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Interpolation and Approximation for Visual Computing
Winter Term 2022
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Interpolation and Approximation for Visual Computing
Lecturer: Vassillen Chizhov
Examiner:
Dr. Joachim Weickert
Winter Term 2022
Lectures (3h) with exercises (1h);
(6 ETCS points)
Lectures: Sessions with Q&A and Tutorial Sections
The lectures will be held online (Zoom link shared over e-mail)
Monday, 14:15-16:00
Thursday, 14:15-16:00
Announcements – Description – Prerequisites – Tutorials – Registration – Exam – Contents – Assignments – Literature
Target group: Students in the Master Programme Visual Computing
Lecture aim: Give an introduction to the concepts of interpolation
and (function) approximation. This includes
- interpolation with polynomials,
- least-square fitting,
- polynomial splines,
- some Fourier theory,
- radial basis functions, and
- applications in image processing.
This course is suitable for students of visual computing, mathematics, and
computer science.
Students attending this course should be familiar with basic concepts of
(multi-dimensional) calculus and linear algebra as covered in introductory
maths course (such as Mathematik für Informatiker I-III). Mathematical
prerequisites which exceed the basic mathematics courses are provided within
the lecture notes. All material will be in English. Knowledge from image
processing may be helpful, but is not required.
In order to register for the lecture, write an e-mail to
Vassillen Chizhov.
The subject line must begin with the tag [IAVC22].
Please use the following template for the e-mail:
First name: myFirstName
Last name: myLastName
Date of birth: dd.mm.yyyy
Student ID number: ...
Course of study: Bachelor/Master/...
Subject: Computer Science/Visual Computing/Mathematics/...
Note that the e-mail address from which you send this information will be used
to provide you with urgent information concerning the lecture.
Such information may include further regulations or urgent additional
remarks regarding assignment.
The registration is completely independent of LSF/HISPOS. They require a separate registration.
According to the regulations concerning storage and processing of personal data (Art. 6 (1) Datenschutzgrundverordnung (DSGVO)) we store and process your personal data for the purpose of lecture and tutorial organisation only. I.e. we may use them to contact you, to inform you about your grade, and to transmit your grades to the examination office.
There will be two written exams: the first on 21.02, 14-17 (E1 3, HS002), and the second on 21.03, 14-17. You are allowed to take part in both exams. The better grade counts, but each exam will count as an attempt individually. Please remember that you have to register online for the exam in the HISPOS system of the Saarland University for each attempt separately.
| Title | Date |
| Mock Exam 1: Polynomials and Splines | 17.11.2022 |
Course material will be made available on this homepage.
Additional organizational information, examples and explanations
that may be relevant for your understanding and the exam are provided
in the online sessions and tutorials.
Introductory Slides
Here you can find: Dr. Augustin's notes.
We will follow the above notes for some topics (e.g. polynomials).
However, I will occasionally provide more details on specific topics, and
less on others. This will be made clear during the lectures.
For instance, I plan to cover some more applications for
interpolation and approximation for higher dimensions
(e.g. finite elements, PDE inpainting).
| Title | Date |
| Piecewise Constant Voronoi Interpolation and Approximation | 06.12.2022 |
| Tiled DCT-II Image Approximation | 21.12.2022 |
| Title | Date |
| Mairhuber-Curtis Theorem | 12.12.2022 |
| Diagonalizing Properties of the Discrete Cosine Transforms | 12.12.2022 |
| The Discrete Cosine Transform | 12.12.2022 |
| Matrices Diagonalized by the Discrete Cosine and Discrete Sine Transforms | 12.12.2022 |
| Polyharmonic Splines Interpolation (Duchon) | 05.01.2023 |
| Ployharmonic Splines Interpolation (Meinguet) | 05.01.2023 |
| Title | Date |
| Newton Interpolation, Least Squares | 06.11.2022 |
| Splines I | 10.11.2022 |
There is no specific text book for this class as it touches on many topics for which specialized books exist.
-
Introduction to Numerical Analysis
J. Stoer, R. Bulirsch, Springer, 1993.
English translation of the originally german version. -
Numerical Methods
W. Boehm, H. Prautzsch, CRC Press, 1993.
-
Interpolation and Approximation
P. Davis, Blaisdell, 1963.
Reprinted by Dover, 2014. -
Approximation Theory
O. Christensen, K. Christensen, Springer, 2005. -
Mathematics of Approximation
J. de Villiers, Springer, 2012. -
Fourier Analysis and Applications
C. Gasquet, P. Witomski, Springer, 1999. -
The Fourier Transform and its Applications
R. N. Bracwell, McGraw Hill, 1999. -
A Practical Guide to Splines
C. de Boor, Springer, 2001. -
Multivariate Splines
C. Chui, SIAM, 1991. -
Scattered Data Approximation
H. Wendland, Cambridge University Press, 2005.
Most of these and further books can be found in the
mathematics and computer science library.
Further references will be provided during the lecture.
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