# FADIT: Fast Document Image Thresholding
## 4 Experimental Results
### Grid-based FADIT Compared with Other Algorithms  
The grid-based FADIT method is compared with [PERSON] method [17], grid-based [PERSON] method [18], and GLGM (gray-level and gradient-magnitude) histogram method [24]. We also present the results of grid-based [PERSON] et al.'s method. [18] obtain a conclusion that grid-based [PERSON] et al.'s method is better than the grid-based [PERSON]'s method, so we do not show the grid-based [PERSON] method in this section.  
In all of grid-based methods, \(s_{G}\) is set to  
\[s_{G}=\frac{\min(r,c)}{2} \tag{29}\]  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{4}{c}{**Peak Signal-to-Noise Ratio (dB)**} \\ \hline  & **[PERSON]** & **[PERSON]** & **FADIT** \\ \hline Image 1 & 9.2647 & 7.1802 & 11.5618 \\ Image 2 & 20.1543 & 20.3800 & 20.9538 \\ Image 3 & 7.2727 & 6.2408 & 16.0214 \\ Image 4 & 16.5733 & 13.1810 & 16.7075 \\ Image 5 & 20.3387 & 19.9889 & 21.5522 \\ \hline \hline \multicolumn{4}{c}{**Misclassification Error**} \\ \hline  & **[PERSON]** & **[PERSON]** & **FADIT** \\ \hline Image 1 & 0.1184 & 0.1914 & 0.0698 \\ Image 2 & 0.0097 & 0.0092 & 0.0080 \\ Image 3 & 0.1874 & 0.2376 & 0.0250 \\ Image 4 & 0.0220 & 0.0481 & 0.0213 \\ Image 5 & 0.0092 & 0.0100 & 0.0070 \\ \hline \hline \multicolumn{4}{c}{**Running Time in MATLAB (Microsecond)**} \\ \hline  & **[PERSON]** & **[PERSON]** & **FADIT** \\ \hline Image 1 & 2.5779 & 3.4130 & 1.6194 \\ Image 2 & 2.5601 & 3.3707 & 1.6029 \\ Image 3 & 2.5841 & 3.4544 & 1.6101 \\ Image 4 & 2.5750 & 3.4324 & 1.6071 \\ Image 5 & 2.5761 & 3.4037 & 1.6105 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Objective performance of different methods.  
where \(r\) and \(c\) denote numbers of row and column of the image, respectively.  
The image results of the mentioned methods are in Figure 3. Different from [PERSON]'s, [PERSON] et al.'s or FADIT method, [PERSON] method selects a threshold for each pixel, then obtains a thrshold matrix with the same size of the input image. Every threshold is calculated in the window centering on the corresponding pixel, so the algorithm runs quite slow, and the running time can been seen in Figure 3. From Figure 3a,f,k,p,u, we can see that the method can successfully extract the characters but can not obtain good result for the whole image as the background contains so much black noise. [PERSON] et al. (2018) have demonstrated that the grid-based technique greatly improved the results of [PERSON] et al.'s method, which can be seen from Figure 3b,g,l,q,v. As such, we apply grid-based technique into [PERSON] et al.'s and FADIT method. Figure 3 shows that grid-based technique indeed improves the results of [PERSON] et al.'s and FADIT method. However, grid-based [PERSON] et al.'s method still suffers from the problem in Figure 2m (see Figure 3m) while grid-based FADIT method obtains results all quite close to ground-truth images. GLGM method is a novel thresholding method which selects a global threshold based on the GLGM histogram, and it obtains satisfying results with natural images ([PERSON] et al., 2018) while not with document images (see Figure 3x).  
The quantitative evaluation result of different methods with the five images is listed in Table 3. According to the metrics, a grid-based FADIT method have outperformed the above methods.  
Figure 3: Results obtained by different thresholding methods: Each column from left to right shows the results of [PERSON] (**a**,f**,**k**,**p**,u**), Grid-based [PERSON] et al.’s (**b**,g**,l**,q**,v**), Grid-based [PERSON] et al.’s (**c**,h**,**m**,_r**,**w**), GLGM (**d**,i**,n**,s**,x**), and Grid-based FADIT method (**e**,j**,o**,t**,y**), respectively.