Morphological operations (erosion, dilation) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of erosion on a binary image

What is the output array after applying erosion with a 3x3 square structuring element on the given binary image?

SciPy

import numpy as np
from scipy.ndimage import binary_erosion

image = np.array([
  [0, 0, 0, 0, 0],
  [0, 1, 1, 1, 0],
  [0, 1, 1, 1, 0],
  [0, 1, 1, 1, 0],
  [0, 0, 0, 0, 0]
], dtype=bool)

structure = np.ones((3,3), dtype=bool)
eroded = binary_erosion(image, structure=structure)
print(eroded.astype(int))

A

[[0 0 0 0 0]
 [0 1 1 1 0]
 [0 1 1 1 0]
 [0 1 1 1 0]
 [0 0 0 0 0]]

B

[[0 0 0 0 0]
 [0 0 1 0 0]
 [0 1 1 1 0]
 [0 0 1 0 0]
 [0 0 0 0 0]]

C

[[0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 1 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]]

D

[[0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]]

💡 Hint

Erosion shrinks the white regions by removing pixels on the edges.

Erosion with a 3x3 structuring element removes pixels on the border of the white square, leaving only the center pixel as 1.

❓ Predict Output

intermediate

Result of dilation on a sparse binary image

What is the output after applying dilation with a 3x3 cross-shaped structuring element on the binary image below?

SciPy

import numpy as np
from scipy.ndimage import binary_dilation

image = np.array([
  [0, 0, 0, 0, 0],
  [0, 0, 1, 0, 0],
  [0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0]
], dtype=bool)

structure = np.array([
  [0, 1, 0],
  [1, 1, 1],
  [0, 1, 0]
], dtype=bool)
dilated = binary_dilation(image, structure=structure)
print(dilated.astype(int))

A

[[0 0 1 0 0]
 [0 1 1 1 0]
 [0 0 1 0 0]
 [0 0 0 0 0]
 [0 0 0 0 0]]

B

[[0 0 0 0 0]
 [0 1 1 1 0]
 [0 1 1 1 0]
 [0 0 1 0 0]
 [0 0 0 0 0]]

C

[[0 0 0 0 0]
 [0 1 1 1 0]
 [0 1 1 1 0]
 [0 1 0 1 0]
 [0 0 0 0 0]]

D

[[0 0 0 0 0]
 [0 0 1 0 0]
 [0 1 1 1 0]
 [0 0 1 0 0]
 [0 0 0 0 0]]

💡 Hint

Dilation adds pixels around existing white pixels according to the structuring element shape.

The cross-shaped structuring element dilates the single pixel to its immediate neighbors in a cross shape.

❓ visualization

advanced

Visualize erosion and dilation effects

Which option shows the correct pair of images after applying erosion and dilation respectively on the given binary image with a 3x3 square structuring element?

SciPy

import numpy as np
from scipy.ndimage import binary_erosion, binary_dilation
import matplotlib.pyplot as plt

image = np.array([
  [0, 0, 0, 0, 0],
  [0, 1, 1, 1, 0],
  [0, 1, 1, 1, 0],
  [0, 1, 1, 1, 0],
  [0, 0, 0, 0, 0]
], dtype=bool)

structure = np.ones((3,3), dtype=bool)
eroded = binary_erosion(image, structure=structure)
dilated = binary_dilation(image, structure=structure)

fig, axs = plt.subplots(1, 2)
axs[0].imshow(eroded, cmap='gray')
axs[0].set_title('Erosion')
axs[1].imshow(dilated, cmap='gray')
axs[1].set_title('Dilation')
plt.show()

A Left image: 3x3 white square with holes; Right image: 5x5 white square with holes

B Left image: 3x3 white square; Right image: 3x3 white square

C Left image: 5x5 white square; Right image: single pixel in center

D Left image: single pixel in center; Right image: 5x5 white square

💡 Hint

Erosion shrinks white areas, dilation expands them.

Erosion reduces the 3x3 white square to a single pixel, dilation expands it to fill the entire 5x5 area.

🧠 Conceptual

advanced

Effect of structuring element shape on dilation

Which statement correctly describes how the shape of the structuring element affects the dilation result on a binary image?

A The dilation result shape matches the structuring element shape centered on each white pixel.

B A larger structuring element always produces a smaller dilated area.

C The structuring element shape does not affect dilation, only erosion.

D Dilation removes pixels from the edges of white regions based on the structuring element.

💡 Hint

Think about how dilation adds pixels around existing ones.

Dilation adds pixels in the shape of the structuring element around each white pixel, so the output shape depends on the structuring element shape.

🔧 Debug

expert

Identify the error in morphological operation code

What error will occur when running the following code snippet for erosion, and why?

SciPy

import numpy as np
from scipy.ndimage import binary_erosion

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

structure = np.array([
  [1, 1],
  [1, 1]
])
eroded = binary_erosion(image, structure=structure)
print(eroded)

A ValueError because structuring element is not square

B TypeError because image array is not boolean

C No error, code runs and outputs eroded image

D IndexError due to structuring element size larger than image

💡 Hint

Check the data type required by binary_erosion for the input image.

binary_erosion expects a boolean array for the image. Using integers without converting to boolean causes a TypeError.