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

TY - GEN

T1 - Generalizations of Ripley’s K-function with Application to Space Curves

AU - Sporring, Jon

AU - Waagepetersen, Rasmus Plenge

AU - Sommer, Stefan Horst

PY - 2019/6

Y1 - 2019/6

N2 - 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.

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.

UR - https://arxiv.org/abs/1812.06870

U2 - 10.1007/978-3-030-20351-1_57

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

M3 - Article in proceedings

SN - 978-3-030-20350-4

T3 - Lecture Notes in Computer Science

SP - 731

EP - 742

BT - Information Processing in Medical Imaging - 26th International Conference, IPMI 2019, Hong Kong, China, 2019, Proceedings

PB - Springer

T2 - 26th International Conference on Information Processing in Medical Imaging (IPMI)

Y2 - 2 June 2019 through 7 June 2019

ER -