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The variogram of a spectral band ratio with a considerable correlation between the bands

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Abstract

The subject of this paper is to show how the variogram of a spectral band ratio u = arctan(x/y) is controlled by the statistical parameters and spatial variation of the individual bands x and y, as well as the correlation coefficient ρ between the bands. Based on certain assumptions about the histograms and variograms of x and y, an approximate mathematical expression for the variogram of the band ratio is derived, which shows that the sill of the variogram of u depends on the ratio of the variance of x to the variance of y. As long as the correlation coefficient ρ increases, the sill decreases. The spatial variation of u for various distances h between pixels depends on the ranges of the variograms of bands x and y, as well as on the correlation coefficient between the bands. Experimentation with satellite images shows a good agreement between theoretically calculated and actual variograms of u, in qualitative terms and, in a considerable extent, in quantitative terms. The proposed methodology may be useful in assessing the efficiency of spectral bands and vegetation indices in environmental and geological remote sensing.

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Acknowledgments

This paper is a part of a research project funded by ELKE, University of Athens (grant code number 10812).

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Authors and Affiliations

  1. Faculty of Geology and Geo-environment, Department of Geography and Climatology, Remote Sensing Laboratory, University of Athens, Panepistimiopolis, Athens, 157 84, Greece

    Georgios Aim Skianis

  2. Faculty of Geology and Geo-environment, Remote Sensing Laboratory, University of Athens, Panepistimiopolis, Athens, 157 84, Greece

    Aristidis D. Vaiopoulos

Authors
  1. Georgios Aim Skianis
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  2. Aristidis D. Vaiopoulos
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Correspondence to Georgios Aim Skianis.

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Communicated by: H. A. Babaie

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Skianis, G.A., Vaiopoulos, A.D. The variogram of a spectral band ratio with a considerable correlation between the bands. Earth Sci Inform 8, 161–169 (2015). https://doi.org/10.1007/s12145-014-0147-5

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