469.1: Scale Space and PDE methods in image analysis and processing

Teaching language will be English.
Registration is probably possible, and you're welcome to attend the lectures.

Day & Time: Monday 14:25-16:05
Weeks: 17 (20.4) - 29 (13.7).
Location: S3/073 (IGD building)



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



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:

Besides the slides that will e made available during the course, examination 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).

Possible topics:
From Handbook of Mathematical Models in Computer Vision - Paragios, Nikos; Chen, Yunmei; Faugeras, Olivier (Eds.)
Diffusion Filters and Wavelets: What Can They Learn from Each Other?
PDE-Based Image and Surface Inpainting
Variational Segmentation with Shape Priors
Curve Propagation, Level Set Methods and Grouping
Segmentation of Diffusion Tensor Images
Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images

From Geometric Level Set Methods in Imaging, Vision, and Graphics - Osher, Stanley; Paragios, Nikos (Eds.)
Fast methods for implicit active contour models
Fast edge integration
Multiplicative denoising and deblurring
Adaptive segmentation of vector-valued images
Joint image registration and segmentation
Variational problems and partial differential equations on implicit surfaces: Bye bye triangulated surfaces?
Other sources:
Structure-texture Image Decomposition - Modeling, Algorithms, and Parameter Selection, Jean-Francois Aujol, Guy Gilboa, Tony Chan, Stanley Osher 2006, IJCV 67(1) 111-136
Discrete Representation of Top Points via Scale Space Tessellation Scale-Space 2005, LNCS 3459, pp. 73-84, 2005.
On Image Reconstruction from Multiscale Top Points Scale-Space 2005, LNCS 3459, pp. 431-442, 2005.
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's. IJCV, Volume 68, Number 1 pp. 65-82, June 2006.
Vector-Valued Image Regularization with PDE's : A Common Framework for Different Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 27, No 4, pp 506-517, April 2005.

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Arjan Kuijper / arjan.kuijper@igd.fraunhofer.de / updated December 26, 2008