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)

_images/labeled-1.png

This results in an image with 3 values:

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

_images/labeled-2.png

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)

_images/labeled-3.png

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)

_images/labeled-4.png

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)

_images/labeled-5.png

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)

_images/labeled-6.png

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)

_images/labeled-7.png

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:

f : integer ndarray

as_slice : boolean, optional

Whether to return slice objects instead of integer coordinates (default: False).

Returns:

bboxes : ndarray

See also

mh.bbox
the binary version of this function
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.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:

labeled : labeled array

remove_bordering : bool, optional

whether to remove regions that touch the border

min_size : int, optional

Minimum size (in pixels) of objects to keep (default is no minimum)

max_size : int, optional

Maximum size (in pixels) of objects to keep (default is no maximum)

Returns:

filtered : labeled array

nr : int

number of new labels

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, 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:

array : ndarray of any type

labeled : int ndarray

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

minlength : int, optional

Minimum size of return array. If labeled has fewer than minlength regions, 0s are added to the result. (optional)

Returns:

sums : 1-d ndarray of array.dtype

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:

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.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:

labeled0 : ndarray of int

A labeled array

labeled1 : ndarray of int

A labeled array

Returns:

same : bool

True if the labelings passed as argument are equivalent

See also

label
function
relabel
function
mahotas.labeled.perimeter(bwimage, n=4, mode="constant")

Calculate total perimeter of all objects in binary image.

Parameters:

bwimage : array

binary image

n : int, optional

passed to bwperim as is

mode : str, optional

passed to bwperim as is

Returns:

p : float

total perimeter of all objects in binary image

See also

bwperim
function Finds the perimeter region

References

[R1]K. Benkrid, D. Crookes. Design and FPGA Implementation of a Perimeter Estimator. The Queen’s University of Belfast. http://www.cs.qub.ac.uk/~d.crookes/webpubs/papers/perimeter.doc
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:

labeled : ndarray

Labeled array

rsize : int 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.

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.
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