Section: New Results

Image assimilation

Sequences of images, such as satellite acquisitions, display structures evolving in time. This information is recognized of major interest by forecasters (meteorologists, oceanographers, etc.) in order to improve the information provided by numerical models. However, the satellite images are mostly assimilated in geophysical models on a point-wise basis, discarding the space-time coherence visualized by the evolution of structures such as clouds. Assimilating image data in an optimal way is of major interest. This issue is twofold:

  • from the model's viewpoint, the location of structures on the observations is used to control the state vector.

  • from the image's viewpoint, a model of the dynamics and structures is built from the observations.

Estimation of motion and acceleration from image data

Participants : Dominique Béréziat [UPMC] , Isabelle Herlin.

Image sequences allow visualizing dynamic systems and understanding their intrinsic characteristics. One first component of this dynamics is obtained by retrieving the velocity of the structures displayed on the sequence. This motion estimation issue has been extensively studied in the literature of image processing and computer vision. In this research, we step beyond the traditional optical flow methods and address the problem of recovering the acceleration from the whole temporal sequence, which has been poorly investigated, even if this is of major importance for some data types, such as fluid flow images. Acceleration is here viewed as the space-time function resulting from the forces applied to the studied system. To solve this issue, we propose a variational approach where a specific energy is designed to model both the motion and the acceleration fields. The contributions are twofold: first, we introduce a unified variational formulation of motion and acceleration under space-time constraints; second, we define the minimization scheme, which allows retrieving the estimations, and provide the full information on the discretization schemes. Experiments are conducted on synthetic and real image sequences, visualizing fluid-like flows, where direct and precise calculation of acceleration is of primary importance.

Rain nowcasting from radar image acquisitions

Participants : Isabelle Herlin, Étienne Huot.

This research concerns the design of an operational method for rainfall nowcasting that aims at prevention of flash floods. The nowcasting method includes two main components:

  • a data assimilation method, based on radar images, estimates the state of the atmosphere: this is the estimation phase.

  • a forecast method uses this estimation to extrapolate the state of the atmosphere in the future: this is the forecast phase.

Results are analyzed on space-time neighborhoods in order to prevent consequences of flash floods on previously defined zone.

Current research concerns the following issues:

  • the use of object components in the state vector. The objective is to improve the description of the image data in order to get a better motion estimation and a more accurate localization of endangered regions.

  • the extension of the estimation phase to a multiscale process.

  • the merging with measures acquired by a network of pluviometers.

Ensemble Kalman filter based on the image structures

Participants : Dominique Béréziat [UPMC] , Isabelle Herlin.

One major limitation of the motion estimation methods that are available in the literature concerns the availability of the uncertainty on the result. This is however assessed by a number of filtering methods, such as the ensemble Kalman filter (EnKF). Our research consequently concerns the use of a description of the displayed structures in an ensemble Kalman filter, which is applied for estimating motion on image acquisitions. Compared to the Kalman filter, EnKF does not require propagating in time the error covariance matrix associated to the estimation, resulting in reduced computational requirements. However, EnKF is also known for exhibiting a shrinking effect when taking into account the observations on the studied system at the analysis step. Various methods are available in the literature for correcting this effect, but they do not involve the structures displayed on the image sequence. We defined two alternative solutions to that shrinking effect: a dedicated localization function and an adaptive decomposition domain. These methods are both well suited for fluid flows images and applied on satellite images of the atmosphere.