Image colormaps in Matplotlib - Time & Space Complexity

Time Complexity: Image colormaps

O(n)

Understanding Time Complexity

We want to understand how the time to apply a colormap to an image changes as the image size grows.

How does the processing time grow when we increase the number of pixels?

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(512, 512)
plt.imshow(image, cmap='viridis')
plt.colorbar()
plt.show()

This code creates a 512x512 random image and applies the 'viridis' colormap to display it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Applying the colormap to each pixel value in the image array.
• How many times: Once for every pixel, so total pixels = width x height.

How Execution Grows With Input

As the image size grows, the number of pixels grows, so the work grows proportionally.

Input Size (n = total pixels)	Approx. Operations
10 x 10 = 100	100 operations
100 x 100 = 10,000	10,000 operations
1000 x 1000 = 1,000,000	1,000,000 operations

Pattern observation: Doubling the image width and height quadruples the number of pixels and operations.

Final Time Complexity

Time Complexity: O(n)

This means the time to apply the colormap grows linearly with the number of pixels in the image.

Common Mistake

[X] Wrong: "Applying a colormap takes the same time no matter the image size."

[OK] Correct: Each pixel must be processed, so more pixels mean more work and more time.

Interview Connect

Understanding how image size affects processing time helps you explain performance in real data visualization tasks.

Self-Check

What if we used a smaller colormap lookup table instead of mapping each pixel individually? How would the time complexity change?

Practice

1. What does the cmap parameter do in plt.imshow() when displaying an image?

easy

A. It changes how numbers map to colors in the image.

B. It changes the image size.

C. It adds a title to the image.

D. It saves the image to a file.

Solution

1. Step 1: Understand the role of cmap in plt.imshow()

   The cmap parameter controls the colormap, which maps numeric values to colors in the image.

2. Step 2: Identify what cmap affects visually

   Changing cmap changes the colors shown, helping interpret data better.

3. Final Answer:

   It changes how numbers map to colors in the image. -> Option A

4. Quick Check:

   Colormap = color mapping [OK]

Hint: Remember: cmap controls colors, not size or titles [OK]

Common Mistakes:

• Thinking cmap changes image size
• Confusing cmap with adding titles
• Assuming cmap saves the image

2. Which of the following is the correct way to apply the 'viridis' colormap to an image using matplotlib?

easy

A. plt.imshow(image, color='viridis')

B. plt.imshow(image, cmap='viridis')

C. plt.imshow(image, cmap=viridis)

D. plt.imshow(image, colormap='viridis')

Solution

1. Step 1: Recall the correct parameter name for colormap

   The parameter to set colormap in plt.imshow() is cmap, and it expects a string name.

2. Step 2: Check the syntax for passing the colormap

   Passing cmap='viridis' is correct. Using color or colormap is incorrect, and omitting quotes causes an error.

3. Final Answer:

   plt.imshow(image, cmap='viridis') -> Option B

4. Quick Check:

   Use cmap='name' syntax [OK]

Hint: Use cmap='colormap_name' exactly [OK]

Common Mistakes:

• Using color instead of cmap
• Forgetting quotes around colormap name
• Using colormap instead of cmap

3. What will the following code display?

import matplotlib.pyplot as plt
import numpy as np
image = np.array([[0, 1], [2, 3]])
plt.imshow(image, cmap='gray')
plt.colorbar()
plt.show()

medium

A. A 2x2 image with shades of gray from black (0) to white (3) and a colorbar showing values 0 to 3.

B. A 2x2 image with random colors and no colorbar.

C. A 2x2 image with rainbow colors and a colorbar showing values 0 to 1.

D. An error because 'gray' is not a valid colormap.

Solution

1. Step 1: Understand the image data and colormap

   The image is a 2x2 array with values 0 to 3. The 'gray' colormap maps low values to black and high values to white.

2. Step 2: Analyze the colorbar and display

   The colorbar shows the numeric range from 0 to 3, matching the image values. The image colors range from black (0) to white (3).

3. Final Answer:

   A 2x2 image with shades of gray from black (0) to white (3) and a colorbar showing values 0 to 3. -> Option A

4. Quick Check:

   Gray cmap maps 0-3 to black-white [OK]

Hint: Gray cmap means black to white shades [OK]

Common Mistakes:

• Thinking 'gray' is invalid
• Ignoring the colorbar range
• Assuming rainbow colors with 'gray'

4. The code below is intended to show an image with the 'hot' colormap and a colorbar, but it raises an error. What is the problem?

import matplotlib.pyplot as plt
import numpy as np
image = np.random.rand(3,3)
plt.imshow(image, cmap=hot)
plt.colorbar()
plt.show()

medium

A. plt.colorbar() must be called before plt.imshow().

B. The image array shape is invalid for imshow.

C. The colormap name 'hot' should be a string: cmap='hot'.

D. np.random.rand() cannot be used for images.

Solution

1. Step 1: Check the cmap parameter usage

   The colormap name must be a string. Here, hot is used without quotes, causing a NameError.

2. Step 2: Verify other code parts

   The image shape is valid, and colorbar usage is correct. np.random.rand() is valid for image data.

3. Final Answer:

   The colormap name 'hot' should be a string: cmap='hot'. -> Option C

4. Quick Check:

   Colormap names need quotes [OK]

Hint: Always put colormap names in quotes [OK]

Common Mistakes:

• Forgetting quotes around colormap name
• Thinking image shape is wrong
• Misordering colorbar and imshow

5. You have a 5x5 numpy array with values from 0 to 24. You want to display it using plt.imshow() with the 'coolwarm' colormap but only show colors for values between 5 and 20. Which code snippet correctly applies this?

hard

A. plt.imshow(data, cmap='coolwarm'); plt.colorbar(vmin=5, vmax=20)

B. plt.imshow(data, cmap='coolwarm', min=5, max=20); plt.colorbar()

C. plt.imshow(data, cmap='coolwarm', clip=(5,20)); plt.colorbar()

D. plt.imshow(data, cmap='coolwarm', vmin=5, vmax=20); plt.colorbar()

Solution

1. Step 1: Understand how to limit color range in imshow

   Use vmin and vmax parameters to set the data range for colormap scaling.

2. Step 2: Check each option for correct syntax

   plt.imshow(data, cmap='coolwarm', vmin=5, vmax=20); plt.colorbar() uses vmin=5 and vmax=20, which is correct. Other options use invalid parameters or place them incorrectly.

3. Final Answer:

   plt.imshow(data, cmap='coolwarm', vmin=5, vmax=20); plt.colorbar() -> Option D

4. Quick Check:

   Use vmin and vmax to clip colors [OK]

Hint: Use vmin and vmax to set color limits [OK]

Common Mistakes:

• Using min/max instead of vmin/vmax
• Trying to clip with non-existent parameters
• Passing vmin/vmax to colorbar instead of imshow