Currents and K-functions for Fiber Point Processes

Pernille E.H. Hansen; Rasmus Waagepetersen; Anne Marie Svane; Jon Sporring; Hans J.T. Stephensen; Stine Hasselholt; Stefan Sommer

doi:10.1007/978-3-030-80209-7_15

Currents and K-functions for Fiber Point Processes

Pernille E.H. Hansen^*, Rasmus Waagepetersen, Anne Marie Svane, Jon Sporring, Hans J.T. Stephensen, Stine Hasselholt, Stefan Sommer

^*Corresponding author for this work

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

Abstract

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.

Original language	English
Title of host publication	Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings
Editors	Frank Nielsen, Frédéric Barbaresco
Number of pages	8
Publisher	Springer Science+Business Media
Publication date	2021
Pages	127-134
ISBN (Print)	9783030802080
DOIs	https://doi.org/10.1007/978-3-030-80209-7_15
Publication status	Published - 2021
Event	5th International Conference on Geometric Science of Information, GSI 2021 - Paris, France Duration: 21 Jul 2021 → 23 Jul 2021

Conference

Conference	5th International Conference on Geometric Science of Information, GSI 2021
Country/Territory	France
City	Paris
Period	21/07/2021 → 23/07/2021

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12829 LNCS
ISSN	0302-9743

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Keywords

Fibers
K-function
Myelin sheaths
Point processes
Shape analysis

Access to Document

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

https://arxiv.org/pdf/2102.05329.pdf

AUB Link

Search for the material in Aalborg University Library's search engine

Cite this

Hansen, P. E. H., Waagepetersen, R., Svane, A. M., Sporring, J., Stephensen, H. J. T., Hasselholt, S., & Sommer, S. (2021). Currents and K-functions for Fiber Point Processes. In F. Nielsen, & F. Barbaresco (Eds.), Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings (pp. 127-134). Springer Science+Business Media. https://doi.org/10.1007/978-3-030-80209-7_15

Hansen, Pernille E.H. ; Waagepetersen, Rasmus ; Svane, Anne Marie et al. / Currents and K-functions for Fiber Point Processes. Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. editor / Frank Nielsen ; Frédéric Barbaresco. Springer Science+Business Media, 2021. pp. 127-134 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12829 LNCS).

@inproceedings{9f62eada863e4d9988ff0f98d8da10ea,

title = "Currents and K-functions for Fiber Point Processes",

abstract = "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{\textquoteright}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.",

keywords = "Fibers, K-function, Myelin sheaths, Point processes, Shape analysis",

author = "Hansen, {Pernille E.H.} and Rasmus Waagepetersen and Svane, {Anne Marie} and Jon Sporring and Stephensen, {Hans J.T.} and Stine Hasselholt and Stefan Sommer",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 5th International Conference on Geometric Science of Information, GSI 2021 ; Conference date: 21-07-2021 Through 23-07-2021",

year = "2021",

doi = "10.1007/978-3-030-80209-7_15",

language = "English",

isbn = "9783030802080",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science+Business Media",

pages = "127--134",

editor = "Frank Nielsen and Fr{\'e}d{\'e}ric Barbaresco",

booktitle = "Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings",

address = "United States",

}

Hansen, PEH, Waagepetersen, R , Svane, AM, Sporring, J, Stephensen, HJT, Hasselholt, S & Sommer, S 2021, Currents and K-functions for Fiber Point Processes. in F Nielsen & F Barbaresco (eds), Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. Springer Science+Business Media, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12829 LNCS, pp. 127-134, 5th International Conference on Geometric Science of Information, GSI 2021, Paris, France, 21/07/2021. https://doi.org/10.1007/978-3-030-80209-7_15

Currents and K-functions for Fiber Point Processes. / Hansen, Pernille E.H.; Waagepetersen, Rasmus ; Svane, Anne Marie et al.
Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. ed. / Frank Nielsen; Frédéric Barbaresco. Springer Science+Business Media, 2021. p. 127-134 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12829 LNCS).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

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

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 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 - Article in proceeding

AN - SCOPUS:85112569235

SN - 9783030802080

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 127

EP - 134

BT - Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings

A2 - Nielsen, Frank

A2 - Barbaresco, Frédéric

PB - Springer Science+Business Media

T2 - 5th International Conference on Geometric Science of Information, GSI 2021

Y2 - 21 July 2021 through 23 July 2021

ER -

Hansen PEH, Waagepetersen R , Svane AM, Sporring J, Stephensen HJT, Hasselholt S et al. Currents and K-functions for Fiber Point Processes. In Nielsen F, Barbaresco F, editors, Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. Springer Science+Business Media. 2021. p. 127-134. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 12829 LNCS). doi: 10.1007/978-3-030-80209-7_15