Semivariogram calculation optimization for object-oriented image classification

[EN] In this paper we propose and evaluate different mathematical parameters extracted from the experimental semivariogram for land use/land cover classification using high-resolution images and cadastral mapping limits for the definition of the objects of analysis. First, we describe the process of calculating the semivariogram from the gray level values in an image object. In order to optimize the computation time we present two pixel selection techniques that preserve the original shape of the semivariogram. Several parameters are then extracted from the semivariogram. Finally, we use various statistical techniques to select the most discriminant parameters. Last section shows the results obtained using aerial digital images of an agricultural area on the Mediterranean coast of Spain. The study of the practical application presented in this paper facilitates the understanding of the relationship between the behaviour of the experimental semivariogram and the variability of the intensity values in a digital image. In order to follow the development of this work, the reader should know some basis of classification methods and digital image processing techniques.[ES] En este trabajo se proponen y evalúan diferentes parámetros matemáticos extraídos del semivariograma experimental para la clasificación de los usos del suelo mediante imágenes de alta resolución, usando los límites catastrales para la definición de los objetos de análisis. En primer lugar, se describe el proceso de cálculo del semivariograma a partir de los valores de niveles de gris del objeto imagen. Con el fin de optimizar el tiempo de cálculo se presentan dos técnicas de selección de píxeles que conservan la forma original del semivariograma. A continuación se definen varios parámetros del semivariograma. Final- mente, se usan diferentes técnicas estadísticas para la selección de los parámetros más discriminantes. La última sección muestra los resultados obtenidos con las imágenes digitales aéreas de una zona agrícola en la costa mediterránea de España. El estudio de la aplicación práctica que se presenta facilita la comprensión de la relación entre el comportamiento del semivariograma experimental y la variabilidad de los valores de intensidad en una imagen digital. Con el fin de seguir el desarrollo de este trabajo, el lector debe conocer algunos métodos estadísticos de clasificación y algunas técnicas de procesamiento digital de imágenes.The authors appreciate the financial support provided by the Spanish Ministry of Science and Innovation and the FEDER in the framework of the Projects CGL2009-14220-C02-01 and CGL2010-19591/BTE.Balaguer-Beser, A.; Hermosilla, T.; Recio, J.; Ruiz, L. (2011). Semivariogram calculation optimization for object-oriented image classification. Modelling in Science Education and Learning. 4:91-104. https://doi.org/10.4995/msel.2011.3057SWORD911044Curran, P. J. (1988). The semivariogram in remote sensing: An introduction. Remote Sensing of Environment, 24(3), 493-507. doi:10.1016/0034-4257(88)90021-1J.P. Chilés, P. Delfinder, 1999, Geostatistics. Modeling Spatial Uncertainty, John Wiley and Sons, New York.P. Goovaerts, 1997, Geostatistics for Natural Resources Evaluation. Oxford University Press: New York.E.H. Isaaks, R.M. Srivastava, 1989, An introduction to applied geostatistics. Oxford. [10] D.K. McIver, M.A. Friedl, 2002, Using prior probabilities in decision tree classification of remotely sensed data. Remote Sensing of Environment 81, 253-261.M.J. Pyrcz, C.V. Deutsch, 2003, The Whole Story on the Hole Effect. In: Searston, S. (Eds.) Geostatistical Association of Australasia, Newsletter 18.J.R. Quinlan, 1993, C4.5: Programs For Machine Learning. Morgan Kaufmann, Los Altos.L.A. Ruiz, J.A. Recio, T. Hermosilla, 2007, Methods for automatic extraction of regularity patterns and its application to object-oriented image classification. In: International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, XXXVI, Munich, Germany, 117-121.M. Story, R. G. Congalton, 1986, Accuracy assessment: a user's perspective, Photogram- metric Engineering and Remote Sensing, 52(3), 397-399

Compressing Random Microstructures via Stochastic Wang Tilings

This paper presents a stochastic Wang tiling based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics. Unlike the existing approaches based on a single unit cell, it utilizes a finite set of tiles assembled by a stochastic tiling algorithm, thereby allowing to accurately reproduce long-range orientation orders in a computationally efficient manner. Although the basic features of the method are demonstrated for a two-dimensional particulate suspension, the present framework is fully extensible to generic multi-dimensional media.Comment: 4 pages, 6 figures, v2: minor changes as suggested by reviewers, v3: corrected two typos in the revised versio

Multivariate Operator-Self-Similar Random Fields

Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar stable random fields $X=\{X(t), t \in \R^d\}$ with values in $\R^m$ are constructed by utilizing homogeneous functions and stochastic integral representations.Comment: 27 page

Multiscale análisis of heavy metal contents in Spanish agricultural topsoils

This study characterized and mapped the spatial variability patterns of seven topsoil heavy metals (Cr, Ni, Pb, Cu, Zn, Hg and Cd) within the Ebro river basin (9.3 million ha) by Multivariate Factorial Kriging. The variograms and cross-variograms of heavy metal concentrations showed the presence of multiscale variation that was modeled using three variogram models with ranges of 20 km (short-range), 100 km (medium-range) and 225 km (long-range). Our results indicate that the heavy metal concentration is influenced by bedrock composition and dynamics at all the spatial scales, while human activities have a notorious effect only at the short- and medium- range scale of variation. Sources of Cu, Pb and Zn (and secondary Cd) are associated with agricultural practices (at the short-range scale of variation), whereas Hg variation at the short- and medium-range scale of variation is related to atmospheric deposition

An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach

Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a computational bottleneck in many applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the precision matrix involved sparse, which enables the use of numerical algorithms for sparse matrices, that for fields in R-2 only use the square root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parameterization. We show that, using an approximate stochastic weak solution to (linear) stochastic partial differential equations, we can, for some GFs in the Matern class, provide an explicit link, for any triangulation of R-d, between GFs and GMRFs, formulated as a basis function representation. The consequence is that we can take the best from the two worlds and do the modelling by using GFs but do the computations by using GMRFs. Perhaps more importantly, our approach generalizes to other covariance functions generated by SPDEs, including oscillating and non-stationary GFs, as well as GFs on manifolds. We illustrate our approach by analysing global temperature data with a non-stationary model defined on a sphere