Abstract
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.
Highlights
Statistical analysis of images can be grouped into two main branches (Molchanov, 1997): (a) describing/classifying an observed scene or (b) considering the scene to be generated by a random process and inferring properties of this process
We examine parallels between non-parametric random closed set (RACS) summary functions and landscape pattern indices (LPI)
The percentage of core area is an estimator of the core probability which is related to the spherical contact distribution for a RACS
Summary
Statistical analysis of images can be grouped into two main branches (Molchanov, 1997): (a) describing/classifying an observed scene or (b) considering the scene to be generated by a random process and inferring properties of this process. We are concerned mostly with the latter, and especially those processes observed in remotely sensed maps of categorical variables Such analysis occurs when comparing different regions, comparing the same region at different times, gaining understanding of random processes (e.g. spatial dependence), or model fitting. A random closed set (RACS) is a generic framework for modelling randomness in processes that generate spatial patterns of patches It encompasses common models in remote sensing, such as those derived from Markov random fields and Gaussian random fields, and a wide range of other models (e.g. germ-grain models, birth-growth models, fibre processes, and tessellations). Other RACS models can describe complex geometrical shapes and infinite-order characteristics (Descombes, 2012) These models reveal new methods for describing the geometry of random scenes such as contact distributions (Baddeley and Gill, 1994) and tangent point analysis (Barbour and Schmidt, 2001).
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