# Multiple-View Geometry

### Chapter 1: Introduction

#### Projective Geometry

* preserve straightness
* Projective in homogeneous coordinates: both$$(x, y, 1)$$and$$(x, y, 0)$$are defined

#### Affine Geometry

* In Projective Space, we single out a particular line and call it the line at infinity.
* With this line at infinity, we are able to define parallelism, and equal length of two intervals.

#### Euclidean Geometry

* In Affine Geometry, we further single out two circular points in the line at infinity. 
* Two circular points: $$(1, ±i, 0)^\mathrm{T}$$which satisfy a pair of real equations: $$x^2 + y^2 = 0; w = 0$$. 
* With two circular points, we are able to define angle and length ratios.
* Representation: $$(x, y)$$