This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on ℝ2 based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package—from model assumptions to algorithmic recovery of the deformation—for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.
"Estimating deformations of isotropic Gaussian random fields on the plane." Ann. Statist. 36 (2) 719 - 741, April 2008. https://doi.org/10.1214/009053607000000893