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.

Practice

1. What is the main purpose of connected component labeling in image processing?

easy

A. To enhance image contrast

B. To convert color images to grayscale

C. To identify and label groups of connected pixels in binary images

D. To compress image file size

Solution

1. Step 1: Understand connected component labeling

   It finds groups of connected pixels in binary images and assigns unique labels to each group.

2. Step 2: Compare with other image tasks

   Other options like grayscale conversion, contrast enhancement, and compression do not involve labeling connected pixels.

3. Final Answer:

   To identify and label groups of connected pixels in binary images -> Option C

4. Quick Check:

   Connected component labeling = identify connected pixel groups [OK]

Hint: Remember: labeling means assigning unique IDs to connected pixels [OK]

Common Mistakes:

• Confusing labeling with color conversion
• Thinking it compresses images
• Mixing it up with image enhancement

2. Which of the following is the correct way to import the connected component labeling function from scipy.ndimage?

easy

A. import scipy.ndimage.label

B. from scipy.ndimage import label

C. from scipy import label

D. import label from scipy.ndimage

Solution

1. Step 1: Recall correct import syntax in Python

   The correct syntax to import a function is 'from module import function'.

2. Step 2: Match with scipy.ndimage.label

   The function 'label' is inside 'scipy.ndimage', so 'from scipy.ndimage import label' is correct.

3. Final Answer:

   from scipy.ndimage import label -> Option B

4. Quick Check:

   Correct import syntax = from module import function [OK]

Hint: Use 'from module import function' to import specific functions [OK]

Common Mistakes:

• Using 'import scipy.ndimage.label' which is invalid
• Trying 'from scipy import label' which misses submodule
• Incorrect 'import label from scipy.ndimage' syntax

3. Given the following code, what will be the output of num_features?

import numpy as np
from scipy.ndimage import label

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

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

medium

A. 1

B. 3

C. 4

D. 2

Solution

1. Step 1: Identify connected groups in the array

   There are two groups of connected 1s: one cluster at top-left (positions (0,0),(1,0),(1,1)) and one cluster at bottom-right (positions (0,3),(2,2),(2,3),(3,2)).

2. Step 2: Count the connected components

   Counting these groups gives 2 connected components.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Count connected 1s groups = 2 [OK]

Hint: Count distinct connected 1s clusters in the array [OK]

Common Mistakes:

• Counting isolated 1s as separate components incorrectly
• Ignoring connectivity rules
• Misreading array layout

4. What is wrong with the following code snippet for connected component labeling?

import numpy as np
from scipy.ndimage import label

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

labeled, num = label(binary_image, structure=1)
print(num)

medium

A. The 'structure' parameter should be an array, not an integer

B. The input array must be float type, not integer

C. The 'label' function does not accept a 'structure' parameter

D. The print statement syntax is incorrect

Solution

1. Step 1: Check 'structure' parameter type

   The 'structure' parameter expects an array defining connectivity, not a single integer.

2. Step 2: Identify correct usage

   Passing 'structure=1' is invalid; it should be an array like np.ones((3,3)) for full connectivity.

3. Final Answer:

   The 'structure' parameter should be an array, not an integer -> Option A

4. Quick Check:

   'structure' must be array, not int [OK]

Hint: Remember: 'structure' needs an array defining connectivity [OK]

Common Mistakes:

• Passing integer instead of array for 'structure'
• Assuming 'label' lacks 'structure' parameter
• Confusing data types of input array

5. You have a binary image with noise: small isolated pixels scattered randomly. How can you use connected component labeling with scipy to remove noise by keeping only components larger than 2 pixels?

hard

A. Label components, count sizes, then remove components with size ≤ 2

B. Apply Gaussian blur before labeling to remove noise

C. Use label function with parameter 'min_size=3' to filter components

D. Invert the image and label the background instead

Solution

1. Step 1: Label connected components in the binary image

   Use scipy.ndimage.label to assign unique labels to each connected group of pixels.

2. Step 2: Count the size of each labeled component and filter

   Calculate the size of each component and remove those with size less than or equal to 2 pixels to eliminate noise.

3. Final Answer:

   Label components, count sizes, then remove components with size ≤ 2 -> Option A

4. Quick Check:

   Filter small components after labeling to remove noise [OK]

Hint: Label, count sizes, remove small components to clean noise [OK]

Common Mistakes:

• Expecting label() to filter by size automatically
• Using image blur instead of component filtering
• Inverting image does not remove noise directly