# Fi-Fo Detector: Figure and Formula Detection Using Deformable Networks
## 4 Experimental Results
### Results and Discussions
This is one of the primary reasons why purely data-driven techniques were not found to be very effective for this dataset in comparison to using hand-defined heuristics. This provides a clear edge to the Fi-Fo detector over [PERSON] et al. 's [9] method, in terms of generalization. Fi-Fo detector demonstrated to be a generic network by pointing out discrepancies in the ICDAR-2017 POD dataset, highlighted in Figure 5. Secondly, the Fi-Fo detector does not rely on any pre/post-processing, rather simple image transforms providing a clear edge not only in terms of efficiency and computation costs, but also the state-of-the-art results, as shown in Figure 6a,b. We also report results from the ablation study where we removed components from the Fi-Fo detector to identify the contribution of the individual components to the system. To further validate the performance and potential of Fi-Fo detector, we present an ablation study that covers the potential of Fi-Fo image representation and deformable neural networks in comparison to raw image representation and non deformable neural networks. We observed a clear performance boost from raw image representation to Fi-Fo image representation and non-deformable neural networks to deformable neural networks, results are furnished in Table 4. The state-of-the-art \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Trained: ICDAR-2017 POD, Tested: ICDAR-2017 POD (corrected)**} & \multicolumn{4}{c}{\(IoU=0.8\)} \\ \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Class**} & \multicolumn{4}{c}{\(IoU=0.6\)} & \multicolumn{4}{c}{\(IoU=0.8\)} \\ \cline{3-10}  & & **Precision** & **Recall** & **F1-score** & **AP** & **Precision** & **Recall** & **F1-Score** & **AP** \\ \hline \multirow{2}{*}{[PERSON] et al. [9]} & Formula & 0.935 & 0.331 & 0.489 & 0.312 & 0.877 & 0.310 & 0.459 & 0.274 \\  & Figure & 0.918 & 0.292 & 0.443 & 0.271 & 0.888 & 0.283 & 0.429 & 0.253 \\ \hline \multirow{2}{*}{Fi-Fo Detector} & Formula & 0.949 & 0.945 & 0.947 & 0.967 & 0.897 & 0.893 & 0.895 & 0.941 \\  & Figure & 0.930 & 0.932 & 0.931 & 0.97 & 0.899 & 0.900 & 0.899 & 0.952 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of Fi-Fo with existing state-of-the-art methods using ICDAR-2017 POD in training and ICDAR-2017 POD (corrected) for testing. performance is achieved by using the combination of Fi-Fo image representation with deformable neural networks. Using an IoU threshold of 0.6 as per ICDAR-2017 POD competition standards, we achieved state-of-the-art results for formula detection with a precision of 0.957 and recall of 0.952 which translates to an F1-score of 0.954. Results with an IoU of 0.8 are 0.913, 0.908, and 0.91 in terms of precision, recall, and F1-score for formula detection, respectively. In figure detection, at an IoU threshold of 0.6, Fi-Fo detector achieved a precision of 0.931, recall of 0.913 along with an F1-score of 0.905. Setting the IoU threshold to 0.8 translated into a precision of 0.901, recall of 0.885 along with F1-score of 0.893. In terms of average precision, Fi-Fo detector outperformed other methods with a significant margin. At IoU=0.6, average precision of figure and formula detection was found to be 0.949 and 0.905, while at IoU=0.8, the average precision of 0.898 and 0.870 for formulas and figures was achieved, respectively. The obtained results highlight the superiority of the deformable model family for this task where the models either outperformed or achieved performance on par with heuristic-based methods.