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VU : Mathematische Grundlagen in Vision & Grafik, 710.100

Teaching language will be English. Subtitle: "Scale Space and PDE methods in image analysis and processing"
Registration in TUGonline is possible, and you're welcome to attend the lectures.

Day & Time: Monday 12:00-16:00
Weeks: 11, 15, 17, 19, 23, 24, 26.
Location: HS FSI 1 (week 15), HSi2 (other weeks)



Image analysis & processing deals with the investigation of images and the application of specific tasks on them, like enhancement, denoising, deblurring, and segmentation. In this course, mathematical methods that are commonly used are presented and discussed. The focus will be on the axiomatic choice for the models, their mathematical properties, and their practical use.

Course slides


The following groups and topics are formed:
David Herrgesell, Martin Godec
1 Diffusion Filters and Wavelets: What Can They Learn from Each Other?
J. Weickert, G. Steidl, P. Mrazek, M. Welk, and T. Brox,
B1, ch1

Rene Ranftl, Gernot Margreitner
2 PDE-Based Image and Surface Inpainting
M. Bertalmio, V. Caselles, G. Haro, and G. Sapiro
B1, ch3

Jakob Santner, Markus Storer, Christian Bauer
3 Variational Segmentation with Shape Priors
M. Bergtholdt, D. Cremers and C. Schnorr
B1 ch 8
Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation
Daniel Cremers, Stanley J. Osher, Stefano Soatto 2006, IJCV 69(3) 335-351

Arnold Irschara, Surinder Ram
4 Curve Propagation, Level Set Methods and Grouping
N. Paragios,
B1, ch 9
Prior Knowledge, Level Set Representations & Visual Grouping
Mikael Rousson ˇ Nikos Paragios
2007, IJCV 76(3) 231-243

Kerstin Pötsch, Markus Demuth
5 Segmentation of Diffusion Tensor Images
Z. Wang and B. Vemuri
B1 Ch 31
Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images
R. Deriche, D. Tschumperle, C. Lenglet and M. Rousson
B1 Ch 32
A Riemannian Framework for Tensor Computing Xavier Pennec, Pierre Fillard, Nicholas Ayache 2006, IJCV 66(1) 41-66

Marc Steiner,Franz-Gerold Url
6 Fast methods for implicit active contour models
Weickert, Kuehne
B2 Ch3

Georg Macher, Bernhard Schlegl
7 Fast edge integration
B2 Ch4

Markus Rettenbacher, Hayko Riemenschneider
8 Multiplicative denoising and deblurring
Rudin, Lions, Osher
B2 Ch6

Inayatullah Khan,Michal Recky
9 Adaptive segmentation of vector-valued images
Rousson, Deriche
B2 Ch 11

Christian Kurz, Matthias Straka
10 Joint image registration and segmentation
Vemuri, Chen
B2 Ch 14

Georg Pacher, Manfred Klopschitz
11 Variational problems and partial differential equations on implicit surfaces: Bye bye triangulated surfaces?
Bertalmio, Memoli, Cheng, Sapiro, Osher
B2 Ch20

Johannes Höller, Bettina Muenzer
12 Multiscale optic flow
B3 Ch17
Highly Accurate Optic Flow Computation with Theoretically Justified Warping Nils Papenberg, Andres Bruhn, Thomas Brox, Stephan Didas, Joachim Weickert 2006, IJCV 67(2) 141-158

Thomas Huber, Patrick Reinbacher
13 Structure-texture Image Decomposition - Modeling, Algorithms, and Parameter Selection
Jean-Francois Aujol, Guy Gilboa, Tony Chan, Stanley Osher 2006, IJCV 67(1) 111-136

Andreas Hartl,Georg Waltner
14 Discrete Representation of Top Points via Scale Space Tessellation
B. Platel, M. Fatih Demirci, A. Shokoufandeh, L.M.J. Florack,
F.M.W. Kanters, B.M. ter Haar Romeny, and S.J. Dickinson
In R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale-Space 2005, LNCS 3459, pp. 73-84, 2005.
On Image Reconstruction from Multiscale Top Points
Frans Kanters, Martin Lillholm, Remco Duits, Bart Janssen,
Bram Platel, Luc Florack, and Bart ter Haar Romeny
In R. Kimmel, N. Sochen, J.Weickert (Eds.): Scale-Space 2005, LNCS 3459, pp. 431-442, 2005.

Joerg Teubl, Peter Teufl, and Clemens Orthacker
16 Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's.
D. Tschumperlé
IJCV, Volume 68, Number 1 pp. 65-82, June 2006.
Vector-Valued Image Regularization with PDE's : A Common Framework for Different Applications.
D. Tschumperlé, R. Deriche
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 27, No 4, pp 506-517, April 2005.

B1: Handbook of Mathematical Models in Computer Vision - Paragios, Nikos; Chen, Yunmei; Faugeras, Olivier (Eds.)
B2: Geometric Level Set Methods in Imaging, Vision, and Graphics - Osher, Stanley; Paragios, Nikos (Eds.)
B3: Front-End Vision & Multi-Scale Image Analysis - B. M. ter Haar Romeny.

Some key words:

Filtering (Edge detection, enhancement, Wiener, Fourier, ...)
Images & Observations: Scale space, regularisation, distributions.
Objects: Differential structure, invariants, feature detection
Deep structure: Catastrophes & Multi-scale Hierarchy
Variational Methods & Partial Differential Methods: Perona Malik, Anisotropic Diffusion, Total Variation, Mumford-Shah, Chan-Vese, geometric PDEs, level sets.
Curve Evolution: Normal Motion, Mean Curvature Motion, Euclidian Shortening Flow.


As image analysis and processing is a mixture of several disciplines, like physics, mathematics, vision, computer science, and engineering, this course is aimed at a broad audience. Therefore, only basic knowledge of analysis is assumed and necessary mathematical tools will be outlined during the meetings.

Examination material:

Course material exists of a collection of papers, covering the presented themes. For the Gaussian scale space part: For the non-linear part:

Other on-line available material worth reading:

References & further reading:


Investigation and public presentation of recent work in image analysis (e.g. book chapter) provided at the course, and an written/oral exam on contents of the course (material & slides).

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Arjan Kuijper / / updated Februari 26, 2008