# Lectures on Projective Geometry

# EEFN (First Frensh-Nordic Summerschool in Geometry)

# 010626-010703

# Lectures:

# Description

The course in projective geometry will cover both the basic theory
and some applications. We will start with the definition and
properties of projective spaces. Special emphasis will be on the
connection between projective, affine and Euclidean spaces; the so
called stratified approach. Another aspect of special important to
applications is projections from a higher dimensional projective
space to another with lower dimension. We will also introduce some
classical construction problems and invariant theory.
One application that we will look into in a little bit more detail
is multiple view geometry, a topic arising from trying to
reconstruct a rigid three-dimensional world from a number of its two-
dimensional images. We will introduce some tensor formalism to
describe the relations between corresponding point in different images.
In this case the projections are from 3D to 2D or sometimes from 2D
to 1D.

# Goals

- To understand and being able to use the basic concepts of
projective geometry
- Knowledge of synthetic projective geometry
- To understand and being able to use coordinate based
projective geometry (homogeneous coordinates)
- To understand the concept of multiple view geometry in
computer vision

# Contents

This tutorial focuses on the understanding and use of multiple view
tensors in computer vision. We will cover the following topics:
- Lecture 1: Projective geometry I (introduction+synthetic)
- Lecture 2: Projective geometry II (synthetic)
- Lecture 3: Projective geometry III (analytic)
- Lecture 4: Projective geometry IV (analytic+stratification)
- Lecture 5: Cartesian tensors
- Lecture 6: Tensors and projective geometry
- Lecture 7: Multiple view geometry in computer vision
- Lecture 8: Auto-calibration
- References:

Lecture manuscript will be handed out during the course.

My home page

My ECCV'98 paper about multiple view tensors:

A Common Framework for Multiple-View Tensors

Anders Heyden

Department of Mathematics (LTH)

Lund Institute of Technology / Lund University

P.O. Box 118, S-221 00 LUND

Room: 453A

Direct Phone: +46 46 22 204 91

Dept. Phone: +46 46 22 285 37

Fax: +46 46 22 240 10

e-mail:
Anders.Heyden@math.lth.se

*Last edited, 1999-03-05,
*