# Analysis of Score-Level Fusion Rules for Deepfake Detection
## 5 Discussion and Conclusions
Furthermore, the following considerations can be extracted from this analysis:  
* The designer, on the basis of the application context, should define whether they expect known (controlled tests) or unknown (uncontrolled or partially controlled tests) types of data and manipulations. * The designer should define at which operational point the detection system will have to work on the basis of the desired weight of first or second type errors. * The designer should use a validation set to analyze the distributions of the scores and select the fusion rule closest to their needs. Figure 9: Example of inferences from real images of the DFDC dataset (22093_5 (**a**) and 21309_6 (**b**)) of three of the analyzed score-level fusion methods from the scores of the single classification models (scores greater than or equal to 0.5 are identified by a red border and by a green border otherwise). Based on these considerations, it is important to highlight that:  
* In an optimal application context given by controlled tests, the designer should select the fusion rule that allows them to have the two distributions of the real and fake scores of the validation set unimodal with a small variability and centered, respectively, on 0 and 1. * The methods based on the weighted average generate single-model distributions with high variability and are therefore more suitable for applications with a decision threshold set to the system's EER. * The methods based on classification models generate bimodal distributions centered in 0 and 1 with a small variability and low density for the mode related to the wrong classifications; they are therefore more suitable for applications with a stringent decision threshold set, for example, at 1% FPR or 1% FNR. However, it should be noted that, although parametric methods are more suitable for fusion purposes, they require a weight estimation (or training) phase, which is time-consuming and can be influenced by biases present in the data used for such an estimation [49, 51]. Since the weight estimation phase is generally performed offline, the related time complexity may be regarded as minor in most application circumstances. The analysis of the online inference time highlights that it is not necessarily required to search for a trade-off between the computational complexity and performance of the fusion method because these are not always in opposition. Furthermore, in the previous investigation, it is also possible to observe that these would not represent the bottleneck of  
Figure 10: Example of inferences from fake images of the DFDC dataset (20010_23 (**a**) and 19970_16 (**b**)) of three of the analyzed score-level fusion methods from the scores of the single classification models (scores greater than or equal to 0.5 are identified by a red border and by a green border otherwise). the deepfake detection system, and therefore the eventually aimed real-time capability will mainly depend on the single classification systems included in the fusion, which generally require a considerably greater inference time (e.g., [52; 53; 54]). In any case, this applies to the score-level fusion across the analyzed methods, as other, more complex models (e.g., neural networks with multiple layers) could compromise the overall processing time. In conclusion, the employment of fusion methods appears to be able to exploit the complementarity of state-of-the-art models, thus, making the detection of deepfakes more robust even concerning the bias towards the acquisition sensors and the image features characterizing both deepfakes and the real samples employed in training. Among the explored fusion approaches, the parametric ones revealed greater robustness to the presence of less performing detection systems in the fusion as well as a more noticeable capability of exploiting the complementarity of the single deepfake detector.