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Rotational integral geometry and local stereology - with a view to image analysis

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Standard

Rotational integral geometry and local stereology - with a view to image analysis. / Jensen, Eva B Vedel; Rasmusson, Allan.

Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. red. / Volker Schmidt. Springer Publishing Company, 2014. s. 233-255 (Lecture Notes in Mathematics, Bind 2120).

Publikation: Bidrag til bog/antologi/rapport/proceedingBidrag til bog/antologiForskningpeer review

Harvard

Jensen, EBV & Rasmusson, A 2014, Rotational integral geometry and local stereology - with a view to image analysis. i V Schmidt (red.), Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. Springer Publishing Company, Lecture Notes in Mathematics, bind 2120, s. 233-255. https://doi.org/10.1007/978-3-319-10064-7_8

APA

Jensen, E. B. V., & Rasmusson, A. (2014). Rotational integral geometry and local stereology - with a view to image analysis. I V. Schmidt (red.), Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms (s. 233-255). Springer Publishing Company. Lecture Notes in Mathematics Bind 2120 https://doi.org/10.1007/978-3-319-10064-7_8

CBE

Jensen EBV, Rasmusson A. 2014. Rotational integral geometry and local stereology - with a view to image analysis. Schmidt V, red. I Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. Springer Publishing Company. s. 233-255. (Lecture Notes in Mathematics, Bind 2120). https://doi.org/10.1007/978-3-319-10064-7_8

MLA

Jensen, Eva B Vedel og Allan Rasmusson "Rotational integral geometry and local stereology - with a view to image analysis". Schmidt, Volker (redaktører). Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. Springer Publishing Company. (Lecture Notes in Mathematics, Bind 2120). 2014, 233-255. https://doi.org/10.1007/978-3-319-10064-7_8

Vancouver

Jensen EBV, Rasmusson A. Rotational integral geometry and local stereology - with a view to image analysis. I Schmidt V, red., Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. Springer Publishing Company. 2014. s. 233-255. (Lecture Notes in Mathematics, Bind 2120). https://doi.org/10.1007/978-3-319-10064-7_8

Author

Jensen, Eva B Vedel ; Rasmusson, Allan. / Rotational integral geometry and local stereology - with a view to image analysis. Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms. red. / Volker Schmidt. Springer Publishing Company, 2014. s. 233-255 (Lecture Notes in Mathematics, Bind 2120).

Bibtex

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title = "Rotational integral geometry and local stereology - with a view to image analysis",
abstract = "This chapter contains an introduction to rotational integral geometry that is the key tool in local stereological procedures for estimating quantitative properties of spatial structures. In rotational integral geometry, focus is on integrals of geometric functionals with respect to rotation invariant measures. Rotational integrals of intrinsic volumes are studied. The opposite problem of expressing intrinsic volumes as rotational integrals is also considered. It is shown how to express intrinsic volumes as integrals with respect to geometric functionals defined on lower dimensional linear subspaces. Rotational integral geometry of Minkowski tensors is shortly discussed as well as a principal rotational formula. These tools are then applied in local stereology leading to unbiased stereological estimators of mean intrinsic volumes for isotropic random sets. At the end of the chapter, emphasis is put on how these procedures can be implemented when automatic image analysis is available. Computational procedures play an increasingly important role in the stereological analysis of spatial structures and a new sub-discipline, computational stereology, is emerging.",
author = "Jensen, {Eva B Vedel} and Allan Rasmusson",
year = "2014",
doi = "10.1007/978-3-319-10064-7_8",
language = "English",
isbn = "978-3-319-10063-0",
series = "Lecture Notes in Mathematics",
publisher = "Springer Publishing Company",
pages = "233--255",
editor = "Volker Schmidt",
booktitle = "Stochastic Geometry, Spatial Statistics and Random Fields",

}

RIS

TY - CHAP

T1 - Rotational integral geometry and local stereology - with a view to image analysis

AU - Jensen, Eva B Vedel

AU - Rasmusson, Allan

PY - 2014

Y1 - 2014

N2 - This chapter contains an introduction to rotational integral geometry that is the key tool in local stereological procedures for estimating quantitative properties of spatial structures. In rotational integral geometry, focus is on integrals of geometric functionals with respect to rotation invariant measures. Rotational integrals of intrinsic volumes are studied. The opposite problem of expressing intrinsic volumes as rotational integrals is also considered. It is shown how to express intrinsic volumes as integrals with respect to geometric functionals defined on lower dimensional linear subspaces. Rotational integral geometry of Minkowski tensors is shortly discussed as well as a principal rotational formula. These tools are then applied in local stereology leading to unbiased stereological estimators of mean intrinsic volumes for isotropic random sets. At the end of the chapter, emphasis is put on how these procedures can be implemented when automatic image analysis is available. Computational procedures play an increasingly important role in the stereological analysis of spatial structures and a new sub-discipline, computational stereology, is emerging.

AB - This chapter contains an introduction to rotational integral geometry that is the key tool in local stereological procedures for estimating quantitative properties of spatial structures. In rotational integral geometry, focus is on integrals of geometric functionals with respect to rotation invariant measures. Rotational integrals of intrinsic volumes are studied. The opposite problem of expressing intrinsic volumes as rotational integrals is also considered. It is shown how to express intrinsic volumes as integrals with respect to geometric functionals defined on lower dimensional linear subspaces. Rotational integral geometry of Minkowski tensors is shortly discussed as well as a principal rotational formula. These tools are then applied in local stereology leading to unbiased stereological estimators of mean intrinsic volumes for isotropic random sets. At the end of the chapter, emphasis is put on how these procedures can be implemented when automatic image analysis is available. Computational procedures play an increasingly important role in the stereological analysis of spatial structures and a new sub-discipline, computational stereology, is emerging.

U2 - 10.1007/978-3-319-10064-7_8

DO - 10.1007/978-3-319-10064-7_8

M3 - Book chapter

AN - SCOPUS:84921665819

SN - 978-3-319-10063-0

T3 - Lecture Notes in Mathematics

SP - 233

EP - 255

BT - Stochastic Geometry, Spatial Statistics and Random Fields

A2 - Schmidt, Volker

PB - Springer Publishing Company

ER -