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Classification of non-reflectance corrected hyperspectral images in wheat fields

nathalie gorretta 1 ; Xavier Hadoux 1 ; Sylvain Jay 1
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1. INTRODUCTION
The analysis of multiple hyperspectral images requires the images to be independent from the illumination conditions. Thus, the measured radiance images are generally transformed into reflectance image before further processing. This reflectance transformation requires the lighting condition available on the scene to be estimated or measured for each image acquired and is very tedious to perform. In this paper we propose an automatic procedure to compensate for the lighting conditions that is adapted to the classification paradigm.

2. THEORY

Let L be a matrix of dimension (N×P) that corresponds to N spectra-radiance signal of P wavelengths extracted from a hyperspectral image.With Lambertian materials, for a pixel i,j, the measured radiance is given by equation (1):
L_(i,j) ()=r_(i,j) ().E() (1)
Where〖 r〗_(i,j) () is the reflectance in radiance and E() is the spectral irradiance.
Let X^((R)) and X(L) be matrices containing log-reflectance and log-radiance spectra respectively.
Let consider a discrimination method that first maps the high dimensional spectra into alower dimensional feature space. The scores obtained for each spectrum in this lower dimensional space are then use to compute a discrimination rule.
Dimension reduction models D^((R)) and D^((L)) built on X^((R)) and X(L) respectively transformed these matrices into lower dimensional score matrix S(R) and S(L) of dimension (N×Q) with Q<<P .
Due to similar lighting at each pixel and because the first step of (most) dimension reduction methods is to center the matrices X^((R)) and X^((L)), the models obtained from either centered log-radiance or centered log-reflectance spectra are the same and equal to D.
We can further demonstrate that the scores obtained from the matrix X^((L)) using D are only translated versions of that of X^((R) ):
S^((L) )=X^((L) ) D=(X^((R) )+〖1_N x〗^((E) ) )D=S^((R) )+〖1_N s〗^((E) ) (3)
With x^((E) ) the log-irradiance vector, 1_N the all-ones N dimensional vector and S^((E) ) the log-irradiance reduced vector.
Indeed, the use of a discrimination model built on a log-radiance image and applied on other log-radiance images with lighting variations is therefore possible. Translation correction of news log-radiance images is however a pre-requisite to apply the discrimination model.
To compensate for this translation, we borrowed a registration technique. Classes are clustered in the low dimensional space and their densities can be estimated. The main difference between these densities corresponds to the translation factor which is then compensated for with registration. Once registered, the decision rule can be applied.

RESULTS AND DISCUSSION

The methodology described above was applied on remotely-sensed hyperspectral images acquired in a wheat field using a Hyspex camera in the visible and near-infrared range (VNIR 1600, Norks Elektro Optikk, Norway). The classification maps obtained using a on the reflectance and the translated radiance images are similar, with around 8% of classification error. On the contrary, results obtained without correction are, due to the change in lighting conditions, completely wrong with up to 40% of misclassification and thus prove the effectiveness of the proposed method.