Colormap and colorbar in MATLAB - Deep Dive

Overview - Colormap and colorbar

What is it?

A colormap is a set of colors used to represent data values visually in plots. It assigns colors to numbers, making patterns easier to see. A colorbar is a small legend next to a plot that shows how colors map to data values. Together, they help us understand data by turning numbers into colors.

Why it matters

Without colormaps and colorbars, it would be hard to quickly see differences or trends in data, especially in images or heatmaps. They make complex data understandable at a glance, helping scientists, engineers, and analysts make better decisions. Without them, visual data would be confusing and less useful.

Where it fits

Before learning colormaps and colorbars, you should know basic plotting and how to create graphs in MATLAB. After this, you can learn advanced visualization techniques like 3D plots, interactive graphics, and custom color schemes.

Mental Model

Core Idea

A colormap translates numbers into colors, and a colorbar shows the color-to-number mapping so you can read the data visually.

Think of it like...

Imagine a weather map where different temperatures are shown in colors from blue (cold) to red (hot). The colormap is the color scale used, and the colorbar is the key that tells you which color means which temperature.

Data values ──> Colormap (color scale) ──> Colors on plot
          │
          └──> Colorbar shows mapping

┌───────────────┐
│   Plot Area   │
│  (colored)    │
└───────────────┘  ┌─────────────┐
                   │ Colorbar    │
                   │ (legend)    │
                   └─────────────┘

Build-Up - 7 Steps

1

Foundation

Understanding Basic Colormaps

Concept: Learn what a colormap is and how MATLAB uses it to color data.

In MATLAB, a colormap is a matrix of colors. Each row is an RGB triplet (red, green, blue) with values from 0 to 1. When you plot data that uses colors, MATLAB assigns colors from this matrix based on data values. For example, the 'jet' colormap goes from blue to red through green and yellow.

Result

You see your data colored according to the colormap, making patterns visible.

Understanding that colormaps are just lists of colors helps you realize you can customize how data looks by changing these colors.

2

Foundation

What a Colorbar Does

Concept: Learn how a colorbar shows the mapping between data values and colors.

A colorbar is a small bar next to your plot that shows the colors used and the data values they represent. It helps you read the plot by explaining what each color means. In MATLAB, you add a colorbar by calling the 'colorbar' function after your plot.

Result

A colorbar appears next to your plot, acting like a legend for colors.

Knowing that a colorbar is a visual guide prevents confusion when interpreting colored data.

3

Intermediate

Applying Colormaps to Different Plots

🤔Before reading on: Do you think colormaps work the same for images and surface plots? Commit to your answer.

Concept: Explore how colormaps apply to various plot types like images, surfaces, and heatmaps.

Colormaps work by mapping data values to colors. For images, each pixel's value is colored. For surface plots, colors show height or intensity. You can set the colormap using 'colormap(name)' or create your own. Different plots may need different colormaps for best clarity.

Result

Your plots use colors that reflect data values correctly across different plot types.

Understanding that colormaps adapt to plot types helps you choose the right colors for clear data communication.

4

Intermediate

Customizing Colormaps

🤔Before reading on: Can you create a colormap with only three colors? Commit to your answer.

Concept: Learn how to create and apply your own colormaps for specific needs.

You can make a custom colormap by creating an N-by-3 matrix of RGB values. For example, to make a colormap with three colors: red, green, and blue, define a matrix with those RGB rows and apply it with 'colormap(yourMatrix)'. This lets you highlight specific data ranges or themes.

Result

Your plot uses the custom colors you defined, making it unique and tailored.

Knowing how to customize colormaps empowers you to make visuals that fit your exact message or data story.

5

Intermediate

Adjusting Color Limits for Better Contrast

🤔Before reading on: Does changing color limits affect the colorbar? Commit to your answer.

Concept: Learn how to control which data values map to the colormap's start and end colors.

MATLAB uses 'caxis' to set color limits. By changing these limits, you control which data values correspond to the lowest and highest colors in the colormap. This can improve contrast and highlight important data ranges. The colorbar updates to reflect these limits.

Result

Your plot colors focus on the data range you care about, and the colorbar matches this range.

Understanding color limits lets you emphasize important data features and avoid misleading visuals.

6

Advanced

Using Colorbars with Multiple Axes

🤔Before reading on: Do you think one colorbar can represent multiple plots with different data ranges? Commit to your answer.

Concept: Learn how to manage colorbars when you have multiple plots or axes in one figure.

When you have multiple plots, each can have its own colormap and color limits. You can add separate colorbars for each axis or share one colorbar. To share, you must align color limits and colormaps. MATLAB functions like 'colorbar' accept axis handles to control placement and association.

Result

Your figure shows correct colorbars for each plot or a shared colorbar that accurately represents all data.

Knowing how to handle multiple colorbars prevents confusion and keeps your visualizations clear in complex figures.

7

Expert

Internals of Colormap Interpolation

🤔Before reading on: Does MATLAB use exact colors from the colormap matrix or interpolate between them? Commit to your answer.

Concept: Understand how MATLAB calculates colors for data values between defined colormap entries.

MATLAB interpolates colors between rows in the colormap matrix. If your colormap has 64 colors but your data has 100 levels, MATLAB blends colors smoothly between the closest entries. This interpolation creates smooth gradients instead of abrupt color jumps. You can control interpolation by changing colormap size or data scaling.

Result

Plots show smooth color transitions that accurately represent continuous data.

Understanding interpolation explains why colors look smooth and helps you control color precision in your plots.

Under the Hood

MATLAB stores colormaps as matrices of RGB values. When plotting, it normalizes data values to an index range matching the colormap size. For each data point, MATLAB finds the closest colors in the colormap and interpolates between them to get the final color. The colorbar is a graphical object that displays this mapping as a gradient with tick labels showing data values.

Why designed this way?

This design balances flexibility and performance. Using a fixed-size colormap matrix with interpolation allows smooth color gradients without storing every possible color. The colorbar as a separate object lets users customize and place it independently. Alternatives like discrete color assignments would look blocky and less informative.

┌───────────────┐
│   Data Values │
└──────┬────────┘
       │ Normalize to colormap index
       ▼
┌───────────────┐
│ Colormap Matrix│
│ (RGB colors)   │
└──────┬────────┘
       │ Interpolate between colors
       ▼
┌───────────────┐
│ Colored Plot  │
└───────────────┘
       │
       ▼
┌───────────────┐
│   Colorbar    │
│ (shows mapping│
│  of colors to │
│  data values) │
└───────────────┘

Myth Busters - 4 Common Misconceptions

Quick: Does changing the colormap affect the actual data values? Commit to yes or no.

Common Belief: Changing the colormap changes the data itself because colors represent data.

Reality: Changing the colormap only changes how data is displayed, not the data values themselves.

Why it matters: Believing this can lead to confusion, making people think data changed when only the colors did, causing wrong conclusions.

Quick: Do you think the colorbar automatically updates if you change data limits? Commit to yes or no.

Common Belief: The colorbar always updates automatically to match any data or axis changes.

Reality: The colorbar updates automatically when data limits or colormap change, but in some cases, you may need to refresh or redraw it; otherwise, it may show outdated mappings.

Why it matters: This can cause mismatches between colors and the colorbar, misleading viewers about data interpretation.

Quick: Is it true that all colormaps are equally good for all data types? Commit to yes or no.

Common Belief: Any colormap works well for any kind of data visualization.

Reality: Some colormaps are better suited for certain data types; for example, perceptually uniform colormaps avoid misleading interpretations, while others can distort data perception.

Why it matters: Using poor colormaps can hide important data features or create false impressions, leading to bad decisions.

Quick: Does MATLAB use exact colors from the colormap matrix without blending? Commit to yes or no.

Common Belief: MATLAB uses only the exact colors defined in the colormap matrix without any blending.

Reality: MATLAB interpolates between colors in the colormap to create smooth gradients for continuous data.

Why it matters: Not knowing this can confuse users about why colors appear smooth and how to control color precision.

Expert Zone

1

Colormaps can be perceptually uniform or non-uniform; choosing perceptually uniform colormaps avoids misleading visual effects.

2

Colorbar tick labels can be customized to show meaningful data ranges or units, improving interpretability.

3

When sharing colorbars across multiple plots, aligning color limits is crucial to avoid misinterpretation.

When NOT to use

Colormaps and colorbars are not suitable for categorical data where colors represent distinct groups; instead, use discrete color assignments or legends. For very large datasets, interactive or dynamic color mapping tools may be better.

Production Patterns

Professionals often use standardized colormaps like 'parula' for consistency and accessibility. They customize colorbars with labels and ticks to match domain-specific units. In dashboards, shared colorbars ensure consistent interpretation across multiple visualizations.

Connections

Perceptual Color Theory

Builds-on

Understanding how humans perceive color differences helps in choosing colormaps that accurately represent data without visual bias.

Data Normalization

Builds-on

Colormaps rely on normalized data values to map colors correctly; knowing normalization helps control color scaling and contrast.

Music Equalizer Visualization

Analogy in different field

Like a music equalizer uses bars of different heights and colors to show sound intensity, colormaps and colorbars visually represent data intensity, helping cross-domain understanding of visual encoding.

Common Pitfalls

#1 Using a colormap that is not perceptually uniform, causing misleading color differences.

Wrong approach:

colormap(jet)
colorbar

Correct approach:

colormap(parula)
colorbar

Root cause:

Not understanding that some colormaps distort perception of data differences.

#2 Not setting color limits, leading to poor contrast and misleading colors.

Wrong approach:

imagesc(data)
colormap(hot)
colorbar

Correct approach:

imagesc(data)
caxis([minVal maxVal])
colormap(hot)
colorbar

Root cause:

Assuming MATLAB automatically chooses the best color limits for all data.

#3 Adding multiple colorbars without linking them to the correct axes, causing confusion.

Wrong approach:

plot(ax1, data1)
colorbar
plot(ax2, data2)
colorbar

Correct approach:

plot(ax1, data1)
colorbar(ax1)
plot(ax2, data2)
colorbar(ax2)

Root cause:

Not associating colorbars explicitly with their axes in multi-plot figures.

Key Takeaways

Colormaps convert numerical data into colors, making complex data easier to understand visually.

Colorbars act as legends that explain how colors relate to data values, preventing misinterpretation.

Customizing colormaps and color limits lets you highlight important data features effectively.

Understanding interpolation in colormaps explains smooth color transitions in plots.

Choosing the right colormap and managing colorbars carefully is essential for accurate and clear data visualization.