Welcome to the homepage of the lecture

Interpolation and Approximation for Visual Computing

Winter Term 2022

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

AnnouncementsDescriptionPrerequisitesTutorialsRegistrationExamContents 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, 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).

Date Please prepare Pages
27.10.2022 Polynomial Interpolation, Lagrange Basis 1--4
31.10.2022 Polynomial Interpolation, Newton Interpolation 5--12
03.11.2022 Interpolation Error, Polynomial Approximation 13--22
07.11.2022 Splines I 23--34
10.11.2022 Splines II: B-Splines 34--46
14.11.2022 Splines III: Approximation and Smoothing Splines 46--53
17.11.2022 Solving Mock Exam I
21.11.2022 Solving Mock Exam I
24.11.2022 Higher Dimensions: Mairhuber-Curtis Theorem and Multivariate Polynomials 55--59
28.11.2022 Higher Dimensions: Tensor Product Splines, Affine Transformations 59--67
01.12.2022 Higher Dimensions: Voronoi, Delaunay, and Multiharmonic Reconstruction 67--74

Here you will have the possibility to download material for the programming assignments.

Assignments will be available here during the semester.

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 Interpolation
    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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