# Publications

### BOOK

G. Christakos and D.T. Hristopulos, Spatiotemporal Environmental Health Modeling, Kluwer Academic Publishers, Boston (1998).

### SELECTED RECENT PUBLICATIONS

I. Spiliopoulos, D. T. Hristopulos, E. Petrakis and A. Chorti (2011).

A Multigrid Method for the Estimation of Geometric Anisotropy in Environmental Data from Sensor Networks, Computers and Geosciences, doi

Dubois, G., Cornford, D., Hristopulos, D., Pebesma, E., Pilz, J., (2011).

Introduction to this special issue on geoinformatics for environmental surveillance, Computers and Geosciences, doi

D. T. Hristopulos and M. Zukovic (2011).

Relationships between correlation lengths and integral scales for covariance models with more than two parameters, Stochastic Environmental Research and Risk Assessment,in press, doi

M. Zukovic and D. T. Hristopulos (2009a).

Classification of missing values in spatial data using spin models, Physical Review E, 80(1), 011116 (2009). doi

D. T. Hristopulos and S. N. Elogne (2009b).

Computationally efficient spatial interpolators based on Spartan spatial random fields, IEEE Transactions on Signal Processing, 57(9), 3475-3487.

M. Zukovic and D. T. Hristopulos (2009c).

The method of normalized correlations: a fast parameter estimation method for random processes and isotropic random fields that focuses on short-range dependence, Technometrics, 15(2), 173-185. doi

M. Zukovic and D.T. Hristopulos (2009).

Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data, Journal of Statistical Mechanics: Theory and Experiment, P02023, doi

M. Zukovic and D.T. Hristopulos (2008).

Environmental Time Series Interpolation Based on Spartan Random Processes, Atmospheric Environment, 42(33), 7669-7678.

A. Chorti and D.T. Hristopulos (2008).

Non-parametric Identification of Anisotropic (Elliptic) Correlations in Spatially Distributed Data Sets, IEEE Transactions on Signal Processing, 56(10), 4738-4751.

S. Elogne, D.T. Hristopulos and E. Varouchakis (2008).

An application of Spartan spatial random fields in environmental mapping: focus on automatic mapping capabilities, Stochastic Environmental Research and Risk Assessment, 52(5), 633 - 646.

A. Moustakas and D.T. Hristopulos (2008).

Estimating tree abundance from remotely sensed imagery in semi-arid and arid environments: bringing small trees to the light, Stochastic Environmental Research and Risk Assessment, in press.

M. Zukovic and D.T. Hristopulos (2008).

Spartan random processes in time series modeling , Physica A-Statistical Mechanics And Its Applications, 387(15), 3995-4001. Preprint.

D.T. Hristopulos and M. Demertzi (2008).

A semi-analytical equation for the Young's modulus of isotropic ceramic materials, Journal of the European Ceramic Society, 28(6), 1111-1120.

D.T. Hristopulos and S. Elogne (2007).

Analytic properties and covariance functions for a new class of generalized Gibbs random fields, IEEE Transactions on Information Theory, 53(12), 4667-4679.

A. Moustakas, A. Chorti and D.T. Hristopulos (2007\oint).

Geostatistical analysis of tree size distributions in the Southern Kalahari, obtained from remotely sensed data, Proceedings of SPIE - The International Society for Optical Engineering, Volume 6742, 2007, Article number 67420G.

D.T. Hristopulos, (2006).

Identification of Spatial Anisotropy by means of the Govariance Tensor Identity, In: Automatic Mapping Algorithms for Routine and Emergency Monitoring Data: Spatial Interpolation Comparison 2004, (edited by G. Dubois), Office for Official Publications of the European Communities, Luxembourg, ISBN 92-894-9400-X, pp. 103-124. Online at: http://www.ai-geostats.org/events/sic2004.htm.

D.T. Hristopulos, L. Leonidakis and A. Tsetsekou, (2006).

A Discrete Nonlinear Mass Transfer Equation with Applications in Solid-State Sintering of Ceramic Materials, European Physical Journal B - Condensed Matter Physics, 50(1-2), 83-87. Preprint.

D.T. Hristopulos, (2006).

Spartan Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences, Physica A: Statistical Mechanics and its Applications, 365(1-2), 211-216. Preprint.

D.T. Hristopulos, (2004a).

Anisotropic Spartan Random Field Models for Geostatistical Analysis, Advances in Mineral Resources Management and Environmental Geotechnology, Chania, June 2004, Greece. Pdf preprint.

D.T. Hristopulos, (2004b).

Numerical Simulations of Spartan Gaussian Random Fields for Geostatistical Applications on Lattices and Irregular Supports, Journal of Computational Methods in Sciences and Engineering, in press. Pdf preprint.

D.T. Hristopulos, (2003a).

Renormalization Group Methods in Subsurface Hydrology: Overview and Applications in Hydraulic Conductivity Upscaling, Advances in Water Resources, 26(12), 1279-1308. Pdf preprint.

D.T. Hristopulos, (2003b).

Spartan Gibbs Random Field Models for Geostatistical Applications, SIAM Journal on Scientific Computing, 24(6), 2125-2162. Pdf preprint.

D.T. Hristopulos, (2003c).

Permissibility of Fractal Exponents and Models of Band-Limited Two-Point Functions for fGn and fBm random fields, Stochastic Environmental Research and Risk Assessment, 17(3), 191-216 (2003). Pdf preprint.

D.T. Hristopulos and T. Uesaka, (2002).

A Model of Machine-Direction Tension Variations in Paper Webs with Runnability Applications, Journal of Pulp and Paper Science<, 28(12), 389-394 (2002). Pdf preprint.

D.T. Hristopulos, (2002).

New Anisotropic Covariance Models and Estimation of Anisotropic Parameters Based on the Covariance Tensor Identity, Stochastic Environmental Research and Risk Assessment, 16(1), 43-62. Pdf preprint.

D.T. Hristopulos and G. Christakos, (2001).

Practical Calculation of Non-Gaussian Multivariate Moments in Spatiotemporal BME Analysis, Mathematical Geology, 33(5), 543-568.

D.T. Hristopulos and G. Christakos, (1999).

Renormalization Group Analysis of Permeability Upscaling,Stochastic Environmental Research and Risk Assessment, 13, 1-26.

D.T. Hristopulos and G. Christakos, (1997).

A Variational Calculation of the Effective Fluid Permeability of Heterogeneous Media, Physical Review E, 55(6), 7288-7298.

G. Christakos, D.T. Hristopulos and C.T. Miller, (1995).

Stochastic Diagrammatic Analysis of Groundwater Flow in Heterogeneous Porous Media, Water Resources Research, 31(7), 1687-1703.

## Anisotropy Identification Code

Non-parametric Identification of Anisotropic (Elliptic) Correlations in Spatially Distributed Data Sets, by Arsenia Chorti and Dionissios T. Hristopulos

The relevant paper was published in IEEE Transactions on Signal Processing (October 2008).

Random fields are useful models of spatially variable quantities, such as those occurring in environmental 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 Covariance Hessian Identity (CHI) 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 Matern 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.

Four Matlab .m files are provided for download (Code.)

To use, decompress the zip archive and place the files in a folder that is in the Matlab path. The .m files include comments that can be read using the Matlab help function, e.g., by typing help aniso_cc_grid. In interpreting results keep in mind the symmetries: (R, THETA) --> (1/R, 90 +/- THETA).

rf_gen: This program simulates Gaussian random fields with specified geometric anisotropy. aniso_cc_grid: This program uses finite centered differences to estimate the geometric anisotropy of random fields sampled on a regular grid. aniso_sg_grid: This program uses Savitsky - Golay derivatives to estimate the geometric anisotropy of random fields sampled on a regular grid. aniso_interp_scatter: This program uses interpolation followed by finite centered differences to estimate the geometric anisotropy of random fields sampled on a scattered grid. Scattered samples are generated using rf_gen and then randomly removing a number of points from the grid. The anisotropy estimation code has been extended to the case of clustered data by means of the clustered CHI method. The relevant paper (Spiliopoulos et al. 2011) will be published in Computers and Geosciences. The main idea is to use image processing filters to define clusters based on the variations of the sampling density, to estimate the anisotropy in each cluster, and then --if so desired -- to derive a coarse-grained estimate of the anisotropy for the entire area. The code in R implementing the clustered CHI method can be downloaded as a component of the Intamap packaged from INTAMAP

or it can be obtained by emailing me at: dionisi@mred.tuc.gr