Sobel and Laplace edge detection in SciPy - 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 image using scipy.ndimage.sobel with axis=0?

SciPy

import numpy as np
from scipy import ndimage

image = np.array([[10, 10, 10],
                  [20, 20, 20],
                  [30, 30, 30]])
sobel_vertical = ndimage.sobel(image, axis=0)
print(sobel_vertical)

A

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

B

[[10 10 10]
 [20 20 20]
 [20 20 20]]

C

[[10 10 10]
 [20 20 20]
 [0 0 0]]

D

[[10 10 10]
 [20 20 20]
 [10 10 10]]

💡 Hint

Think about how the Sobel filter calculates the gradient along the vertical axis.

The Sobel filter computes the gradient by subtracting pixel values above and below. The output shows positive values where intensity increases downward and negative where it decreases.

❓ data_output

intermediate

Number of edges detected by Laplace filter

After applying the Laplace filter on the given 5x5 image, how many pixels have a non-zero value indicating edges?

SciPy

import numpy as np
from scipy import ndimage

image = np.array([
    [10, 10, 10, 10, 10],
    [10, 50, 50, 50, 10],
    [10, 50, 100, 50, 10],
    [10, 50, 50, 50, 10],
    [10, 10, 10, 10, 10]
])
laplace = ndimage.laplace(image)
non_zero_count = np.count_nonzero(laplace)
print(non_zero_count)

A 8

B 12

C 20

D 16

💡 Hint

Edges are where the Laplace output is not zero, usually around intensity changes.

The Laplace filter highlights regions with rapid intensity changes. Counting non-zero pixels gives the number of detected edges.

🔧 Debug

advanced

Identify the error in Sobel filter application

What error will this code raise when applying the Sobel filter incorrectly?

SciPy

import numpy as np
from scipy import ndimage

image = np.array([[1, 2], [3, 4]])
sobel = ndimage.sobel(image, axis=2)
print(sobel)

A ValueError: input array must be 3D

B TypeError: unsupported operand type(s) for +: 'int' and 'str'

C IndexError: axis 2 is out of bounds for array of dimension 2

D No error, prints the Sobel filtered array

💡 Hint

Check the axis parameter against the image array dimensions.

The image is 2D, so axis=2 is invalid and causes an IndexError.

❓ visualization

advanced

Visual difference between Sobel and Laplace filters

Which option best describes the visual difference when applying Sobel and Laplace filters on the same image?

A Sobel and Laplace produce identical edge maps.

B Sobel produces a blurred image; Laplace produces a sharpened image.

C Sobel detects color changes; Laplace detects brightness changes only.

D Sobel highlights edges in one direction; Laplace highlights edges regardless of direction with zero-crossings.

💡 Hint

Think about directional vs. non-directional edge detection.

Sobel calculates gradient in a specific direction, while Laplace detects edges by second derivatives and zero-crossings.

🚀 Application

expert

Combining Sobel and Laplace for edge enhancement

Given an image, which code snippet correctly combines Sobel filters on both axes and the Laplace filter to create an enhanced edge image?

A

sobel_x = ndimage.sobel(image, axis=0)
sobel_y = ndimage.sobel(image, axis=1)
laplace = ndimage.laplace(image)
enhanced = np.sqrt(sobel_x**2 + sobel_y**2) + laplace

B

sobel_x = ndimage.sobel(image, axis=0)
sobel_y = ndimage.sobel(image, axis=1)
laplace = ndimage.laplace(image)
enhanced = sobel_x + sobel_y + laplace

C

sobel = ndimage.sobel(image)
laplace = ndimage.laplace(image)
enhanced = sobel * laplace

D

sobel_x = ndimage.sobel(image, axis=0)
laplace = ndimage.laplace(image)
enhanced = sobel_x - laplace

💡 Hint

Combine gradients from both directions using Pythagorean theorem before adding Laplace.

The combined magnitude of Sobel x and y gradients gives edge strength; adding Laplace enhances edges further.

Practice

1. What is the main purpose of using the Sobel filter in image processing?

easy

A. To detect edges by highlighting horizontal and vertical changes

B. To blur the image and reduce noise

C. To increase the brightness of the image

D. To convert the image to grayscale

Solution

1. Step 1: Understand Sobel filter function

   The Sobel filter detects edges by calculating gradients in horizontal and vertical directions separately.

2. Step 2: Identify the purpose of edge detection

   Edges are found by highlighting where brightness changes sharply, which Sobel does by combining horizontal and vertical gradients.

3. Final Answer:

   To detect edges by highlighting horizontal and vertical changes -> Option A

4. Quick Check:

   Sobel = edge detection [OK]

Hint: Sobel finds edges by checking horizontal and vertical changes [OK]

Common Mistakes:

• Confusing Sobel with blurring filters
• Thinking Sobel changes brightness directly
• Mixing Sobel with color conversion

2. Which of the following is the correct way to apply the Sobel filter on a 2D image array named img using SciPy?

easy

A. scipy.ndimage.sobel(img, axis=2)

B. scipy.ndimage.laplace(img, axis=1)

C. scipy.ndimage.sobel(img, axis=0)

D. scipy.ndimage.gaussian_filter(img, sigma=1)

Solution

1. Step 1: Recall Sobel filter usage in SciPy

   The Sobel filter is applied using scipy.ndimage.sobel with the image and axis (0 for vertical, 1 for horizontal).

2. Step 2: Check axis validity

   For a 2D image, valid axes are 0 or 1. Axis=2 is invalid and will cause an error.

3. Final Answer:

   scipy.ndimage.sobel(img, axis=0) -> Option C

4. Quick Check:

   Sobel syntax = scipy.ndimage.sobel(img, axis) [OK]

Hint: Use axis 0 or 1 for 2D images with sobel [OK]

Common Mistakes:

• Using axis=2 on 2D images causes errors
• Confusing laplace and sobel functions
• Using gaussian_filter instead of sobel for edges

3. Given the following code, what is the shape of the output array edges?

import numpy as np
from scipy import ndimage
img = np.array([[1, 2, 1], [0, 1, 0], [2, 1, 2]])
sobel_x = ndimage.sobel(img, axis=0)
sobel_y = ndimage.sobel(img, axis=1)
edges = np.hypot(sobel_x, sobel_y)

medium

A. (3, 3)

B. (2, 2)

C. (3, 2)

D. (1, 3)

Solution

1. Step 1: Check input image shape

   The input image img is a 3x3 array, so shape is (3, 3).

2. Step 2: Understand Sobel output shape

   Sobel filter preserves the input shape, so sobel_x and sobel_y are also (3, 3).

3. Step 3: Calculate edges shape

   Using np.hypot combines two (3, 3) arrays element-wise, resulting in (3, 3).

4. Final Answer:

   (3, 3) -> Option A

5. Quick Check:

   Input shape = output shape for sobel [OK]

Hint: Sobel keeps input shape; hypot combines same shapes [OK]

Common Mistakes:

• Assuming output shape shrinks after sobel
• Confusing axis with shape dimensions
• Thinking hypot changes array shape

4. The following code attempts to apply the Laplace filter but raises an error. What is the mistake?

from scipy import ndimage
img = [[1, 2, 3], [4, 5, 6], [7, 8]]
laplace_img = ndimage.laplace(img)

medium

A. ndimage.laplace does not exist in SciPy

B. Laplace filter requires axis parameter

C. The image must be grayscale

D. The input image must be a NumPy array, not a list

Solution

1. Step 1: Check input type for ndimage filters

   ndimage functions require NumPy arrays, not Python lists, for image input.

2. Step 2: Identify error cause

   Passing a list causes a TypeError because ndimage.laplace expects an array.

3. Final Answer:

   The input image must be a NumPy array, not a list -> Option D

4. Quick Check:

   ndimage needs np.array input [OK]

Hint: Convert lists to np.array before filtering [OK]

Common Mistakes:

• Passing lists instead of arrays
• Thinking laplace needs axis parameter
• Believing laplace function is missing

5. You want to detect edges in a noisy grayscale image using SciPy. Which approach best combines Sobel and Laplace filters to improve edge detection?

hard

A. Apply Gaussian blur, then Sobel filter on axis=0 only

B. Apply Sobel filters on both axes, combine results, then apply Laplace to sharpen edges

C. Use only Laplace filter because Sobel does not work on noisy images

D. Apply Laplace filter first, then Sobel on axis=2

Solution

1. Step 1: Understand Sobel and Laplace roles

   Sobel detects edges by gradients on horizontal and vertical axes; combining both gives full edge info.

2. Step 2: Use Laplace to enhance edges

   Applying Laplace after Sobel can sharpen edges by detecting second-order changes.

3. Step 3: Evaluate options

   Apply Sobel filters on both axes, combine results, then apply Laplace to sharpen edges correctly combines Sobel on both axes and Laplace for sharpening; others misuse axis or filters.

4. Final Answer:

   Apply Sobel filters on both axes, combine results, then apply Laplace to sharpen edges -> Option B

5. Quick Check:

   Sobel + Laplace = better edge detection [OK]

Hint: Combine Sobel axes then Laplace for sharper edges [OK]

Common Mistakes:

• Applying Sobel on invalid axis
• Skipping combination of horizontal and vertical Sobel
• Using Laplace alone without Sobel for noisy images