**4.2 Chemometric model**

Because hyperspectral images include hundreds of contiguous spectral bands, they have a very high potential for spectral discrimination, compared to classical colour or multispectral images. Unfortunately, in a classification context, these kinds of high-dimensional datasets are difficult to handle and tend to suffer from the problem of the "curse of dimensionality", well known as "Hughes phenomenon" (Hughes, 1968) which causes inaccurate classification (figure 14).

Fig. 14. Illustration of Hughes phenomenon

In this context, it is important to note that some news techniques already exist to overcome this problem. Among all possible methods, many recent works have focused on the area of dimensionnality reduction approaches in order to reduce this highdimensional datasets while maintaining the relevance of the information contained in the signal.(Journaux et al., 2008). One of these approaches is the Partial Least Square Regression (PLS-R) , which builds a low-dimension subspace by determining a set of spectral "latent variables". Compared to other reduction methods such as Principal Component Analysis (PCA), the PLS takes into account both inputs and outputs to build its subspace, leading to better performances. The PLS-DA (PLS Discriminant Analysis) is an adaptation of PLS-R to discrimination problems.

In our case, a total of 335 spectra was increased step by step on a first reflectance image (figure 15) in three categories, namely wheat (157 spectra), dicotyledons (60 spectra) and ground (118 spectra).

A PLS-DA model was then determined on this data set by cross-validation using commercial software in chemometrics (The Unscrambler v9.7, CAMO Software AS, Oslo, Norway).

The resulting discriminant model, which involves 8 latent variables, was then exported and applied to all pixels in an image test, using a dedicated software developed in C + +.

Fig. 15. Calibration image and sample positions (the reference ceramic can be seen on the left)
