title: Automatic sorting of point pattern sets using Minkowski functionals.
abstract: 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 distiguishable. This heterogeneity can be elucidated by looking at statistical measures of the patterns sets and using these measures to divide the pattern sets into distinct groups representing like spatial processes. We introduce here a numerical procedure for sorting point pattern sets into spatially homogenous 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 second-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.
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland 20740, USA.
authors.forename: Joshua
authors.initials: J
authors.lastname: Parker
authors.forename: Eilon
authors.initials: E
authors.lastname: Sherman
authors.forename: Matthias
authors.initials: M
authors.lastname: van de Raa
authors.forename: Devaraj
authors.initials: D
authors.lastname: van der Meer
authors.forename: Lawrence E
authors.initials: LE
authors.lastname: Samelson
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Losert
mesh_terms: D001331:Automation; D005110:Extracellular Space / Q000378:metabolism; D006801:Humans; D007109:Immunity; D008962:Models, Theoretical; D025341:Principal Component Analysis; D021381:Protein Transport; D011506:Proteins / Q000378:metabolism; D013269:Stochastic Processes
chemical_list: D011506:Proteins
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 2):066111
references.pmid: 15697438
references.citation: Biophys J. 2012 Apr 4;102(7):1524-33
references.pmid: 22500752
references.citation: Immunity. 2011 Nov 23;35(5):705-20
references.pmid: 22055681
references.citation: Science. 2006 Sep 15;313(5793):1642-5
references.pmid: 16902090
references.citation: Biom J. 2005 Aug;47(4):473-88
references.pmid: 16161805
references.citation: J Microsc. 2003 Nov;212(Pt 2):122-31
references.pmid: 14629561
references.citation: J Exp Med. 1984 Oct 1;160(4):1126-46
references.pmid: 6090574