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
APA
Vancouver
Author
Bibtex
}
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