# Cascade Network with Deformable Composite Backbone for Formula Detection in Scanned Document Images
## 4 Experimental Results
### Result and Discussion
#### 4.3.2. Marmot  
We follow similar evaluation criteria to report results on the Marmot dataset in order to draw a direct comparison with the prior work. Our network separately detects the isolated and embedded formulas in a document image due to their variable sizes between isolated and embedded formulas. Table 4 summarizes the performance of our method on the Marmot dataset. As explained in Section 4.2.6, we calculate the accuracies of correct and partial detections. Our proposed mathematical formula identification system achieves the correct detection accuracy of 93% and 92.5% on isolated formulas with and without incorporating the pre-processing method, respectively. In embedded formulas, the system obtains the correct detection accuracy of 81.3% and 80.6% equipped with and without the proposed dilation method, respectively. Besides calculating detection accuracy, we compute AP at an IoU threshold of 0.5 and 0.75 for both the isolated and embedded formula detection on the Marmot dataset. The achieved results are highlighted in Figure 10. Moreover, in Figure 11, we present the performance of correct detection accuracy over various IoU thresholds ranging from 0.5 to 1.0. Figure 8. Performance evaluation of the proposed method on the ICDAR-2017-POD dataset. The green colour depicts the ground truth, while red denotes the predicted bounding boxes. (**a,b**) exhibit true positives on a two-column and a single column document image, respectively. The qualitative performance analysis of the presented method on the Marmot dataset is exhibited in Figures 12-14. We predict correct regions for 236 out of 253 formulas present in the test set in detecting isolated formulas. In the case of embedded formulas, the network is able to precisely detect 777 out of the 956 formulas from the test set. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Formula** & **Correct (\%)** & **Partial (\%)** & **Total** \\ \hline \multirow{3}{*}{[PERSON] et al. [55]} & Isolated & 26.87 & 44.87 & 71.76 \\ \cline{2-5}  & Embedded & 1.74 & 28.87 & 30.61 \\ \hline \multirow{3}{*}{[PERSON] et al. [11]} & Isolated & 50.37 & 39.14 & 91.18 \\ \cline{2-5}  & Embedded & 22.9 & 58.45 & 81.35 \\ \hline \multirow{3}{*}{[PERSON] et al. [18]} & Isolated & 93 & - & - \\ \cline{2-5}  & Embedded & 73 & - & - \\ \cline{2-5}  & Isolated & 92.5 & 4.64 & 97.14 \\ \cline{2-5}  & Embedded & 80.6 & 6.23 & 86.83 \\ \hline \multirow{3}{*}{Ours (Without Pre-processing)} & Isolated & 93 & 4.86 & 97.86 \\ \cline{2-5}  & Embedded & 81.3 & 6.77 & 88.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison between our method and previous state-of-the-art approaches on the Marmot dataset. Figure 9: Performance evaluation of the proposed method on the ICDAR-2017-POD dataset. The green colour depicts the ground truth, while red denotes the predicted bounding boxes. (**a**) represents an example of both true positives and a single false positive case, whereas (**b**) shows three false positives with one false negative. Comparison with State-of-the-Art Methods  
We compare our results with earlier approaches on the Marmot dataset in Table 4. From the table, It is evident that our cascade network with a deformable composite backbone has clearly outsmarted the prior state-of-the-art method [18] in detecting embedded formulas while accomplishing identical results in the case of isolated formulas. We reduce the relative error of 30% by achieving a detection accuracy of 81.3% on embedded formulas. Another point that is worth mentioning is the partial detection accuracy. The proposed system partly predicts 4.86% from the remaining 7% missing isolated formulas, which makes the total detection accuracy 97.86%. For embedded formulas, we achieve a partial detection accuracy of 6.77%, which adds up to an 88.07% total detection accuracy. Therefore, our network only missed 2.14% and 11.93% of isolated formulas and embedded formulas from the test set, respectively.