Motion fields describing the ocean surface dynamics live in vectorial spaces of high dimension. Consequently, their estimation from satellite images requires huge computational resources. The issue of dimensionality reduction, that is the determination of representative low dimensional structures in these high dimensional spaces, is of major importance for any application that demands real-time or short-term results. Proper Order Decomposition allows to determine such sub-space of motion fields on which estimation may be assessed with reduced complexity. A reduced model is obtained by Galerkin projection of evolution equations on this subspace. Motion is estimated by assimilating the observed image sequence with the reduced model. The paper describes how to derive the reduced space from a database of ocean model's outputs and explains how to estimate surface circulation from satellite sequences. Results are given on images acquired on the Black Sea basin by NOAA-AVHRR sensors.

This paper describes modeling and numerical computation of orthogonal bases, which are used to describe images and motion fields. Motion estimation from image data is then studied on subspaces spanned by these bases. A reduced model is obtained as the Galerkin projection on these subspaces of a physical model, based on Euler and optical flow equations. A data assimilation method is studied, which assimilates coefficients of image data in the reduced model in order to estimate motion coefficients. The approach is first quantified on synthetic data: it demonstrates the interest of model reduction as a compromise between results quality and computational cost. Results obtained on real data are then displayed so as to illustrate the method.

The paper presents a motion estimation method based on data assimilation in a dynamic model, named Image Model, expressing the physical evolution of a quantity observed on the images. The application concerns the retrieval of apparent surface velocity from a sequence of satellite data, acquired over the ocean. The Image Model includes a shallow-water approximation for the dynamics of the velocity field (the evolution of the two components of motion are linked by the water layer thickness) and a transport equation for the image field. For retrieving the surface velocity, a sequence of Sea Surface Temperature (SST) acquisitions is assimilated in the Image Model with a 4D-Var method. This is based on the minimization of a cost function including the discrepancy between model outputs and SST data and a regularization term. Several types of regularization norms have been studied. Results are discussed to analyze the impact of the different components of the assimilation system.

The objective of this study is to compute the surface circulation velocity from oceanographic image sequences. Data assimilation provides a mathematical solution to combine optimally observations and models. We define a dedicatedImageModelconsistent with the physical knowledge of ocean dynamics. Satellite images are then assimilated into this model using a variational data assimilation scheme. This technique relies on the adjoint model definition to compute the minimum of a cost function measuring the discrepancy between model's outputs and observations. The method takes into account the physical knowledge of the ocean circulation, which is relevant for explaining images evolution and, in case of missing data due to clouds occlusion or lack of acquisitions, the estimation is still consistent with the physical evolution laws.

We tackle the problem of coupling a geophysical simulation model with data coming from image processing. It needs to define the image observation space and to design an operator to transform results from the image space to the model space. In this study, we use a shallow-water oceanographic circulation model developed at MHI. We propose a processing chain first based on an image processing step relying on a dedicated motion estimation operator, and then a data assimilation step of the estimated velocity. We illustrate the method on different results without and with assimilation

This paper aims at estimating the apparent velocity from sequences of satellite images. This study is an illustration of a more general methodology for generating, from satellite images, pseudo-observations of physical variables, that are assimilated within a geophysical forecast model in view of improving the quality of its results. In the case of the presented study, the used satellite images are sequences of sea surface temperature (SST), from which pseudo-observations of sea surface velocities are generated, and assimilated within an ocean circulation model. The originality of the approach lies in the definition of an image model, that predicts the evolution of image information -here, SST- as a function of the pseudo-observations -here, surface velocity-. Satellite data are then assimilated within the image model, yielding an estimation of the pseudo-observations. In the case of this paper, this methods allows the estimation of sea surface velocities, even when large parts of the satellite images are corrupted by clouds. The image model plays the role of an intermediate model, between satellite data and the forecast model, and allows the assimilation of image information which is not directly linked to the state variables of the forecast model.

We are interested in the problem of modeling the propagation of landslides. We use an image processing approach based on the computation of a geodesic distance map. We determine the evolution of an initial curve along a given surface. The model can incorporate various properties coming from the geometry of the surface or independant measures. In an application, we focus on landslides study in the context of natural risk management The model is driven by geometrical constraints and SAR interferometric measures.

The general problem of surface matching is considered in this study. The process described in this work hinges on a geodesic distance equation for a family of surfaces embedded in the graph of a cost function. The cost function represents the geometrical matching criterion between the two 3D surfaces. This graph is a hypersurface in 4-dimensional space, and the theory presented herein is a generalization of the geodesic curve evolution method introduced by R. Kimmel et al. (1995). It also generalizes the 2D matching process developed in Cohen and Herlin (1998). An Eulerian level-set formulation of the geodesic surface evolution is also used, leading to a numerical scheme for solving partial differential equations originating from hyperbolic conservation laws, which has proven to be very robust and stable. The method is applied on examples showing both small and large deformations, and arbitrary topological changes.

Tackles the general problem of surface tracking. The authors present a new method based on the computation of geodesic distance maps between a source and a destination surface. The method used in this case is a generalization to the case of surfaces of a 2D matching process introduced by Cohen and Herlin (1998). It relies on a level-set formulation, thus providing stable and robust resolution schemes. The obtained matching method accommodates both small and large deformations. Actually, the matching constraints are explicitly expressed by the definition of a hypersurface. The connecting paths between the two surfaces lie on this hypersurface. The authors construct a hypersurface that allows the matching process to preserve geometric similarities in the case of small deformations, and loosen these geometric constraints when large deformations occur. The applicative framework is the study of the Earth's crustal evolution to characterize the deformation of digital elevation models.

Repeat-pass SAR interferometric data are multitemporal and display changes occurring between two acquisitions. As a consequence, phase and correlation images contains meaningful information that are usable for cropland monitoring. This paper proposes a statistical model to segment high phasimetric structures. It is expressed in a Markov random field framework by using cooperatively phase and correlation information.

Important SAR phasimetric effects can be observed on the evolution of vegetation subjected to rainy periods. We present a segmentation model to detect these artefacts. It is based on a statistical model, expressed in a Markovian random field framework. The novelty of the approach resides in the use of both interferometric phase and coherence.

Presents a segmentation method to detect effects due to high temporal evolution of the interferometric phase. The segmentation of these phasimetric artefacts is performed, taking into consideration both phase image and interferometric correlation. The process is based on a statistical model, robust in a noisy environment. It is expressed in a Markovian random field framework. This work is particularly original in respect to its application domain. The major novelty of the approach resides on the use of two pieces of information in order to correspond exactly to the effects definition. It is used to segment phasimetric effects, appearing on some kind of ground occupation, due to rainy events.

To analyze SAR interferometric data, an unwrapping process must be first performed. Most so far proposed solutions use either local or global methods. In this paper we propose a mixed method to solve this problem, based on a 3-step iterative process: a local unwrapping is first performed and then improved through a Markovian segmentation, false unwrapped residues are finally detected and corrected. A deterministic algorithm is used for the relaxation process; wrong unwrapped areas are corrected by a backtracking mechanism. Some results obtained by this approach, which presents a lower computational cost compared to complex stochastic unwrapping methods, are also presented.