Automatic sorting of point pattern sets using Minkowski Functionals

TL;DR

This paper presents a numerical method that uses Minkowski functionals and FPCA to automatically classify point pattern sets into homogeneous groups, aiding the analysis of complex spatial patterns in various scientific fields.

Contribution

The authors introduce a novel procedure combining Minkowski functionals and FPCA for sorting point pattern sets, effectively distinguishing patterns from different spatial processes.

Findings

Successfully sorts pattern sets from similar processes

Distinguishes patterns with identical second-order characteristics

Applicable to biological spatial pattern analysis

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 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.