A causal hierarchical markov framework for the classification of multiresolution and multisensor remote sensing images

In this paper, a multiscale Markov framework is proposed in order to address the problem of the classification of multiresolution and multisensor remotely sensed data. The proposed framework makes use of a quadtree to model the interactions across different spatial resolutions and a Markov model with respect to a generic total order relation to deal with contextual information at each scale in order to favor applicability to very high resolution imagery. The methodological properties of the proposed hierarchical framework are investigated. Firstly, we prove the causality of the overall proposed model, a particularly advantageous property in terms of computational cost of the inference. Secondly, we prove the expression of the marginal posterior mode criterion for inference on the proposed framework. Within this framework, a specific algorithm is formulated by defining, within each layer of the quadtree, a Markov chain model with respect to a pixel scan that combines both a zig-zag trajectory and a Hilbert space-filling curve. Data collected by distinct sensors at the same spatial resolution are fused through gradient boosted regression trees. The developed algorithm was experimentally validated with two very high resolution datasets including multispectral, panchromatic and radar satellite images. The experimental results confirm the effectiveness of the proposed algorithm as compared to previous techniques based on alternate approaches to multiresolution fusion.