Image Processing in Physics

This module covers a wide range of basic and advanced techniques used for image processing and image reconstruction, with a special focus on physical science applications. Following a problem-solving philosophy, the module motivates all techniques and fundamental concepts with problems drawn from real-life applications.

The topics covered may be roughly divided into three parts, one focusing on basics of image processing and data analysis, one part based on image formation in optical devices, its requirements and limitations, and one part on more abstract algorithmic approaches to data analysis and optimization.

The module gives a rather broad overview over recurring topics in all fields of imaging, focusing more on an understanding of underlying principles than on rigorous mathematical derivations.

The lecture covers the following topics:

1. Image processing in spatial domain
2. Image processing in Fourier domain
3. Sampling, interpolation & pixel representations
4. Resolution & Noise
5. Segmentation
6. Tomography
7. Wave propagation
8. Wavelets and windowed Fourier transform
9. Optimization (Constrained + Least Squares)
10. Phase-contrast Imaging
11. Grating-based imaging

After successful lecture participation the student is able to:

• apply the basic principles of the discussed image processing techniques (filtering in spatial and in fourier domain, interpolation, segmentation, noise and resolution analysis, tomographic reconstruction, wave propagation and phase retrieval).
• identify the imaging technique to address specific biomedical questions.
• analyze images with respect to the used image-processing technique with its advantages and disadvantages.

The exercises will be given in python. No specific computer science or programming knowledge is required. The practicals offered together with the course also do not require any specific knowledge.
Some basic mathematics knowledge is expected: this includes basics of calculus, statistics, linear algebra & functional analysis (matrices, vectorspaces, bases, Fourier transformation, etc). In general the mathematical content will not be the focus of the course.

Each class will address a specific technique, yet all will be linked by recurrent essential topics including for example Fourier analysis, linear algebra, iterative techniques, maximum likelihood and convex optimization.

Together with each class, an exercise lesson is offered, where the student can directly apply and test the studied method. Typically this will involve writing a few lines of code (<10) in python to complete an existing program.

The following methods will be applied:

Oral presentation

Quiz

Discussions

Textbook/Scientific article

Power point slides filled in class

Online quiz/Quiz

Textbook/Scientific article

• Rafael Gonzales, Richard Woods, “Digital Image Processing”, 3rd ed.
• Bernd Jähne, “Digitale Bildverarbeitung und Bildgewinnung”, 7th ed.
• Lipson, Lipson, Tannhauser, “Optik” (German) 3rd ed., [english edition “Optical physics”  available as “Vollansicht” from TUM library]
• Bishop, “Pattern Recognition and Machine Learning” 1st ed.
• Max Born, Emil Wolf, “Principles of Optics”, 7th ed.
• Joseph Goodman, “Introduction to Fourier Optics”, 3rd ed.

free downloads:

• William Pratt, “Digital Image Processing” http://onlinelibrary.wiley.com/book/10.1002/0470097434
• Stephen Smith, “The Scientist and Engineer’s Guide To Digital Signal Processing”  http://www.dspguide.com
• Roger Easton, “Fourier Methods in Imaging” http://onlinelibrary.wiley.com/book/10.1002/9780470660102
• Gabriel Cristobal, “Optical and Digital Image Processing: Fundamentals and Applications” http://onlinelibrary.wiley.com/book/10.1002/9783527635245
• Tinku Acharya, “Image Processing: Principles and Applications” http://onlinelibrary.wiley.com/book/10.1002/0471745790
• Avinash Kak, Malcolm Slaney, “Principles of computerized tomographic imaging” http://www.slaney.org/pct/
• Richard Szileski, “Computer Vision: Algorithms and Applications” http://szeliski.org/Book/
• David Barber, “Bayesian Reasoning and Machine Learning” http://www.cs.ucl.ac.uk/staff/d.barber/brml/
• Simon J.D. Prince, “Computer Vision: Models, Learning, and Inference” http://www.computervisionmodels.com/
• Trevor Hastie “The Elements Of Statistical Learning”, 2nd ed. http://www-stat.stanford.edu/~tibs/ElemStatLearn/
• Otmar Scherzer. “Handbook of Mathematical Methods in imaging” http://link.springer.com/book/10.1007/978-0-387-92920-0

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and case studies.

For example an assignment in the exam might be:

• Explain the concept of spatial frequencies and indicate them in an exemplary image.
• How do you get 3D volumes from 2D projections?
• What is the difference between standard attenuation-based and phase-contrast imaging?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.