Currents and K-functions for Fiber Point Processes

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 fiber-v...

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Bibliographic Details
Published inGeometric Science of Information pp. 127 - 134
Main Authors Hansen, Pernille E. H., Waagepetersen, Rasmus, Svane, Anne Marie, Sporring, Jon, Stephensen, Hans J. T., Hasselholt, Stine, Sommer, Stefan
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Fibers
function
Myelin sheaths
Point processes
Shape analysis
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Summary: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 fiber-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 complete spatial randomness of point processes to fiber data. The paper provides a theoretical account of the statistical foundation of the K-function, and we apply the K-function on simulated data and a data set of myelin sheaths. This includes a fiber data set consisting of myelin sheaths configurations at different debts.
ISBN:9783030802080
3030802086
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-80209-7_15