MODELS OF COVARIANCE FUNCTIONS OF GAUSSIAN RANDOM FIELDS ESCAPING FROM ISOTROPY, STATIONARITY AND NON NEGATIVITY

• Main Authors: Pablo Gregori, Emilio Porcu, Jorge Mateu
• Format: Article
• Language: English
• Published: Slovenian Society for Stereology and Quantitative Image Analysis 2014-03-01
• Series: Image Analysis and Stereology
• Subjects: anisotropy; covariance model; Gaussian random field; non negativity; non stationarity
• Online Access: http://www.ias-iss.org/ojs/IAS/article/view/1077

This paper represents a survey of recent advances in modeling of space or space-time Gaussian Random Fields (GRF), tools of Geostatistics at hand for the understanding of special cases of noise in image analysis. They can be used when stationarity or isotropy are unrealistic assumptions, or even when negative covariance between some couples of locations are evident. We show some strategies in order to escape from these restrictions, on the basis of rich classes of well known stationary or isotropic non negative covariance models, and through suitable operations, like linear combinations, generalized means, or with particular Fourier transforms.