2 research outputs found
Automatic sorting of point pattern sets using Minkowski Functionals
Point pattern sets arise in many different areas of physical, biological, and
applied research, representing many random realizations of underlying pattern
formation mechanisms. These pattern sets can be heterogeneous with respect to
underlying spatial processes, which may not be visually distinguishable. This
heterogeneity can be elucidated by looking at statistical measures of the
patterns sets and using these measures to divide the pattern set into distinct
groups representing like spatial processes. We introduce here a numerical
procedure for sorting point pattern sets into spatially homogeneous groups
using Functional Principal Component Analysis (FPCA) applied to the
approximated Minkowski functionals of each pattern. We demonstrate that this
procedure correctly sorts pattern sets into similar groups both when the
patterns are drawn from similar processes and when the 2nd-order
characteristics of the pattern are identical. We highlight this routine for
distinguishing the molecular patterning of fluorescently labeled cell membrane
proteins, a subject of much interest in studies investigating complex spatial
signaling patterns involved in the human immune response.Comment: 11 pages, 6 figures, submitted to Physical Review E (05 March 2013