  Analysis of images of sets of fibers such as myelin sheaths or skeletal
muscles must account for both the spatial distribution of fibers and
differences in fiber shape. This necessitates a combination of point process
and shape analysis methodology. In this paper, we develop a K-function for
shape-valued point processes by embedding shapes as currents, thus equipping
the point process domain with metric structure inherited from a reproducing
kernel Hilbert space. We extend Ripley's K-function which measures deviations
from spatial homogeneity of point processes to fiber data. The paper provides a
theoretical account of the statistical foundation of the K-function and its
extension to fiber data, and we test the developed K-function on simulated as
well as real data sets. This includes a fiber data set consisting of myelin
sheaths, visualizing the spatial and fiber shape behavior of myelin
configurations at different debts.
