Label images

Conceptionally, label images are an extension of binary images. In a label image, all pixels with value 0 correspond to background, a special region which is not considered as any object. Pixels with a value larger than 0 denote that the pixel belongs to an object and identifies that object with the given number. A pixel with value 1 belongs to first object and pixels with value 2 belongs to a second object and so on. Ideally, objects are labeled subsequently, because then, the maximum intensity in a label image corresponds to the number of labeled objects in this image.

Connected component labeling

We can technially use both alternatives for connected components labeling, depending on the connectivity that is used for connecting pixels in the label function.

Connectivity

1. von Neumann, 4-connected

2. Moore, 8-connected

4-connected component labeling

See also

• Connected-component labeling

We start with a made up binary image.

import numpy as np
import pyclesperanto_prototype as cle
from pyclesperanto_prototype import imshow

binary_image = np.asarray([
    [1, 1, 0, 0, 0, 0 ,0],
    [0, 0, 1, 0, 0, 0 ,0],
    [0, 0, 0, 1, 1, 1 ,0],
    [0, 0, 0, 1, 1, 1 ,0],
    [1, 1, 0, 0, 0, 0 ,0],
    [1, 1, 0, 0, 1, 1 ,1],
    [1, 1, 0, 0, 1, 1 ,1],    
])

imshow(binary_image, color_map='Greys_r')

C:\Users\rober\miniconda3\envs\bio_39\lib\site-packages\pyclesperanto_prototype\_tier9\_imshow.py:46: UserWarning: The imshow parameter color_map is deprecated. Use colormap instead.
  warnings.warn("The imshow parameter color_map is deprecated. Use colormap instead.")

This binary image can be interpreted in two ways: Either there are five rectangles with size ranging between 1 and 6. Alternatively, there are two rectangles with size 6 and one snake-like structure of size 9 pixels.

from skimage.measure import label
labeled_4_connected = label(binary_image, connectivity=1)

imshow(labeled_4_connected, labels=True)

8-connected component labeling

from skimage.measure import label
labeled_8_connected = label(binary_image, connectivity=2)

imshow(labeled_8_connected, labels=True)

In practice, for counting cells, the connectivity is not so important. This is why the connectivity parameter is often not provided.

Connected component labeling in clesperanto

In clesperanto, both connectivity options for connected component labeling is implemented in two different functions. When labeling objects using the 4-connected pixel neighborhood, we consider the “diamond” neighborhood of all pixels.

labeled_4_connected2 = cle.connected_components_labeling_diamond(binary_image)

imshow(labeled_4_connected2, labels=True)

The 8-connected neighborhood considers a “box” around all pixels.

labeled_8_connected2 = cle.connected_components_labeling_box(binary_image)

imshow(labeled_8_connected2, labels=True)

Labeling in practice

To demonstrate labeling in a practical use case, we label the blobs.tif image.

# Load data
from skimage.io import imread
blobs = imread("../../data/blobs.tif")

# Thresholding
from skimage.filters import threshold_otsu
threshold = threshold_otsu(blobs)
binary_blobs = blobs > threshold

# Connected component labeling
from skimage.measure import label
labeled_blobs = label(binary_blobs)

# Visualization
import matplotlib.pyplot as plt
fig, axs = plt.subplots(1, 3, figsize=(15,15))

cle.imshow(blobs, plot=axs[0])
cle.imshow(binary_blobs, plot=axs[1])
cle.imshow(labeled_blobs, plot=axs[2], labels=True)

Exercise

Find out experimentally what the default setting of the connectivity parameter of the skimage.measure.label function is.