*3.2. Similarity Measures*

Let *ρi* be a spectral signature, *ρi*,*<sup>λ</sup>* its reflectance at wavelength *λ* and [1, ..., *L*] its spectral range. Several criteria have been used (Table 4). Some criteria characterize the difference between reflectance levels (like the distances) and other ones are related to the difference of the spectral shape (e.g., SAM) and other ones are related to probabilistic behaviour (e.g., SID, ...). Table 4 inventories main similarity measurement techniques described in the literature.


#### **Table 4.** Similarity measures.

#### *3.3. Relative Spectral Discriminatory Probability*

To determine if a spectral signature belongs to a class, the method proposed by [45] is used. Let {*ρj*}*Jj*=<sup>1</sup> *J* spectral signatures in Δ an existing spectral reference database and *τ* be a target signature to be identified using Δ. Let *<sup>m</sup>*(·, ·) be a given hyperspectral measure, the spectral discriminatory probabilities of all *ρj* in Δ with respect to *τ* as is defined as follows:

$$p^m\_{\tau,\Lambda}(i) = \frac{m(\tau,\rho\_i)}{\sum\_{j=1}^l m(\tau,\rho\_j)}, \text{ for } i = 1,2,...,l,\tag{2}$$

where *J* ∑ *j*=1 *<sup>m</sup>*(*<sup>τ</sup>*, *ρj*) is a normalization constant determined by *τ* and Δ. The resulting probability vector isdefinedas

$$\mathbf{p}^{m}\_{\tau,\Lambda} = \left( p^{m}\_{\tau,\Lambda}(1), p^{m}\_{\tau,\Lambda}(2), \dots, p^{m}\_{\tau,\Lambda}(J) \right)^{T}.\tag{3}$$

Using Equation (3), the target signature can be identified by selecting the one with the smallest spectral discriminatory probability because *τ* and the selected one have the minimum spectral discrimination.
