An interpolation procedure for generalizing a look-up table
inversion method
J.P. Gastellu-Etchegorry
*
, F. Gascon, P. Este
`
ve
Centre d’Etudes Spatiales de la BIOsphe
`
re (CESBIO), (CNES/CNRS/UPS), BPi 2801, 18 Av. Edouard Belin, 31401 Toulouse ce
´
dex 4, France
Received 28 December 2001; received in revised form 23 May 2003; accepted 1 June 2003
Abstract
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 c
i
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 c
i
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 c
i
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 c 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.
D 2003 Elsevier Inc. All rights reserved.
Keywords: LAI; DART; SPOT images
1. Introduction
The study of continental biosphere implies that vegeta-
tion variables be known worldwide, continuously and at
different scales of time and space. Fortunately, (1) vegeta-
tion variables affect more or less directly the spectral
reflectance of earth surfaces, (2) vegetation reflectance
models can simulate the reflectance of earth surfaces using
input parameters that correspond to vegetation variables and
view-sun configurations, and (3) remote sensing allows one
to measure the reflectance of earth surfaces, continuously,
worldwide and at different scales of time and space. In this
context, physically based reflectance models (Gastellu-Etch-
egorry, Demarez, Pinel, & Zagolski, 1996; Goel & Thomp-
son, 2000; Myneni & Ross, 1991; Quin & Liang, 2000) are
very useful tools because they can relate accurately a
large number of vegetation optical and structural variables
to satellite measurements (e.g., SPOT, MODIS, MISR,
POLDER, Ve
´
ge
´
tation). Being designed to model physical
processes that explain vegetation reflectance, these models
are potentially more robust and accurate than other
vegetation reflectance models such as empirical models,
including spectral indices.
Physically based models range in complexity from sim-
ple nonlinear models to complex numerical radiative trans-
fer models (e.g., Monte Carlo, ray tracing) in realistic three-
dimensional computer simulations of vegetation canopies.
Usually, they require a large number of input parameters
because they need to address the entire radiative transfer
problem in order to simulate accurate vegetation reflectance
values for any experimental conditions (e.g., sun and view
directions) and any type of Earth surfaces (e.g., forests,
savannas, etc.). For most studies, it is often assumed that a
large number of variables are more or less well known (e.g.,
tree architecture variables depend on the type of landscape
0034-4257/03/$ - see front matter D 2003 Elsevier Inc. All rights reserved.
doi:10.1016/S0034-4257(03)00146-9
* Corresponding author. Tel.: +33-5-61-55-61-30; fax: +33-5-61-55-
85-00.
E-mail address: gastellu@cesbio.cnes.fr (J.P. Gastellu-Etchegorry).
www.elsevier.com/locate/rse
Remote Sensing of Environment 87 (2003) 55 – 71