Connected component labeling

Conceptionally, label images are an extension of binary images. Binary images have only two values, e.g. 0 and 1, describing background and foreground. 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, which means in an image with 7 objects, all integer intensities between 0 and 7 exist. None is missing. Then, the maximum intensity in the label image corresponds to the number of labeled objects in the image.

See also

• Connected-component labeling

import numpy as np
from skimage.measure import label
import stackview
from skimage.io import imread
from skimage.filters import threshold_otsu
import matplotlib.pyplot as plt

We start with a simple mock binary image.

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],    
])

stackview.imshow(binary_image)

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.

labeled_4_connected = label(binary_image, connectivity=1)

stackview.imshow(labeled_4_connected)

8-connected component labeling

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

stackview.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.

# Load data
blobs = imread("data/blobs.tif")

# Thresholding
threshold = threshold_otsu(blobs)
binary_blobs = blobs > threshold

# Connected component labeling
labeled_blobs = label(binary_blobs)

# Visualization
fig, axs = plt.subplots(1, 3, figsize=(15,15))

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

Visualizing segmentation results

To gain trust in segmentation results, it is key to visualize the segmented image on top of the original image.

stackview.animate_curtain(blobs, labeled_blobs)

stackview.curtain(blobs, labeled_blobs)

stackview.animate_blend(blobs, labeled_blobs)

stackview.blend(blobs, labeled_blobs)

Exercise

In a single line of code, find out the number of objects in the labeled_blobs image.