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Institute for Biomedical Imaging
Logo Institute for Biomedical Imaging
Institute for Biomedical Imaging
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IBI > Teaching

Lectures

The Institute for Biomedical Imaging lectures on various topics ranging from theoretical computer science to computer graphics to medical imaging. The following lectures are currently offered:

Summer Semester

Scientific Programming
since 2021

Content

  • Elementary data types and the connection to mathematics
  • Scientific data types: Multidimensional arrays, sparse arrays, data frames, missing data
  • Multiple Dispatch as an efficient paradigm for scientific programming
  • Literate Programming
  • Profiling and Benchmarks
  • Acceleration techniques: caching, multi-threading, SIMD, GPGPU
  • Scientific Data Formats: CSV, TOML, HDF5, and selected examples
  • Data visualization
  • Standard numerical techniques and efficient program libraries (BLAS, LAPACK, FFTW, ...)
  • Tests, code management, documentation
  • Reproducible science
Computer Graphics
since 2016

Content

  • Light, color & perception
  • Mathematical foundation of computer graphics
  • Algorithmic concepts of computer graphics
  • Basic rendering techniques
  • Basic shading techniques

Winter Semester

Medical Imaging
since 2015

Content

  • Overview of common imaging techniques
  • Signal processing
  • Inverse problems
  • Computed tomography
  • Magnetic Resonance Imaging
  • Compressed Sensing
  • Magnetic Particle Imaging
Image Processing
since 2021

Content

  • Mathematical image definition, volume data sets, illumination, radiometry, multispectral imaging, reflectivities, shading and shape.
  • Luminance and color perception, color spaces and color transformations, spectral value curves, visual perception, models of color perception
  • Image sensors (CMOS, CCD, HDR, X-ray sensors, IR), sensor characterization (EMVA1288), lenses
  • Spatio-temporal discretization (interpolation, decimation, aliasing, leakage, moiré, flicker, aperture)
  • Features (filters, edges, morphology, invariance, statistical features, texture)
  • Optical flow (calculus of variations, quadratic optimization, Euler-Lagrange equations)
  • Segmentation (distance measures, region growth, clusters, contours, levels, energy minimization, graph partitioning)
  • Registration (distance and similarity, calculus of variations, iterative nearest neighbors)

Past Lectures

Automata Theory and Formal Languages
2014 - 2021

Content

  • Propositional logic, Boolean algebra, propositional resolution, SAT-2KNF
  • Predicate logic, unification, predicate logic resolution
  • Temporal Logics (LTL, CTL)
  • Deterministic finite automata, definition and construction
  • Regular languages, closure properties, word problem, string matching
  • Nondeterministic automata: Rabin-Scott transformation of nondeterministic into deterministic automata
  • Epsilon automata, minimization of automata, elimination of e-edges, uniqueness of the minimal automaton (modulo renaming of states)
  • Myhill-Nerode Theorem: Correctness of the minimization procedure, equivalence classes of strings induced by automata
  • Pumping Lemma for regular languages: provision of a tool which, in some cases, can be used to show that a finite automaton principally cannot be expressive enough to solve a word problem for some given language
  • Regular expressions vs. finite automata: Equivalence of formalisms, systematic transformation of representations, reductions
  • Pushdown automata and context-free grammars: Definition of pushdown automata, definition of context-free grammars, derivations, parse trees, ambiguities, pumping lemma for context-free grammars, transformation of formalisms (from pushdown automata to context-free grammars and back)
  • Chomsky normal form
  • CYK algorithm for deciding the word problem for context-free grammrs
  • Deterministic pushdown automata
  • Deterministic vs. nondeterministic pushdown automata: Application for parsing, LL(k) or LR(k) grammars and parsers vs. deterministic pushdown automata, compiler compiler
  • Regular grammars
  • Outlook: Turing machines and linear bounded automata vs general and context-sensitive grammars
  • Chomsky hierarchy
  • Mealy- and Moore automata: Automata with output (w/o accepting states), infinite state sequences, automata networks
  • Omega automata: Automata for infinite input words, Büchi automata, representation of state transition systems, verification w.r.t. temporal logic specifications (in particular LTL)
  • LTL safety conditions and model checking with Büchi automata, relationships between automata and logic
  • Fixed points, propositional mu-calculus
  • Characterization of regular languages by monadic second-order logic (MSO)
TU Hamburg
Institute for Biomedical Imaging
Lottestraße 55, 2nd floor
22529 Hamburg
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MNPDynamics.jl
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