## 2 Methods
### Evaluation Metrics  
This experiment uses three image-quality evaluation indicators to evaluate the performance of the method--peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and the bit error rate (BER)--and uses the Confusion Matrix to evaluate the effect and accuracy of the model. The detailed definition of each indicator is as follows. Peak signal-to-noise ratio (PSNR) is a measure of image quality. The larger the ratio calculated by PSNR, the closer the copied image is to the input image, and the image quality is good. The typical PSNR value is between 30 dB and 40 dB. The higher the value, the lower the distortion. The PSNR value is defined as Equation (1):  
\[PSNR=10\times log\frac{255^{2}}{MSE} \tag{1}\] \[\text{where }MSE=\frac{1}{H\times W}\sum_{i=0}^{H-1}\sum_{j=0}^{W-1 }[I(i,j)-K(i,j)]^{2}\]  
where \(H\) and \(W\) are the width and height of the image, respectively, \(I(i,j)\) represents the pixel value of the original image at position \((i,j)\), and \(K(i,j)\) represents the pixel value of the original image at \((i,j)\). Structural similarity (SSIM) is an index that measures the similarity of two images. When the SSIM value is 1, it means that the two images are exactly the same. Generally speaking, the SSIM value must be at least 0.95 for the image quality to be acceptable. \(SSIM\) is defined as Equation (2):  
\[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+C_{1}\right)\left(2\sigma_{xy}+C_{2} \right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+C_{1}\right)\left(\sigma_{x}^{2}+\sigma _{y}^{2}+C_{2}\right)} \tag{2}\]  
where \(x\) and \(y\) stand for the original image and the restored (retrieved) image, respectively, \(\mu_{x}\) and \(\mu_{y}\) are the average values of \(x\) and \(y\), \(\sigma_{xy}\) is the covariance of the sum, \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variation of x and y, respectively, and \(C_{1}\) and \(C_{2}\) are constants. The bit error rate (Bit Error Rate) represents the error rate of the restored (retrieved) image. The lower the error rate, the more similar the restored image is to the original image. \(BER\) is defined as Equation (3):  
\[BER=\frac{N_{e}}{H\times W} \tag{3}\]  
where \(H\) and \(W\) are the length and width of the image, and \(N_{e}\) is the number of bits to restore the error. The confusion matrix is an index to measure the accuracy of the classification model. The confusion matrix has two dimensions: Actual condition and Predicted condition, and each has two situations: Positive and Negative. Therefore, the following four indicators can be obtained:  
Figure 4: Part of the binary image of National Chung Hsing University LOGO and CIFAR. (**a**) NCHU logo, (**b**) Man, (**c**) paw, (**d**) bike, (**e**) camel, (**f**) women. True positive (\(TP\)): Represents that the real situation is true, and the model prediction is true. False positive (\(FP\)): Represents that the real situation is not true, and the model prediction is true. False negative (\(FN\)): Represents that the real situation is true, and the model prediction is not true. True negative (\(TN\)): Represents that the real situation is not true, and the model predicts it is not true. For the classification model, the more accurate the prediction performance, the better. Therefore, corresponding to the confusion matrix, the higher the number of \(TP\) and \(TN\), the better, and the smaller the number of \(FP\) and \(FN\), the better. With the above four indicators, four other advanced indicators can be calculated accordingly: Accuracy, Precision, Recall, and F1 Score. The definitions of the four indicators are as shown in Equations (4)-(7). Accuracy represents the proportion of correct judgments among the results predicted by all models. Precision represents the proportion of the true situation in the model judged to be true. The Recall rate represents the proportion of all the results that are judged to be true by the model. The F1 Score combines precision and recall.