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.
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Acknowledgments
This work was funded by the Villum Foundation through the Center for Stochastic Geometry and Advanced Bioimaging (http://csgb.dk).
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Sporring, J., Waagepetersen, R., Sommer, S. (2019). Generalizations of Ripley’s K-function with Application to Space Curves. In: Chung, A., Gee, J., Yushkevich, P., Bao, S. (eds) Information Processing in Medical Imaging. IPMI 2019. Lecture Notes in Computer Science(), vol 11492. Springer, Cham. https://doi.org/10.1007/978-3-030-20351-1_57
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DOI: https://doi.org/10.1007/978-3-030-20351-1_57
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