# Privacy Preserving Face Recognition in Cloud Robotics: A Comparative Study
## 5 Performance Analysis of CNN Based Robot Face Recognition Models
### Accuracy  
The accuracy of the studied CNN models depends on the efficient feature extraction from encrypted images. Although a CNN model can easily extract features from clear images, it is a challenging task for it to extract features from encrypted images. The studied CNN models use different filters in convolution layers, pooling layers, and followed different strategies for features extraction, which leads to different accuracy of face recognition. Moreover, images with different poses, illumination effects, and disguise might lead to low face recognition accuracy value. Regarding encryption algorithms, they introduce some distortion in the images features. Thus, image features are distorted after encryption and consequently CNN models can lead to different results. Moreover, among the studied encryption algorithms some are linear and some are nonlinear. Therefore, they have different effect on the accuracy of the CNN models. According to the results shown in Table 4 the **Bit Slice**, **Chacos** and **GA** encryption algorithms preserve the features after encryption, and therefore, give better accuracy compared to other encryption algorithms. More precisely, for the studied CNN based face recognition models, their accuracy obtained using these encrypted algorithms is close to the accuracy obtained using clear images. Table 4 shows the accuracy obtained with various algorithms including PCA. It It is clearly noted from the table that the face recognition accuracy of CNN models is better than accuracy of PCA for clear images and encrypted images. From the studied CNN models, Effnet gives the best accuracy and outperforms other models with all encrypted algorithms. Compared to PCA, EffNet improves accuracy by 16.2%, 6.16%, 20.4%, 22.1%, 279.88%, 9.56%, 392.1%, 366.32%, and 480 % for plain image, AES, Bit slice, Chacos, DNA, GA, Hill, RSA and RCP, respectively. Additionally, Tables 5 and 6 show the testing and training time of various CNN models. The testing time of all CNN models for one image is less than one second, and training time is 6 to 8 minutes for the used ORL database. Figures 13-17 show the loss and accuracy curves of LeNet, AlexNet, Vgg16 Net, ResNet, and DenseNet, respectively. To train the CNN model, Softmax loss function is used in this paper. It is a cascaded combination of softmax function, the last fully connected layer of corresponding CNN model, and cross-entropy loss. In training CNN models, weights \(wk\) (where k is number of training class, here 40) of connected layers are normalized to scale parameter \(s\), and, in the same way, outcome features of last convolution layers amplitudes are normalized to \(s\)[36]. As a result, softmax loss is calculated from the below equation for a given input vector feature \(x\), and, assuming respective ground truth label \(y\), then  
\[L_{1}=-log\frac{e^{\textit{sc}(\theta_{xy},x)}}{e^{\textit{sc}(\theta_{xy},x)} +\sum_{k\
eq y}^{k}e^{\textit{sc}(\theta_{xy},x)}} \tag{21}\]  
where \(\textit{sc}(\theta_{xy},x)=w_{k}^{T}x\) is the cosine similarity and \(\theta_{xy},x\) is the angle between \(w_{k}\) and \(x\). The learned features with softmax loss are prone to be separable, rather than to be discriminative for robot face recognition. In addition, the time needed to produce recognition results (with LeNet) for one image for the cloud turned out to be smaller than that required for the robot as depicted in Table 7.  
Figure 14: Loss and Accuracy of **Vgg16 Net** from left to right and top to bottom: DNA, AES, Bit Slice, Chaco, GA, Hill, RCP, and RSA. Figure 13: Loss and Accuracy of **AlexNet** from left to right and top to bottom: DNA, AES, Bit Slice, Chaco, GA, Hill, RCP, and RSA. Figure 16: Loss and Accuracy of **ResNet** from left to right and top to bottom: DNA, AES, Bit Slice, Chaco, GA, Hill, RCP, and RSA. Figure 15: Loss and Accuracy of **GoogleNet** from left to right and top to bottom: DNA, AES, Bit Slice, Chaco, GA, Hill, RCP, and RSA. _Appl. Sci._**2021**, _11_, 6522