Differential Equations in Image Processing and Computer Vision
Three Computer Science Teaching Awards (Summer Terms 2003 and 2006, Winter Term 2015)
One Mathematics Teaching Award (Summer Term 2009)
Lecturer:
Prof. Joachim Weickert
Coordinator of tutorials:
Aaron Wewior
Winter Term 2017 / 2018
Lectures (4h) with theoretical exercises (2h)
(9 ETCS points)
Lectures:
Tuesday, 810 a.m., Building E 1.3, Lecture Hall 001
Friday, 1012 a.m., Building E 1.3, Lecture Hall 001
First lecture: Tuesday, October 17, 2017
Tutorials: 2 hours each week; see below.
News –
Synopsis –
Prerequisites –
Tutorials –
Registration –
Written Exams –
Contents –
Self Test –
Material for the Programming Assignments –
Example Solutions for the Assignments –
References
27.10.
The lecture from Tuesday, October 31, will be moved to
Monday, October 30, 68 p.m., Building E1.3, Lecture Hall 001.
The tutorial for group T1 from Tuesday, October 31, will be moved to
Thursday, November 2, 46 p.m., Building E1.3, Seminar Room 016.
The tutorial for group T2 from Tuesday, October 31, will be moved to
Thursday, November 2, 68 p.m., Building E1.3, Seminar Room 016.
20.10.
Registration is closed.
20.10.
The lectures on Tuesday start at 8:20 a.m.
17.10.
Registration is open.
Many modern techniques in image processing and computer vision make
use of methods based on partial differential equations (PDEs) and
variational calculus. Moreover, many classical methods may be
reinterpreted as approximations of PDEbased techniques. In this
course we will get an indepth insight into these methods.
For each of these techniques, we will discuss the basic ideas
as well as theoretical and algorithmic aspects. Examples from
the fields of medical imaging and computer aided quality control
illustrate the various application possibilities.
Since this class guides its participants to many
research topics in our group, its attendance is required for
everyone who wishes to pursue a master thesis in our group.
Equally suited for students of visual computing, mathematics and
computer science.
Requires undergraduate knowledge in mathematics (e.g. ''Mathematik
für Informatiker IIII''). Knowledge in image processing or differential
equations is useful, but not required. The lectures will be given
in English.
A combination of classroom and homework assignments (including theoretical
as well as programming problems) is offered.
The classroom assignments are intended to be solved in the tutorials and are
not graded.
The homework assignments are intended to be solved at home and have
to be submitted on Friday before the lecture.
In order to qualify for the exam you must
 attend 80% of the tutorials (we do check)
 gain 50% of all points from the homework assignments
Working in groups of up to 3 people is permitted, but all persons must be in
the same tutorial group.
Both classroom as well as homework assignments will be discussed in the
tutorials.
If you have questions concerning the assignments or tutorials,
please do not hesitate to contact
Aaron Wewior.
Two groups are scheduled:
 Group T1:
Tuesday, 1012 a.m., Building E1.3, Seminar Room 016
Tutor: Aaron Wewior
 Group T2:
Tuesday, 24 p.m., Building E1.3, Seminar Room 016
Tutor: Tobias Alt
The tutorial group can be reached via the mail addresses:
dicx  at  mia.unisaarland.de
where x has to be replaced by the group name
(t1 or t2).
Registration is now closed. You can still check in which group you are via
here.
Please do not forget to register also in the HISPOS system.
The first written exam will take place on
Thursday, February 8, 2018 from 2:00 p.m. to 5:00 p.m.
in the Günther Hotz Lecture Hall.
The second written exam will take place on
Thursday, April 5, 2018 from 2:00 p.m. to 5:00 p.m.
in the Günther Hotz Lecture Hall.
In order to qualify for the exams you must
 attend 80% of the tutorials (we do check)
 gain 50% of all points from the homework assignments
In case of qualification, you are allowed to take part in both exams.
The better grade counts.
The exams will be closed book. These are
the rules during the exams:

You are allowed and obliged to bring three things
to your desk only:
Your student ID card (Studierendenausweis), a ballpen that has no
function other than writing, and a socalled cheat sheet.
This cheat sheet is a A4 page with formulas or important equations
from the lecture. Please note that the cheat sheet has to be
handwritten by yourself. It will be collected at the end of the
exam, and you can get it back at the exam inspection.

In particular, electronic devices (including your cell phone), bags,
jackets, briefcases, lecture notes, homework and
classroom work solutions, additional handwritten notes, books,
dictionaries, and paper are not allowed at
your desk.

Please keep your student ID card ready for an attendance check during
the exam.
 Do not use pencils or pens that are erasable with a normal rubber.
 You are not allowed to take anything with you that contains
information about the exam.
A violation of this rule means failing the
DIC course.
 You must stay until the exam is completely over.
Course material will be made available on this webpage in order to
support the classroom teaching and the tutorials, not to replace
them. Additional organisational information, examples and explanations
that may be relevant for your understanding and the exam are provided
in the lectures and tutorials. It is solely your responsibility
 not ours  to make sure that you receive this infomation.
The following table shows a preliminary list of topics that will be
covered during the semester.
At the end of the semester, there will be a selftest problem sheet
that contains 6 problems, which
are intended to be similar in style and difficulty to a 180minutes
written exam.
Here you can download the material for the programming assignments:
Here you can download example solutions for the assignments:
Date 
Assignment 
27/10 
Assignment C1: Partial Derivatives, Otsu's Axiomatic Derivation of
Gaussian ScaleSpace 
27/10 
Assignment H1: Derivatives, Gaussian Convolution and Linear Diffusion 
03/11 
Assignment C2: 1D Linear Diffusion 
03/11 
Assignment H2: Finite Difference Approximation, Diffusivities,
Linear Diffusion 
10/11 
Assignment C3: Stencils and Discrete Diffusion Processes 
10/11 
Assignment H3: MaximumMinimum Principle and Average Grey Level Invariance,
Discrete ScaleSpace Properties of the SemiImplicit Scheme,
Consistency of the AOS Scheme, Nonlinear Isotropic Diffusion 
17/11 
Assignment C4: Diffusion Tensor of EED 
17/11 
Assignment H4: Discretisation of Anisotropic Nonlinear Diffusion,
Integration Model for Anisotropic Diffusion,
Anisotropic Diffusion 
24/11 
Assignment C5: Fast Explicit Diffusion 
24/11 
Assignment H5: Filter Factorisations into Explicit Diffusion Steps,
Parameter Adaption under Rescaling 
01/12 
Assignment C6: Continuous Variational Regularisation, Convex
Functionals and Forward Diffusion 
01/12 
Assignment H6: Gradient Domain Methods, Discrete Energy Minimisation,
Stability of DiffusionReaction Discretisations,
DiffusionReaction Methods 
08/12 
Assignment C7: ForwardBackward Splitting 
08/12 
Assignment H7: Proximal Problems and Energy Minimisation, HalfQuadratic
Regularisation, PrimalDual Methods for TV Regularisation 
15/12 
Assignment C8: Multiple Choice, Windowed Smoothness Terms 
15/12 
Assignment H8: MatrixValued Diffusion Filtering, Mean and Median
Filtering, Iterated Bilateral Filtering 
22/12 
Assignment C9: Transition Matrix for 1D Osmosis 
22/12 
Assignment H9: Average Grey Value Invariance of Osmosis,
Analysis of the Explicit Osmosis Scheme, Osmosis Filtering 
05/01 
Assignment C10: Eigenvalues and Eigenvectors of Nagel's Method,
Photometric Invariants 
05/01 
Assignment H10: Optic Flow Regularisation, Design of Global Optic Flow Methods,
Motion Tensors 
12/01 
Assignment C11: Data Terms for Large Displacements 
12/01 
Assignment H11: JIF Regularisation, Parabolic and Elliptic Problem,
FlowDriven Isotropic Optic Flow 
19/01 
Assignment C12: Discretisation of 1D Erosion 
19/01 
Assignment H12: Slope Transform, Dilation and Erosion 
 J. Weickert:
Anisotropic Diffusion in Image Processing.
Teubner, Stuttgart, 1998.
 G. Aubert and P. Kornprobst:
Mathematical Problems in Image Processing: Partial Differential
Equations and the Calculus of Variations.
Second Edition, Springer, New York, 2006.
 T. F. Chan and J. Shen:
Image Processing and Analysis: Variational, PDE, Wavelet,
and Stochastic Methods.
SIAM, Philadelphia, 2005.
 F. Cao:
Geometric Curve Evolutions and Image Processing.
Lecture Notes in Mathematics, Vol. 1805, Springer, Berlin, 2003.
 R. Kimmel:
The Numerical Geometry of Images.
Springer, New York, 2004.
 G. Sapiro:
Geometric Partial Differential Equations in Image Analysis.
Cambridge University Press, 2001.
 Articles from journals and conferences.
