Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-62-17-M-7

Image Analysis for Stochastic Structures (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-62-17-M-7 Image Analysis for Stochastic Structures 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-62-17-K-7
Image Analysis for Stochastic Structures
P 56 h 79 h - - PL1 4.5 irreg.
  • About [MAT-62-17-K-7]: Title: "Image Analysis for Stochastic Structures"; Presence-Time: 56 h; Self-Study: 79 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86256 ("Image Analysis for Stochastic Structures")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Processing and statistical analysis of three-dimensional image data, in particular:
  • Random closed sets and their characteristics,
  • Discretisation and three-dimensional context,
  • Mathematical morphology,
  • Methods of image processing: filtering, segmentation, Euclidean distance transformation, labeling,watershed transformation,
  • Estimates of geometrical characteristics for random closed sets of image data.

Competencies / intended learning achievements

Upon successful completion of the module, the students have learned the basic classes of algorithms for the processing and analysis of three-dimensional image data. Assuming that the pictured structure is a random closed set, they can estimate geometric structure characteristics from the image data. They are also able to process and to analyse the given image data by means of suitable image processing software.

By solving the exercise problems, they have gained a precise and independent handling of terms, propositions and methods of the lecture. They understand the proofs presented in the lecture and are able to reproduce and explain them. They can in particular outline the conditions and assumptions that are necessary for the validity of the statements.

Literature

  • D. Stoyan, W.S. Kendall, J. Mecke: Stochastic Geometry and its Applications,
  • R. Schneider, W. Weil: Stochastic and Integral Geometry,
  • J. Ohser, K. Schladitz: 3D Images of Materials Structures: Processing and Analysis.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

More advanced knowledge in Stochastics (e.g. from the courses [MAT-60-12-K-4] or [MAT-60-11-K-4]) is useful but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-62-17-M-7]

Module-Pool Name
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)