ComputerVision101_Week1_WhatIsAnImage

university computervision week1 theory

What Is An Image

Source:

• HC1a Images and Interpolation
• https://rvdboomgaard.github.io/ComputerVision_LectureNotes/LectureNotes/IP/Images/index.html

Short idea

In everyday language, an image looks like a collection of pixels.

In the lecture, the deeper idea is:

$$\text{image}=\text{a function that gives a value at each position}$$

So an image is not only a grid of squares on your screen. A grid of pixels is only the stored discrete version.

Intuition

Think of a photograph as a sheet where every location has some amount of light.

• A camera measures light
• The measurement depends on position
• So we model the image as a function over space

For a grayscale image:

$$f(x,y)$$

tells you the brightness at position $(x,y)$.

Why the lecture says computers see images differently

Humans think:

• picture
• scene
• object

Computers store:

• numbers
• arranged on a grid

So there are really two views:

1. The continuous mathematical idea

$$f:{\mathbb{R}}^2\to \mathbb{R}$$

2. The discrete stored image

$$F:{\mathbb{Z}}^2\to \mathbb{R}$$

The whole lecture is mostly about moving between these two views.

Pixels

Pixels are called the “atoms” of an image because they are the smallest stored units in the digital image.

But a pixel is not a tiny real square in nature. It is just:

• one sample location
• with one stored value

That is why zooming in too much makes an image look blocky.

The handwritten lecture notes make this explicit:

• pixels are not true rectangular image elements in the physical world
• the rectangular grid is part of the discrete representation, not part of reality

Links

• ComputerVision101_Week1_ImageDefinition_DomainAndRange
• ComputerVision101_Week1_Discretization