Non-parametric Identification of anisotropic (Elliptic) correlations in spatially distributed data setsNon-parametric Identification of anisotropic (Elliptic) correlations in spatially distributed data sets Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-09-252008enRandom fields are useful models of spatially variable quantities, such as those occurring in en- vironmental processes and medical imaging. The fluctuations obtained in most natural data sets are typically anisotropic. The parameters of anisotropy are often determined from the data by means of empirical methods or the computationally expensive method of maximum likelihood. In this paper we propose a systematic method for the identification of geometric (elliptic) anisotropy parameters of scalar fields. The proposed method is computationally efficient, non-parametric, non-iterative, and it applies to differentiable random fields with normal or lognormal probability density functions. Our approach uses sample based estimates of the random field spatial derivatives that we relate through closed form expressions to the anisotropy parameters. This paper focuses on two spatial dimensions. We investigate the performance of the method on synthetic samples with Gaussian and Mate ́rn correlations, both on regular and irregular lattices. The systematic anisotropy detection provides an important pre-processing stage of the data. Knowledge of the anisotropy parameters, followed by suitable rotation and rescaling transformations restores isotropy thus allowing classical interpolation and signal processing methods to be applied.http://creativecommons.org/licenses/by/4.0/ IEEE Transactions on Signal Processing 56104738-4751 Chorti Arsenia Christopoulos Dionysios Χριστοπουλος Διονυσιος Institute of Electrical and Electronics Engineers Anisotropic magnetoresistance Biomedical imaging Fluctuations Maximum likelihood detection Maximum likelihood estimation Probability density function Lattices Signal restoration Interpolation Signal processing