CVPR 2001 Short Course

Multiple View Geometry

Instructors: Anders Heyden (Lund University, Sweden) and Marc Pollefeys (K.U. Leuven, Belgium)

Duration: 4 hours

Description

The course will deal with multiple view geometry and especially the process of making 3D-models from a collection of two-dimensional images. We will start with some background material on basic mathematical tools, such as tensor calculus and projective geometry, that will be needed later on. We will also describe the process of modelling cameras, from the basic pinhole model to the mostly used uncalibrated camera model. The main part of the course contains the description of multiple view geometry both from a theoretical and from a practical point of view. We will define all multiple view invariants - epipoles, fundamental matrices, trifocal tensors and quadrifocal tensors - and show some of their properties. Then we will use this knowledge to solve the structure and motion problem, including finding point-matches using RANSAC methods. Both factorization methods and non-linear methods such as bundle adjustment will be explained. We will also deal with self-calibration methods and the more general flexible calibration methods in order to obtain a Euclidean reconstruction of the scene without using pre-calibrated cameras. The 3D-modelling will be accomplished using dense depth maps for obtaining a realistic texture mapping to the scene. Finally, we will also deal with plenoptic modelling, which gives an estimate of the reflectance properties of the scene.

Goals

1. To give a theoretical understanding of multiple view geometry and

3D-modelling.

2. To give working knowledge of solving the structure and motion problems.

3. To show how multiple view geometry can be used in some different

applications:

Structure and motion

View synthesis

The correspondance problem

Plenoptic modelling

Contents

This tutorial focuses on the understanding and use of multiple view geometry in computer vision. We will cover the following topics:

1. Introduction

2. Tensor Calculus and Projective Geometry

3. Modeling cameras

4. Multiple view geometry

5. Structure and motion

6. Factorization and bundle adjustment

7. Flexible calibration

8. Dense depth estimation

9. Plenoptic modelling

10. Conclusions

Intended Audience:

The target audience is anyone interested in knowing about the principles and applications of multiple view geometry and its latest developments. The tutorial is directed towards both researchers in closely related areas, application-oriented peaple and PhD-students. The course is self-contained in the sense that no background about tensor calculus is needed. Some knowledge about multiple view geometry might be helpful but is not essential.

Notes: Lecture manuscript will be handed out during the course.

Background material can be found on here and here.

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