2. Some Basic Principles

Perspective Projection

camera obscura
A camera obscura of 1772.
Source: Wikimedia Commons

Cameras are perfect for recording wonderful moments. Plenty of memories cross our mind just by viewing a photograph.

It may not occur to you every time, but by taking a picture, you actually convert the three-dimensional surroundings into a two-dimensional image.

The transformation of a higher-dimensional space into a lower-dimensional image plan is called projection.

In the last few years, there has been an evolution to digital cameras. But do you still remember the first camera, the camera obscura? Let's have a look at what happens there.

The camera obscura (in English, 'dark chamber') is a dark box with a hole on one side. As the sun (or any other source of light) shines on an object, each visible point of the scene reflects a ray of light that passes through the hole and forms a unique image point on the film placed on the inner side opposite the hole.

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pinhole camera
Principle of a camera obscura (represented by the box). Light rays from an object pass through a small hole to form an image.
Source: Wikimedia Commons
Question: What is so remarkable in this projection?

The image displayed in the box is coming from one point, the aperture in the opposite side of the box. This point is called the perspective center. In a later phase of photography, a lens is added at this point to get a sharper image.

A perspective view is one which is seen out of one point, with the result that closer objects appear bigger on the image and more distant objects smaller.

Making a photograph from an airplane or even from space...

The principles of perspective projection can also be applied in aerial photography and remote sensing, where there are two possibilities:

  1. projection on a negative plane, as in the camera obscura, where the lens of the camera (which acts as the perspective center) is located between the surface and the image plane.
  2. projection on a positive plane where the image plane is located between the lens and the surface that has to be imaged.
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perspective projection
Perspective projection with P serving as the perspective center (the lens) on a negative plane (a) and a positive plane (b).
The three-dimensional points in the object space are transformed via a perspective projection into a two-dimensional image plan, with the lens of the sensor acting as the perspective center.

The counterpart of perspective projection is orthographic projection.