Image gradients (Sobel, Laplacian) in Computer Vision - ML Experiment: Train & Evaluate

Experiment - Image gradients (Sobel, Laplacian)

Problem:You want to detect edges in images using gradient filters. Currently, you apply Sobel filters but the edges are noisy and unclear.

Current Metrics:Edge clarity score: 60/100 (subjective visual score), Noise level: high

Issue:The Sobel filter output has too much noise and weak edge definition, making it hard to identify clear edges.

Your Task

Improve edge detection by reducing noise and enhancing edge clarity using image gradients. Target a clearer edge map with less noise.

Use only Sobel and Laplacian filters for gradient calculation.

Do not use advanced denoising or deep learning methods.

Work with grayscale images only.

Hint 1

Hint 2

Hint 3

Solution

Computer Vision

import cv2
import numpy as np
import matplotlib.pyplot as plt

# Load image in grayscale
img = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)

# Apply Sobel filter in x and y directions
sobel_x = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=3)
sobel_y = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=3)

# Calculate gradient magnitude
grad_mag = np.sqrt(sobel_x**2 + sobel_y**2)

# Normalize gradient magnitude to 0-255
grad_mag = np.uint8(255 * grad_mag / np.max(grad_mag))

# Apply threshold to reduce noise
_, thresh_grad = cv2.threshold(grad_mag, 50, 255, cv2.THRESH_BINARY)

# Apply Laplacian filter
laplacian = cv2.Laplacian(img, cv2.CV_64F)
laplacian = np.uint8(np.absolute(laplacian))

# Display results
plt.figure(figsize=(12,6))
plt.subplot(1,3,1)
plt.title('Original Grayscale')
plt.imshow(img, cmap='gray')
plt.axis('off')

plt.subplot(1,3,2)
plt.title('Sobel Gradient Magnitude + Threshold')
plt.imshow(thresh_grad, cmap='gray')
plt.axis('off')

plt.subplot(1,3,3)
plt.title('Laplacian Filter Output')
plt.imshow(laplacian, cmap='gray')
plt.axis('off')

plt.show()

Combined Sobel x and y gradients to get gradient magnitude for better edge strength representation.

Normalized gradient magnitude to 0-255 scale for visualization.

Applied thresholding to gradient magnitude to reduce noise and keep strong edges only.

Added Laplacian filter output to compare edge detection results.

Results Interpretation

Before: Sobel filter alone produced noisy edges with unclear boundaries.

After: Combining Sobel x and y gradients and thresholding reduced noise and enhanced edge clarity. Laplacian filter provided a complementary edge map highlighting different edge features.

Using gradient magnitude from Sobel filters and thresholding helps reduce noise and improve edge detection. Laplacian filter offers an alternative edge detection method that can complement Sobel results.

Bonus Experiment

Try applying Gaussian blur before gradient calculation to see if smoothing the image further reduces noise in edge detection.

💡 Hint

Use cv2.GaussianBlur with a small kernel size (e.g., 3x3) before applying Sobel and Laplacian filters.

Practice

1. What is the main purpose of using image gradients like Sobel and Laplacian in computer vision?

easy

A. To increase the color saturation of an image

B. To convert the image into grayscale

C. To blur the image and reduce noise

D. To detect edges by highlighting rapid changes in pixel brightness

Solution

1. Step 1: Understand what image gradients do

   Image gradients detect changes in pixel brightness, which correspond to edges in images.

2. Step 2: Match purpose with options

   Sobel and Laplacian filters highlight edges by showing where brightness changes quickly, not color or blur.

3. Final Answer:

   To detect edges by highlighting rapid changes in pixel brightness -> Option D

4. Quick Check:

   Image gradients = edge detection [OK]

Hint: Edges = brightness changes, gradients highlight these [OK]

Common Mistakes:

• Confusing edge detection with color changes
• Thinking gradients blur images
• Assuming gradients convert images to grayscale

2. Which of the following is the correct way to apply a Sobel filter in OpenCV to detect horizontal edges?

easy

A. cv2.Laplacian(image, cv2.CV_64F)

B. cv2.Sobel(image, cv2.CV_64F, 0, 1, ksize=3)

C. cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=3)

D. cv2.Canny(image, 100, 200)

Solution

1. Step 1: Recall Sobel filter parameters

   In OpenCV, Sobel's dx=1 and dy=0 detects horizontal edges (changes along x-axis).

2. Step 2: Match parameters to options

   cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=3) uses dx=1, dy=0, which is correct for horizontal edge detection.

3. Final Answer:

   cv2.Sobel(image, cv2.CV_64F, 1, 0, ksize=3) -> Option C

4. Quick Check:

   dx=1, dy=0 means horizontal edges [OK]

Hint: dx=1, dy=0 for horizontal Sobel edges [OK]

Common Mistakes:

• Swapping dx and dy values
• Using Laplacian instead of Sobel for directional edges
• Confusing Canny edge detector with Sobel

3. Given the following Python code using OpenCV, what will be the shape of the output image after applying the Laplacian filter?

import cv2
image = cv2.imread('photo.jpg', cv2.IMREAD_GRAYSCALE)
laplacian = cv2.Laplacian(image, cv2.CV_64F)
print(laplacian.shape)

medium

A. Same height and width as the input grayscale image

B. One channel smaller than input image

C. A 3-channel color image

D. A single pixel value

Solution

1. Step 1: Understand Laplacian output size

   Laplacian filter outputs an image of the same size as input, preserving height and width.

2. Step 2: Check input image type

   Input is grayscale (single channel), so output remains single channel with same dimensions.

3. Final Answer:

   Same height and width as the input grayscale image -> Option A

4. Quick Check:

   Laplacian output size = input size [OK]

Hint: Laplacian keeps image size same as input [OK]

Common Mistakes:

• Expecting output to have fewer channels
• Thinking Laplacian converts grayscale to color
• Assuming output is a single pixel value

4. You wrote this code to apply Sobel filter but get an error:

import cv2
image = cv2.imread('img.png')
sobel = cv2.Sobel(image, cv2.CV_64F, 1, 0)

What is the likely cause of the error?

medium

A. Image path is incorrect

B. Sobel filter cannot be applied to color images

C. cv2.CV_64F is not a valid depth argument

D. Missing kernel size parameter 'ksize' in cv2.Sobel call

Solution

1. Step 1: Check image loading

   cv2.imread('img.png') returns None if file does not exist, causing Sobel to fail.

2. Step 2: Validate other parameters

   Sobel works on color images channel-wise, CV_64F is valid, ksize defaults to 3.

3. Final Answer:

   Image path is incorrect -> Option A

4. Quick Check:

   Check image is not None after imread [OK]

Hint: Always check if cv2.imread returns None [OK]

Common Mistakes:

• Forgetting to verify image loaded
• Assuming Sobel cannot handle color images
• Believing ksize parameter is mandatory

5. You want to detect edges in all directions in a noisy grayscale image. Which approach is best to get clear edges while reducing noise?

hard

A. Apply Sobel filter directly without preprocessing

B. Apply Gaussian blur first, then use Laplacian filter

C. Use only Gaussian blur without edge detection

D. Apply Laplacian filter first, then Gaussian blur

Solution

1. Step 1: Understand noise effect on edge detection

   Noise causes false edges; smoothing reduces noise before edge detection.

2. Step 2: Choose correct filter order

   Applying Gaussian blur first smooths noise, then Laplacian detects edges in all directions clearly.

3. Final Answer:

   Apply Gaussian blur first, then use Laplacian filter -> Option B

4. Quick Check:

   Smooth then detect edges = clear edges [OK]

Hint: Blur noisy image before Laplacian for better edges [OK]

Common Mistakes:

• Applying edge detection before noise reduction
• Using Sobel only for all-direction edges
• Skipping noise reduction step