Morphological operations in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of dilation on a binary image

What is the output of the following MATLAB code snippet that performs dilation on a binary image?

BW = [0 0 0 0 0; 0 1 1 0 0; 0 1 0 0 0; 0 0 0 0 0];
se = strel('square', 3);
BW2 = imdilate(BW, se);
disp(BW2)

MATLAB

BW = [0 0 0 0 0; 0 1 1 0 0; 0 1 0 0 0; 0 0 0 0 0];
se = strel('square', 3);
BW2 = imdilate(BW, se);
disp(BW2)

A [0 0 0 0 0; 0 1 1 0 0; 0 1 0 0 0; 0 0 0 0 0]

B [0 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 0 1 1 0 0]

C [0 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 0 1 1 1 0]

D [1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 0 0 0 0 0]

💡 Hint

Dilation expands the white regions by the shape of the structuring element.

The 3x3 square structuring element expands the white pixels in BW by one pixel in all directions, resulting in the output matrix shown in option C.

❓ Predict Output

intermediate

Result of erosion on a binary image

What is the output of this MATLAB code that performs erosion on a binary image?

BW = [1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 0 0 0 0 0];
se = strel('disk', 1, 0);
BW2 = imerode(BW, se);
disp(BW2)

MATLAB

BW = [1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 0 0 0 0 0];
se = strel('disk', 1, 0);
BW2 = imerode(BW, se);
disp(BW2)

A [1 1 0 0 0; 1 1 0 0 0; 1 1 0 0 0; 0 0 0 0 0]

B [1 0 0 0 0; 1 0 0 0 0; 1 0 0 0 0; 0 0 0 0 0]

C [0 0 0 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 0 0 0 0]

D [1 1 1 0 0; 1 1 1 0 0; 1 1 1 0 0; 0 0 0 0 0]

💡 Hint

Erosion shrinks white regions by removing pixels near edges based on the structuring element.

The disk structuring element with radius 1 removes pixels on the edges of the white region, shrinking it as shown in option A.

🔧 Debug

advanced

Identify the error in morphological closing code

The following MATLAB code is intended to perform morphological closing on a binary image. What error will it produce when run?

BW = imread('text.png');
se = strel('line', 5, 45)
BW2 = imclose(BW, se);
imshow(BW2);

MATLAB

BW = imread('text.png');
se = strel('line', 5, 45)
BW2 = imclose(BW, se);
imshow(BW2);

A Runtime error: 'text.png' file not found

B SyntaxError due to missing semicolon after strel line

C No error, code runs and shows the closed image

D TypeError because imclose expects a binary image but BW is uint8

💡 Hint

Check the input type expected by imclose function.

imclose expects a binary image (logical), but imread returns uint8. Without converting BW to logical, imclose will error.

🧠 Conceptual

advanced

Effect of structuring element shape on morphological operations

Which statement best describes how the shape of the structuring element affects morphological operations like dilation and erosion?

A The structuring element shape only affects the color of the output image, not the shape.

B The structuring element shape determines the direction and extent of pixel expansion or shrinking in the image.

C The structuring element shape has no effect; only its size matters.

D The structuring element shape affects only grayscale images, not binary images.

💡 Hint

Think about how the shape controls which neighbors are considered during the operation.

The shape of the structuring element defines which pixels around a target pixel are included in the operation, thus controlling how the image is modified.

❓ Predict Output

expert

Output of morphological gradient on a binary image

What is the output of this MATLAB code that computes the morphological gradient of a binary image?

BW = [0 0 0 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 0 0 0 0];
se = strel('square', 3);
BWd = imdilate(BW, se);
BWe = imerode(BW, se);
BWg = BWd - BWe;
disp(BWg)

MATLAB

BW = [0 0 0 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 0 0 0 0];
se = strel('square', 3);
BWd = imdilate(BW, se);
BWe = imerode(BW, se);
BWg = BWd - BWe;
disp(BWg)

A [0 1 1 1 0; 1 0 0 1 0; 1 0 0 1 0; 0 1 1 1 0]

B [0 1 1 1 0; 1 1 1 1 0; 1 1 1 1 0; 0 1 1 1 0]

C [0 0 0 0 0; 0 1 1 0 0; 0 1 1 0 0; 0 0 0 0 0]

D [1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1]

💡 Hint

Morphological gradient highlights edges by subtracting eroded image from dilated image.

The dilation expands the white region, erosion shrinks it, and their difference highlights the border pixels as shown in option A.

Practice

1. Which MATLAB function is used to create a structuring element for morphological operations?

easy

A. imerode

B. strel

C. imopen

D. imdilate

Solution

1. Step 1: Understand structuring element creation

   The structuring element defines the shape used in morphological operations.

2. Step 2: Identify the MATLAB function for structuring elements

   In MATLAB, strel creates structuring elements like disks or lines.

3. Final Answer:

   strel -> Option B

4. Quick Check:

   Structuring element = strel [OK]

Hint: Remember: strel makes shapes for morphology [OK]

Common Mistakes:

• Confusing strel with imopen or imerode
• Using imdilate to create structuring elements
• Thinking imopen creates structuring elements

2. Which of the following is the correct syntax to perform erosion on a binary image BW using a disk structuring element of radius 3?

easy

A. BW2 = imopen(BW, strel('disk', 3));

B. BW2 = imdilate(BW, strel('disk', 3));

C. BW2 = imerode(BW, strel('disk', 3));

D. BW2 = imclose(BW, strel('disk', 3));

Solution

1. Step 1: Identify the erosion function

   In MATLAB, imerode performs erosion on images.

2. Step 2: Check the syntax for erosion with a disk structuring element

   The correct syntax is imerode(image, strel('disk', radius)).

3. Final Answer:

   BW2 = imerode(BW, strel('disk', 3)); -> Option C

4. Quick Check:

   Erosion syntax = imerode(image, strel) [OK]

Hint: imerode + strel('disk', radius) erodes image [OK]

Common Mistakes:

• Using imdilate instead of imerode
• Wrong order of arguments
• Missing quotes around 'disk'

3. What will be the output size of the binary image BW2 after applying BW2 = imdilate(BW, strel('square', 3)); if BW is a 5x5 matrix?

medium

A. Cannot determine without image content

B. 7x7

C. 3x3

D. 5x5

Solution

1. Step 1: Understand dilation size effect

   Dilation expands shapes but does not change image size in MATLAB.

2. Step 2: Check MATLAB behavior on image size

   MATLAB morphological functions keep the output image size same as input.

3. Final Answer:

   5x5 -> Option D

4. Quick Check:

   Output size = input size for imdilate [OK]

Hint: Morphology keeps image size same in MATLAB [OK]

Common Mistakes:

• Assuming dilation increases image size
• Confusing structuring element size with output size
• Thinking output depends on image content

4. Consider the code snippet:
se = strel('line', 5, 45);
BW2 = imerode(BW, se);
What is the likely error if BW is a grayscale image instead of binary?

medium

A. No error; imerode works on grayscale images

B. Error because strel cannot create line elements

C. Error because imerode expects binary images only

D. Error due to missing image conversion to binary

Solution

1. Step 1: Check imerode input types

   MATLAB's imerode supports both binary and grayscale images.

2. Step 2: Verify structuring element creation

   strel('line', 5, 45) correctly creates a line structuring element.

3. Final Answer:

   No error; imerode works on grayscale images -> Option A

4. Quick Check:

   imerode supports grayscale and binary [OK]

Hint: imerode works on grayscale too, no conversion needed [OK]

Common Mistakes:

• Thinking imerode only works on binary
• Assuming strel('line') is invalid
• Forgetting imerode supports grayscale images

5. You want to remove small noise dots from a binary image BW without changing the main shapes. Which morphological operation and structuring element combination is best?

hard

A. imopen with strel('disk', 2)

B. imclose with strel('square', 5)

C. imerode with strel('line', 3, 0)

D. imdilate with strel('diamond', 1)

Solution

1. Step 1: Understand noise removal by morphology

   Opening removes small objects (noise) while preserving shape size.

2. Step 2: Choose suitable structuring element

   A disk with radius 2 is good for removing small dots without harming main shapes.

3. Final Answer:

   imopen with strel('disk', 2) -> Option A

4. Quick Check:

   Opening + disk removes noise best [OK]

Hint: Use imopen with small disk to clean noise [OK]

Common Mistakes:

• Using imclose which fills holes
• Using erosion alone which shrinks shapes
• Using dilation alone which enlarges noise