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.

Camera model

1-view

2-views

Reconstruction via Point Triangulation

Using the Reconstruction