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Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
Hyperspectral images show similar statistical properties to natural grayscale or color photographic images. However, the classification of hyperspectral images is more challenging because of the very high dimensionality of the pixels and…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
This work concerns a detailed review of data analysis methods used for remotely sensed images of large areas of the Earth and of other solid astronomical objects. In detail, it focuses on the problem of inferring the materials that cover…
Hyperspectral sensors enable the study of the chemical properties of scene materials remotely for the purpose of identification, detection, and chemical composition analysis of objects in the environment. Hence, hyperspectral images…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
Hyperspectral unmixing is an important remote sensing task with applications including material identification and analysis. Characteristic spectral features make many pure materials identifiable from their visible-to-infrared spectra, but…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…
To improve the classification performance in the context of hyperspectral image processing, many works have been developed based on two common strategies, namely the spatial-spectral information integration and the utilization of neural…
Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…
Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic…
Flood extent mapping plays a crucial role in disaster management and national water forecasting. Unfortunately, traditional classification methods are often hampered by the existence of noise, obstacles and heterogeneity in spectral…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
A visual system has to learn both which features to extract from images and how to group locations into (proto-)objects. Those two aspects are usually dealt with separately, although predictability is discussed as a cue for both. To…
Image-level regression is an important task in Earth observation, where visual domain and label shifts are a core challenge hampering generalization. However, cross-domain regression within remote sensing data remains understudied due to…
We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…