Image resizing and cropping in MATLAB - Time & Space Complexity

Time Complexity: Image resizing and cropping

O(n)

Understanding Time Complexity

When resizing and cropping images in MATLAB, it is important to understand how the time taken grows as the image size changes.

We want to know how the processing time increases when the image gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

% Resize and crop an image
img = imread('photo.jpg');
resized_img = imresize(img, [new_height, new_width]);
cropped_img = imcrop(resized_img, [x, y, crop_width, crop_height]);
imshow(cropped_img);
    

This code reads an image, resizes it to new dimensions, then crops a part of it before displaying.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Processing each pixel during resizing and cropping.
• How many times: Each pixel in the resized image is visited once for cropping; resizing touches pixels proportional to the new image size.

How Execution Grows With Input

As the image size grows, the number of pixels to process grows too.

Input Size (pixels)	Approx. Operations
100 x 100	10,000
500 x 500	250,000
1000 x 1000	1,000,000

Pattern observation: The operations grow roughly with the total number of pixels, so if width and height double, operations increase about four times.

Final Time Complexity

Time Complexity: O(n)

This means the time grows linearly with the number of pixels in the resized image.

Common Mistake

[X] Wrong: "Cropping an image is always very fast and does not depend on image size."

[OK] Correct: Cropping still processes pixels in the cropped area, so if the crop size is large, it takes more time.

Interview Connect

Understanding how image size affects processing time helps you explain performance in real projects, showing you can think about efficiency clearly.

Self-Check

"What if we resize the image to half its size before cropping? How would the time complexity change?"

Practice

1. What does the imresize function do in MATLAB when working with images?

easy

A. Converts an image to grayscale

B. Extracts a rectangular part of an image

C. Changes the size of an image by scaling or specifying new dimensions

D. Rotates an image by a specified angle

Solution

1. Step 1: Understand the purpose of imresize

   The imresize function is used to change the size of an image either by scaling it up or down or by specifying exact new dimensions.

2. Step 2: Differentiate from cropping

   Unlike cropping, which extracts a part of the image, resizing changes the entire image size.

3. Final Answer:

   Changes the size of an image by scaling or specifying new dimensions -> Option C

4. Quick Check:

   imresize = Resize image size [OK]

Hint: Resize changes whole image size, crop extracts part [OK]

Common Mistakes:

• Confusing resize with crop
• Thinking resize changes image colors
• Assuming resize rotates image

2. Which of the following is the correct syntax to crop an image img to a rectangle starting at (50, 30) with width 100 and height 80 in MATLAB?

easy

A. cropped = imcrop(img, [50 30 100 80]);

B. cropped = imresize(img, [50 30 100 80]);

C. cropped = crop(img, 50, 30, 100, 80);

D. cropped = imcrop(img, [30 50 80 100]);

Solution

1. Step 1: Recall imcrop syntax

   The imcrop function takes the image and a rectangle vector [x y width height]. Here, x=50, y=30, width=100, height=80.

2. Step 2: Check option correctness

   cropped = imcrop(img, [50 30 100 80]); matches the correct syntax. cropped = imresize(img, [50 30 100 80]); uses imresize which is wrong. cropped = crop(img, 50, 30, 100, 80); uses a non-existent function. cropped = imcrop(img, [30 50 80 100]); swaps x and y and width and height incorrectly.

3. Final Answer:

   cropped = imcrop(img, [50 30 100 80]); -> Option A

4. Quick Check:

   imcrop(img, [x y width height]) = correct crop syntax [OK]

Hint: imcrop uses [x y width height] rectangle vector [OK]

Common Mistakes:

• Swapping x and y coordinates
• Using imresize instead of imcrop
• Incorrect rectangle vector order

3. What will be the size of the output image resized_img after running the following MATLAB code?

img = imread('peppers.png');
resized_img = imresize(img, 0.5);

medium

A. Half the width and half the height of the original image

B. Double the width and double the height of the original image

C. Same size as the original image

D. Width halved but height unchanged

Solution

1. Step 1: Understand imresize with scale factor

   Using imresize(img, 0.5) scales the image to 50% of its original size in both width and height.

2. Step 2: Determine output size

   The output image will have half the width and half the height of the original image.

3. Final Answer:

   Half the width and half the height of the original image -> Option A

4. Quick Check:

   imresize with 0.5 scales both dimensions by 0.5 [OK]

Hint: Scale 0.5 halves both width and height [OK]

Common Mistakes:

• Thinking only width or height changes
• Assuming scale factor doubles size
• Confusing imresize with imcrop

4. Identify the error in this MATLAB code snippet intended to crop an image img to a 100x100 square starting at (20, 20):

cropped_img = imcrop(img, [20 20 100]);

medium

A. The image variable name is incorrect

B. The rectangle vector is missing the height value

C. imcrop cannot crop square images

D. The starting coordinates should be (100, 100)

Solution

1. Step 1: Check imcrop rectangle vector format

   The rectangle vector must have four values: [x y width height]. Here only three values are given.

2. Step 2: Identify missing parameter

   The height value is missing, causing a syntax error or unexpected behavior.

3. Final Answer:

   The rectangle vector is missing the height value -> Option B

4. Quick Check:

   imcrop needs [x y width height] vector [OK]

Hint: Rectangle vector must have 4 values [OK]

Common Mistakes:

• Providing only 3 values instead of 4
• Confusing coordinates with size
• Assuming imcrop auto-fills missing values

5. You want to resize an image img to exactly 200x150 pixels and then crop a 100x100 square from the center. Which MATLAB code sequence correctly achieves this?

hard

A. cropped = imcrop(img, [75 50 100 100]); resized = imresize(cropped, [200 150]);

B. resized = imresize(img, [200 150]); cropped = imcrop(resized, [50 25 100 100]);

C. cropped = imcrop(img, [50 25 100 100]); resized = imresize(cropped, [200 150]);

D. resized = imresize(img, [150 200]); cropped = imcrop(resized, [50 25 100 100]);

Solution

1. Step 1: Resize image to 200x150 pixels

   Use imresize(img, [150 200]) to set width=200 and height=150.

2. Step 2: Crop 100x100 square from center

   The center of resized image is at (100, 75). To crop 100x100, start at (50, 25) because 50 = 100 - 100/2 and 25 = 75 - 100/2.

3. Step 3: Verify option correctness

   resized = imresize(img, [150 200]); cropped = imcrop(resized, [50 25 100 100]); matches the correct order and coordinates. resized = imresize(img, [200 150]); cropped = imcrop(resized, [50 25 100 100]); swaps width and height. Options C and D crop before resizing, which is not what is asked.

4. Final Answer:

   resized = imresize(img, [150 200]); cropped = imcrop(resized, [50 25 100 100]); -> Option D

5. Quick Check:

   Resize first, then crop center rectangle [OK]

Hint: Resize first, then crop center using half-dimensions [OK]

Common Mistakes:

• Swapping width and height in resize
• Cropping before resizing
• Incorrect crop start coordinates