# Forgery Detection for Anti-Counterfeiting Patterns Using Deep Single Classifier
## 4 Experimental Results and Analysis
### Genuine and Forged Anti-Counterfeiting Pattern Identification Test  
As mentioned above, after the completion of the auto-encoder training, a set of feature vectors corresponding to the positive samples can be extracted by taking the smartphone-captured genuine pattern images as input, and a set of feature vectors corresponding to the abnormal sample is extracted by taking the smartphone-captured counterfeit pattern images as input. Then, the second stage of the one-class classifier randomly selects 30% positive sample feature vectors as the training set, and all positive sample and abnormal sample feature vectors are the test set.  
The comparative experiment in the two stages is conducted, and the obtained classifiers are named C1, C2, C3, and C4. For C1 and C2, the U-Net-based feature extractor is trained by standard collected patterns without artificially blurring in the first module, while for C3 and C4, the feature extractor is trained by artificially blurred patterns. In the second stage, for C1 and C3, the boundary is generated by the standard OCSVM method, while the boundary generated by OCSVM is optimized for C2 and C4. The discrimination ability of different classifiers is measured by the recognition rate of the test samples. The results are shown in Table 2. The TP rate is the recognition rate of genuine patterns indicating the proportion of the input genuine patterns that are also recognized as normal samples, and the FP rate is the misclassification rate of counterfeit patterns indicating the proportion of the counterfeit patterns that are misjudged as normal samples.  
The sample scatterplot obtained by feature extraction in the first stage and the decision boundary obtained in the second stage corresponding to each classifier are shown in Figure 11a-d, where the label ori corresponds to positive samples (genuine patterns), while cop and scan correspond to duplicating and scan-reprinting negative samples (counterfeit patterns), respectively.  
It can be seen from the chart that classifier C1 does not use blurred patterns in the first stage of training, and there is an intersection between positive and negative sample points in the feature space. At the same time, because there are relatively few samples used in training OCSVM, most of the positive sample points fall outside the generated decision boundary, and the recognition rate of authentic products is very low. Classifier C2 modifies the boundary on the basis of C1, and all positive sample points fall within the modified decision boundary. However, due to the intersection of positive and negative samples, it is inevitable that a small number of negative sample points also fall within the boundary and are judged as positive sample points. Classifier C3 uses blurred patterns to train the U-Net in the first stage, and it can be seen that the model has a good restoration ability for the blurred pattern images taken by mobile phones. The distribution of positive and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Classifier** & **C1**1  & **C2** & **C3** & **C4 (Proposed)** \\ \hline TP rate & 10.5 & 100 & 41.5 & **100** \\ FP rate & 0 & 5.5 & 0 & **0** \\ Precision & 100 & 94.7 & 100 & 100 \\ Recall & 10.5 & 100 & 41.5 & 100 \\ F\({}_{1}\) score & 19.0 & 97.3 & 58.7 & **100** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of different classifiers (%).  
negative sample points in the feature space is not overlapped, which makes it easier for the classifier to identify the sample points. On the basis of C3, classifier C4 conducts boundary correction, all the positive sample points fall within the decision boundary, and at the same time, it can completely distinguish negative samples. The recognition rate of authentic products reaches 100%, and the false classification rate reduces to 0%, which verifies the effectiveness of the proposed classifier.