Computer Vision Mid-Level Vision Projective Geometry The - PowerPoint PPT Presentation

Computer Vision Mid-Level Vision

Projective Geometry • The projective projection of a 3D point: For the fundamental matrix: Ambiguity

Projective ambiguity

2D projective plane

Ideal points:

Conics FIVE POINTS DEFIN E A CONIC

Dual conics

Projective transformation

Transformation of lines and conics

Transformation types Similarity Affine Projective

Decomposition

Invariants

The line at infinity

Circular points

The conic dual to the circular points

Metric rectification

Planes 3 points define a plane. 3 planes define a point. A lines may be identified by its points intersecting two planes.

Projective transforms

Quadrics

Protectively equivalent

The plane at infinity

The absolute conics Absolute dual quadric