## 2 Proposed Approach and Its Verification
### Combined Metrics and Discussion of Results  
The experimental results presented as the correlations of individual metrics used for the computation of aggregated mutual similarities with Levenshtein Distances obtained for all 1760 images are shown in Table 1. As it may be noticed, for some of the metrics, correlation values are very small, and therefore they cannot be considered useful for predicting the quality of final OCR results. The best results have been obtained for F-Measure and pseudo-F-Measure; hence, these two metrics are the most appropriate for the analyzed application. Considering the encouraging results obtained by the combination of metrics presented in some earlier papers, including their application to binary images [20], the next conducted  
Figure 5: Illustration of the idea of calculation of mutual similarities for binary images. experiments have been related to the validation of the combination of the two abovementioned \"best\" metrics. The first model is defined as the weighted product of two metrics:  
\[CM_{1}=\prod_{i=1}^{2}Q_{i}{}^{\text{{\tiny{2v_{i}}}}}=(\text{F-Measure})^{\text{{ \tiny{2v_{1}}}}}\cdot(\text{pseudo-F-Measure})^{\text{{\tiny{2v_{2}}}}}\, \tag{1}\]  
where \(Q_{i}\) are the averaged mutual similarities obtained using the individual metrics being combined and \(w_{i}\) are their weights obtained as the result of optimization using MATLAB's (version R2024a) minsearch function. The second considered model is defined as the weighted sum of two individual metrics, also used as the averaged mutual similarities:  
\[CM_{2}=\sum_{i=1}^{2}(a_{i}\cdot Q_{i}{}^{\text{{\tiny{2v_{i}}}}})=a_{1}\cdot( \text{F-Measure})^{\text{{\tiny{2v_{1}}}}}+a_{2}\cdot(\text{pseudo-F-Measure})^{ \text{{\tiny{2v_{2}}}}}. \tag{2}\]  
The main motivation of the use of the above defined combined metrics originates from the application of a similar approach for natural images for which a significant increase in the correlation between the objective and subjective quality scores has been reported. Some initial experiments have been conducted for the nonlinear combination of three metrics, MS-SSIM, VIF, and R-SVD, further changed into the combination of MS-SSIM, VIF, and FSIM\({}_{\text{c}}\), leading to CISI metric [21], which is highly correlated with the subjective quality scores available in image quality assessment (IQA) datasets. Further extensions and applications of this approach for many various types of images, including binary images [20], remote sensing, or stitched images, fully confirmed the validity of this approach. A similar approach has also been applied by Netflix researchers in their Video Multi-Method Assessment Fusion (VMAF) metric [22]. Particularly interesting results have been obtained applying the combined metric based on the weighted sum, according to Formula (2), for multiply distorted images, proposed in the paper [23]. Although some attempts at the use of neural networks for designing the combined metrics have also been made [24], leading to comparable performance, the use of simpler combinations is more convenient for the considered application. As it may be seen in Table 2, the combination of two metrics has led to a noticeable improvement in correlation between the obtained IQA values and Levenshtein Distances, \begin{table}
\begin{tabular}{l c} \hline \hline
**Quality Metric** & **PLCC for Tesseract** \\ \hline Precision & 0.5594 \\ Recall/Sensitivity & 0.1003 \\ F-Measure & **0.8460** \\ Pseudo-Precision & 0.5972 \\ Pseudo-Recall & 0.1127 \\ Pseudo-F-Measure & **0.8810** \\ Specificity & 0.2957 \\ Balanced Classification Rate (BCR) & 0.1397 \\ S-F-Measure & 0.2019 \\ Accuracy & 0.2590 \\ Geometric Accuracy & 0.2165 \\ Peak Signal-to-Noise Ratio (PSNR) & 0.2543 \\ Border Distance (chessboard) [10] & 0.2939 \\ Border Distance (city block) [10] & 0.2805 \\ Border Distance (Euclidean) [10] & 0.2932 \\ Distance Reciprocal Distortion (DRD) [7] & 0.3662 \\ Misclassification Penalty Metric (MPM) [8] & 0.1928 \\ \hline \hline \end{tabular}
\end{table}