Currents and K-functions for Fiber Point Processes

Research output: Book/Report › Report › Research

Standard

Currents and K-functions for Fiber Point Processes. / Hansen, Pernille Emma Hartung; Waagepetersen, Rasmus Plenge; Svane, Anne Marie; Sporring, Jon; Stephensen, Hans Jacob Teglbjærg; Hasselholt, Stine; Sommer, Stefan Horst.

arXiv preprint, 2021. 12 p.

Research output: Book/Report › Report › Research

Harvard

Hansen, PEH, Waagepetersen, RP, Svane, AM, Sporring, J, Stephensen, HJT, Hasselholt, S & Sommer, SH 2021, Currents and K-functions for Fiber Point Processes. arXiv preprint. https://doi.org/10.48550/arXiv.2102.05329

APA

Hansen, P. E. H., Waagepetersen, R. P., Svane, A. M., Sporring, J., Stephensen, H. J. T., Hasselholt, S., & Sommer, S. H. (2021). Currents and K-functions for Fiber Point Processes. arXiv preprint. https://doi.org/10.48550/arXiv.2102.05329

Vancouver

Hansen PEH, Waagepetersen RP, Svane AM, Sporring J, Stephensen HJT, Hasselholt S et al. Currents and K-functions for Fiber Point Processes. arXiv preprint, 2021. 12 p. https://doi.org/10.48550/arXiv.2102.05329

Author

Hansen, Pernille Emma Hartung ; Waagepetersen, Rasmus Plenge ; Svane, Anne Marie ; Sporring, Jon ; Stephensen, Hans Jacob Teglbjærg ; Hasselholt, Stine ; Sommer, Stefan Horst. / Currents and K-functions for Fiber Point Processes. arXiv preprint, 2021. 12 p.

Bibtex

@book{bd64f23f05084331835a11268a9922bb,
title = "Currents and K-functions for Fiber Point Processes",
abstract = "Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis methodology. In this paper, we develop a K-function for shape-valued point processes by embedding shapes as currents, thus equipping the point process domain with metric structure inherited from a reproducing kernel Hilbert space. We extend Ripley's K-function which measures deviations from spatial homogeneity of point processes to fiber data. The paper provides a theoretical account of the statistical foundation of the K-function and its extension to fiber data, and we test the developed K-function on simulated as well as real data sets. This includes a fiber data set consisting of myelin sheaths, visualizing the spatial and fiber shape behavior of myelin configurations at different debts.",
author = "Hansen, {Pernille Emma Hartung} and Waagepetersen, {Rasmus Plenge} and Svane, {Anne Marie} and Jon Sporring and Stephensen, {Hans Jacob Teglbj{\ae}rg} and Stine Hasselholt and Sommer, {Stefan Horst}",
year = "2021",
doi = "10.48550/arXiv.2102.05329",
language = "English",
publisher = "arXiv preprint",

}

RIS

TY - RPRT

T1 - Currents and K-functions for Fiber Point Processes

AU - Hansen, Pernille Emma Hartung

AU - Waagepetersen, Rasmus Plenge

AU - Svane, Anne Marie

AU - Sporring, Jon

AU - Stephensen, Hans Jacob Teglbjærg

AU - Hasselholt, Stine

AU - Sommer, Stefan Horst

PY - 2021

Y1 - 2021

N2 - Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis methodology. In this paper, we develop a K-function for shape-valued point processes by embedding shapes as currents, thus equipping the point process domain with metric structure inherited from a reproducing kernel Hilbert space. We extend Ripley's K-function which measures deviations from spatial homogeneity of point processes to fiber data. The paper provides a theoretical account of the statistical foundation of the K-function and its extension to fiber data, and we test the developed K-function on simulated as well as real data sets. This includes a fiber data set consisting of myelin sheaths, visualizing the spatial and fiber shape behavior of myelin configurations at different debts.

AB - Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis methodology. In this paper, we develop a K-function for shape-valued point processes by embedding shapes as currents, thus equipping the point process domain with metric structure inherited from a reproducing kernel Hilbert space. We extend Ripley's K-function which measures deviations from spatial homogeneity of point processes to fiber data. The paper provides a theoretical account of the statistical foundation of the K-function and its extension to fiber data, and we test the developed K-function on simulated as well as real data sets. This includes a fiber data set consisting of myelin sheaths, visualizing the spatial and fiber shape behavior of myelin configurations at different debts.

U2 - 10.48550/arXiv.2102.05329

DO - 10.48550/arXiv.2102.05329

M3 - Report

BT - Currents and K-functions for Fiber Point Processes

PB - arXiv preprint

ER -

ID: 324971648