Spacebender

This paper presents an algorithm that deforms geographical space such that local spatial variation is more regular in the transformed space than in the original space. Geographical-space deformation may be useful in situations where there is an indication that the assumption of stationarity of the variance is unrealistic. In this paper we present an algorithm, Spacebender, a variance equalising algorithm that can be used for generating the non-affine transform between geographic space and the transformed space. This transformed space, which takes care of the non-stationary spatial covariance structure in the geographic space, is the one in which regularly spaced points would be optimal for sampling. This transformed space is a kind of enviro-geographic space as opposed to a simple geographic one. Two examples are given; one is based on a digital elevation model, and the other used a data from a soil gamma radiometric potassium survey.