Basic Mathematical Tools for Imaging and Visualization - IN2124

Administrative Info Lecture by Prof. Nassir Navab, Tobias Lasser, Jakob Vogel, and Richard Brosig Organization by Maximilian Baust IN2124: 2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach IN2124: 2+2 SWS, 5 ECTS, Biomedical Computing, required module (For CSE students, this lecture is credited with 2 ECTS with the restriction that it has to be taken together with either the Computer Aided Medical Procedures lecture or the 3D Computer Vision lecture.) The lecture is given in English.

Time & Location Lecture and exercise: Tuesday 16:00-18:00, MI 03.013.010. Thursday 16:00-18:00, MI 03.013.010. Exam: 15.02.2011 11:30 - 13:00 Room: MW 2050

Site Content Overview Script Course Schedule Literature

Announcements REMINDER: THE EXAM IS CLOSED-BOOK!!! QUESTION CATALOGUE OUT NOW:  questions EXAM 15.02.2011, 11:30 - 13:00 Room: MW 2050

Overview

Not only for the developement but also for the application of many image processing techniques and computer vision algortihms a deep mathematical understanding is of fundamental importance. This lecture aims in providing interested students with a solid mathematical basis for imaging and visualization applications.

Script

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Course Schedule

For questions regarding the organization (e.g. exam date and time, exam admission, exercises,...) plase contact Maximilian Baust.

For questions regarding the content (e.g. content of lecture, relevant topics for exam,...) please contact the corresponding lecturer.

Week	Topic	Lecturer	Slides	Material
18/10/10 - 22/10/10	no lecture	-	-	-
26/10/10, 28/10/10	Basics, Linear Equation Systems	Jakob Vogel	-	-
02/11/10, 04/11/10	Least Squares Problems	Jakob Vogel	-	-
09/11/10, 11/11/10	Eigenvalue Problems	Jakob Vogel	-	-
16/11/10, 18/11/10	Matrix Decompositions	Jakob Vogel	-	-
23/11/10	no lecture	-	-	-
25/11/10	Case Study (part I)	Maximilian Baust	CaseStudy_I	CaseStudy_I.zip
30/11/10	Analysis Basics (Metric spaces, Topology, Convergence and compactness)	Tobias Lasser	analysis1	-
02/12/10	no lecture	-	-	-
07/12/10, 09/12/10	Analysis Basics (Continuity, Differentiability)	Tobias Lasser	analysis2  analysis3	-
14/12/10, 16/12/10	Analysis Basics (Taylor expansion, Extrema, Optimization, Convexity, Gauss-Newton)	Tobias Lasser	analysis4  analysis5	-
21/12/10	Analysis Basics (Gradient descent, Fixed point iteration)	Tobias Lasser	analysis6	exercises
27/12/10 - 31/12/10	24/12/10 - 06/01/11 Chistmas	-	-	-
03/01/11 - 07/01/11	24/12/10 - 06/01/11 Chistmas	-	-	-
11/01/11	Case Study (part II)	Maximilian Baust	CaseStudy_II	CaseStudy_II.zip
13/01/11	Graphs, Random Walks, and Conjugate Gradients	Maximilian Baust	Graphs, Random Walks, and Conjugate Gradients	-
18/01/11	PDEs Basics	Richard Brosig	Error Corrections  Advection demo	-
20/01/11	PDEs Basics	Maximilian Baust	PDEs part II	-
25/01/11, 27/01/11	Elliptic and Parabolic Problems	Richard Brosig	Poisson demo  Poisson Example	-
01/02/11, 03/02/11	Image Processing Applications	Richard Brosig and Maximilian Baust	PDEs part III Level Sets	Poisson Editing
08/02/11, 10/02/11	Questions	-	-	-
15/02/2011	Exam 11:30 am - 13:00 pm Room: MW 2050

Literature

Linear Algebra

• Yousef Saad, Iterative Methods for Sparse Linear Systems, SIAM (You can download the book for free!)

• Lloyd N. Trefethen and David Bau, Numerical Linear Algebra, SIAM (Available in the library!)

• Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press (Available in the library! Check out his video-lectures on youtube!)

MATLAB

• Cleve Moler, first chapter of Numerical Computing with MATLAB, SIAM (You can download the book for free!)

Calculus

• Walter Rudin, Real and Complex Analysis, McGraw-Hill (Available in the library!)

PDEs

• Lloyd Nick Trefethen , Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations (You can download the book for free!)
• Cleve Moler, chapter 11 of Numerical Computing with MATLAB, SIAM (You can download the book for free!)