On the combination of multi-sensor data using

On the combination of multi-sensor data using meta-Gaussian distributions B˚ard Storvik, Geir Storvik and Roger Fjørtoft Member, IEEE Abstract—With the ever-increasing number and diversity of earth observation satellites, it steadily becomes more important to be able to analyze compound data sets consisting of different types of images acquired by different sensors. In this paper we examine different ways of obtaining joint distributions of such images, and we propose a method that enables incorporation of correlations between images while keeping a good fit to the marginal distributions. The approach basically consists of two steps. First the marginal densities are specified. Based on this specification, each marginal variable is transformed to a normal distributed variable. The joint distribution of the transformed variables is assumed multivariate normal. Transforming back to the original scale gives a joint distribution with dependence, where the initial marginal distributions are preserved. The parameters of the new joint distribution can be estimated. The focus is on marginal distributions that are Gamma, K or Gaussian although any distribution could be considered. The joint distributions produced by the transformation method can e.g. be used in supervised classification of radar and optical images. Results obtained for a set of 4-look SAR images, as well as a combination of SAR and optical images, are presented. Index Terms—Gaussian copula, meta-Gaussian distribu-B˚ard Storvik is senior researcher at the Norwegian Computing

On the combination of multi-sensor data using meta-Gaussian distributions B˚ard Storvik, Geir Storvik and Roger Fjørtoft Member, IEEE Abstract—With the ever-increasing number and diversity of earth observation satellites, it steadily becomes more important to be able to analyze compound data sets consisting of different types of images acquired by different sensors. In this paper we examine different ways of obtaining joint distributions of such images, and we propose a method that enables incorporation of correlations between images while keeping a good fit to the marginal distributions. The approach basically consists of two steps. First the marginal densities are specified. Based on this specification, each marginal variable is transformed to a normal distributed variable. The joint distribution of the transformed variables is assumed multivariate normal. Transforming back to the original scale gives a joint distribution with dependence, where the initial marginal distributions are preserved. The parameters of the new joint distribution can be estimated. The focus is on marginal distributions that are Gamma, K or Gaussian although any distribution could be considered. The joint distributions produced by the transformation method can e.g. be used in supervised classification of radar and optical images. Results obtained for a set of 4-look SAR images, as well as a combination of SAR and optical images, are presented. Index Terms—Gaussian copula, meta-Gaussian distributions, multi-sensor data, multivariate Gamma distribution, multivariate

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