Currents and K-functions for Fiber Point Processes

TY - GEN

T1 - Currents and K-functions for Fiber Point Processes

AU - Hansen, Pernille E. H.

AU - Waagepetersen, Rasmus

AU - Svane, Anne Marie

AU - Sporring, Jon

AU - Stephensen, Hans J. T.

AU - Hasselholt, Stine

AU - Sommer, Stefan

PY - 2021/7

Y1 - 2021/7

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 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.

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 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.

KW - Fibers

KW - K-function

KW - Myelin sheaths

KW - Point processes

KW - Shape analysis

UR - http://www.scopus.com/inward/record.url?scp=85112569235&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-80209-7_15

DO - 10.1007/978-3-030-80209-7_15

M3 - Conference article

SN - 0302-9743

VL - 12829

SP - 127

EP - 134

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - Geometric Science of Information

Y2 - 21 July 2021 through 23 July 2021

ER -