Generalizations of Ripley’s K-function with Application to Space Curves

Jon Sporring; Rasmus Plenge Waagepetersen; Stefan Horst Sommer

doi:10.1007/978-3-030-20351-1_57

Generalizations of Ripley’s K-function with Application to Space Curves

Jon Sporring, Rasmus Plenge Waagepetersen, Stefan Horst Sommer

1 Citation (Scopus)

Abstract

The intensity function and Ripley’s K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley’s K-function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracks. In this paper, we take a computational perspective and construct new and very general variants of Ripley’s K-function for curves pieces, surface patches etc. We discuss the method from [3] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.

Original language	English
Title of host publication	Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings : 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings
Publisher	Springer
Publication date	Jun 2019
Pages	731-742
ISBN (Print)	978-3-030-20350-4
ISBN (Electronic)	978-3-030-20351-1
DOIs	https://doi.org/10.1007/978-3-030-20351-1_57
Publication status	Published - Jun 2019
Event	26th International Conference on Information Processing in Medical Imaging (IPMI) - Hong Kong, China Duration: 2 Jun 2019 → 7 Jun 2019

Conference

Conference	26th International Conference on Information Processing in Medical Imaging (IPMI)
Country/Territory	China
City	Hong Kong
Period	02/06/2019 → 07/06/2019

Series	Lecture Notes in Computer Science
Volume	11492
ISSN	0302-9743

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10.1007/978-3-030-20351-1_57

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Sporring, J., Waagepetersen, R. P., & Sommer, S. H. (2019). Generalizations of Ripley’s K-function with Application to Space Curves. In Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings (pp. 731-742). Springer. Lecture Notes in Computer Science Vol. 11492 https://doi.org/10.1007/978-3-030-20351-1_57

Generalizations of Ripley’s K-function with Application to Space Curves. / Sporring, Jon; Waagepetersen, Rasmus Plenge; Sommer, Stefan Horst.

Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings. Springer, 2019. p. 731-742 (Lecture Notes in Computer Science, Vol. 11492).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Sporring, J, Waagepetersen, RP & Sommer, SH 2019, Generalizations of Ripley’s K-function with Application to Space Curves. in Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings. Springer, Lecture Notes in Computer Science, vol. 11492, pp. 731-742, 26th International Conference on Information Processing in Medical Imaging (IPMI), Hong Kong, China, 02/06/2019. https://doi.org/10.1007/978-3-030-20351-1_57

Sporring J, Waagepetersen RP, Sommer SH. Generalizations of Ripley’s K-function with Application to Space Curves. In Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings. Springer. 2019. p. 731-742. (Lecture Notes in Computer Science, Vol. 11492). doi: 10.1007/978-3-030-20351-1_57

Sporring, Jon ; Waagepetersen, Rasmus Plenge ; Sommer, Stefan Horst. / Generalizations of Ripley’s K-function with Application to Space Curves. Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings: 26th International Conference, IPMI 2019, Hong Kong, China, June 2–7, 2019, Proceedings. Springer, 2019. pp. 731-742 (Lecture Notes in Computer Science, Vol. 11492).

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abstract = "The intensity function and Ripley{\textquoteright}s K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley{\textquoteright}s K-function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracks. In this paper, we take a computational perspective and construct new and very general variants of Ripley{\textquoteright}s K-function for curves pieces, surface patches etc. We discuss the method from [3] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.",

author = "Jon Sporring and Waagepetersen, {Rasmus Plenge} and Sommer, {Stefan Horst}",

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AB - The intensity function and Ripley’s K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley’s K-function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracks. In this paper, we take a computational perspective and construct new and very general variants of Ripley’s K-function for curves pieces, surface patches etc. We discuss the method from [3] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.

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Generalizations of Ripley’s K-function with Application to Space Curves

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