On the use of geodesic distances for spatial interpolation

Spatially distributed estimates of ecological variables are generally required for use in geographic information systems (GIS) and models when dealing with many environmental phenomena [2]. In particular, the quality of GIS products depends often on local properties that vary in space. In this context, increased interest has been demonstrated to geostatistics, or spatial statistics, as an analytical tool in the eld of environmental sciences. Indeed, the problem of estimating local values of variables at unsampled sites within an area covered by sample points, using the data from those points, is at the core of geostatistics [2]. The most common geostatistic tools involve kriging for data interpolation and mapping. Most methods to date have focused on the estimation, with the variogram, of the spatial autocorrelation structure used in kriging. A topic less covered concerns the use of di erent (non-Euclidean) measures for determining related inter-point distances. Some recent references include [1], [6] and [8]. This paper will investigate the use of the so-called geodesic distances for geostatistical related applications. Namely, using techniques derived from mathematical morphology in the eld of image processing, new non-Euclidean distances are introduced while the de nition of those proposed in previous studies are generalised. Geodesic distances enable both for characterizing isotropic spatial dependence and for taking account of natural barriers in heterogeneous domains. Algorithms described in [9, 10] are employed for computing the geodesic distances; the publicly available source code of [5] is employed to incorporate these non-euclidean distances into geostatistical algorithms.