Statistics for patch observations

In the application of remote sensing it is common to investigate processes that generate patches of material. This is especially true when using categorical land cover or land use maps. Here we view some existing tools, landscape pattern indices (LPI), as non-parametric estimators of random closed sets (RACS). This RACS framework enables LPIs to be studied rigorously. A RACS is any random process that generates a closed set, which encompasses any processes that result in binary (two-class) land cover maps. RACS theory, and methods in the underlying field of stochastic geometry, are particularly well suited to high-resolution remote sensing where objects extend across tens of pixels, and the shapes and orientations of patches are symptomatic of underlying processes. For some LPI this field already contains variance information and border correction techniques. After introducing RACS theory we discuss the core area LPI in detail. It is closely related to the spherical contact distribution leading to conditional variants, a new version of contagion, variance information and multiple border-corrected estimators. We demonstrate some of these findings on high resolution tree canopy data.