In this paper, a hierarchical probabilistic graphical model is proposed to tackle joint classification of multiresolution and multisensor remote sensing images of the same scene. This problem is crucial in the study of satellite imagery and jointly involves multiresolution and multisensor image fusion. The proposed framework consists of a hierarchical Markov model with a quadtree structure to model information contained in different spatial scales, a planar Markov model to account for contextual spatial information at each resolution, and decision tree ensembles for pixelwise modeling. This probabilistic graphical model and its topology are especially fit for application to very high resolution (VHR) image data. The theoretical properties of the proposed model are analyzed: the causality of the whole framework is mathematically proved, granting the use of time-efficient inference algorithms such as the marginal posterior mode criterion, which is non-iterative when applied to quadtree structures. This is mostly advantageous for classification methods linked to multiresolution tasks formulated on hierarchical Markov models. Within the proposed framework, two multimodal classification algorithms are developed, that incorporate Markov mesh and spatial Markov chain concepts. The results obtained in the experimental validation conducted with two datasets containing VHR multispectral, panchromatic, and radar satellite images, verify the effectiveness of the proposed framework. The proposed approach is also compared to previous methods that are based on alternate strategies for multimodal fusion.

In this paper, the problem of the classification of multiresolution and multisensor remotely sensed data is addressed by proposing a multiscale Markov mesh model. Multiresolution and multisensor fusion are jointly achieved through an explicitly hierarchical probabilistic graphical classifier, which uses a quadtree structure to model the interactions across different spatial resolutions, and a symmetric Markov mesh random field to deal with contextual information at each scale and favor applicability to very high resolution imagery. Differently from previous hierarchical Markovian approaches, here, data collected by distinct sensors are fused through either the graph topology itself (across its layers) or decision tree ensemble methods (within each layer). The proposed model allows taking benefit of strong analytical properties, most remarkably causality, which make it possible to apply time-efficient non-iterative inference algorithms.

In this paper, we address the problem of the joint classification of multiple images acquired on the same scene at different spatial resolutions. From an application viewpoint, this problem is of importance in several contexts, including, most remarkably, satellite and aerial imagery. From a methodological perspective, we use a probabilistic graphical approach and adopt a hierarchical Markov mesh framework that we have recently developed and models the spatial-contextual classification of multiresolution and possibly multisensor images. Here, we focus on the methodological properties of this framework. First, we prove the causality of the model, a highly desirable property with respect to the computational cost of the inference. Then, we prove the expression of the marginal posterior mode criterion for this model and discuss the related assumptions. Experimental results with multispectral and panchromatic satellite images are also presented.

Abstract. 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.

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