Image Representation Formula

Image representation is the way a computer stores a picture as numeric data.

The Formula

file size≈width×height×bits per pixel\text{file size} \approx \text{width} \times \text{height} \times \text{bits per pixel}

When to use: A digital image is a giant colored spreadsheet: each square has a position and a color value.

Quick Example

A 100 by 100 image has 10,000 pixels. If each pixel stores RGB color, the file needs data for red, green, and blue at every pixel.

What This Formula Means

Image representation is the way a computer stores a picture as numeric data. Most digital images are made of pixels arranged in a grid, where each pixel stores color information such as red, green, and blue values.

A digital image is a giant colored spreadsheet: each square has a position and a color value.

Formal View

A raster image is a function from pixel coordinates (x,y)(x, y) to color values. Storage size depends on the number of pixels and the number of bits used for each pixel's color data.

Worked Examples

Example 1

medium
An image is enlarged on screen from 100x100 to 400x400 pixels by repeating each pixel 4x4 times. Does the file size change, and what visual effect appears?

Answer

file size same; pixelation appears\text{file size same; pixelation appears}

First step

1
The underlying data is still 100×100100 \times 100 pixel values.

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Example 2

hard
Compare 8-bit and 10-bit per channel for one channel: how many MORE levels does 10-bit provide, and by what factor?

Common Mistakes

  • Thinking a larger displayed image must contain more pixels - Fix this by naming the input, process, output, evidence, and checking "Am I explaining how data is encoded, organized, transformed, or interpreted rather than only naming the information?" before using the concept.
  • Confusing image resolution with compression format - Fix this by naming the input, process, output, evidence, and checking "Am I explaining how data is encoded, organized, transformed, or interpreted rather than only naming the information?" before using the concept.
  • Ignoring that more color depth increases file size - Fix this by naming the input, process, output, evidence, and checking "Am I explaining how data is encoded, organized, transformed, or interpreted rather than only naming the information?" before using the concept.
  • Using image representation from a keyword alone - Signal words like data, binary, bits only point to a possible model; the computing structure must match too.

Why This Formula Matters

Students use image representation ideas whenever they work with photos, graphics, screenshots, and game art. The concept also explains why higher quality images usually need more storage.

Frequently Asked Questions

What is the Image Representation formula?

Image representation is the way a computer stores a picture as numeric data. Most digital images are made of pixels arranged in a grid, where each pixel stores color information such as red, green, and blue values.

How do you use the Image Representation formula?

A digital image is a giant colored spreadsheet: each square has a position and a color value.

Why is the Image Representation formula important in CS Thinking?

Students use image representation ideas whenever they work with photos, graphics, screenshots, and game art. The concept also explains why higher quality images usually need more storage.

What do students get wrong about Image Representation?

Resolution and file format are different ideas. Two images can have the same resolution but different file sizes.

What should I learn before the Image Representation formula?

Before studying the Image Representation formula, you should understand: data representation, binary.

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