Welcome to the homepage of the lecture

Interpolation and Approximation for Visual Computing

Winter Term 2018

Interpolation and Approximation for Visual Computing

Dr. Matthias Augustin
Office hour: Friday, 13:00 - 14:00.

Winter Term 2018

Lectures (3h) with exercises (1h);
(6 ETCS points)

Lectures:
Monday, 12:00-14:00, Building E1.3, Lecture Hall 001
Wednesday, 16:00-18:00, Building E1.3, Lecture Hall 003

First lecture: Wednesday, October 17, 2018

Tutor: Jón Arnar Tómasson

First tutorial: Wednesday, November 07, 2018; see also below.

Announcements – Description – Prerequisites – Tutorials – Registration – Exam – Contents – Assignments – Literature

• 2019-02-15: Uploaded solutions to classroom and homework assignments 07.
• 2019-01-28: Classroom assignment 07 is online.
  Updated Chapter 04, final extension. Content is now complete, but may still contain typos.
• 2019-01-09: Homepage now contains more information about the oral exams.

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,
• Fourier Series, Fourier Transform, and related concepts,
• discrete Fourier transform and FFT,
• splines,
• 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. Lectures and tutorials will be in English. Knowledge from image processing may be helpful, but is not required.

There will be a total of 7 tutorials which will take place instead of regular lectures on

• 2018-11-07,
• 2018-11-21,
• 2018-12-05,
• 2018-12-19,
• 2019-01-09,
• 2019-01-23, and
• 2019-02-06.

The tutorials include homework assignments which have to be submitted in the lecture break, or earlier and which will be graded. Working together in groups of up to 3 students is permitted and encouraged. Some assignments may contain programming exercises.

In order to qualify for the final exam, it is necessary to achieve 50% of the points of all homework assignment sheets in total. There will be either oral exams or written exams, depending on the number of participants.

Registration is closed since the submitting date of the first assignment passed (2018-11-05).

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.

In order to qualify for the final exam, it is necessary to achieve 50% of the points of all assignment sheets in total.

There will be two oral exams, one at the beginning and one at the end of the semester break. In case of qualification, 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.

The first round of oral exams takes place on
Wednesday, February 20, 2019, in
Office 4.12, Building E1 7.

The second round of oral exam takes place on
Friday, March 22, 2019, in
Office 4.12, Building E1 7.

Please note that each individual exam takes 30 minutes.

Exams can be taken in English (default) or German.

Internal Registration:

For internal uses, register per email to Matthias Augustin.
(Deadline first exam: February 13, 2019)
(Deadline second exam: March 15, 2019)
Subject: [IAVC18] exams Content:
First name: [myFirstName]
Last name: [myLastName]
Date of birth: [dd.mm.yyyy]
Student ID number: [...]
Registration for: [first/second] exam
Prefered language: [English/German]

I will arrange the time slots and let you know.

Lecture notes in separate chapters

No.	Title	Date
Slides	Organizational Issues, Introduction	10/22	[download]
Chapter 1	Polynomials	11/12	[download]
Chapter 2	Fourier Theory	11/15	[download]
Chapter 3	Splines	01/16	[download]
Chapter 4	Techniques in Higher Dimensions	02/04	[download]
Appendix A	Supplementary Material	12/18	[download]

No.	Title	Date
Assignment 01	Interpolation with Derivative Information	11/05	[download]
Assignment 02	Discrete Least-Square, Orthogonal Polynomials	11/19	[download]
Assignment 03	Fourier Series, Gram Polynomials	12/03	[download]
Assignment 04	Estimates, Cubic Splines, Not-a-knot Condition	12/17	[download]
Assignment 05	Quadratic splines, B-splines with repeated knots	01/07	[download]
Assignment 06	B-Splines with Repeated Knots	01/21	[download]
Assignment 07	Simple 3D Surface Modeling	02/04	[download]

No.	Title	Date		Submit until
Assignment 01	Interpolation, Estimates, Bernstein Polynomials	10/29	[download]	11/05
Assignment 02	Programming Interpolation, Discrete Least-Square, Gram-Schmidt	11/12	[download]	11/19
Assignment 03	Chebyshev Polynomials, Fourier Series	11/26	[download]	12/03
Assignment 04	Fourier, Convolution, Sampling	12/10	[download]	12/10
Assignment 05	Convolution, Cubic Splines, B-Splines	12/17	[download]	01/07
Assignment 06	B-Splines, Derivatives, Integrals	01/14	[download]	01/21
Assignment 07	Unisolvency, Tensor Products, Method of Plates	01/28	[download]	02/04

No.	Title	Date		Submit until
Assignment 02	Newton Interpolation	11/12	[download]	11/19
Assignment 05	Cubic Spline Interpolation	12/17	[download]	01/07

No.	Title	Date
Homework Assignment 01	Interpolation, Estimates, Bernstein Polynomials	11/12	[download]
Classroom Assignment 01	Interpolation with Derivative Information	11/12	[download]
Homework Assignment 02	Discrete Least-Square, Gram-Schmidt	11/23	[download]
Programming Assignment 02	Newton Interpolation	11/23	[download]
Classroom Assignment 02	Discrete Least-Square, Orthogonal Polynomials	11/23	[download]
Homework Assignment 03	Chebyshev Polynomials, Fourier Series	12/10	[download]
Classroom Assignment 03	Fourier Series, Gram Polynomials	12/10	[download]
Homework Assignment 04	Fourier, Convolution, Sampling	12/20	[download]
Classroom Assignment 04	Estimates, Cubic Splines, Not-a-knot Condition	12/20	[download]
Homework Assignment 05	Convolution, Cubic Splines, B-Splines	01/14	[download]
Classroom Assignment 05	Quadratic splines, B-splines with repeated knots	01/14	[download]
Programming Assignment 05	Cubic Spline Interpolation	01/14	[download]
Homework Assignment 06	B-Splines, Derivatives, Integrals	01/28	[download]
Classroom Assignment 06	B-Splines with Repeated Knots	01/28	[download]
Homework Assignment 07	Unisolvency, Tensor Products, Method of Plates	02/15	[download]
Classroom Assignment 07	Simple 3D Surface Modeling	02/15	[download]

There is no specific text book for this class as it touches on many topics for which specialized books exists.

• Introduction to Numerical Analysis
  J. Stoer, R. Bulirsch, Springer, 1993.
  English translation of the originally german version.
• Mathematics of Approximation
  J. de Villiers, Springer, 2012.
• A Practical Guide to Splines
  C. de Boor, Springer, 2001.
• Fourier Analysis and Applications
  C. Gasquet, P. Witomski, Springer, 1999.
• Approximation Theory
  O. Christensen, K. Christensen, Springer, 2005.
• Multivariate Splines
  C. Chui, SIAM, 1991.
• Interpolation and Approximation
  P. Davis, Blaisdell, 1963.
  Reprinted by Dover, 2014.
• 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.

MIA Group
©2001-2023
The author is not
responsible for
the content of
external pages.

Imprint - Data protection