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: $(x, y)$