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?"

Practice

1. What does the imshow function in matplotlib do?

easy

A. Displays image data as a picture

B. Creates a line plot from data points

C. Generates a histogram of values

D. Saves an image file to disk

Solution

1. Step 1: Understand the purpose of imshow

   imshow is designed to display image data visually as a picture.

2. Step 2: Compare with other plotting functions

   Other functions like line plots or histograms serve different purposes, so they don't match imshow's role.

3. Final Answer:

   Displays image data as a picture -> Option A

4. Quick Check:

   imshow = display image [OK]

Hint: Remember: imshow means 'image show' [OK]

Common Mistakes:

• Confusing imshow with plot or hist functions
• Thinking imshow saves images instead of displaying
• Assuming imshow creates charts, not images

2. Which of the following is the correct way to display a 2D numpy array named img as an image using matplotlib?

easy

A. plt.hist(img)

B. plt.plot(img)

C. plt.imshow(img)

D. plt.show(img)

Solution

1. Step 1: Identify the function to display images

   To show an image from a 2D array, plt.imshow() is the correct function.

2. Step 2: Check other options for correctness

   plt.plot() is for line plots, plt.hist() for histograms, and plt.show() displays the current figure but does not take data as argument.

3. Final Answer:

   plt.imshow(img) -> Option C

4. Quick Check:

   Image display = plt.imshow() [OK]

Hint: Use imshow to display arrays as images [OK]

Common Mistakes:

• Using plt.plot for image data
• Passing data to plt.show() incorrectly
• Confusing histogram with image display

3. What will the following code display?

import matplotlib.pyplot as plt
import numpy as np
img = np.array([[0, 1], [1, 0]])
plt.imshow(img, cmap='gray')
plt.show()

medium

A. A 2x2 image with black and white pixels

B. A line plot of the array values

C. An error because cmap='gray' is invalid

D. A blank plot with no image

Solution

1. Step 1: Understand the array and cmap

   The array has values 0 and 1 arranged in a 2x2 grid. Using cmap='gray' maps 0 to black and 1 to white.

2. Step 2: Predict the image output

   The image will show a 2x2 grid with black and white pixels arranged as per the array.

3. Final Answer:

   A 2x2 image with black and white pixels -> Option A

4. Quick Check:

   Array + cmap='gray' = black/white image [OK]

Hint: cmap='gray' shows 0 as black, 1 as white [OK]

Common Mistakes:

• Expecting a line plot instead of image
• Thinking cmap='gray' causes error
• Assuming image will be blank

4. Identify the error in this code snippet:

import matplotlib.pyplot as plt
import numpy as np
img = np.random.rand(5,5)
plt.imshow(img, cmap='viridis', interpolation='none')
plt.show()

medium

A. The interpolation value 'none' is invalid

B. The cmap 'viridis' does not exist

C. np.random.rand cannot create 2D arrays

D. The code runs without error and shows the image

Solution

1. Step 1: Check interpolation parameter

   In matplotlib, interpolation='none' is valid and means no smoothing.

2. Step 2: Verify cmap and array creation

   'viridis' is a standard colormap, and np.random.rand(5,5) creates a 5x5 array of floats between 0 and 1.

3. Step 3: Confirm code behavior

   The code runs without error and displays a 5x5 colored image with viridis colors and no interpolation smoothing.

4. Final Answer:

   The code runs without error and shows the image -> Option D

5. Quick Check:

   interpolation='none' and cmap='viridis' are valid [OK]

Hint: Check docs: 'none' is valid interpolation [OK]

Common Mistakes:

• Assuming 'none' is invalid interpolation
• Thinking 'viridis' cmap is missing
• Believing np.random.rand can't make 2D arrays

5. You have a grayscale image stored as a 2D numpy array with values from 0 to 255. You want to display it with matplotlib so that the darkest pixel is black and the brightest is white. Which code snippet achieves this correctly?

hard

A. plt.imshow(image_array, cmap='viridis', vmin=0, vmax=255)

B. plt.imshow(image_array, cmap='gray', vmin=0, vmax=255)

C. plt.imshow(image_array, cmap='gray', vmin=255, vmax=0)

D. plt.imshow(image_array)

Solution

1. Step 1: Understand grayscale display with imshow

   To show grayscale correctly, use cmap='gray' and set vmin=0 (black) and vmax=255 (white) to map pixel values properly.

2. Step 2: Evaluate other options

   plt.imshow(image_array, cmap='gray', vmin=255, vmax=0) reverses vmin and vmax, causing inverted colors. plt.imshow(image_array, cmap='viridis', vmin=0, vmax=255) uses wrong colormap 'viridis'. plt.imshow(image_array) lacks vmin/vmax, so colors may not map correctly.

3. Final Answer:

   plt.imshow(image_array, cmap='gray', vmin=0, vmax=255) -> Option B

4. Quick Check:

   Grayscale with correct vmin/vmax = plt.imshow(image_array, cmap='gray', vmin=0, vmax=255) [OK]

Hint: Set vmin=0 and vmax=255 for correct grayscale [OK]

Common Mistakes:

• Reversing vmin and vmax values
• Using wrong colormap for grayscale
• Not setting vmin and vmax for pixel range