Algorithm 1. AdaBoost training procedure

Given example images (${\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}})$, $\mathrm{i}=1,\dots ,\mathrm{n}$, where ${\mathrm{y}}_{\mathrm{i}}=0, 1$ for negative and positive examples, respectively. Initialize the weights ${\mathrm{w}}_{1,\mathrm{i}}=\frac{1}{2\mathrm{m}},\frac{1}{2\mathrm{l}}$ for ${\mathrm{y}}_{\mathrm{i}}=0, 1$, for $\mathrm{m}$ negative and $\mathrm{l}$ positive samples, respectively. For $\mathrm{t}=1,\dots ,\mathrm{T}$: Step 1. Weight normalization $${\mathrm{w}}_{\mathrm{t},\mathrm{i}}={\mathrm{w}}_{\mathrm{t},\mathrm{i}}/{\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{t},\mathrm{j}}$$ (3) Step 2. For each feature $\mathrm{j}$, a classifier ${\mathrm{h}}_{\mathrm{j}}$ is trained, whose error is calculated with respect to the weight, which enables the algorithm to emphasize on the most incorrectly classified instances in order to address them in further steps: $${\mathrm{e}}_{\mathrm{j}}={\displaystyle \sum }_{\mathrm{i}}{\mathrm{w}}_{\mathrm{i}}\left|{\mathrm{h}}_{\mathrm{j}}\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right)\right|$$ (4) Step 3. Select the classifier that exhibits the smallest error. Step 4. Update the weights $${\mathrm{w}}_{\mathrm{t}+1,\mathrm{i}}={\mathrm{w}}_{\mathrm{t},\mathrm{i}}{\mathsf{\beta }}_{\mathrm{t}}^{1-{\mathrm{c}}_{\mathrm{i}}}$$ (5) where $$c_i=\{\begin{array}{ll}0& \mathrm{correctly} \mathrm{classified} \mathrm{examples}\\ 1& otherwise\end{array}$$ (6) and $${\mathsf{\beta }}_{\mathrm{t}}=\frac{{\mathrm{e}}_{\mathrm{t}}}{1-{\mathrm{e}}_{\mathrm{t}}}$$ (7) The final strong classifier is given by: $$h_j\left(x\right)=\{\begin{array}{ll}1& {\displaystyle {\displaystyle \sum }_{t=1}^T}{\propto }_t{h}_t\left(x\right)\ge \frac{1}{2}{\displaystyle {\displaystyle \sum }_{t=1}^T}{\propto }_t\\ 0& otherwise\end{array}$$ (8)