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

2018

  • Bruno Ebner AND Norbert Henze AND Michael A. Klatt AND Klaus Mecke
  • Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images
  • Electronic Journal of Statistics 12(2), 2873–2904 (2018)
  • Khmaladze, Estate and Weil, Wolfgang
  • Fold-up derivatives of set-valued functions and the change-set problem: A Survey
  • Ann. Inst. Statist. Math. 70(1), 1–38 (2018)

2017

  • Hörrmann, Julia and Svane, Anne Marie
  • Local Digital Algorithms Applied to Boolean Models
  • Scand. J. Stat. 44(2), 369–395 (2017)
  • Hug, Daniel and Kiderlen, Markus and Svane, Anne Marie
  • Voronoi-Based Estimation of Minkowski Tensors from Finite Point Samples
  • Discrete Comput. Geom. 57(3), 545–570 (2017)
  • Klatt, Michael A. and Schröder-Turk, Gerd E. and Mecke, Klaus
  • Mean-intercept anisotropy analysis of porous media. I. Analytic formulae for anisotropic Boolean models
  • Med. Phys. 44(7), 3650–3662 (2017)
  • Klatt, Michael A. and Schröder-Turk, Gerd E. and Mecke, Klaus
  • Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative
  • Med. Phys. 44(7), 3663–3675 (2017)
  • Astrid Kousholt and Johanna F. Ziegel and Markus Kiderlen and Eva B. Vedel Jensen
  • Stereological estimation of mean particle volume tensors in $\mathbb R^3$ from vertical sections.
  • pages 423–434 in: Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014, Cham: Springer, 2017
  • Svane, Anne Marie
  • Valuations in image analysis
  • pages 435–454 in: Lecture Notes in Math., Vol. 2177: Tensor valuations and their applications in stochastic geometry and imaging, Springer, Cham, 2017
  • Anne Marie Svane
  • Valuations in image analysis.
  • pages 435–454 in: Tensor valuations and their applications in stochastic geometry and imaging. Based on the presentations at the workshop, Sandbjerg Manor, Denmark, September 21–26, 2014, Cham: Springer, 2017
  • Astrid Kousholt
  • Reconstruction of $n$-dimensional convex bodies from surface tensors.
  • Adv. Appl. Math. 83, 115–144 (2017)
  • Julia Hörrmann and Anne Marie Svane
  • Local digital algorithms applied to Boolean models.
  • Scand. J. Stat. 44(2), 369–395 (2017)
  • Prokešová, Michaela and Dvorák, Jiri and Jensen, Eva B. Vedel
  • Two-step estimation procedures for inhomogeneous shot-noise Cox processes
  • Ann. Inst. Statist. Math. 69(3), 513–542 (2017)

2016

  • Sabrina T. Christensen and Markus Kiderlen
  • Comparison of two global digital algorithms for Minkowski tensor estimation
  • CSGB Research Report 2016-10 (2016)
  • Astrid Kousholt and Markus Kiderlen
  • Reconstruction of convex bodies from surface tensors
  • Adv. Appl. Math. 76, 1–33 (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)
  • Hahn, Ute and Vedel Jensen, Eva B.
  • Hidden second-order stationary spatial point processes
  • Scand. J. Stat. 43(2), 455–475 (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)
  • Anne Marie Svane
  • Estimation of Minkowski tensors from digital grey-scale images.
  • Image Anal. Stereol. 34(1), 51–61 (2015)
  • Anne Marie Svane
  • Asymptotic variance of grey-scale surface area estimators.
  • Adv. Appl. Math. 62, 41–73 (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)
  • Ólöf Thórisdóttir, Ali Rafati, and Markus Kiderlen
  • Estimating the surface area of non-convex particles from central planar sections
  • Journal of Microscopy 255(1), 49-64 (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)
  • Prokešová, Michaela and Jensen, Eva B. Vedel
  • Asymptotic Palm likelihood theory for stationary point processes
  • Ann. Inst. Statist. Math. 65(2), 387–412 (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)