Connected component labeling in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of connected components labeling on a binary image

What is the output of the following code that labels connected components in a binary image using scipy.ndimage.label?

SciPy

import numpy as np
from scipy.ndimage import label

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

labeled_array, num_features = label(binary_image)
print((labeled_array, num_features))

A (array([[1, 0, 0, 1], [1, 1, 0, 0], [0, 0, 2, 2], [0, 0, 2, 0]]), 2)

B (array([[1, 0, 0, 2], [1, 1, 0, 0], [0, 0, 3, 3], [0, 0, 3, 0]]), 3)

C (array([[1, 0, 0, 2], [1, 1, 0, 0], [0, 0, 2, 2], [0, 0, 2, 0]]), 2)

D (array([[1, 0, 0, 2], [1, 1, 0, 0], [0, 0, 3, 3], [0, 0, 4, 0]]), 4)

💡 Hint

Look at how connected pixels with value 1 are grouped. Each group gets a unique label starting from 1.

The function label assigns a unique integer to each connected group of 1s. Here, there are three groups: top-left corner, top-right corner, and bottom-right corner. So, the labeled array shows 1, 2, and 3 for these groups, and the total number of features is 3.

❓ data_output

intermediate

Number of connected components in a 3D array

Given the following 3D binary array, how many connected components does scipy.ndimage.label find?

SciPy

import numpy as np
from scipy.ndimage import label

array_3d = np.zeros((3, 3, 3), dtype=int)
array_3d[0, 0, 0] = 1
array_3d[0, 0, 1] = 1
array_3d[2, 2, 2] = 1

labeled, num = label(array_3d)
print(num)

A 2

B 1

C 3

D 0

💡 Hint

Check if the two 1s at positions (0,0,0) and (0,0,1) are connected.

The two 1s at (0,0,0) and (0,0,1) are adjacent and form one connected component. The single 1 at (2,2,2) is isolated, so total connected components are 2.

❓ visualization

advanced

Visualizing labeled connected components

Which option shows the correct matplotlib code to visualize the labeled connected components of a 2D binary image with distinct colors for each component?

SciPy

import numpy as np
from scipy.ndimage import label
import matplotlib.pyplot as plt

binary_image = np.array([
    [1, 0, 1, 1],
    [1, 1, 0, 0],
    [0, 0, 1, 1],
    [0, 0, 1, 0]
])
labeled_array, num_features = label(binary_image)

# Which code below correctly plots labeled_array with distinct colors?

A

plt.imshow(binary_image, cmap='nipy_spectral')
plt.colorbar()
plt.show()

B

plt.imshow(labeled_array, cmap='gray')
plt.colorbar()
plt.show()

C

plt.imshow(labeled_array, cmap='nipy_spectral')
plt.colorbar()
plt.show()

D

plt.imshow(binary_image, cmap='gray')
plt.colorbar()
plt.show()

💡 Hint

Use the labeled array and a color map that shows distinct colors for different labels.

The labeled array contains integer labels for each connected component. Using a color map like 'nipy_spectral' shows each label in a different color. Using the binary image or grayscale color map won't distinguish components clearly.

🔧 Debug

advanced

Identify the error in connected components labeling code

What error will the following code raise when trying to label connected components?

SciPy

import numpy as np
from scipy.ndimage import label

image = np.array([[1, 2], [3, 4]])
labeled, num = label(image)
print(num)

A RuntimeWarning: Non-binary values ignored

B ValueError: The input array must be 2D

C No error, output is (array([[1, 0], [0, 0]]), 1)

D TypeError: Input array must be binary or boolean

💡 Hint

Check the input array values. Are they binary (0 or 1)?

The label function expects a binary or boolean array. Here, the input has values other than 0 or 1, so it raises a RuntimeWarning and treats non-zero values as 1.

🚀 Application

expert

Counting connected components with custom connectivity

Using scipy.ndimage.label, how many connected components are found in the following binary image if connectivity=1 (only direct neighbors up, down, left, right) is used?

SciPy

import numpy as np
from scipy.ndimage import label

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

structure = np.array([
    [0,1,0],
    [1,1,1],
    [0,1,0]
])

labeled_array, num_features = label(binary_image, structure=structure)
print(num_features)

A 1

B 2

C 4

D 3

💡 Hint

Connectivity=1 means only vertical and horizontal neighbors are connected, not diagonals.

With the given structure, diagonal neighbors are not connected. The image has three distinct connected groups under this connectivity rule.