## 3 Results
### Final Results and Discussion  
As shown throughout this section, the best results are obtained by RBC with a recognition rate of 95.12%, followed by LBP and LTP with a recognition rate of 89.43 %. These results show the validity of applying Radon Barcodes to facial emotion recognition, as seen in Section 2, and it can be then concluded that the RBC descriptor is a reliable, robust texture descriptor against noise and scale and rotation invariance.  
Figure 8: Recognition rate according to LTP threshold.  
Figure 9: Recognition rate according to RBC projections.  
Taking into account the cross-validation values of each method, LBP has a value of 7.69%, LTP obtains 19.23%, and RBC a cross-validation score of 11.54%. With these results, it can be said that, in terms of being independent from the training images, LBP is better than LTP and RBC. Considering the runtime to identify the pain in an input image, LBP takes around 20 ms in processing a frame, LTP around 300 ms, and RBC around 30 ms. Therefore, in terms of cross-validation score and execution time results, LBP obtains better results. However, RBC behaves much better in terms of recognition rate. In Table 1, there is a summary of the obtained results.  
Considering that typically videos work at 25-30 frames per second, it can be said that both LBP and RBC would be able to analyze all frames detected in a second, allowing the system to be integrated in a mobile app or a wearable device. However, since facial expressions do not change drastically in less than a second, the recognition process would not lose accuracy by just analyzing a few frames per second, instead of 25-30. This would also reduce workload, getting a more efficient tool in terms of speed, as a result.  
Finally, in Table 2, there is a comparison between our research and some previous works. All of these works have made use of the Infant COPE database and different feature extraction methods and classifiers such as texture descriptors, deep learning methods, or supervised learning methods.  
From the comparison of Table 2, it can be observed that the proposed method with Radon Barcode achieves the best recognition rate, over 10%, compared with previous works working with the same database. Therefore, it can be said that the proposed method can be used as a reliable tool to classify infant face expressions as pain or non-pain. Moreover, the time to process the algorithm makes it feasible to be implemented in a mobile app or a wearable device.  
Finally, from the results in Table 2, it must be pointed out that different research that has used the same algorithms may provide different recognition rate results. This may be the result of the pre-processing stage in each work or due to the input parameters of the different feature extraction methods and/or the classifier used.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Recognition Rate (\%)** & **Cross-Validation (\%)** & **Execution Time per Frame (ms)** \\ \hline LBP & 89.43 & **7.96** & **20** \\ LTP & 89.43 & 19.23 & 300 \\ RBC & **95.12** & 11.54 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 1: A summary of texture descriptors’ results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Article** & **Algorithm** & **Recognition Rate (\%)** \\ \hline [PERSON] et. al. [3] & PCA+SVM & 82.55 \\ [PERSON] et. al. [10] & PCA+SVM & 88 \\ [PERSON] and [PERSON] [11] & LBP+Gaussian & 87.74–88 \\ LBP+K-NN & 76–80 \\ [PERSON] et. al [12] & LBP+SVM & 82.6 \\ [PERSON] and [PERSON] [13] & LBP+HOG+ CNN & 82.95 \\ [PERSON] et. al [14] & CNN+Strain+NB & 92.71 \\ [PERSON] et. al [15] & N-CNN & 84.5 \\ The proposed method & LBP+SVM & 89.43 \\ The proposed method & LTP+SVM & 89.43 \\ The proposed method & RBC+SVM & **95.12** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison with other works.