Instructors: Prof. Dr. Arjan Kuijper
Event type:
Seminar
Org-unit: Dept. 20 - Computer Science
Displayed in timetable as:
Scale space and PDE methods in image analysis and processing
Subject:
Crediting for:
Hours per week:
2
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Course 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.
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, Euclidean shortening flow.
Literature:
Main:
- B. M. ter Haar Romeny, Front-End Vision and Multi-scale Image Analysis, Dordrecht, Kluwer Academic Publishers, 2003.
Recommended:
- T. Lindeberg: Scale-Space Theory in Computer Vision, Dordrecht, Kluwer Academic Publishers, 1994.
- J. Weickert: Anisotropic Diffusion in Image Processing, Teubner-Verlag, Stuttgart, Germany, 1998.
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.
Preconditions:
Da Bildanalyse und -verarbeitung eine Mischung aus verschiedenen Disziplinen, wie Physik, Mathematik, Vision, Informatik und Engineering, ist, ist dieser Kurs gezielt auf ein breites Publikum zugeschnitten. Daher werden nur Grundkenntnisse in Analysis angenommen. Weitere notwendige mathematische Werkzeuge werden in den Sitzungen skizziert.
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