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 12:0016:00
Weeks: 11, 15, 17, 19, 23, 24, 26.
Location: HS FSI 1 (week 15), HSi2 (other weeks)
Contents:
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
 Week 11:
Scale space introduction, axioms: part 1 (pps, 8.5 MB), or
part 1 (pdf, 1.4 MB).
the Gaussian kernel, regularisation: part 2 (pps, 1.5 MB), or
part 2 (pdf, 661 KB), and
extra info(66 KB).
 Week 15: Gaussian derivatives, deblurring: part 1 (pps, 5.0 MB), or
part 1 (pdf, 1.0 MB).
Features, image geometry, differential structure: part 2 (pps, 7.6 MB), or
part 2 (pdf, 1.9 MB).
 Week 17: nonlinear PDEs: Perona Malik part 1 (pdf, 397 kB),
Total Variation part 1 (pdf, 795 kB),
Mean Curvature Motion part 1 (pdf, 635 kB),
 Week 19: nonlinear PDEs 2: Mathematical Morphology, MumfordShah, Snakes/Active Contours
3 pdfs (zipped, 625 kB),
Introduction to Level Sets single file (pdf, 400 kB),
Applications of Level Sets (TV, MCM, ChanVese)3 pdfs (zipped, 1,68 MB),

Week 23: Presentations: Group 5, 8, 11, 4, 3

Week 24: Presentations: Group 6, 9, 10, 16
Some Deep Structure too.

Week 26: Presentations: Group 1, 2, 13, 7, 12, 14
Presentations:
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 PDEBased 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) 335351
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) 231243
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) 4166
Marc Steiner,FranzGerold Url
6 Fast methods for implicit active contour models
Weickert, Kuehne
B2 Ch3
Georg Macher, Bernhard Schlegl
7 Fast edge integration
Kimmel
B2 Ch4
Markus Rettenbacher, Hayko Riemenschneider
8 Multiplicative denoising and deblurring
Rudin, Lions, Osher
B2 Ch6
Inayatullah Khan,Michal Recky
9 Adaptive segmentation of vectorvalued 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) 141158
Thomas Huber, Patrick Reinbacher
13 Structuretexture Image Decomposition  Modeling, Algorithms, and Parameter Selection
JeanFrancois Aujol, Guy Gilboa, Tony Chan, Stanley Osher
2006, IJCV 67(1) 111136
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.): ScaleSpace 2005, LNCS 3459, pp. 7384, 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.): ScaleSpace 2005, LNCS 3459, pp. 431442, 2005.
Joerg Teubl, Peter Teufl, and Clemens Orthacker
16 Fast Anisotropic Smoothing of MultiValued Images using CurvaturePreserving PDE's.
D. Tschumperlé
IJCV, Volume 68, Number 1 pp. 6582, June 2006.
VectorValued 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 506517, April 2005.
(online)
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: FrontEnd Vision & MultiScale 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 & Multiscale Hierarchy
Variational Methods & Partial Differential Methods: Perona Malik,
Anisotropic Diffusion, Total Variation, MumfordShah, ChanVese,
geometric PDEs, level sets.
Curve Evolution: Normal Motion, Mean Curvature Motion, Euclidian Shortening Flow.
Audience:
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 nonlinear part:
Other online available material worth reading:
 Frédéric Guichard and JeanMichel Morel: Image Analysis and P.D.E.'s, IPAM GBM Tutorials, March 27 – April 6, 2001.
Especially the chapters 16, 2022
are a nice introduction to the second part of the course.
References & further reading:
 G. Aubert & P. Kornprobst: Mathematical problems in image processing:
Partial Differential Equations and the Calculus of Variations (second edition), Springer, Applied Mathematical Sciences, Vol 147, 2006.
 Tony
F. Chan & Jianhong (Jackie) Shen, mage Processing and Analysis:
Variational, PDE, Wavelet, and Stochastic Methods, SIAM, 2005.
 L. M. J. Florack: The Structure of Scalar Images, Dordrecht, Kluwer Academic Publishers, 1996.
 B. M. ter Haar Romeny, FrontEnd Vision and Multiscale Image Analysis,
Dordrecht, Kluwer Academic Publishers, 2003.
 B. M. ter Haar Romeny, Ed.: GeometryDriven
Diffusion in Computer Vision. Dordrecht, Kluwer Academic Publishers, 1994.
 T. Lindeberg: ScaleSpace Theory in Computer Vision, Dordrecht, Kluwer Academic Publishers, 1994.
 G. Sapiro: Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001
 J. Weickert: Anisotropic Diffusion in Image Processing, TeubnerVerlag, Stuttgart, Germany, 1998.
Examination:
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).
Arjan Kuijper / arjan.kuijper@oeaw.ac.at
/ updated Februari 26, 2008