Multiple-View Geometry

Chapter 1: Introduction

Projective Geometry

  • preserve straightness

  • Projective in homogeneous coordinates: both(x,y,1)(x, y, 1)and(x,y,0)(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)T(1, ±i, 0)^\mathrm{T}which satisfy a pair of real equations: x2+y2=0;w=0x^2 + y^2 = 0; w = 0.

  • With two circular points, we are able to define angle and length ratios.

  • Representation: (x,y)(x, y)

Last updated