Morphological operations (erosion, dilation, opening, closing) in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of erosion on a binary image

Given the following 5x5 binary image and a 3x3 square structuring element, what is the output after applying one iteration of erosion?

Computer Vision

import numpy as np
import cv2

image = np.array([
  [1, 1, 1, 1, 0],
  [1, 1, 1, 1, 0],
  [1, 1, 1, 1, 0],
  [1, 1, 1, 1, 1],
  [0, 0, 0, 1, 1]
], dtype=np.uint8)

kernel = np.ones((3,3), np.uint8)
eroded = cv2.erode(image, kernel, iterations=1)
print(eroded)

A

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

B

[[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]]

C

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

D

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

💡 Hint

Erosion shrinks white regions by removing pixels on object boundaries where the structuring element does not fit entirely.

Erosion with a 3x3 kernel removes pixels from the edges of white regions. Only the central 2x2 block in the top-left square remains white because the kernel fits fully there. The bottom-right white region is too small for the kernel, so it disappears.

🧠 Conceptual

intermediate

Effect of dilation on image noise

Which of the following best describes the effect of applying dilation to a binary image with small isolated noise pixels?

A Dilation enlarges white regions and can cause isolated noise pixels to grow.

B Dilation removes isolated noise pixels by shrinking white regions.

C Dilation converts white pixels to black pixels in isolated noise areas.

D Dilation has no effect on isolated noise pixels.

💡 Hint

Think about how dilation changes the size of white areas.

Dilation expands white regions by adding pixels around them. Isolated noise pixels, which are white, will grow larger after dilation, making noise more prominent.

❓ Hyperparameter

advanced

Choosing kernel size for opening operation

You want to remove small white noise dots from a binary image without affecting larger objects. Which kernel size for the opening operation is most appropriate?

A A kernel size slightly larger than the noise dots but smaller than the smallest object.

B A kernel size smaller than the noise dots but larger than the smallest object.

C A very large kernel that is bigger than the largest object in the image.

D A kernel size equal to the entire image size.

💡 Hint

Opening removes small objects smaller than the kernel size.

Opening is erosion followed by dilation. It removes small white noise smaller than the kernel. To keep larger objects intact, the kernel must be bigger than noise but smaller than objects.

❓ Metrics

advanced

Evaluating closing operation effect

After applying a closing operation on a binary image, which metric would best indicate that small black holes inside white objects have been filled?

A Increase in the number of connected white components.

B Increase in the total white pixel area inside objects.

C Decrease in the number of white pixels.

D Decrease in the total black pixel area outside objects.

💡 Hint

Closing fills small black holes inside white regions.

Closing is dilation followed by erosion. It fills small black holes inside white objects, increasing the white pixel area inside those objects.

🔧 Debug

expert

Identifying error in morphological operation code

What error will this code raise when applying dilation with an invalid kernel shape? import numpy as np import cv2 image = np.array([[0,1,0],[1,1,1],[0,1,0]], dtype=np.uint8) kernel = np.array([1,1,1]) # Incorrect kernel shape result = cv2.dilate(image, kernel)

A ValueError: invalid kernel shape

B TypeError: kernel must be a 2D array

C cv2.error: (-215:Assertion failed) !ksize.empty() in function 'dilate'

D No error, code runs successfully

💡 Hint

Check the expected shape of the kernel argument in OpenCV dilation.

OpenCV expects the kernel to be a 2D array. Passing a 1D array causes an assertion failure with a specific error message about kernel size.