TeachingWs11BasicMathTools

Chair for Computer Aided Medical Procedures & Augmented Reality
Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

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

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

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

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




TeachingForm
Title: Basic Mathematical Tools for Imaging and Visualization
Professor: Dr. Tobias Lasser
Tutors: Richard Brosig, Jakob Vogel
Type: Lecture
Information: 2 + 2 SWS, 5 ECTS Credits (Module IN 2124)
Term: 2011WiSe
Abstract: 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.


Edit | Attach | Refresh | Diffs | More | Revision r1.85 - 16 Apr 2012 - 06:27 - TobiasLasser

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