## 4 Experimental Setup
### The Learning Framework  
The structure of the experimental WI-SV framework draws its inspiration mainly from the seminal work of [PERSON] et al. [28], which highlights the use of blind, or disjoint, subsets for the development and testing of the model or verifier. It adheres to the underlying assumption that the learning, or development, subset \(\mathbb{L}\) of writers used for building and validating the model is sufficient for the testing or exploitation stage. Therefore, in accordance with the Section 1, we make use of two blind sets: (a) the learning set \(\mathbb{L}\) and (b) the testing set \(\mathbb{TS}\). The origin of the \(\mathbb{L}\) and \(\mathbb{TS}\) sets depends on the intra-lingual or inter-lingual nature of the experimental framework. In the case of the intra-lingual framework, denoted hereafter with \(\mathcal{F}_{intra}\), any signature dataset \(\mathcal{D}_{i}\) splits its initial population of writers into two equally populated subsets, \(\mathbb{L}\) and \(\mathbb{TS}\). During one fold, the learning set \(\mathbb{L}\) is further divided into the training \(\mathbb{T}_{\mathbb{R}}\) and validation sets \(\mathbb{V}\) so that \(\mathbb{L}=\{\mathbb{T}_{\mathbb{R}}\cup\mathbb{V}\}\). In the course of the training stage, the \(\mathbb{T}_{\mathbb{R}}\) set is employed for evaluation of the current operating parameters of the model under learning, while the validation set \(\mathbb{V}\) is employed in order to select the optimal operating parameters of the model. In the course of the testing stage, the \(\mathbb{TS}\) subset is employed in order to evaluate the efficiency of the model. Then, in order to conclude the fold, the \(\mathbb{L}\) and \(\mathbb{TS}\) subsets swap roles so that the model learns the new \(\mathbb{L}\leftarrow\mathbb{TS}\) and \(\mathbb{TS}\leftarrow\mathbb{L}\). We randomly repeat the selection of the \(\mathbb{L},\mathbb{TS}\) writers five times; this is the so-called \(5\times 2\) fold, which has been followed in our experiments [37; 55; 56]. As for the case of the inter-lingual framework, denoted hereafter with \(\mathcal{F}_{inter}\), a kind of a transfer learning concept in which the model learns an entire dataset \(\mathcal{D}_{i}\), it is then tested over the remaining datasets \(\mathcal{D}_{j}\), \(j\
eq i\). Figure 5: Example of the preprocessing procedure and the applied filters. Top left: the original handwritten signature. Top right: the output of the preprocessing (threshold and thinning). The remaining images depict the visual output of each image filter: \(I_{x}\), \(I_{y}\), \(I_{xx}\), \(I_{yy}\), \(I_{yy}\), \(\sqrt{{I_{x}}^{2}+{I_{y}}^{2}}\), \(tan^{-1}\big{(}I_{y}/I_{x}\big{)}\), \(x,y\). We now provide details regarding the generation of the learning set \(\mathbb{L}=\{\mathbb{T}_{\mathbb{R}}\cup\mathbb{V}\}\). Therefore, let us denote the cardinality of writers for each dataset \(\mathcal{D}_{i}\) with \(\mathbb{N}_{\mathcal{D}_{i}}=|\mathcal{D}_{i}|\). At each \(\mathcal{F}_{intra}\) fold, the cardinality of the learning set \(\mathbb{L}\) is \(\mathbb{N}_{\mathbb{L}}=\lceil|\mathcal{D}_{i}|/2\rceil\). Each one of the \(\mathbb{N}_{\mathbb{L}}\) writers is populated by \(\mathbb{N}_{\mathbb{G}}\) and \(\mathbb{N}_{\mathbb{SF}}\) genuine and skilled forgery samples. The \(\mathbb{T}_{\mathbb{R}}\) and \(\mathbb{V}\) subsets are formed by representatives of both the similar and the dissimilar \(\omega_{\mathbb{T}_{\mathbb{R}}}^{\pm}\), \(\omega_{\mathbb{V}}^{\pm}\) classes. To do so, \(\mathbb{N}_{\mathbb{GT}_{\mathbb{R}}}=\lceil 0.7\mathbb{N}_{\mathbb{G}}\rceil\) and \(\mathbb{N}_{\mathbb{SF}_{\mathbb{R}}}=\lceil 0.7\mathbb{N}_{\mathbb{SF}}\rceil\) samples were reserved for the \(\mathbb{T}_{\mathbb{R}}\) subset, and \(\mathbb{N}_{\mathbb{GV}}=\lfloor 0.3\mathbb{N}_{\mathbb{G}}\rfloor\) and \(\mathbb{N}_{\mathbb{SFV}}=\lfloor 0.3\mathbb{N}_{\mathbb{SF}}\rfloor\) were reserved for the \(\mathbb{V}\) subset.