**Aims**

**Imaging_spectrometers**

**Methods**

**Partnership**

**Publications**

**Reports**

**Conferences**

**Meetings**

**Software**

**Funding**

**Index**

[[methods]]

We organize our research and developments according to four work-packages (WP):

- Statistical image processing
- Mathematical and Physical models
- Inversion algorithms
- Visualization system

**Statistical image processing** detects, delineates, and extracts objects of interest (planetary surface units, galaxies, meteoritic mineral assemblages, etc.) by segmentating and classifying hyperspectral images. In that matter we innovate by applying state-of-the-art methods that reduce the dimensionality of data (BPSS, HDDA-HDDC, etc.) and regularize spatially their classification (Markov fields, chains and trees). In addition the statistical processing of the image aims at correcting several artifacts related to the acquisition by an imaging spectrometer (noise, missing data, etc.) or related to forefront media which often disturb the signal of interest (atmosphere for surface studies).

Classification of a hyperspectral high resolution CRISM image covering the northern polar cap edge of Mars (left) into 5 spectral classes (right) |
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**Mathematical and Physical models** respectively provide a parametric and/or statistical conceptual representation of the entire image (or portions of it) and establish a numerical relation between object properties and signals measured for each pixel. First the statistical models are instrumental in designing classification algorithms by making explicit the attachment to the data. Physical models simulate the propagation of light from sources to the sensor through different media in order to relate numerically the chemical, physical and structural properties of objects, for instance atmospheric and surface materials, with the measurements. In the specific case of planetary remote sensing, we propose to develop a new generation of surface reflectance models based on stochastic, discrete and multi-scale formulations and using Monte-Carlo, ray tracing and global illumination methods. These models will improve considerably our capabilities to model the photometric properties of surfaces, precisely those properties that will be far better sampled from space thanks to HMA instruments. In addition physical models can generate well calibrated synthetic data used to validate the statistical image processing methods.

**Inversion algorithms** can reverse the models in order to estimate the mathematical (e.g. morphologic) or physical (e.g. compositional) properties of the objects of interest from hyperspectral images. We investigate trained algorithms (KNN, GRSIR, SVM, etc.) based on huge collections of synthetic spectra generated by the physical models and used as knowledge databases.

Mapping dust abundance across the south permanent polar cap of Mars by three different methods (KNN, weighted KNN, and Gaussian Regularized Slice Inverse Regression) and comparison. |
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The **Visualization system** aims at providing the user with the ability to view in a synthetic and enhanced manner the meaningful astrophysical content of a given image or of a group of related images and easily interact with it. The visualization platform rests heavily on fast statistical and/or physical treatments that provide a small number of indicators. The latter are mapped to an optimal colorimetric space and the result is superimposed on a control image.