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Currents and K-functions for Fiber Point Processes

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Geometric Science of Information (GSI 2021)


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.

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Zhiheng Xu and Yaqing Wang from Institute of Genetics and Developmental Biology, Chinese Academy of Sciences are thanked for providing the mouse tissue used for generation of the dataset. The work was supported by the Novo Nordisk Foundation grant NNF18OC0052000.

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Correspondence to Pernille E. H. Hansen .

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Hansen, P.E.H. et al. (2021). Currents and K-functions for Fiber Point Processes. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham.

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  • Print ISBN: 978-3-030-80208-0

  • Online ISBN: 978-3-030-80209-7

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