Geometric Foundations of Computer Vision

Winter Term 2009/10

Geometric Foundations of Computer Vision

Lectures: Dr. Martin Welk (bld. E1.1, room 3.10.1, phone 0681-302-57343)
Tutorials: Dr. Andrés Bruhn (bld. E1.1, room 3.09.1, phone 0681-302-57344)

Winter 2009/10

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 geometric ideas in computer vision models and algorithms.

Breaking newsEntrance requirementsContentsAssessments / ExamsReferencesDownload

First written exam: The results can be queried via our online query form.
To inspect your exam sheet appoint by e-mail with Andrés Bruhn.

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.

General notice: 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).

Online registration 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 algorithms.

Topics include:

  • Basic topology
  • Euclidean, affine, and projective geometries
  • Scene representation
  • Camera geometry
  • Epipolar geometry and stereo vision
  • Stitching
  • 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.
  • O. Faugeras. 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 (access password-protected):


No. Title Date Last update
1 Introduction October 14 2009.10.14.2131
2 Topology, Metrics, Manifolds October 21 2009.10.21.2035
3 Matrix Groups October 28 2009.10.28.2141
4 Euclidean and Affine Geometry; Camera Geometry November 4 2009.11.04.2038
5 Projective Geometry and Camera Geometry November 11 2009.11.11.1832
6 Epipolar Geometry November 18 2009.11.18.1957
7 Calibration and Rectification November 25 2009.11.26.1343
8 Triangulation and Matching December 2 2009.12.02.2119
9 Full 3D Reconstruction and Three Views December 9 2009.12.17.2022
10 Multiple Views and Continuous Epipolar Geometry December 16 2010.01.10.1934
11 Image Stitching January 6 2010.01.06.2254
12 Principles of Gestalt Theory January 13 2010.01.13.1907
13 Gestalt Theory Based Image Analysis January 20 2010.01.20.2304
14 Geometry of the Human Visual Field; Quaternions January 27 2010.01.27.1851
15 Resume February 3 2010.02.03.1750

Exercises (H homework, C classroom)

To be
H1   21.10. 28.10. H1S
C1   22.10. C1S
H2   04.11. 11.11. H2S
C2 gfcv09_ex01.tgz 05.11. C2S
H3   25.11. 01.12. H3S
C3   26.11. C3S
H4   02.12. 09.12. H4S
C4 gfcv09_ex02.tgz 03.12. C4S
H5   16.12. 06.01. H5S
C5   17.12. C5S
H6   13.01. 20.01. H6S
C6 gfcv09_ex03.tgz 14.01. C6S
C7   28.01. C7S

Martin Welk / April 22, 2010

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