Contact (Karlsruhe)
Prof. Dr. Günter Last
Karlsruhe Institute of Technology
Institut für Stochastik
Kaiserstraße 89
76133 Karlsruhe
Germany
Phone: +49-721-608 43265
Fax: +49-721-608 46691
Contact (Erlangen)
Prof. Dr. Klaus Mecke
Universität Erlangen-Nürnberg
Institut für Theoretische Physik
Staudtstraße 7
91058 Erlangen
Germany
Phone: +49-9131-85 28442
Fax: +49-9131-85 28444
Contact (Aarhus)
CSGB
Department of Mathematical Sciences
Ny Munkegade 118
building 1530
8000 Aarhus C
Denmark

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6. Image analysis and spatial statistics

The goal of this project is to develop methods of extracting geometric characteristics and features from physical data in a quantitative, robust and efficient manner. This project is therefore an auxiliary tool for several of the other projects in the Research Unit.

One key-issue is the extraction of geometric characteristics, like Minkowski functionals or general tensor valuations, from digital images of a continuous object (see Software below). The analysis and improvement of existing algorithms serving this purpose requires a combination of image analysis on the one hand and geometric concepts from mathematical morphology, discrete, stochastic and integral geometry on the other hand.

Besides digital data, we also treat continuous input. For instance, estimators for tensor valuations (or derived quantities) based on lower dimensional central sections are derived. Concerning the model based approach, we work on estimation of the radius distribution of the stationary planar Boolean model, and on statistical inference for random field models based on local morphological measurements, exemplified by the analysis of H.E.S.S. sky maps.

Project Members

Cooperating partners

Software

  • Papaya calculates the Minkowski Tensors of planar patterns
  • Karambola is a program to calculate the Minkowski Tensors of three-dimensional bodies and surfaces.

Publications

2016

  • Sabrina T. Christensen and Markus Kiderlen
  • Comparison of two global digital algorithms for Minkowski tensor estimation
  • Preprint, CSGB Research Reports 2016-10. (2016)
  • Julia Hörrmann and Anne Marie Svane
  • Local digital algorithms applied to Boolean models
  • Scand. J. Stat. (to appear) (2016)
  • Daniel Hug and Markus Kiderlen and Anne Marie Svane
  • Voronoi-based estimation of Minkowski tensors from finite point samples
  • Preprint (2016)
  • Astrid Kousholt and Markus Kiderlen
  • Reconstruction of convex bodies from surface tensors
  • Adv. Appl. Math. 76, 1–33 (2016)
  • Astrid Kousholt, Johanna F. Ziegel, Markus Kiderlen and Eva B. Vedel Jensen
  • Stereological estimation of mean particle volume tensors in R^3 from vertical sections
  • to appear in: Tensor Valuations and their Applications in Stochastic Geometry and Imaging (edited by Markus Kiderlen and Eva B. Vedel Jensen), Lecture Notes in Mathematics (2016)
  • Ali H. Rafati, Johanna F. Ziegel, Jens R. Nyengaard and Eva B. Vedel Jensen
  • Stereological estimation of particle shape and orientation from volume tensors
  • J. Microsc. 261, 229–237 (2016)
  • Svane, Anne Marie
  • Valuations in digital geometry
  • to appear in: Tensor Valuations and their Applications in Stochastic Geometry and Imaging (edited by Markus Kiderlen and Eva B. Vedel Jensen), Lecture Notes in Mathematics (2016)

2015

  • Evgeny Spodarev, Peter Straka and Steffen Winter
  • Estimation of fractal dimension and fractal curvatures from digital images
  • Chaos Solitons Fractals 75, 134–152 (2015)
  • Svane, Anne Marie
  • Local digital algorithms for estimating the integrated mean curvature of r-regular sets
  • Discrete Comput. Geom. 54, 316–338 (2015)
  • Svane, Anne Marie
  • Estimation of Minkowski tensors from digital grey-scale images
  • Image Anal. Stereol. 34, 51–61 (2015)
  • Svane, Anne Marie
  • Asymptotic variance of grey-scale surface area estimators
  • Adv. Appl. Math. 62, 41–73 (2015)
  • Ziegel, Johanna F., Nyengaard, Jens R. and Jensen, Eva B. Vedel
  • Estimating particle shape and orientation using volume tensors
  • Scand. J. Stat. 42, 813–831 (2015)

2014

  • Daniel Hug, Günter Last, Zbynek Pawlas, and Wolfgang Weil
  • Statistics for Poisson models of overlapping spheres
  • Adv. in Appl. Probab. 46, 937–962 (2014)
  • Estate Khmaladze and Wolfgang Weil
  • Differentation of sets – the general case
  • J. Math. Anal. Appl. 413, 291–310 (2014)
  • Svane, Anne Marie
  • Estimation of intrinsic volumes from digital grey-scale images
  • J. Math. Imaging Vision 49, 352–376 (2014)
  • Svane, Anne Marie
  • On multigrid convergence of local algorithms for intrinsic volumes
  • J. Math. Imaging Vision 49, 148–172 (2014)
  • Svane, Anne Marie
  • Estimation of Minkowski tensors from digital grey-scale images
  • Preprint (2014)
  • Svane, Anne Marie
  • Asymptotic variance of grey-scale surface area estimators
  • Preprint (2014)

2013

  • Jérémy Auneau-Cognacq, Johanna Ziegel, and Eva B. Vedel Jensen
  • Rotational integral geometry of tensor valuations
  • Adv. in Appl. Math. 50, 429–444 (2013)
  • Kristjana Ý. Jónsdóttir and Eva B. Vedel Jensen
  • Lévy based error prediction in circular systematic sampling
  • Image Anal. Stereol. 32, 117–125 (2013)
  • Kristjana Y. Jónsdóttir, Anders Rønn-Nielsen, Kim Mouridsen, and Eva B. Vedel Jensen
  • Lévy based modelling in brain imaging
  • Scand. J. Stat. 40, 511–529 (2013)
  • Jürgen Kampf and Markus Kiderlen
  • Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
  • Doc. Math. 18, 275–295 (2013)
  • Ólöf Thórisdóttir and Markus Kiderlen
  • Wicksell's problem in local stereology
  • Adv. in Appl. Probab. 45 (2013)
  • Ólöf Thórisdóttir, Ali Rafati, and Markus Kiderlen
  • Estimating the surface area of non-convex particles from central planar sections
  • Preprint (2013)

2012

  • Jérémy Auneau-Cognacq, Jan Rataj, and Eva B. Vedel Jensen
  • Closed form of the rotational Crofton formula
  • Math. Nachr. 285, 164–180 (2012)