Edge detection (Sobel, Laplacian) in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to apply the Sobel filter on the image.

Signal Processing

sobel_x = cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=[1])

Drag options to blanks, or click blank then click option'

A3

B5

C1

D7

Attempts:

3 left

💡 Hint

Common Mistakes

Using an even number for kernel size causes errors.

Using kernel size 1 does not apply the filter properly.

The Sobel filter kernel size is commonly set to 3 for edge detection.

2fill in blank

medium

Complete the code to compute the Laplacian of the image.

Signal Processing

laplacian = cv2.Laplacian(image, cv2.CV_64F, ksize=[1])

Drag options to blanks, or click blank then click option'

A1

B3

C5

D7

Attempts:

3 left

💡 Hint

Common Mistakes

Using kernel size 1 may not detect edges well.

Using even kernel sizes causes errors.

The Laplacian kernel size is often set to 3 for detecting edges.

3fill in blank

hard

Fix the error in the Sobel filter call by completing the missing argument.

Signal Processing

sobel_y = cv2.Sobel(image, cv2.CV_64F, 0, [1], ksize=3)

Drag options to blanks, or click blank then click option'

A0

B-1

C1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Setting dy=0 results in no vertical edge detection.

Using dy=2 is invalid for Sobel.

The first order derivative in y direction is set by dy=1 for Sobel.

4fill in blank

hard

Fill both blanks to create a dictionary of edge components using Sobel filters.

Signal Processing

edges = { 'sobel_x': cv2.Sobel(image, cv2.CV_64F, [1], 0, ksize=3), 'sobel_y': cv2.Sobel(image, cv2.CV_64F, 0, [2], ksize=3) }

Drag options to blanks, or click blank then click option'

A1

B0

C-1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using dx=0 and dy=0 results in no edge detection.

Using dx or dy as 2 is invalid.

To detect edges in x and y directions, dx and dy should be 1 and 0 or 0 and 1 respectively.

5fill in blank

hard

Fill all three blanks to compute the combined edge magnitude from Sobel x and y.

Signal Processing

magnitude = np.sqrt(np.square(edges['[1]']) + np.square(edges['[2]']))
result = np.uint8(magnitude / np.max(magnitude) * [3])

Drag options to blanks, or click blank then click option'

Asobel_x

Bsobel_y

C255

D128

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up keys in edges dictionary.

Scaling magnitude incorrectly.

We combine 'sobel_x' and 'sobel_y' to get magnitude, then scale to 255 for image display.

Practice

1. What is the main purpose of the Sobel operator in edge detection?

easy

A. To detect color changes in an image

B. To smooth the image by averaging pixel values

C. To find edges by calculating gradients in horizontal and vertical directions

D. To reduce noise using a median filter

Solution

1. Step 1: Understand Sobel operator function

   The Sobel operator calculates the gradient of image intensity in horizontal and vertical directions.

2. Step 2: Identify purpose in edge detection

   Gradients highlight sharp changes in intensity, which correspond to edges.

3. Final Answer:

   To find edges by calculating gradients in horizontal and vertical directions -> Option C

4. Quick Check:

   Sobel = gradient edge detection [OK]

Hint: Sobel finds edges by gradients horizontally and vertically [OK]

Common Mistakes:

• Confusing Sobel with smoothing filters
• Thinking Sobel detects color changes
• Mixing Sobel with noise reduction methods

2. Which of the following is the correct 3x3 Sobel kernel for detecting vertical edges?

easy

A. [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]

B. [[1, 2, 1], [0, 0, 0], [-1, -2, -1]]

C. [[0, 1, 0], [1, -4, 1], [0, 1, 0]]

D. [[1, 0, -1], [2, 0, -2], [1, 0, -1]]

Solution

1. Step 1: Recall Sobel vertical kernel

   The Sobel vertical kernel detects edges by emphasizing horizontal intensity changes and is defined as [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]].

2. Step 2: Compare options

   [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]] matches the known vertical Sobel kernel; others are horizontal or Laplacian kernels.

3. Final Answer:

   [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]] -> Option A

4. Quick Check:

   Vertical Sobel kernel = [[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]] [OK]

Hint: Vertical Sobel kernel has -1 and 1 on sides, 0 in middle column [OK]

Common Mistakes:

• Confusing vertical and horizontal Sobel kernels
• Selecting Laplacian kernel instead
• Mixing signs in kernel values

3. Given the following 3x3 image patch:
[[10, 10, 10], [10, 0, 10], [10, 10, 10]]
What is the approximate output of applying the Laplacian kernel [[0, 1, 0], [1, -4, 1], [0, 1, 0]] at the center pixel?

medium

A. -40

B. 0

C. -10

D. 40

Solution

1. Step 1: Overlay kernel on image patch

   Center pixel [1,1]=0. Relevant positions: top-center [0,1]=10, mid-left [1,0]=10, mid-right [1,2]=10, bottom-center [2,1]=10. Others have kernel weight 0.

2. Step 2: Compute weighted sum

   (1*10) + (1*10) + (-4*0) + (1*10) + (1*10) = 10 + 10 + 0 + 10 + 10 = 40.

3. Final Answer:

   40 -> Option D

4. Quick Check:

   Laplacian = sum(neighbors) - 4*center = 40 - 0 = 40 [OK]

Hint: Sum neighbors times 1 minus 4 times center pixel [OK]

Common Mistakes:

• Ignoring kernel sign and weights
• Mixing neighbor and center pixel values
• Calculating sum incorrectly

4. Consider this Python code snippet applying Sobel filter:

import numpy as np
image = np.array([[1,2,1],[0,1,0],[2,1,2]])
sobel_x = np.array([[1,0,-1],[2,0,-2],[1,0,-1]])
result = np.zeros_like(image)
for i in range(1,2):
    for j in range(1,2):
        region = image[i-1:i+2, j-1:j+2]
        result[i,j] = np.sum(region * sobel_x)
print(result[1,1])

What is the output and is there any error?

medium

A. Output is 0; error due to incorrect loop range

B. Output is 0; no error

C. Output is 2; no error

D. Output is 2; error due to incorrect loop range

Solution

1. Step 1: Analyze loop ranges and region extraction

   Loops run for i=1 and j=1 only, extracting 3x3 region around center pixel (1,1).

2. Step 2: Calculate convolution sum

   Region = [[1,2,1],[0,1,0],[2,1,2]]
   sobel_x = [[1,0,-1],[2,0,-2],[1,0,-1]]
   Element-wise multiply and sum:
   (1*1)+(2*0)+(1*-1)+(0*2)+(1*0)+(0*-2)+(2*1)+(1*0)+(2*-1) = 1+0-1+0+0+0+2+0-2 = 0

3. Step 3: Check for errors

   Loop ranges are correct for this small image to avoid index errors.
   No error occurs.

4. Final Answer:

   0; no error -> Option B

5. Quick Check:

   Convolution sum = 0; loops correct [OK]

Hint: Check loop ranges match image size to avoid errors [OK]

Common Mistakes:

• Using wrong loop ranges causing index errors
• Miscomputing convolution sum
• Assuming output is non-zero without calculation

5. You want to detect edges in a noisy grayscale image. Which approach best improves edge detection results using Sobel and Laplacian filters?

hard

A. Apply Gaussian smoothing before Sobel, then use Laplacian on result

B. Apply Laplacian first, then Sobel without smoothing

C. Use Sobel only without any smoothing

D. Apply median filter after Laplacian to sharpen edges

Solution

1. Step 1: Understand noise effect on edge detection

   Noisy images cause false edges; smoothing reduces noise before edge detection.

2. Step 2: Combine smoothing and edge detection

   Applying Gaussian smoothing before Sobel reduces noise impact.
   Then applying Laplacian on Sobel result enhances edge detection.

3. Step 3: Evaluate other options

   Applying Laplacian first without smoothing amplifies noise.
   Using Sobel only misses benefits of combined filters.
   Median filter after Laplacian may remove edges, not sharpen.

4. Final Answer:

   Apply Gaussian smoothing before Sobel, then use Laplacian on result -> Option A

5. Quick Check:

   Smoothing before edge detection improves results [OK]

Hint: Smooth noisy image before edge detection [OK]

Common Mistakes:

• Skipping smoothing step on noisy images
• Applying filters in wrong order
• Assuming median filter sharpens edges