## 4 Experimental Setup
### Description of the Testing Protocol  
The returned, now-fixed model verifiers \(\Delta_{SVM}\) (or \(\Delta_{DSC-BFS}\)) are now utilized at the testing stage. For each writer of the testing set \(\mathbb{TS}\), a reference set \(\mathbb{N}_{REF}\) of \(|\mathbb{N}_{REF}|=10\) signature samples is reserved out of its \(\mathbb{N}_{\mathbb{G}}\) genuine samples. The remaining \(\mathbb{Q}^{+}=\{\mathbb{N}_{\mathbb{G}}-\mathbb{N}_{REF}\}\) and \(\mathbb{Q}^{-}=\mathbb{N}_{\mathbb{SF}}\) samples form the \(|\mathbb{Q}^{+}|\) positive and \(|\mathbb{Q}^{-}|\) negative members of the questioned set \(\mathbb{Q}^{\pm}=\{\mathbb{Q}^{+},\mathbb{Q}^{-}\}\). Typically, the \(\mathbb{N}_{REF}\), \(\mathbb{Q}^{\pm}\) corresponding covariance matrices are now paired in order to create the RDV's \(\Psi^{\mu}_{\{g,S,I\}}\) and \(\Psi^{L\mu}_{\{g,S,I\}}\), along with their vectored forms \(v^{\pm}_{\{g,S,I\}}\) and \(dv^{\mu\pm}_{\{g,S,I\}}\), \(a=1:14\). Since we have two learning procedures, the serial \(LFW1\) and the parallel \(LFW2\), we also now provide details regarding their equivalent testing companion, namely the serial \(TFW1\) and the parallel \(TFW2\). The implementation steps of \(TFW1\) are graphically depicted in Figure 6. For a single covariance pair, \(\mathbf{\mathcal{R}}\in\mathbb{N}_{REF}\) and \(\mathbf{Q}\in\mathbb{Q}^{\pm}\), we begin by evaluating a vector of 14 scores \(sc_{\Delta}=\{sc_{\Delta}(a)\leftarrow\Delta_{a}\}\in\mathbb{R}^{14}\) each with \(a\)-component \(\Delta_{a}\), \(a=1:14\) to correspond to the local spatial segments of Figure 2. Then, the following steps are applied:  
* Sort \(sc_{\Delta}\) in a descending order, thus creating the \(sc_{s\Delta}=\{sc_{s\Delta}(a)\equiv s\Delta_{a}\}\in\mathbb{R}^{14}\) score vector. * Generate the final score vector \(sc^{f}_{s\Delta}\in\mathbb{R}^{14}\) by (a) assigning its first component \(sc^{f}_{s\Delta}(1)\) to the original \(\Delta_{1}\) value and (b) assigning its value as \(sc^{f}_{s\Delta}(a)\equiv\overline{s\Delta_{a}}=\underline{means_{s\Delta} }(1:a)\) for every \(a=1:14\) local segment. Then, for all \(|\mathbb{N}_{REF}|\times|\mathbb{Q}^{\pm}|\) pairs, a stack \(D=\{D_{a}\},\ a=1:14\), \(D_{a}\in\mathbb{R}^{|\mathbb{Q}^{\pm}|\times|\mathbb{N}_{REF}|}\) is formed in which the \"\(D_{a}\)-level\" has elements, which are the corresponding \(\overline{s\Delta_{a}}(\mathbf{\mathcal{R}},\mathbf{Q})\) values. In conclusion, a final score vector \(FSV(a|\mathbb{Q}^{\pm})\in\mathbb{R}^{|\mathbb{Q}^{\pm}|}\) is derived by assigning the maximum distance of \(\mathbf{Q}\) over the entire reference set \(\mathbb{N}_{REF}\). The \(FSV(a)\) scores are a function of the segment parameter \(a\) and are conditioned on the positive or/and negative class. Following the evaluation of the \(FSV(a|\mathbb{Q}^{\pm})\) scores, a sliding threshold evaluates the per-writer false acceptance rates \(FAR_{SF}\) (i.e., skilled forgeries that have been accepted as genuine), the false rejection rates \(FRR\) (i.e., genuine samples that have been rejected as forgery), and the corresponding equal error rates \(EEK^{user}_{SF}\) as the point in which \(FAR_{SF}=FRR\). The above process is repeated ten times for each writer, and the averages are reported as a function of the \(a\) parameter in the following section. The implementation steps of \(TFW2\) are much simpler. Following the learning stage of the \(\Delta_{SVM}\) (or \(\Delta_{DSC-BFS}\)) verifiers with the 770-dimensional feature vectors \(\{v^{\mu\pm}_{\{g,S,I\}}\}\), \(\{dv^{\mu\pm}_{\{g,S,I\}}\}\) depicted in Figure 4, we utilize the same \(\mathbb{TS}\) set of the TFW1 framework by means of the same reference \(\mathbb{N}_{REF}\) and questioned \(\mathbb{Q}^{\pm}=\{\mathbb{Q}^{+},\mathbb{Q}^{-}\}\) sets. The output of the \(\Delta_{SVM}\) (or \(\Delta_{DSC-BFS}\)) verifiers is a set of scores conditioned on the \(\mathbb{Q}^{+}\) or \(\mathbb{Q}^{-}\) classes. In a similar approach, the \(EEK^{user}_{SF}\) is evaluated for each writer.