Causal Markov Mesh Hierarchical Modeling for the Contextual Classification of Multiresolution Satellite Images

Abstract

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.

A Causal Hierarchical Markov Framework for the Classification of Multiresolution and Multisensor Remote Sensing Images

“…This notion of causal Markovianity on a planar lattice extends the one discussed in (Montaldo et al, 2019a, Montaldo et al, 2019b, in which the order relation was referred to a 2D mesh. We also recall that it can be proved for several planar causal Markov models (including Markov meshes of second and third order and Markov chains) that the following factorization holds (Abend et al, 1965):…”

“…The proposed framework 2.2.1 Model assumptions In this paper, we formulate a general framework for the joint fusion of multisensor and multiresolution images in a supervised classification scenario. The key-idea of the proposed framework is to generalize the approaches in (Montaldo et al, 2019a, Montaldo et al, 2019b by introducing a hierarchical Markov model with respect to a quadtree topology and to an arbitrary total order relation on each layer of the tree. Considering a set of well-registered images acquired by distinct VHR sensors at different spatial resolutions on the same area, each image is included in a corresponding layer of the quadtree.…”

“…First, we extend the approach developed in (Montaldo et al, 2019a, Montaldo et al, 2019b, in which hierarchical MRFs on quadtrees have been combined with planar Markov meshes and with various pixelwise probabilistic models, to a broader framework in which each layer of the quadtree is associated with a Markov model with respect to an arbitrary total order relation. The resulting framework is highly general and includes the Markov meshes in (Montaldo et al, 2019a, Montaldo et al, 2019b as a special case. Secondly, within this generalized framework, we develop a novel algorithm that is based on a Markov chain model (Fjortoft et al, 2003) on each layer of the quadtree.…”

“…On the other hand, when data sources from distinct sensors are available at the same resolution, multisensor fusion is addressed by incorporating a nonparametric ensemble method within the proposed algorithm. Similar to (Montaldo et al, 2019a, Montaldo et al, 2019b, gradient boosting regression trees (GBRT) (Friedman, 2001) are employed in this role.…”

Multisensor and Multiresolution Remote Sensing Image Classification through a Causal Hierarchical Markov Framework and Decision Tree Ensembles

“…Multiresolution fusion is intrinsically supported by the topology of the proposed framework, while multisensor (optical and radar) fusion is addressed by the integration of nonparametric ensemble modeling, e.g., decision tree ensembles [17], into the proposed hierarchical Markov model. From this perspective, the developed framework generalizes and completes the preliminary formulations that were presented in the conference papers [18][19][20][21].…”