## 3 Results
Therefore, it makes more sense to compare our cross-validation results with state-of-the-art solutions because they also excluded the test set from the training process. Table 3 compares the best average \(FM\) obtained using the proposed method in all four scenarios with state-of-the-art methods based on deep learning and traditional methods. It might seem counterintuitive to compute \(\overline{FM}_{I}\) and \(\overline{FM}_{D}\) for the winners of the DIBCO competitions, because they are entirely different solutions, but the scores for the other solutions were also computed for different model instances obtained using different training and test sets. The results for DIBCO 2019 are highlighted because previous state-of-the-art methods performed significantly worse on that dataset, most likely owing to the increased variance of the images compared with the previous DIBCO datasets. \(\overline{FM}_{19}\) represents the average \(FM\) for the DIBCO 2019 dataset, \(\overline{FM}_{9D}\) represents the average \(FM\) for the nine previous DIBCO datasets, and \(\overline{FM}_{9I}\) represents the average \(FM\) for all the images from the previous nine DIBCO datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & \(\overline{FM}_{9D}\)**(\%)** & \(\overline{FM}_{9I}\)**(\%)** & \(\overline{FM}_{19}\)**(\%)** & \(\overline{FM}_{D}\)**(\%)** & \(\overline{FM}_{I}\)**(\%)** \\ \hline Otsu & 78.74 & 78.75 & 63.87 & 77.25 & 76.56 \\ \hline Sauvola & 79.72 & 80.05 & 63.82 & 78.13 & 77.66 \\ \hline DIBCO winners & 91.33 & 91.30 & 72.88 & 89.49 & 88.59 \\ \hline Howe & 90.93 & 90.97 & 48.20 & 86.66 & 84.68 \\ \hline Jia & 89.94 & 89.93 & 55.87 & 86.53 & 84.92 \\ \hline DeepOtsu & 91.68 & 91.57 & 60.75 & 88.59 & 87.04 \\ \hline SAE & 92.98 & 93.04 & 58.78 & 89.56 & 88.01 \\ \hline DD-GAN & 92.71 & 92.82 & 58.01 & 89.24 & 87.70 \\ \hline MRAM & 91.93 & 91.90 & 49.53 & 87.69 & 85.67 \\ \hline
2 DMIN & 84.46 & 87.49 & 42.76 & 80.29 & 78.61 \\ \hline cGANs & 93.19 & 93.18 & 62.29 & 90.10 & 88.64 \\ \hline CT-Net & 94.03 & 94.05 & - & - & - \\ \hline DE-GAN & 93.33 & 94.13 & 56.03 & 89.60 & 88.52 \\ \hline Suh & 93.33 & 93.25 & 70.63 & 91.06 & 89.92 \\ \hline GDB & 93.84 & 93.82 & 73.84 & 91.84 & 90.89 \\ \hline GDBMO & 94.10 & 94.20 & 73.50 & 92.04 & 91.16 \\ \hline D2 BFormer & **96.02** & **96.05** & 66.69 & 93.08 & 91.73 \\ \hline DocBinFormer & 95.76 & 95.87 & 60.31 & 92.22 & 90.64 \\ \hline Scenario 1 & 91.776 & 91.777 & 91.763 & 91.775 & 91.775 \\ \hline Scenario 2 & 94.367 & 94.368 & 94.351 & 94.366 & 94.365 \\ \hline Scenario 3 & 95.846 & 95.845 & **95.846** & **95.846** & **95.845** \\ \hline Scenario 4 & 95.677 & 95.675 & 95.658 & 95.675 & 95.673 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: State-Of-The-Art Comparison. Figure 1 compares the binarization results for image 9 from the DIBCO 2019 dataset, which is difficult to binarize because of the ink bleeding from the other side of the page. Figure 2 compares the binarization results for image 13 from the DIBCO 2019 dataset, which is difficult to binarize because of the missing parts of the papyrus on which the text is written. In both figures, green signifies false positives (background pixels classified as foreground), and magenta signifies false negatives (foreground pixels classified as background). The proposed solution is compared with a classic global thresholding method (Otsu), a classic local thresholding method (Sauvola), and a state-of-the-art deep learning method that achieved the highest average \(FM\) for the DIBCO 2019 dataset (GDB). Both figures graphically illustrate that the proposed solution performed significantly better than the classical and state-of-the-art methods for exceedingly difficult images. Appendix A contains high-resolution versions of the proposed solution binarization for both images. Figure 1: Comparison of binarization results. Left to right, top to bottom: original image, ground-truth, Otsu binarization, Sauvola binarization, GDB binarization, proposed solution binarization.