Supervised learning on graphs of spatio-temporal similarity in satellite image sequences

High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the information contained in satellite image sequences in a graph representation using Bayesian methods. Based on such a representation, this paper further presents a supervised learning methodology of semantics associated to spatio-temporal patterns occurring in satellite image sequences. It enables the recognition and the probabilistic retrieval of similar events. Indeed, graphs are attached to statistical models for spatio-temporal processes, which at their turn describe physical changes in the observed scene. Therefore, we adjust a parametric model evaluating similarity types between graph patterns in order to represent user-specific semantics attached to spatio-temporal phenomena. The learning step is performed by the incremental definition of similarity types via user-provided spatio-temporal pattern examples attached to positive or/and negative semantics. From these examples, probabilities are inferred using a Bayesian network and a Dirichlet model. This enables to links user interest to a specific similarity model between graph patterns. According to the current state of learning, semantic posterior probabilities are updated for all possible graph patterns so that similar spatio-temporal phenomena can be recognized and retrieved from the image sequence. Few experiments performed on a multi-spectral SPOT image sequence illustrate the proposed spatio-temporal recognition method

An Efficient Algorithm for Video Super-Resolution Based On a Sequential Model

In this work, we propose a novel procedure for video super-resolution, that is the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a "sequential" model (i.e., each high-resolution frame is supposed to be a displaced version of the preceding one) and considers the use of sparsity-enforcing priors. Both the recovery of the high-resolution images and the motion fields relating them is tackled. This leads to a large-dimensional, non-convex and non-smooth problem. We propose an algorithmic framework to address the latter. Our approach relies on fast gradient evaluation methods and modern optimization techniques for non-differentiable/non-convex problems. Unlike some other previous works, we show that there exists a provably-convergent method with a complexity linear in the problem dimensions. We assess the proposed optimization method on {several video benchmarks and emphasize its good performance with respect to the state of the art.}Comment: 37 pages, SIAM Journal on Imaging Sciences, 201

Self-similar prior and wavelet bases for hidden incompressible turbulent motion

This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition involves correlated wavelet coefficients, we are able to handle this dependence in practice. Based on these two wavelet decompositions, we finally provide effective and efficient algorithms to approach the maximum a posteriori. An intensive numerical evaluation proves the relevance of the proposed wavelet-based self-similar priors.Comment: SIAM Journal on Imaging Sciences, 201

Inverse Reduced-Order Modeling

International audienceWe propose a general probabilistic formulation of reduced-order modeling in the case the system state is hidden and characterized by some uncertainty. The objective is to integrate noisy and incomplete observations in the process of building a reduced-order model. We call this problematic inverse reduced-order modeling. This problematic arises in many scientific domains where there exists a need of accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Among others, it concerns geophysical studies dealing with image data, which are important for the characterization of global warming or the prediction of natural disasters

Reduced-Order Modeling of Hidden Dynamics

International audienceThe objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically observed. Within this context, the paper proposes a probabilistic framework for the construction of "POD-Galerkin" reduced-order models. Assuming a hidden Markov chain, the inference integrates the uncertainty of the hidden states relying on their posterior distribution. Simulations show the benefits obtained by exploiting the proposed framework

Sparse representations in nested non-linear models

International audienceFollowing recent contributions in non-linear sparse represen-tations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straight-forwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient computation of the gradient of the objective function. In the particular case of interest, we propose to resort to a well-known technique from the theory of optimal control to estimate the gradient. This computation is then implemented into the optimization procedure proposed byCan es et al., leading to a non-linear extension of it

Three-Dimensional Motion Estimation of Atmospheric Layers From Image Sequences

International audienceIn this paper, we address the problem of estimating three-dimensional motions of a stratified atmosphere from satellite image sequences. The analysis of three-dimensional atmospheric fluid flows associated with incomplete observation of atmospheric layers due to the sparsity of cloud systems is very difficult. This makes the estimation of dense atmospheric motion field from satellite images sequences very difficult. The recovery of the vertical component of fluid motion from a monocular sequence of image observations is a very challenging problem for which no solution exists in the literature. Based on a physically sound vertical decomposition of the atmosphere into cloud layers of different altitudes, we propose here a dense motion estimator dedicated to the extraction of three-dimensional wind fields characterizing the dynamics of a layered atmosphere. Wind estimation is performed over the complete three-dimensional space using a multi-layer model describing a stack of dynamic horizontal layers of evolving thickness, interacting at their boundaries via vertical winds. The efficiency of our approach is demonstrated on synthetic and real sequences

Wavelets to reconstruct turbulence multifractals from experimental image sequences

International audienceIn the context of turbulent fluid motion measurement from image sequences, we propose in this paper to reverse the traditional point of view of wavelets perceived as an analyzing tool: wavelets and their properties are now considered as prior regularization models for the motion estimation problem, in order to exhibit some well-known turbulence regularities and multifractal behaviors on the reconstructed motion field