Discriminant functions

Each of the above mentioned three classes has an associated discriminant function denoted as $g_1$, $g_2$, and $g_3$, respectively. Let $\bf X$ denote a feature vector extracted from an image $K$. Representing the system as classifier in a canonical form through the set of these three discriminant functions, the classifier classifies $\bf X$ and, hence, $K$, to the class $\Omega_i$ if

$$g_i({\bf X}) > g_j({\bf X}), \:\: i \neq j, \:\: i,j \in \{1,2,3\}$$ (26)

For minimum-error-rate classification [25] we may set

$$g_i({\bf X}) = \log[P(\Omega_i\vert{\bf X})]$$ (27)

Figure 2: Some of the images in the database.