Mathematical Image Analysis Group, Saarland University

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Correspondence Problems in Computer Vision

Summer Term 2007

Correspondence Problems in Computer Vision

Lecturer: Dr. Andrés Bruhn
Office hours: Friday, 14:15 - 15:15.

Summer Term 2007

Lectures (2h) with programming/theoretical exercises (1h)
(5 credit points)

Lectures: Wednesday 14-16 c.t., Building E1.3, Lecture Hall 1

First lecture: Wednesday, April 18, 2007

Tutorials: 2 hours each 2 weeks, Thursday 16-18 c.t., ~~Building E1.3, CIP-Pool 012~~
Turorials: New room for tutorials (starting from June 14)
Turorials: Building E2.4 (math building), Cip-Pool U009

Prerequisites – Synopsis – Planned Contents – Assignments – References

Example - Stereo Reconstruction

Example - Motion Estimation

Prerequisites

Requires undergraduate knowledge in mathematics (e.g. ''Mathematik für Informatiker I-III'') . Knowledge in image processing or differential equations is useful. The lectures will be given in English.

Synopsis

Correspondence problems are a central topic in computer vision. Thereby, one is interested in identifying and matching corresponding features in different images/views of the same scene. Typical corresondence problems are the estimation of motion information from consecutive frames of an image sequence (optic flow), the reconstruction of a 3-D scene from a stereo image pair and the registration of medical image data from different image acquisition devices (e.g. CT and MRT). Central part of this lecture is the discussion of the most important correspondence problems as well as the presentation of suitable algorithms for solving them.

This class is particularly useful for those students who wish to to pursue a diploma or master thesis in our group in the field of computer vision.

Contents

Date Topic
18/4 Introduction, Overview
25/4 Block Matching, Correlation Techniques, Interest Points, Feature-Based Methods
2/5 Optic Flow I: Local Differential Methods, Parameterisation Models
9/5 Optic Flow II: Global Differential Methods, Horn and Schunck
23/5 Optic Flow III: Advanced Constancy Assumptions, Large Motion
30/5 Optic Flow IV: Advanced Data and Smoothness Terms
6/6 Optic Flow V: High Accuracy Methods, Advanced Numerics
13/6 Stereo Matching I: Projective and Epipolar Geometry
20/6 Stereo Matching II: Estimation of the Fundamental Matrix
27/6 Stereo Matching III: Correlation and Variational Methods, Graph Cuts
4/7 Medical Image Registration: Mutual Information, Elastic Registration, Landmarks
11/7 Particle Image Velocimetry: Div-Curl-Regularisation, Incompressible Navier Stokes Prior

Tutorials/Assignments

Programming excercises which are sometimes supplemented by small theoretical assignments will be offered. The regular attendence of these excercises is requirement for admission to the exam.

You could enroll for the lecture from Wed, Apr. 18, 2007, 3 PM to Tue, Apr. 24, 2007, 4 PM.

First tutorial: Thursday, April 26, 2007

Written/Oral Exams:

Oral exams took place after personal appointsments. The second chance exams was only available for those students who failed the first exam, or who did not take part in the first exam.

NEWS: The cerfificates (Scheine) are issued by the office of the Mathematics Department. They can be obtained from Mrs. Voss, Building E2.4, Room 111 (math building, ground floor, 8.15-11.30 AM).

References

There is no specific book that covers the complete content of this class. Many lectures will be based on articls from journals and conferences. However, the following four books cover most topics:

Optic Flow
A. Bruhn: Variational Optic Flow Computation: Accurate Modeling and Efficient Numerics.
Ph.D. Thesis, 2006. Available from /bruhn/PhDThesis.pdf
Stereo Reconstruction
O. Faugeras and Q.-T. Luong: The Geometry of Multiple Images. MIT Press, 2001.
Medical Image Registration
J. Modersitzki: Numerical Methods for Image Registration. Oxford Press, 2003.
Optic Flow/Medical Image Registration
O. Scherzer (Ed.): Mathematical Models for Registration and Applications to Medical Imaging, Series: Mathematics in Industry Vol. 10 Springer, New York, 2006.