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19 January 2001 Multisensor data classification with dependence trees
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In order to apply the statistical approach to the classification of multisensor remote sensing data, one of the main problems lies in the estimation of the joint probability density functions (pdfs) f(X|?k) of the data vector X given each class ?k, due to the difficulty of defining a common statistical model for such heterogeneous data. A possible solution is to adopt non-parametric approaches which rely on the availability of training samples without any assumption about the statistical distributions involved. However, as the multisensor aspect involves generally numerous channels, small training sets make difficult a direct implementation of non-parametric pdf estimation. In this paper, the suitability of the concept of dependence tree for the integration of multisensor information through pdf estimation is investigated. First, this concept, introduced by Chow and Liu, is used to provide an approximation of a pdf defined in an N-dimensional space by a product of N-1 pdfs defined in two-dimensional spaces, representing in terms of graph theoretical interpretation a tree of dependencies. For each land cover class, a dependence tree is generated by minimizing an appropriate closeness measure. Then, a non-parametric estimation of the second order pdfs f(xjxj,?k) is carried out through the Parzen approach, based on the implementation of two-dimensional Gaussian kernels. In this way, it is possible to reduce the complexity of the estimation, while capturing a significant part of the interdependence among variables. A comparative study with two other non-parametric multisensor data fusion methods, namely: the Multilayer Perceptron (MLP) and K-nearest neighbors (K-nn) methods, is reported. Experimental results carried out on a multisensor (ATM and SAR) data set show the interesting performances of the fusion method based on dependence trees with the advantage of a reduced computational cost with respect to the two other methods.
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Andrea Piardi, Farid Melgani, Sebastiano Bruno Serpico, and Mihai P. Datcu "Multisensor data classification with dependence trees", Proc. SPIE 4170, Image and Signal Processing for Remote Sensing VI, (19 January 2001);

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