An interpolation procedure for generalizing a look-up table inversion method

The inversion of physically based reflectance models is increasingly efficient for extracting vegetation variables from remote sensing images. It requires a vegetation reflectance model and an inversion method that are accurate and efficient. Usually, the complexity of reflectance models implies to use specific inversion methods (e.g., look-up table and neural network). Unfortunately, these methods are valid only for the view-sun directions for which they are designed. A developed look-up table based inversion method avoids this limitation: it generalizes any look-up table for any view-sun direction, and more generally for any input parameter value. It uses a look-up table made of ci coefficients of any analytical expression h that fits a set of reflectance values simulated by the Discrete Anisotropic Radiative Transfer (DART) model. Interpolation on coefficients ci allows h to give reflectance values for any input parameter value. We settled some options of the inversion method with sensitivity studies: tree covers are simulated with 4-tree scenes, expression h has six coefficients ci and the interpolation is the continuous first derivative interpolation method. Moreover, the robustness of the inversion method was validated. The ability to generalize a look-up table for any view-sun direction was successfully tested with the inversion of SPOT images of Fontainebleau (France) forest. LAI maps proved to be as accurate (i.e., RMSE≈1.3) as those obtained with classical relationships that are calibrated with in situ LAI measurements. Here, the advantage of our inversion method was to avoid this calibration.