Thomas Corpetti

Dense estimation of fluid flows

In this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from computer vision, originally designed for quasi-rigid motions with stable salient features, are not well adapted in this context. We thus investigate a dedicated minimization-based motion estimator. The cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics, which is compatible with large displacements. This term is associated with an original second-order div-curl regularization which prevents the washing out of the salient vorticity and divergence structures. The performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images. In addition, we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence.

Extraction of Singular Points from Dense Motion Fields: An Analytic Approach

In this paper we propose a new method to extract the vortices, sources, and sinks from the dense motion field preliminary estimated between two images of a fluid video. This problem is essential in meteorology for instance to identify and track depressions or convective clouds in satellite images. The knowledge of such points allows in addition a compact representation of the flow which is very useful in both experimental and theoretical fluid mechanics. The method we propose here is based on an analytic representation of the flow. This approach has the advantage of being robust, simple, fast and requires few parameters.

Dynamically consistent optical flow estimation

In this paper, we present a framework for dynamic consistent estimation of dense motion fields over a sequence of images. The originality of the approach is to exploit recipes related to optimal control theory. This setup allows performing the estimation of an unknown state function according to a given dynamical model and to noisy and incomplete measurements. The overall process is formalized through the minimization of a global spatio-temporal cost functional w.r.t the complete sequence of motion fields. The minimization is handled considering an adjoint formulation. The resulting scheme consists in iterating a forward integration of the evolution model and a backward integration of the adjoint evolution model guided by a discrepancy measurement between the state variable and the available noisy observations. Such an approach allows us to cope with several delicate situations (such as the absence of data) which are not well managed with usual estimators.

Combined Use of Multi-Temporal Optical and Radar Satellite Images for Grassland Monitoring

The aim of this study was to assess the ability of optical images, SAR (Synthetic Aperture Radar) images and the combination of both types of data to discriminate between grasslands and crops in agricultural areas where cloud cover is very high most of the time, which restricts the use of visible and near-infrared satellite data. We compared the performances of variables extracted from four optical and five SAR satellite images with high/very high spatial resolutions acquired during the growing season. A vegetation index, namely the NDVI (Normalized Difference Vegetation Index), and two biophysical variables, the LAI (Leaf Area Index) and the fCOVER (fraction of Vegetation Cover) were computed using optical time series and polarization (HH, VV, HV, VH). The polarization ratio and polarimetric decomposition (Freeman–Durden and Cloude–Pottier) were calculated using SAR time series. Then, variables derived from optical, SAR and both types of remotely-sensed data were successively classified using the Support Vector Machine (SVM) technique. The results show that the classification accuracy of SAR variables is higher than those using optical data (0.98 compared to 0.81). They also highlight that the combination of optical and SAR time series data is of prime interest to discriminate grasslands from crops, allowing an improved classification accuracy.

Evaluation of SPOT imagery for the estimation of grassland biomass

In many regions, a decrease in grasslands and change in their management, which are associated with agricultural intensification, have been observed in the last half-century. Such changes in agricultural practices have caused negative environmental effects that include water pollution, soil degradation and biodiversity loss. Moreover, climate-driven changes in grassland productivity could have serious consequences for the profitability of agriculture. The aim of this study was to assess the ability of remotely sensed data with high spatial resolution to estimate grassland biomass in agricultural areas. A vegetation index, namely the Normalized Difference Vegetation Index (NDVI), and two biophysical variables, the Leaf Area Index (LAI) and the fraction of Vegetation Cover (fCOVER) were computed using five SPOT images acquired during the growing season. In parallel, ground-based information on grassland growth was collected to calculate biomass values. The analysis of the relationship between the variables derived from the remotely sensed data and the biomass observed in the field shows that LAI outperforms NDVI and fCOVER to estimate biomass (R2 values of 0.68 against 0.30 and 0.50, respectively). The squared Pearson correlation coefficient between observed and estimated biomass using LAI derived from SPOT images reached 0.73. Biomass maps generated from remotely sensed data were then used to estimate grass reserves at the farm scale in the perspective of operational monitoring and forecasting.

Multitemporal classification of TerraSAR-X data for wetland vegetation mapping

Abstract This paper is concerned with wetland vegetation mapping using multitemporal synthetic aperture radar imagery. Although wetlands play a key role in controlling flooding and nonpoint source pollution, sequestering carbon and providing an abundance of ecological services, knowledge of the flora and fauna of these environments is patchy, and understanding of their ecological functioning is still insufficient for a reliable functional assessment on areas larger than a few hectares. The aim of this paper is to evaluate multitemporal TerraSAR-X imagery to precisely map the distribution of vegetation formations considering flood duration. A series of six dual-polarization TerraSAR-X images (HH-VV) was acquired in 2012 during dry and wet seasons. One polarimetric parameter, the Shannon entropy (SE), and two intensity parameters ( σ ° HH and σ ° VV), which vary with wetland flooding status and vegetation roughness, were first extracted. These parameters were then classified using support vector machine techniques based on a specific kernel adapted to the comparison of time-series data, K-nearest neighbors, and decision tree (DT) algorithms. The results show that the vegetation formations can be identified very accurately ( kappa index = 0.85 ) from the classification of SE temporal profiles derived from the TerraSAR-X images. They also reveal the importance of the use of polarimetric parameters instead of backscattering coefficients alone (HH or VV) or combined (HH and VV).

Estimation of the orientation of textured patterns via wavelet analysis

This paper is concerned with the estimation of the dominant orientation of textured patches that appear in a number of images (remote sensing, biology or natural sciences for instance). It is based on the maximization of a criterion that deals with the coefficients enclosed in the different bands of a wavelet decomposition of the original image. More precisely, we search for the orientation that best concentrates the energy of the coefficients in a single direction. To compare the wavelet coefficients between the different bands, we use the Kullback-Leibler divergence on their distribution, this latter being assumed to behave like a Generalized Gaussian Density. The space-time localization of the wavelet transform allows to deal with any polygon that may be contained in a single image. This is of key importance when one works with (non-rectangular) segmented objects. We have applied the same methodology but using other criteria to compare the distributions, in order to highlight the benefit of the Kullback-Leibler divergence. In addition, the methodology is validated on synthetic and real situations and compared with a state-of-the-art approach devoted to orientation estimation.

Monitoring Urban Areas with Sentinel-2A Data: Application to the Update of the Copernicus High Resolution Layer Imperviousness Degree

Monitoring with high resolution land cover and especially of urban areas is a key task that is more and more required in a number of applications (urban planning, health monitoring, ecology, etc.). At the moment, some operational products, such as the “Copernicus High Resolution Imperviousness Layer”, are available to assess this information, but the frequency of updates is still limited despite the fact that more and more very high resolution data are acquired. In particular, the recent launch of the Sentinel-2A satellite in June 2015 makes available data with a minimum spatial resolution of 10 m, 13 spectral bands, wide acquisition coverage and short time revisits, which opens a large scale of new applications. In this work, we propose to exploit the benefit of Sentinel-2 images to monitor urban areas and to update Copernicus Land services, in particular the High Resolution Layer imperviousness. The approach relies on independent image classification (using already available Landsat images and new Sentinel-2 images) that are fused using the Dempster–Shafer theory. Experiments are performed on two urban areas: a large European city, Prague, in the Czech Republic, and a mid-sized one, Rennes, in France. Results, validated with a Kappa index over 0.9, illustrate the great interest of Sentinel-2 in operational projects, such as Copernicus products, and since such an approach can be conducted on very large areas, such as the European or global scale. Though classification and data fusion are not new, our process is original in the way it optimally combines uncertainties issued from classifications to generate more confident and precise imperviousness maps. The choice of imperviousness comes from the fact that it is a typical application where research meets the needs of an operational production. Moreover, the methodology presented in this paper can be used in any other land cover classification task using regular acquisitions issued, for example, from Sentinel-2.

Monitoring land use and land cover changes in oceanic and fragmented landscapes with reconstructed MODIS time series

Image time series from medium resolution sensors such as NASA EOS/MODIS are frequently used to monitor vegetation phenology at regional and global scales. Facing the limitations of high resolution sensors, that is small coverage areas and low revisit frequencies, data from medium resolution sensors are now assessed to monitor subtle vegetation changes at meso or large scales, even in fragmented landscapes. However, monitoring of subtle changes is difficult to perform with such data without important pre-processing steps. Previous studies showed that time series extracted from original images are often corrupted and hence not exploitable, due to atmospheric and geometric distortions and others artifacts (angle variations, clouds, aerosols for example). In this paper we present an approach to reconstruct high accurate NASA EOS/MODIS time series. Firstly, we propose a method to correct images from atmospheric and geometric distortions. The comparison between different pre-processed NDVI MODIS images and SPOT HRVIR high resolution data points out significant differences, highlighting the necessity of properly pre-processing time serie data. Moreover, on the basis of these first results obtained in using pre-processed series of MODIS images through the smoothing technique developed here to recover the winter vegetation phenology, it is now possible to undertake the identification of subtle changes on land surfaces.

Data Assimilation for Convective-Cell Tracking on Meteorological Image Sequences

This paper focuses on the tracking and analysis of convective cloud systems from Meteosat Second Generation images. The highly deformable nature of convective clouds, the complexity of the physical processes involved, and also the partially hidden measurements available from image data make difficult the direct use of conventional image-analysis techniques for tasks of detection, tracking, and characterization. In this paper, we face these issues using variational-data-assimilation tools. Such techniques enable us to perform the estimation of an unknown state function according to a given dynamical model and to noisy and incomplete measurements. The system state we are setting in this study for the cloud representation is composed of two nested curves corresponding to the exterior frontiers of the clouds and to the interior coldest parts (core) of the convective clouds. Since no reliable simple dynamical model exists for such phenomena at the image grid scale, the dynamics on which we are relying has been directly defined from image-based motion measurements and takes into account an uncertainty modeling of the curve dynamics along time. In addition to this assimilation technique, we show in the Appendix how each cell of the recovered cloud system can be labeled and associated to characteristic parameters (birth or death time, mean temperature, velocity, growth, etc.) of great interest for meteorologists.