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.Comment: 9 pages & 8 figure