Multisource data classification with dependence trees

In order to apply a statistical approach to the classification of multisource remote-sensing data, one of the main problems to face lies in the estimation of probability distribution functions. This problem arises out of the difficulty of defining a common statistical model for such heterogeneous data. A possible solution is to adopt nonparametric approaches, which rely on the availability of training samples without any assumption about the related statistical distributions. The purpose of this paper is to investigate the suitability of the concept of dependence trees for the integration of multisource information through estimation of probability distributions. First, this concept, introduced by Chow and Liu (1968), is used to provide an approximation of a probability distribution defined in an N-dimensional space by a product of N-1 probability distributions defined in two-dimensional (2-D) spaces; this approximation corresponds, in terms of graph theoretical interpretation, to a tree of dependence. For each land cover class, a dependence tree is generated by minimizing an appropriate closeness measure. Then, a nonparametric estimation of the second-order probability distributions is carried out through the Parzen window approach, based on the implementation of 2-D 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 comparison with other multisource data fusion methods, namely, the multilayer perceptron (MLP) method, the k-nearest neighbor (k-NN) method, and a Bayesian hierarchical classifier (BHC), is made. Experimental results obtained on multisensor [airborne thematic mapper (ATM) and synthetic aperture radar (SAR)] and multisource (experimental synthetic aperture radar (E-SAR) and a textural feature) data sets show that the proposed fusion method based on dependence trees is able to provide a classification accuracy similar to those of the other methods considered, but with the advantage of a reduced computational load.