## 3 Proposed Method
### The Reasoning Process and Spoof Scores  
OCT images have rich details. Using only the reconstruction image error as the criterion for abnormal judgment often leads to relatively low accuracy. To accurately identify the input images, the reconstruction distances of the fused features in the high-dimensional space and those of the input images themselves are comprehensively considered. By accumulating the reconstruction distances, the differences in reconstruction distances among different samples are further enlarged, and the overlapping areas of the reconstruction distances between bona fide samples and spoof samples are effectively reduced, thus obtaining a clearer decision-making boundary. The anti-spoofing judgment result, SpoofScore, is expressed as  
\[SpoofScore=(FDis>s1)\cdot(RDis>s2) \tag{16}\]  
where FDis and RDis represent the reconstruction distance of the fused features in the high-dimensional space and the reconstruction distance of the image, respectively. During the training phase, this method only uses bona fide samples for training. Therefore, in the model inference phase, the boundary of the reconstruction distance of bona fide samples, s2, and the reconstruction distance of the fused features in the high-dimensional space, s1, can be obtained. According to the requirements of specific datasets, the threshold of the reconstruction distance can be flexibly adjusted. When both the reconstruction distance of the input image and the reconstruction distance of the features exceed the preset thresholds, it is determined as a bona fide sample; conversely, if either of the distances is lower than the threshold, the image will be regarded as a spoof sample. To ensure a fair and consistent evaluation of the unsupervised method, thresholds \(s_{1}\) and \(s_{2}\) in Equation (16) were calibrated using a validation set. Given the inherent randomness and susceptibility to overfitting in unsupervised training, the validation set serves as a reference to select optimal parameters. Specifically, multiple threshold combinations were evaluated, and the ones achieving the best anti-spoofing performance on the validation set were chosen to serve as \(s_{1}\) and \(s_{2}\) during inference. By constraining the reconstruction scores of the autoencoder, the model can learn the features of bona fide samples, and then distinguish between bona fide and spoof samples. As shown in the density graph in Figure 12, when the overlapping area of the reconstruction distances between bona fide samples and spoof samples is too large, the obtained reconstruction scores cannot effectively distinguish between bona fide and spoof samples. Therefore, by introducing a new reconstruction distance score in the high-dimensional space, the model can obtain more high-dimensional information about bona fide samples, further expanding the partition intervals of bona fide samples and spoof samples. In this subsection, the data distribution of bona fide input images is introduced, and the Gaussian probability density function in the data distribution, along with the mean and variance of the distribution, are intended to be used to comprehensively consider the spoof probability of input samples. Given a training sample \(x\), after segmenting the sample, it is cropped and reshaped into \(N\) feature maps \(x_{i}\) with the same resolution. Through the training of the reconstruction module, the mean \(\mu\) and variance \(\sigma\) of the data distribution of the bona fide sample dataset can be obtained. According to the density graph of the reconstruction distance of the fused features in Figure 12, the reconstruction distance \(d_{r}\) can be regarded as conforming to a Gaussian distribution.