Interpolation and Approximation for Visual Computing

Lecturer: Vassillen Chizhov

Examiner: Dr. Joachim Weickert

Winter Term 2025/2026

Lectures (4h)
(6 ETCS points)

Lectures: Sessions with Q&A and Tutorial Sections
Monday, 12:15-14:00
Friday, 12:15-14:00
 

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Description

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 and approximation with polynomials
• polynomial splines
• least-squares fitting
• some Fourier theory
• PDE-based interpolation
• radial basis functions
• applications in image processing

 

 

Prerequisites

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 mathematics courses (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.

 

Exams

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 written exams. You can bring an A4 "cheat" sheet (you can use both sides) handwritten by you yo the exam. 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.

 

Literature

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

• Mathematics of Approximation
  J. de Villiers, Springer, 2012.
• Curves and Surfaces for CAGD: A Practical Guide
  G. Farin, Morgan Kaufmann, 2002.
• Scattered Data Approximation
  H. Wendland, Cambridge University Press, 2005.
• Meshfree Approximation Methods with MATLAB
  G. Fasshauer, World Scientific, 2007.
• Interpolation and Approximation
  P. Davis, Dover, 1975.
• Splines and Variational Methods
  P. M. Prenter, Wiley, 1989.
• Spline Functions: Basic Theory
  L. L. Schumaker, Cambridge University Press, 2007.

Further references will be provided during the lecture.