Reliable Low-Level Image Analysis

What information give discrete images about the continuous world?

Image analysis uses discrete methods to make statements about the continuous real world. Since an in
finite amount of information is lost by digitization, it is not obviuous whether or when this approa
ch will succeed: Can one prove that certain properties of interest will be preserved, despite the in
formation loss?

This habilitation thesis considers theories which explicitly connect continuous and discrete models,
such as Shannon's famous sampling theorem and a recently discovered geometric sampling theorem. Thi
s analysis reveals important consequences regarding the necessary image quality (e.g. resolution and
signal-to-noise-ratio) and the resulting limits of observation. These findings are subsequently app
lied to a large number of low-level image analysis problems (such edge and corner detection, segment
ation, local estimation, and noise normalization), which leads to significantly improved algorithms
that perform robustly and accurately in accordance to the predictions of theory.