Rotational Integral Geometry and its Applications

Eva B. Vedel Jensen obtained a Doctor of Science degree in 1987 from Aarhus University (AU). She has been a staff member at the Department of Mathematics, AU, since 1976, as full professor since 1998. Since 2020, she has been affiliated to AU as professor emerita. Member of the Danish Natural Science Research Council, 2001-2007, and Royal Danish Academy of Sciences and Letters, 2010-. In 2010, she received The Order of Dannebrog and in 2013 she became honorary doctor at University of Bern. In 2010-2020, she was the scientific director of Centre for Stochastic Geometry and Advanced Bioimaging with rotational integral geometry as one of the focus points. She is the author of two research monographs and approximately 90 scientific papers (stereology, integral geometry, stochastic geometry, geometric measure theory, probability theory, statistics).  Markus Kiderlen obtained an Erasmus Diploma in mathematics from the Université Grenoble Alpes in 1990 and a Doctor of Science degree in 1999 from the Karlsruhe Institute of Technology (KIT). After a postdoc period at KIT, he has been a staff member at the Department of Mathematics, AU, since 2004, as associate professor since 2007. In 2011-2020 he was co-leader of the project Image analysis and spatial statistics within the DFG research unit Geometry and Physics of Random Spatial Systems. He was leader of the Stochastic Geometry Group within the Centre for Stochastic Geometry and Advanced Bioimaging in 2016-2020. He has published an edited volume on Tensor Valuations and Their Applications in Stochastic Geometry and Imaging together with Eva B. Vedel Jensen and approximately 45 peer-reviewed papers on stereology, convex and integral geometry, stochastic geometry, geometric tomography and inverse problems.

• - 1. Introduction.- 2. Convex Bodies and their Classical Integral Geometry.- 3. Integral Geometric Transformations.- 4. Rotational Crofton Formulae for Intrinsic Volumes.- 5. Rotational Crofton Formulae for Minkowski Tensors.- 6. Rotational Slice Formulae.- 7. Further Rotational Integral Geometric Formulae.- 8. Applications to Particle Populations.- 9. Implementation in Optical Microscopy.