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

arXiv: https://arxiv.org/abs/1812.06870 · HTML: https://mlsanity.com/paper/1812.06870/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning](https://mlsanity.com/paper/2402.09529/) (2024)

## Abstract (arXiv)

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 [Chiu, Stoyan, Kendall, & Mecke 2013] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.