Contour Models for Boundaries Enclosing Star-Shaped and Approximately Star-Shaped Polygons

TL;DR

This paper introduces the Gaussian Star-shaped Contour Model (GSCM) for modeling boundary contours of star-shaped and approximately star-shaped polygons, with applications demonstrated on Arctic sea ice data.

Contribution

The paper presents the GSCM, a novel statistical model for sequences of spatial points forming contours of star-shaped regions, including metrics for deviation assessment.

Findings

GSCM effectively models star-shaped contours in simulations.

Metrics quantify how much a polygon deviates from star-shaped.

Application to Arctic sea ice data demonstrates practical utility.

Abstract

Boundaries on spatial fields divide regions with particular features from surrounding background areas. These boundaries are often described with contour lines. To measure and record these boundaries, contours are often represented as ordered sequences of spatial points that connect to form a line. Methods to identify boundary lines from interpolated spatial fields are well-established. Less attention has been paid to how to model sequences of connected spatial points. For data of the latter form, we introduce the Gaussian Star-shaped Contour Model (GSCM). GSMCs generate sequences of spatial points via generating sets of distances in various directions from a fixed starting point. The GSCM is designed for modeling contours that enclose regions that are star-shaped polygons or approximately star-shaped polygons. Metrics are introduced to assess the extent to which a polygon deviates from star-shaped. Simulation studies illustrate the performance of the GSCM in various scenarios and an analysis of Arctic sea ice edge contour data highlights how GSCMs can be applied to observational data.