Image smoothing (Gaussian blur) in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Gaussian blur on a simple 3x3 image

Given the following 3x3 grayscale image and a Gaussian kernel, what is the output after applying Gaussian blur?

Signal Processing

import numpy as np
from scipy.ndimage import gaussian_filter

image = np.array([[10, 20, 30],
                  [20, 30, 40],
                  [30, 40, 50]], dtype=float)

blurred = gaussian_filter(image, sigma=1)
print(np.round(blurred, 1))

A

[[20.7 24.  27.3]
 [24.  27.  30. ]
 [27.3 30.  32.7]]

B

[[15. 25. 35.]
 [25. 35. 45.]
 [35. 45. 55.]]

C

[[25. 30. 35.]
 [30. 35. 40.]
 [35. 40. 45.]]

D

[[10. 20. 30.]
 [20. 30. 40.]
 [30. 40. 50.]]

💡 Hint

Gaussian blur smooths the image by averaging nearby pixels weighted by a Gaussian function.

The gaussian_filter with sigma=1 applies a weighted average that smooths the image values. The output is a blurred version with values between the original pixel intensities.

🧠 Conceptual

intermediate

Effect of increasing sigma in Gaussian blur

What happens to an image when the sigma value in Gaussian blur is increased?

A The image becomes more blurred and details are smoothed out.

B The image becomes sharper with more edges visible.

C The image colors become inverted.

D The image size increases.

💡 Hint

Think about how the Gaussian kernel size and spread change with sigma.

Increasing sigma increases the spread of the Gaussian kernel, causing more smoothing and blurring of details.

🔧 Debug

advanced

Identify the error in Gaussian blur application code

What error will this code produce when applying Gaussian blur? import numpy as np from scipy.ndimage import gaussian_filter image = np.array([[100, 150], [200, 250]]) blurred = gaussian_filter(image, sigma=-1) print(blurred)

A IndexError: index out of bounds

B TypeError: image must be a 3D array

C No error, outputs a blurred image

D ValueError: sigma must be non-negative

💡 Hint

Sigma controls the spread of the Gaussian kernel and cannot be negative.

The gaussian_filter function requires sigma to be zero or positive. Negative sigma values cause a ValueError.

❓ data_output

advanced

Resulting shape after Gaussian blur on a 5x5 image

If you apply Gaussian blur with sigma=1 to a 5x5 image using scipy.ndimage.gaussian_filter, what is the shape of the output?

A (7, 7)

B (5, 5)

C (3, 3)

D (1, 1)

💡 Hint

Gaussian blur does not change the image size by default.

The gaussian_filter function returns an output of the same shape as the input image.

🚀 Application

expert

Choosing sigma for edge-preserving smoothing

You want to smooth an image to reduce noise but keep edges sharp. Which sigma value strategy is best?

A Use a very high sigma to blur everything strongly.

B Use sigma=0 to keep the image unchanged.

C Use a small sigma to smooth noise but preserve edges.

D Use a negative sigma to sharpen edges.

💡 Hint

Small sigma values apply gentle smoothing.

Small sigma values smooth noise while preserving edges better than large sigma values.

Practice

1. What is the main purpose of applying a Gaussian blur to an image?

easy

A. To smooth the image by averaging pixels with a weighted filter

B. To increase the image resolution

C. To convert the image to grayscale

D. To detect edges in the image

Solution

1. Step 1: Understand Gaussian blur function

   Gaussian blur smooths images by averaging pixels using a weighted filter based on a Gaussian function.

2. Step 2: Identify the main effect on the image

   This process reduces noise and smooths details, not increasing resolution or changing color or detecting edges.

3. Final Answer:

   To smooth the image by averaging pixels with a weighted filter -> Option A

4. Quick Check:

   Gaussian blur = smoothing with weighted average [OK]

Hint: Gaussian blur smooths images by weighted averaging [OK]

Common Mistakes:

• Confusing blur with edge detection
• Thinking blur increases resolution
• Assuming blur changes image color

2. Which of the following is the correct Python syntax to apply a Gaussian blur using OpenCV with kernel size 5x5 and sigma 1.0 on image img?

easy

A. cv2.GaussianBlur(img, (5), 1.0)

B. cv2.gaussian_blur(img, 5, 1.0)

C. cv2.GaussianBlur(img, 5, 1.0)

D. cv2.GaussianBlur(img, (5, 5), 1.0)

Solution

1. Step 1: Recall OpenCV GaussianBlur syntax

   The function requires the image, kernel size as a tuple (width, height), and sigma value.

2. Step 2: Check each option's syntax

   cv2.GaussianBlur(img, (5, 5), 1.0) uses correct function name and parameters: cv2.GaussianBlur(img, (5, 5), 1.0). Others have wrong function names or kernel size format.

3. Final Answer:

   cv2.GaussianBlur(img, (5, 5), 1.0) -> Option D

4. Quick Check:

   Correct syntax uses tuple kernel size [OK]

Hint: Kernel size must be a tuple like (5, 5) in OpenCV [OK]

Common Mistakes:

• Using kernel size as single integer instead of tuple
• Wrong function name capitalization
• Passing kernel size without parentheses

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

import cv2
img = cv2.imread('photo.jpg')
blurred = cv2.GaussianBlur(img, (7, 7), 2)
print(blurred.shape)

medium

A. Larger than original image shape

B. Smaller than original image shape

C. Same as original image shape

D. Returns a single number, not shape

Solution

1. Step 1: Understand GaussianBlur effect on image size

   Gaussian blur smooths the image but does not change its dimensions.

2. Step 2: Check output shape behavior

   The output image has the same height, width, and channels as the input image.

3. Final Answer:

   Same as original image shape -> Option C

4. Quick Check:

   Gaussian blur keeps image size unchanged [OK]

Hint: Gaussian blur smooths but keeps image size same [OK]

Common Mistakes:

• Assuming blur crops or resizes image
• Expecting output to be a single value
• Confusing blur with image scaling

4. Identify the error in this code snippet applying Gaussian blur:

import cv2
img = cv2.imread('image.png')
blur = cv2.GaussianBlur(img, 5, 1.5)
cv2.imshow('Blurred', blur)
cv2.waitKey(0)

medium

A. cv2.imshow requires image path, not image array

B. Kernel size should be a tuple, not an integer

C. Sigma value must be an integer, not float

D. cv2.waitKey needs a parameter greater than 1000

Solution

1. Step 1: Check GaussianBlur parameters

   The kernel size must be a tuple like (5, 5), not a single integer.

2. Step 2: Verify other function calls

   Sigma can be float, cv2.imshow accepts image arrays, and cv2.waitKey(0) is valid for waiting indefinitely.

3. Final Answer:

   Kernel size should be a tuple, not an integer -> Option B

4. Quick Check:

   Kernel size = tuple (width, height) [OK]

Hint: Kernel size must be tuple like (5, 5) in GaussianBlur [OK]

Common Mistakes:

• Passing kernel size as single integer
• Misunderstanding cv2.imshow input
• Incorrect sigma type assumptions

5. You want to reduce noise in a grayscale image but keep edges sharp. Which Gaussian blur parameters should you choose to balance smoothing and edge preservation?

hard

A. Small kernel size (3x3) and low sigma (0.5)

B. Large kernel size (15x15) and high sigma (5.0)

C. Kernel size (7x7) and sigma 0 (automatic calculation)

D. Kernel size (1x1) and sigma 10

Solution

1. Step 1: Understand effect of kernel size and sigma

   Small kernel and low sigma cause mild smoothing, preserving edges better.

2. Step 2: Analyze options for noise reduction and edge preservation

   Large kernel and high sigma cause heavy blur, losing edges. Sigma 0 lets OpenCV choose, which may be too strong. Kernel 1x1 means no blur.

3. Final Answer:

   Small kernel size (3x3) and low sigma (0.5) -> Option A

4. Quick Check:

   Small kernel + low sigma = smooth noise, keep edges [OK]

Hint: Use small kernel and low sigma to keep edges sharp [OK]

Common Mistakes:

• Choosing too large kernel causing edge loss
• Using sigma 0 without understanding automatic effect
• Using kernel 1x1 which applies no blur