Displaying images with imshow in Matplotlib - Time & Space Complexity

Time Complexity: Displaying images with imshow

O(n^2)

Understanding Time Complexity

When we use imshow to display images, it processes pixel data. Understanding how the time to display grows with image size helps us know what to expect when working with bigger images.

We want to know: how does the time to show an image change as the image gets larger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import matplotlib.pyplot as plt
import numpy as np

image = np.random.rand(1000, 1000)  # Create a 1000x1000 image
plt.imshow(image, cmap='gray')
plt.show()

This code creates a 1000 by 1000 pixel image with random grayscale values and displays it using imshow.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Processing each pixel in the 2D image array to prepare it for display.
• How many times: Once for every pixel, so for a 1000x1000 image, 1,000,000 times.

How Execution Grows With Input

As the image size grows, the number of pixels grows by width times height. The time to process and display grows roughly with the total number of pixels.

Input Size (n x n)	Approx. Operations
10 x 10	100
100 x 100	10,000
1000 x 1000	1,000,000

Pattern observation: If you double the width and height, the total pixels (and work) increase by about four times.

Final Time Complexity

Time Complexity: O(n^2)

This means the time to display grows roughly with the square of the image width (assuming width and height are similar), because each pixel must be processed.

Common Mistake

[X] Wrong: "Displaying an image takes the same time no matter how big it is."

[OK] Correct: The display time depends on how many pixels there are. Bigger images have more pixels, so they take more time to process and show.

Interview Connect

Knowing how image size affects display time helps you understand performance in data visualization. This skill shows you can think about how data size impacts your tools, which is useful in many data science tasks.

Self-Check

"What if we display a color image with three color channels instead of a grayscale image? How would the time complexity change?"