IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Supervised Classification of Multi-sensor and Multi-resolution Remote Sensing Images with a Hierarchical Copula-based Approach

In this paper we develop a novel classification approach for multi-resolution, multi-sensor (optical and synthetic aperture radar, SAR) and/or multi-band images. This challenging image processing problem is of great importance for various remote sensing monitoring applications and has been scarcely addressed so far. To deal with this classification problem, we propose a two-step explicit statistical model. We first design a model for the multivariate joint class-conditional statistics of the co-registered input images at each resolution by resorting to multivariate copulas. Such copulas combine the class-conditional marginal probability density functions of each input channel that are estimated by finite mixtures of well-chosen parametric families. We consider different distribution families for the most common types of remote sensing imagery acquired by optical and SAR sensors. We then plug the estimated joint probability density functions into a hierarchical Markovian model based on a quad-tree structure, where each tree-scale corresponds to the different input image resolutions and to corresponding multi-scale decimated wavelet transforms, thus preventing a strong resampling of the initial images. To obtain the classification map, we resort to an exact estimator of the marginal posterior mode. We integrate a prior update in this model in order to improve the robustness of the developed classifier against noise and speckle. The resulting classification performance is illustrated on several remote sensing multi-resolution datasets including very high resolution and multi-sensor images acquired by COSMO-SkyMed and GeoEye-1. Index Terms Multi-sensor remote sensing images, supervised classification, hierarchical Markov random fields, multi-resolution data. I