Median and uniform filters in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of median filter on 1D array

What is the output of the following code applying a median filter with size 3 on a 1D array?

SciPy

import numpy as np
from scipy.ndimage import median_filter

arr = np.array([1, 2, 80, 4, 5, 6, 7])
filtered = median_filter(arr, size=3)
print(filtered.tolist())

A [2, 2, 4, 5, 6, 6, 7]

B [1, 2, 80, 4, 5, 6, 7]

C [1, 2, 4, 4, 5, 6, 7]

D [1, 2, 4, 5, 5, 6, 7]

💡 Hint

Median filter replaces each element with the median of neighbors within the window size.

The median filter with size 3 looks at each element and its neighbors (previous and next). For example, at index 2, neighbors are [2, 80, 4], median is 4. This smooths out the spike at 80.

❓ data_output

intermediate

Result of uniform filter on 2D array

What is the resulting 2D array after applying a uniform filter with size 3 on this 3x3 array?

SciPy

import numpy as np
from scipy.ndimage import uniform_filter

arr = np.array([[1, 2, 3],
                [4, 5, 6],
                [7, 8, 9]])
filtered = uniform_filter(arr, size=3, mode='constant', cval=0)
print(filtered)

A

[[1.55555556 2.33333333 1.88888889]
 [3.66666667 5.         4.11111111]
 [3.11111111 4.66666667 3.55555556]]

B

[[1.33333333 2.         1.66666667]
 [3.         5.         3.        ]
 [2.66666667 4.         2.66666667]]

C

[[1. 2. 3.]
 [4. 5. 6.]
 [7. 8. 9.]]

D

[[0.66666667 1.33333333 1.        ]
 [2.33333333 4.         3.        ]
 [2.         3.33333333 2.33333333]]

💡 Hint

Uniform filter computes the average over the window including zero padding outside edges.

The uniform filter with size 3 averages each 3x3 neighborhood. Since mode='constant' with cval=0, zeros pad the edges, lowering averages near borders.

❓ visualization

advanced

Visual effect of median vs uniform filter on noisy image

Which option best describes the visual difference after applying median and uniform filters on a noisy grayscale image?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import median_filter, uniform_filter

np.random.seed(0)
image = np.ones((10,10)) * 100
noise = np.random.randint(0, 50, (10,10))
noisy_image = image + noise
median_img = median_filter(noisy_image, size=3)
uniform_img = uniform_filter(noisy_image, size=3)

plt.subplot(1,3,1)
plt.title('Noisy')
plt.imshow(noisy_image, cmap='gray')
plt.subplot(1,3,2)
plt.title('Median Filter')
plt.imshow(median_img, cmap='gray')
plt.subplot(1,3,3)
plt.title('Uniform Filter')
plt.imshow(uniform_img, cmap='gray')
plt.show()

A Median filter increases noise; uniform filter sharpens edges.

B Median filter removes noise while preserving edges; uniform filter blurs edges and smooths noise.

C Both filters produce identical smoothing and edge preservation.

D Uniform filter removes noise while preserving edges; median filter blurs edges and smooths noise.

💡 Hint

Median filter is good for salt-and-pepper noise; uniform filter averages values.

Median filter replaces each pixel with median of neighbors, preserving edges better. Uniform filter averages neighbors, causing blur and edge smoothing.

🧠 Conceptual

advanced

Effect of filter size on median and uniform filters

How does increasing the filter size affect the output of median and uniform filters on a noisy signal?

A Increasing size increases smoothing for both filters; median filter preserves edges better but may remove small details.

B Increasing size decreases smoothing for both filters; median filter blurs edges more than uniform filter.

C Increasing size has no effect on median filter; uniform filter smoothing decreases.

D Increasing size causes median filter to amplify noise; uniform filter preserves edges perfectly.

💡 Hint

Think about how larger windows affect averaging and median calculations.

Larger filter sizes mean more neighbors considered, increasing smoothing. Median filter still preserves edges better but may remove small features as size grows.

🔧 Debug

expert

Identify the error in applying median filter on a 3D array

What error will this code raise when applying median_filter with size=3 on a 3D array without specifying axis?

SciPy

import numpy as np
from scipy.ndimage import median_filter

arr = np.random.randint(0, 10, (4,4,4))
filtered = median_filter(arr, size=3)
print(filtered.shape)

A ValueError: size must be less than or equal to input size along each axis

B TypeError: size must be a sequence of integers

C No error; output shape is (4,4,4)

D No error; output shape is (2,2,2)

💡 Hint

Check how median_filter handles size parameter for multi-dimensional arrays.

median_filter accepts an integer size and applies it to all axes. The output shape matches input shape. No error occurs.

Practice

1. What is the main purpose of applying a median filter to a dataset?

easy

A. To find the maximum value in the dataset

B. To calculate the average of all values in the dataset

C. To remove noise by replacing each value with the middle value in its neighborhood

D. To sort the dataset in ascending order

Solution

1. Step 1: Understand median filter function

   A median filter replaces each data point with the median (middle) value of its neighbors, reducing spikes and noise.

2. Step 2: Compare options with median filter purpose

   Only To remove noise by replacing each value with the middle value in its neighborhood describes replacing values with the middle value in a neighborhood, which matches the median filter's role.

3. Final Answer:

   To remove noise by replacing each value with the middle value in its neighborhood -> Option C

4. Quick Check:

   Median filter = middle value replacement [OK]

Hint: Median filter picks middle value to reduce spikes [OK]

Common Mistakes:

• Confusing median filter with averaging
• Thinking median filter sorts entire dataset
• Assuming median filter finds max or min values

2. Which of the following is the correct way to import the median filter function from scipy?

easy

A. from scipy.ndimage import median_filter

B. import scipy.median_filter

C. from scipy import median_filter

D. import median_filter from scipy

Solution

1. Step 1: Recall scipy median filter import syntax

   The median_filter function is in scipy.ndimage module, so it is imported as from scipy.ndimage import median_filter.

2. Step 2: Check each option's correctness

   from scipy.ndimage import median_filter matches the correct syntax. The other options are invalid Python import statements.

3. Final Answer:

   from scipy.ndimage import median_filter -> Option A

4. Quick Check:

   Correct import = from scipy.ndimage import median_filter [OK]

Hint: Import median_filter from scipy.ndimage module [OK]

Common Mistakes:

• Trying to import median_filter directly from scipy
• Using invalid import syntax
• Confusing module names

3. What is the output of this code snippet?

import numpy as np
from scipy.ndimage import uniform_filter

arr = np.array([1, 2, 3, 4, 5])
result = uniform_filter(arr, size=3)
print(result)

medium

A. [1 2 3 4 5]

B. [1.66666667 2. 3. 4. 4.33333333]

C. [1 2 3 3 3 3]

D. [1 2 2 3 4]

Solution

1. Step 1: Understand uniform_filter with size=3

   The uniform_filter computes the average over a sliding window of size 3. For edges, it uses 'reflect' mode by default.

2. Step 2: Calculate each element in result

   Using reflect padding:
   - index 0: [2, 1, 2] avg = 1.66666667
   - index 1: [1, 2, 3] avg = 2.0
   - index 2: [2, 3, 4] avg = 3.0
   - index 3: [3, 4, 5] avg = 4.0
   - index 4: [4, 5, 4] avg = 4.33333333
   print(result) shows [1.66666667 2. 3. 4. 4.33333333]

3. Final Answer:

   [1.66666667 2. 3. 4. 4.33333333] -> Option B

4. Quick Check:

   Uniform filter smooths values with reflect padding [OK]

Hint: Uniform filter averages neighbors in window size [OK]

Common Mistakes:

• Confusing median_filter output with uniform_filter
• Ignoring edge effects in uniform_filter
• Expecting original array unchanged

4. Identify the error in this code that applies a median filter:

import numpy as np
from scipy.ndimage import median_filter

arr = np.array([1, 2, 100, 4, 5])
filtered = median_filter(arr, size=0)
print(filtered)

medium

A. missing import for numpy

B. median_filter requires 2D arrays only

C. numpy array must be float type

D. size parameter cannot be zero

Solution

1. Step 1: Check median_filter size parameter

   The size parameter defines the window size and must be a positive integer. Zero is invalid and causes an error.

2. Step 2: Verify other code parts

   Array is 1D which is allowed. numpy is imported. Data type can be int. So only size=0 is wrong.

3. Final Answer:

   size parameter cannot be zero -> Option D

4. Quick Check:

   Window size > 0 for median_filter [OK]

Hint: Window size must be positive integer [OK]

Common Mistakes:

• Using zero or negative size values
• Assuming median_filter only works on 2D arrays
• Forgetting to import numpy

5. You have a noisy 2D image array with salt-and-pepper noise. Which filter and parameters would best reduce noise while preserving edges?

import numpy as np
from scipy.ndimage import median_filter, uniform_filter

image = np.array([[10, 10, 10, 10],
                  [10, 255, 10, 10],
                  [10, 10, 10, 10],
                  [10, 10, 10, 10]])

hard

A. Use median_filter with size=3 to remove salt-and-pepper noise

B. Use uniform_filter with size=3 to blur the image

C. Use median_filter with size=1 to keep image unchanged

D. Use uniform_filter with size=1 to sharpen edges

Solution

1. Step 1: Understand noise type and filter effects

   Salt-and-pepper noise is best removed by median filters because they replace each pixel with the median of neighbors, preserving edges.

2. Step 2: Evaluate filter choices and parameters

   Median_filter with size=3 covers neighbors and removes noise spikes. Uniform_filter averages and blurs edges, not ideal here. Size=1 means no change.

3. Final Answer:

   Use median_filter with size=3 to remove salt-and-pepper noise -> Option A

4. Quick Check:

   Median filter + size=3 removes salt-and-pepper noise [OK]

Hint: Median filter removes salt-and-pepper noise best [OK]

Common Mistakes:

• Using uniform filter which blurs edges
• Using size=1 which does nothing
• Confusing noise types and filter effects