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 news – Entrance requirements – Contents – Assessments / Exams – References – Download

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):

Lectures

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)

Problem sheet	Additional file	Date posted	To be submitted	Solution
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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