Differential Geometry for Image Processing



Mathematical Image Analysis is getting more and more important nowadays in academia and industry. It requires pre-knowledge from various mathematical fields. Many of these fields, like scientific computing and functional analysis, are well-covered in the TU/e curriculum. Other fields such as differential geometry, continuous wavelet theory and Lie group analysis, are less covered. This course aims to bridge this gap, focusing on the Lie group of roto-translations (and the homogeneous space of positions and orientations), as this is most relevant for image analysis in view of multi-orientation processing of images. This course puts direct connections between mathematical theorems and industrial/medical imaging applications. We provide illustrative Mathematica code of such applications, allowing students to get hands-on experience and to see how theory makes a difference in practice. The course and its exam are strictly mathematical. It focusses on image analysis applications, but it is also relevant for students in the fields of scientific computing, applied analysis, mechanics, mathematical physics who are interested in differential geometry.
Course period1/09/19 → …
Course formatCourse