Mathematics for Technical VisualizationLaajuus (5 ECTS)

Objective

After completing the course the student will know different ways to represent the results of technical activity visually. Will be able to tell data and information apart. Will understand basic concepts in statistics, information theory and in colour processing. Will know what kind of information is related to a signal in frequency domain. Will know some principles how to extract information from data.
-----
After completing the course the student will be able to enhance images in frequency domain by a computer. Will be able to carry out colour image processing by a computer.

Content

Applied statistics in image processing: distributions, conditional probabilities, central limit theorem. Basics of information theory, redundancy, compression ratio. Mathematics of colour, colour spaces and colour processing. Fourier analysis of signals esp. digital images: frequency domain processing; sampling principles; amplitude and phase spectrum of a signal. Filtering in frequency domain; image enhancement in frequency domain: e.g. removing noise from a digital image.
-----
Boosting masks; Laplacian of a signal in edge enhancement. Bayer filter pattern of a colour image. Basics of data compression methods: reducing redundancy of data.

Qualifications

Engineering Mathematics and Mathematics for Multimedia