Currents and K-functions for Fiber Point Processes

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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 spatial homogeneity 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.
Original languageEnglish
Title of host publicationGeometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
EditorsFrank Nielsen, Frédéric Barbaresco
Publication date2021
ISBN (Print)978-3-030-80208-0
ISBN (Electronic)978-3-030-80209-7
Publication statusPublished - 2021
Event5th conference on Geometric Science of Information - GSI2021 - Paris, France
Duration: 21 Jul 202123 Jul 2021


Conference5th conference on Geometric Science of Information - GSI2021
SeriesLecture Notes in Computer Science
Volume 12829


ID: 273012378