# Multi-view geometry in Robotics

## Why should I care

Note taken during my study of the course on robotic perception in Coursera.

cite hartley here

## Projective geometry

We now take a first step to projective geometry–the workhorse of mutli-view geometry. We shall see why is projective geometry interesting and relevant. Most importantly, how projective geometry machinery significantly improves calculations and algorithmic development.

Consider a plane \(\mathbb{R}^2\), and now, the projective plane \(\mathbb{P}^2\)

A line is formed from two points.

A point is the intersection of two lines, even parallel ones.

Ideal points, or point at infinity. There are as many of them as
**normal** points.

Projective mappings and where to find them.

Using projective mappings we can see the points and lines at infinity.

Lastly, don’t think if the projective plan \(\mathbb{P}^2\) as rays, because a plane contains points. It is better to think of it as the Eucledian plane with ideal points and lines.