MASTERCLASS

# The geometry of image formation

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In the last lecture we talked about image formation for pinhole cameras and cameras with lenses and we treated it geometrically.

In this lecture we're going to look at image formation again but this time we're going to treat it more formally, more mathematically. We're going to use two mathematical tools to help us do this. The first is linear algebra and that's all about matrices and vectors, a topic you should be quite familiar with. The second topic is one you are perhaps less familiar with and its homogeneous coordinates.

So we'll introduce homogeneous coordinates and then we'll use it to help us with a mathematical formalism of image formation.

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How is an image formed? The real world has three dimensions but an image has only two. We can use linear algebra and homogeneous coordinates to understand what’s going on. This more general approach allows us to model the positions of pixels in the sensor array and to derive relationships between points on the image and points on an arbitrary plane in the scene.

### Skill level

MATLAB experience

This content assumes an understanding of high school level mathematics; for example, trigonometry, algebra, calculus, physics (optics) and experience with MATLAB command line and programming, for example workspace, variables, arrays, types, functions and classes.

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