TeachingWs07BasicMathTools

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

Basic Mathematical Tools for Imaging and Visualization

Administrative Info

Lecture by Prof. Nassir Navab
Exercises by Selim BenHimane, Tobias Lasser, Darko Zikic

2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach

(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

Monday, 14:00 - 15:30
Thursday, 16:00 - 17:30

The lessons will take place in room MI 03.013.010.
The programming exercises will take place in room MI 03.013.008.

Site Content

Announcements

  • Final Results are available. The grades have been sent by e-mail to the people who gave their e-mail address at the final exam. Otherwise, you can get your grade at the MyTUM portal.

  • New regulation for CSE students: For CSE students, the lecture is credited with 2 ECTS with the restriction that it has to be taken together with either the Computer Aided Medical Procedures (CAMP) lecture or the 3D Computer Vision (3DCV) lecture.

Overview

In order to solve real-world problems in applied engineering areas of computer science, knowledge of basic mathematical tools is essential.

The aim of this lecture is to provide a basic mathematical toolbox for selected topics of Imaging and Visualization.

We will present the basic and most common mathematical techniques and use mostly applications from Computer Vision and Image Processing for illustration. The same mathematical tools, however, are also needed in many other engineering fields like Artificial Intelligence and Machine Learning, Computer Graphics, Robotics, and so on.

The lecture will have three main parts: Basics, Tools and Practise. In the first part, we will give a reminder of linear algebra, analysis, geometry, probability and statistics basics. We go on by presenting the use of these basic concepts in methods such as parameter estimation and optimization. And finally, the students will have the opportunity to gain a deep understanding and hands-on experience of the methods by implementing them and/or using them to solve real-world problems during the exercises.

Course Schedule

Thu, Oct 18, 2007 Introduction  
Mon, Oct 22, 2007 Linear Algebra (basics recap) Linear spaces and linear mappings
Thu, Oct 25, 2007 cancelled  
Mon, Oct 29, 2007 Matlab Introduction The lecture takes place in the room MI 03.013.008
MATLABWorkshop.pdf
Thu, Nov 01, 2007 no class ('Allerheiligen')  
Mon, Nov 05, 2007 Linear Algebra (basics recap) Matrices, linear systems and determinants
Thu, Nov 08, 2007 Linear Algebra (basics recap) Subspaces, basis and rank/kernel of matrices
Mon, Nov 12, 2007 Linear Algebra (basics recap) Change of basis, eigenvalues and vectors
Thu, Nov 15, 2007 Linear Algebra (basics recap) exercise
Mon, Nov 19, 2007 Analysis (basics recap) Functions, continuity, differentiability in R
Thu, Nov 22, 2007 Analysis (basics recap) Differentiating higher dimensional functions, Taylor expansion
Mon, Nov 26, 2007 Exercises on Linear Algebra Basics Applications Singular Value Decompostion (SVD)

Pseudo-Inverse
BMexercise01.pdf
Thu, Nov 29, 2007 Function Minimization: Introduction & Theoretical Background
  • Definite Positive
  • Convexity
  • Minimum definition
  • Gradient and Hessian
  • Mon, Dec 03, 2007 Function Minimization: Minimum condition
  • Necessary conditions
  • Sufficient conditions
  • Thu, Dec 06, 2007 no class ('Dies Academicus')  
    Mon, Dec 10, 2007 Function Minimization: Unidimensional minimization
  • Golden number and Fibonacci sequence methods
  • Newton and secant methods
  • Line search method
  • Thu, Dec 13, 2007 Non-Linear Minimization
  • Gradient method
  • Mon, Dec 17, 2007 Non-Linear Minimization
  • Conjugate-Gradients method
  • Thu, Dec 20, 2007 Non-Linear Minimization
  • Newton + Quasi-Newton + Levenberg-Marquardt methods
  • Simplex
  • Christmas Holidays no classes  
    Mon, Jan 07, 2008 Intermediate Exam  
    Thu, Jan 10, 2008 Probability and Statistics (basics recap)
  • Probability Recap: Definition, Conditional Probability, Sum and Chain Rule, Bayes' Rule, Random Variables
  • Homework: Absolute Orientation by Iterative Minimization (exemplary matlab solution)
  • Mon, Jan 14, 2008 Probability and Statistics Tools
  • Probability Recap: Multivariate Random Variables, Probability Density Functions (PDF), Expectation, Variance
  • Covariance and Correlation
  • Principal Component Analysis (PCA)
  • accompanying slides
  • Thu, Jan 17, 2008 Probability and Statistics Tools + Exercise Discussion Principal Component Analysis (PCA)
  • Homework: PCA Exercise, (Matlab script)
  • Supplementary Material: Tutorial on PCA by Jonathon Shlens
  • Mon, Jan 21, 2008 Probability and Statistics Tools
  • PCA application: data compression
  • parameter estimation basics: Bayesian Estimation, Maximum a Posteriori (MAP), Maximum Likelihod Estimation (MLE)
  • parameter estimation basics slides (corrected version: definition of i.i.d. was wrong. The same error occurred in the MLE-recipe slide.)
  • Homework programming assignment: PCA Reconstruction: brief description, script for generating a population from an image
  • Thu, Jan 24, 2008 Probability and Statistics Tools / Calculus of Variations Basics
  • Kernel-based density approximation
  • Mon, Jan 28, 2008 Calculus of Variations Basics
  • handout
  • Thu, Jan 31, 2008 Calculus of Variations Basics  
    Mon, Feb 04, 2008 Final Exam  
    Thu, Feb 07, 2008    

    Literature

    Linear Algebra:

    • [GSLA] Introduction to Linear Algebra, Gilbert Strang. Wellesley Cambridge Pr, 3rd edition, March 1, 2003.

    Linear Algebra and Analysis Basics with many Applications (in German):

    • [HM1] Höhere Mathematik, Kurt Meyberg and Peter Vachenauer. Springer, 6 edition, 2001.
    • [HM2] Höhere Mathematik 2, Kurt Meyberg and Peter Vachenauer. Springer, 4 edition, 2001.

    Probability Therory Basics:

    • [AIMA] Artificial Intelligence: A Modern Approach, Stuart Russell and Peter Norvig. ( Some chapters available online. )
    • [ITIL] Information Theory, Inference, and Learning Algorithms, David MacKay. ( Book available online for on-screen viewing. )
    • [PRML] Pattern Recognition and Machine Learning, Christopher M. Bishop. Springer, 2006. ( Especially Chapters 1 and 2 are of interest for the lecture. )
    • [MAKBM] Multivariate Analysis (Probability and Mathematical Statistics), J. T. Kent, J. M. Bibby, und K. V. Mardia

    Function Minimization

    • [NMDS] Numerical Methods for Unconstrained Optimization and Nonlinear Equations, J. Dennis & R. Schnabel. Prentice Hall, 1983.
    • [POGMW] Practical Optimization, P. Gill, W. Murray & M. Wright. Academic Press, 1981.
    • [NPB] Nonlinear Programming, D. Bertsekas. Athena Scientific, 1999.
    • [NRPTVF] Numerical Recipes in C, W. Press, S. Teukolsky, W. Vetterling, B. Flannery. Cambridge University Press, 2002. ( Book available online. )
    • [COBV] Convex Optimization, S. Boyd & L. Vandenberghe. Cambridge University Press, 2004. ( Book available online. )
    • [OTCBG] Optimization toolbox for use with MATLAB: User’s guide, T. Coleman, M. A. Branch & A. Grace. The Mathworks Inc., 2006. ( Book available online. )



    internal

    TeachingForm
    Title: Basic Mathematical Tools for Imaging and Visualization
    Professor: Prof. Nassir Navab
    Tutors: Selim BenHimane,Tobias Lasser,Darko Zikic
    Type: Lecture
    Information: 2+2 SWS, 5 ECTS, Theoretische Informatik, Wahlpflichtfach
    Term: 2007WiSe
    Abstract: In order to solve real-world problems in applied engineering areas of computer science, knowledge of basic mathematical tools is essential. The aim of this lecture is to provide a basic mathematical toolbox for selected topics of Imaging and Visualization. We will present the basic and most common mathematical techniques and use mostly applications from Computer Vision and Image Processing for illustration. The same mathematical tools, however, are also needed in many other engineering fields like Artificial Intelligence and Machine Learning, Computer Graphics, Robotics, and so on. The lecture will have three main parts: Basics, Tools and Practise. In the first part, we will give a reminder of linear algebra, analysis, geometry, probability and statistics basics. We go on by presenting the use of these basic concepts in methods such as parameter estimation and optimization. And finally, the students will have the opportunity to gain a deep understanding and hands-on experience of the methods by implementing them and/or using them to solve real-world problems during the exercises.


    Edit | Attach | Refresh | Diffs | More | Revision r1.37 - 25 Feb 2008 - 19:56 - DarkoZikic

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