## 3 Results
### Recognition of Intergranular Corrosion Patterns Using the Fuzzy ARTMAP ANN  
The Fuzzy ARTMAP ANN performs learning that minimizes the predictive error and maximizes generalization. This is achieved by a match-tracking process that increases the surveillance parameter by the minimum amount necessary to correct an error in pattern recognition. The implementation of the Fuzzy ARTMAP ANN starts with a data normalization process since both the training and test patterns must correspond to the interval (0, 1). Subsequently, the vigilance parameters were defined, such as the Base Vigilance (\(\rho_{a}\)), Vigilance (\(\rho_{b}\)), and Rho map (\(\rho_{map}\)). Like the training and test sets, the monitoring parameters must be placed in an interval (0.1), so an experimental design is programmed where, for each monitoring parameter, it is increased by 0.1, and the rest are fixed. In this way, the answers are stored, and the architectures found that this minimizes the error in the pattern recognition task.  
Another aspect to consider when programming the Fuzzy ARTMAP ANN is the size of the input and output vectors; however, these values were defined depending on the application case and type of processing applied to the input signal. In the case of the recognition of intergranular corrosion patterns from the Fuzzy ARTMAP ANN, an architecture defined for each type of digital processing was implemented in the metallographic images. The selection criterion between the architectures was the minimization of the MSE, and in this way, it achieves the efficient classification of the corrosion patterns present in the microstructures of AISI 304 stainless steel; see Table 13.  
With the intention of evaluating the performance of the ARTMAP Fuzzy artificial neural network architectures, the indicators of sensitivity, specificity, and accuracy are calculated. See Tables 14 and 15.  
Table 16 shows the average accuracy offered by each of the classification models to recognize the three intergranular corrosion patterns present in AISI 304 stainless steel, based on analyzing the information provided by the digital image processing used in the investigation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Phase Congruence** & **GLCM Matrix** \\ \hline Input vector dimension & [30 \(\times\) 1] & [14 \(\times\) 1] \\ Output vector dimension & 1 & 1 \\ Base Vigilance (\(\rho_{a}\)) & 0.1 & 0.2 \\ Vigilance (\(\rho_{b}\)) & 0.8 & 0.9 \\ Rho map (\(\rho_{map}\)). & 0.9 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Fuzzy ARTMAP artificial neural network architectures.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Sensitivity** & **Specificity** & **Accuracy** \\ \hline No intergranular corrosion (NIC) & 0.93 & 0.93 & 0.92 \\ Presence of intergranular corrosion (PCI) & 0.91 & 0.84 & 0.89 \\ Precipitation of chromium carbides (PCC) & 0.95 & 0.96 & 0.93 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Performance indicators using the phase congruence method.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Sensitivity** & **Specificity** & **Accuracy** \\ \hline No intergranular corrosion (NIC) & 1.00 & 0.96 & 0.97 \\ Presence of intergranular corrosion (PCI) & 1.00 & 0.91 & 0.98 \\ Precipitation of chromium carbides (PCC) & 0.93 & 1.00 & 0.98 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Performance indicators using the GLCM method.  
According to the results obtained, the multilayer perceptron ANN presents a greater efficiency using phase congruence image processing. Regarding the GLCM processing method, the Fuzzy ARTMAP ANN managed to match the efficiency achieved by the multilayer perceptron ANN in the task of intergranular corrosion pattern recognition. The SVM achieves its best recognition efficiency when integrated with the phase congruency image processing method.