Image gradients (Sobel, Laplacian) in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Sobel filter on a simple image

What is the output array after applying the Sobel filter on the given 3x3 grayscale image using OpenCV's Sobel function with dx=1, dy=0, and kernel size 3?

Computer Vision

import cv2
import numpy as np

image = np.array([[10, 10, 10],
                  [10, 20, 10],
                  [10, 10, 10]], dtype=np.uint8)

sobelx = cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=3)
output = sobelx.astype(int)
print(output)

A

[[  0 -10   0]
 [  0   0   0]
 [  0  10   0]]

B

[[  0  10   0]
 [  0   0   0]
 [  0 -10   0]]

C

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

D

[[  0   0   0]
 [ 10   0 -10]
 [  0   0   0]]

💡 Hint

Sobel with dx=1 detects horizontal edges by calculating differences along the x-axis.

The Sobel filter with dx=1 and dy=0 calculates the gradient in the x-direction. The center pixel has a higher value (20) than its neighbors (10), so the gradient is positive on the left and negative on the right, resulting in the output shown in option D.

🧠 Conceptual

intermediate

Understanding Laplacian filter effect

Which statement best describes the effect of applying a Laplacian filter to a grayscale image?

A It detects edges by calculating the first derivative only in the horizontal direction.

B It smooths the image by averaging neighboring pixels to reduce noise.

C It detects edges by calculating the second derivative, highlighting regions of rapid intensity change.

D It converts the image to binary by thresholding pixel values.

💡 Hint

Think about what the second derivative tells us about intensity changes.

The Laplacian filter calculates the second derivative of the image intensity, which highlights areas where the intensity changes rapidly, such as edges and corners.

❓ Hyperparameter

advanced

Choosing kernel size for Sobel filter

What is the effect of increasing the kernel size (ksize) parameter in OpenCV's Sobel function from 3 to 7?

A It decreases the smoothing effect, making the filter more sensitive to noise and fine details.

B It increases the smoothing effect, resulting in detecting broader edges but less noise sensitivity.

C It changes the filter to detect vertical edges instead of horizontal edges.

D It converts the Sobel filter into a Laplacian filter automatically.

💡 Hint

Larger kernels average over more pixels.

Increasing the kernel size makes the Sobel filter consider a larger neighborhood, smoothing the image more and detecting broader edges while reducing sensitivity to noise.

🔧 Debug

advanced

Identifying error in Laplacian filter code

What error will this code produce when applying the Laplacian filter, and why? import cv2 import numpy as np image = np.array([[1,2],[3,4]], dtype=np.uint8) laplacian = cv2.Laplacian(image, cv2.CV_8U) print(laplacian)

Computer Vision

import cv2
import numpy as np

image = np.array([[1,2],[3,4]], dtype=np.uint8)
laplacian = cv2.Laplacian(image, cv2.CV_8U)
print(laplacian)

A The output will be incorrect due to overflow because CV_8U cannot represent negative values from the Laplacian.

B The code will raise a SyntaxError because of missing parentheses.

C The code will raise a TypeError because image is not a float array.

D The output will be a zero matrix because the image is too small.

💡 Hint

Laplacian can produce negative values; unsigned types cannot represent them.

Using CV_8U (unsigned 8-bit) as the output depth causes negative values from the Laplacian to wrap around, producing incorrect results. The correct depth is CV_64F or CV_16S to handle negatives.

❓ Model Choice

expert

Best gradient method for detecting fine edges in noisy images

You want to detect fine edges in a noisy grayscale image. Which gradient method and parameter choice is best to maximize edge detection while minimizing noise?

A Use Laplacian of Gaussian (LoG) filter which combines smoothing and second derivative.

B Use Laplacian filter directly on the noisy image without smoothing.

C Use Sobel filter with kernel size 7 without any smoothing.

D Use Sobel filter with kernel size 3 and apply Gaussian blur before filtering.

💡 Hint

Consider methods that combine smoothing and edge detection.

The Laplacian of Gaussian (LoG) filter smooths the image to reduce noise and then applies the Laplacian to detect edges, making it ideal for noisy images with fine edges.