Geometric Foundations of Computer Vision
Dr. Martin Welk
(bld. E1.1, room 3.10.1, phone 0681-302-57343)
Dr. Andrés Bruhn
(bld. E1.1, room 3.09.1, phone 0681-302-57344)
Lectures (2h) with exercises (1h), winter term 2009/10
Lectures: Wednesdays 16–18 (4–6 p.m.),
Bld. E1.3, Lecture hall 003.
Tutorials: Thursdays 16–18 (4–6 p.m.)
every other week, Bld. E1.3, SR 015/CIP room 104
(after prior notice).
Specialised course in mathematical image analysis,
suitable for students in mathematics, computer science and visual computing programs.
The course is designed to familiarise students with the application of elementary
in computer vision models and algorithms.
Breaking news –
Entrance requirements –
Assessments / Exams –
First written exam:
The results can be queried via our online query form.
To inspect your exam sheet appoint by e-mail with
Second written exam:
I (Martin Welk) would like to apologise for the delay in grading the second
exam. Unfortunately I am by now (April 22)
still stuck in Chicago after attending a conference
due to the interruption in European and transatlantic aviation. Grades will
hopefully be available by the end of April.
Please be aware that this is not a remote study course. This web page does not
(and is not intended to)
replace regular attendance of lectures and tutorials.
Regular participation in
classroom exercises and regular submission of homework assignments is a prerequisite
for admission to the exam (as announced in the lecture).
was open from Wednesday, October 14, 16:00 (4 p.m.),
till Wednesday, October 21, 16:00 (4 p.m.).
Undergraduate knowledge of mathematics. For computer science students,
this requirement is met by successful completion of the
Mathematics for Computer Scientists lecture cycle.
Mathematical prerequisites which exceed the basic mathematics courses
are provided within the lecture.
Previous knowledge in digital image processing
is therefore helpful but not required.
This lecture is designed to familiarise students with geometrical
aspects of computer vision models and algorithms. Emphasis is laid
on the geometry of points, lines, shapes, rather than differential-geometric
and analytic tools.
After providing some mathematical basis, we will study
the geometrical description of scenes and the image acquisition
process. Further, we will consider how geometric parameters of features
in images can be used to infer scene information, or
to transform images. We will also learn about geometric models from
human visual perception which have found their way into computer vision
- Basic topology
- Euclidean, affine, and projective geometries
- Scene representation
- Camera geometry
- Epipolar geometry and stereo vision
- Geometric description of human visual perception
The written exam took place on Monday, February 15, 1000–1200
in Lecture Hall 002, Bld. E1.3.
The second written exam took place on Friday, April 9, 1000–1200
in Lecture Hall 002, Bld. E1.3.
The better grade counts.
Y. Ma, S. Soatto, J. Košecká, S. Shankar Sastry.
An Invitation to 3-D Vision.
Springer, New York 2004.
Max K. Agoston.
Computer Graphics and Geometric Modelling. Mathematics.
Springer, London 2005.
Three-Dimensional Computer Vision. A Geometric Viewpoint.
The MIT Press, Cambridge, Massachusetts, 2001.
E. Trucco, A. Verri.
Introductory Techniques for 3-D Computer Vision.
Prentice Hall, Upper Saddle River, 1998.
R. Hartley, A. Zisserman.
Multiple View Geometry in Computer Vision.
2nd Edition. Cambridge University Press, 2003.
G. Sommer (editor).
Geometric Computing with Clifford Algebras.
Springer, Berlin 2001.
Articles from journals and conferences.
Participants of the course can download the lecture materials here
|| Topology, Metrics, Manifolds
|| Matrix Groups
|| Euclidean and Affine Geometry;
|| Projective Geometry and
|| Epipolar Geometry
|| Calibration and
|| Triangulation and
|| Full 3D
Reconstruction and Three Views
|| Multiple Views
and Continuous Epipolar Geometry
of Gestalt Theory
|| Gestalt Theory
Based Image Analysis
of the Human Visual Field; Quaternions
Exercises (H homework, C classroom)
Martin Welk /
April 22, 2010