Temporal Interpolation of Spatially Dynamic Polygons

In this study we compare two methods of interpolating simple metrics from polygons that change over time. Conventional methodology involves computing values of the metrics at points in time where the polygon is observed, and interpolating between these observed values to estimate values at other points in time. An alternative method applies interpolation techniques to the locations of vertices composing polygons are interpolated between observations and metrics are computed from the interpolated polygon shapes. We conducted a Monte Carlo simulation of both techniques using simulated polygons composed of varying numbers of vertices, which were allowed to move randomly over varying numbers of discrete time periods. We observed differences in the success of the two methods when applied to three metrics: Area, Perimeter, and Area/Perimeter Ratio. We found the two techniques to perform differently depending upon the metric being interpolated. Full results are presented and possible reasons why the techniques succeeded or failed under various conditions are discussed.