Pattern Recognition

In order to use matched filters for classification, one matched filter vi is created for each class ωi to be recognized. The filters are moved over the image and for each position the best match is recorded. More formally, the feature vector at position x = (x,y)T is given by

$m\left(x\right):=\text{col}\left\{\left\{g\left(x\prime \right)|x\prime =x-\alpha ,\forall \alpha \in \mathcal{U}\right\}\right\},\left(7.78\right)$

i.e., the column vector of image pixels within the (shifted) region U around x. The decision function for each filter vi, i= 1, . . . ,c, is given by ki (m(x)) = vT im(x) and the decision vector becomes

$k\left(m\left(x\right)\right)=\left(\begin{array}{c}{v}_1^T\\ ⋮\\ v_c^T\end{array}\right)m\left(x\right)=Vm\left(x\right).\left(7.79\right)$

This decision vectoris evaluated at every pixel of the input image. As there ...