Basic Mathematical Tools for Imaging and Visualization - IN2124

Administrative Info Lecture by Dr. Tobias Lasser Exercises by Richard Brosig and Jakob Vogel 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 16:10-17:40, Room MI 03.013.010     Thursday 16:10-17:40, Room MI 03.013.010 Exam:     Mid-term: Tuesday, 13/12/2011, Room MW 0350, start: 16:30     Final: Thursday, 09/02/2012, Room Interim Hörsaal 1, start: 18:00     Repeat: Tuesday, 03/04/2012, Room MI HS2, start: 11:00     Allowed material: one handwritten DIN A4 sheet

Site Content Overview Script Course Schedule Literature

Announcements

Overview

For the development, but also for the application of many image processing techniques and computer vision algorithms, a deep mathematical understanding is of fundamental importance. This lecture aims to provide interested students with a solid mathematical basis for imaging and visualization applications.

Script

The script to the lecture is available:  bmt2011.pdf.

Course Schedule

Week	Type	Topic	Files
Tue, 18/10/11	L	Introduction and Overview	01Introduction.pdf
Thu, 20/10/11	L	Linear Algebra (linear spaces, bases)	02LinearAlgebra.pdf,  02Script.pdf
Tue, 25/10/11	E		Exercise Sheet 1,  Solution Sheet 1,  Supplementary Material,  MATLABWorkshop.pdf
Thu, 27/10/11	L	Linear Algebra (linear mappings, linear systems)	03LinearAlgebra.pdf,  03Script.pdf
Tue, 01/11/11		no lecture (public holiday)
Thu, 03/11/11	L	Linear Algebra (orthogonality, matrix decompositions)	04LinearAlgebra.pdf,  04Script.pdf
Tue, 08/11/11	E		Exercise Sheet 2,  Solution Sheet 2,  Supplementary Material
Thu, 10/11/11	L	Linear Algebra (least squares problems, eigenvalue problems, SVD)	05LinearAlgebra.pdf,  05Script.pdf
Tue, 15/11/11	E		Exercise Sheet 3,  Solution Sheet 3,  Supplementary Material,  principal_components.pdf
Thu, 17/11/11	L	Analysis (basics, topology, convergence)	06Analysis.pdf,  06Script.pdf
Tue, 22/11/11	E		Exercise Sheet 4,  Solution Sheet 4,  Supplementary Material
Thu, 24/11/11	L	Analysis (continuity, differentiability)	07Analysis.pdf,  07Script.pdf
Tue, 29/11/11	E		Exercise Sheet 5,  Solution Sheet 5,  Supplementary Material
Thu, 01/12/11	L	Analysis (taylor expansion, extrema, case study)	08Analysis.pdf,  08Script.pdf
Tue, 06/12/11	E		Exercise Sheet 6,  Solution Sheet 6,  Supplementary Material
Thu, 08/12/11		no lecture (dies academicus)
Tue, 13/12/11		mid-term exam (start: 16:30, room MW 0350)
Thu, 15/12/11	L	Optimization (existence/uniqueness of minimizer)	09Optimization.pdf,  09Script.pdf
Tue, 20/12/11	E		Exercise Sheet 7,  Solution Sheet 7,  Supplementary Material
Thu, 22/12/11	L	Optimization (Newton, case study, gradient descent)	10Optimization.pdf,  10Script.pdf
24/12/11 – 08/01/12		no lectures (christmas)
Tue, 10/01/12	L	Optimization (conjugate gradient)	11Optimization.pdf,  11Script.pdf
Thu, 12/01/12	L	Optimization (fixed point iteration), Probability Theory (basics)	12OptPT.pdf,  12Script.pdf
Tue, 17/01/12	E		Exercise Sheet 8,  Solution Sheet 8,  Supplementary Material
Thu, 19/01/12	L	Probability Theory (random variables)	13PT.pdf,  13Script.pdf
Tue, 24/01/12	E		Exercise Sheet 9,  Solution Sheet 9
Thu, 26/01/12	L	Probability Theory (expectation, EM, MLEM)	14PT.pdf,  14Script.pdf
Tue, 31/01/12	L	PDEs (basics, applications)	15PDE.pdf,  15Script.pdf
Thu, 02/02/12	E		Exercise Sheet 10,  Solution Sheet 10,  Supplementary Material
Tue, 07/02/12		Question & Answer session
Thu, 09/02/12		final exam (start: 18:00!, 101 Interim Hörsaal 1)

Literature

MATLAB

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

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!)

Analysis

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

Optimization

• Ake Björck, Numerical Methods for Least Squares Problems, SIAM (Available in the library!)
• Jonathan Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
• Uri Ascher, A first course in numerical methods, SIAM (Available in the library!)

Probability Theory

• Heinz Bauer, Measure and Integration Theory, deGruyter (Available in the library!)
• Sheldon Ross, Introduction to probability and statistics for engineers and scientists, Elsevier (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!)