (the only

difference

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 xrange(n):
    if not good_region(labeled, region + 1):
        # This deletes the region:
        labeled[labeled == (region + 1)] = 0
relabel(labeled, inplace=True)

Parameters :

relabeled : ndarray of int

A labeled array

inplace : boolean, optional

Whether to perform relabeling inplace, erasing the values in labeled (default: False)

Returns :

relabeled: ndarray :

nr_objs : int

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 im as out to achieve in-place operation.

Parameters :

labeled : ndarray

Labeled array

rsize : int, optional

Minimum distance to the border (in Manhatan distance) to allow an object to survive.

out : ndarray, optional

If im is passed as out, then it operates inline.

Returns :

slabeled : ndarray

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 :

relabeled : ndarray of int

A labeled array

regions : sequence of int

These regions will be removed

inplace : boolean, optional

Whether to perform removal inplace, erasing the values in labeled (default: False)

Returns :

removed : ndarray

See also

relabel

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