## 3 Multi-Feature Extraction
### Extraction of Image Texture Information Based on Intra-Frame Information  
Deepfake-generated synthetic media achieves visual realism through localized texture manipulation in facial regions. This methodology has gained prominence due to its effectiveness in enhancing visual authenticity through detailed feature reproduction, including micro-expressions, skin texture variations, and lighting effects. Conventional detection approaches typically employ direct texture analysis through comparative evaluation of pixel values and localized texture patterns. However, these techniques are frequently challenged by advanced generation methods that employ region-specific texture modifications capable of deceiving traditional analytical frameworks. Current detection systems demonstrate limited robustness when confronted with sophisticated manipulation algorithms that maintain structural consistency while altering subtle textural properties. [PERSON] et al. [33] proposed using the Gram matrix as a method for describing image textures. To address this limitation, we introduce the Gram matrix as a means to capture the global texture features of an image. Unlike traditional methods that analyze the texture of individual local regions, the Gram matrix provides a more abstract and comprehensive image description by comparing the texture relationships across all regions of the image. Specifically, the Gram matrix utilizes the covariance matrix of feature maps to describe the texture correlations between different locations, thereby capturing the overall texture structure of the image within a broader spatial context. This approach to extracting global texture features is more effective for detecting deepfakes because, even when local textures are fine-tuned, the overall texture structure and relationships retain a certain degree of stability and distinctiveness. Furthermore, current convolutional neural networks often fail to capture long-range information due to their limited receptive fields, which leads to reduced performance on lower-resolution images. By incorporating auxiliary networks to gather texture information, the ability to capture long-range information is enhanced, thereby improving the model's generalization capability. The Gram matrix is defined as shown in Equation (8). \[\Delta(\alpha_{1},\alpha_{2},\ldots,\alpha_{k})= \begin{pmatrix}(\alpha_{1}, \alpha_{1})&(\alpha_{1},\alpha_{2})&\ldots&(\alpha_{1},\alpha_{k})\\ (\alpha_{2},\alpha_{1})&(\alpha_{2},\alpha_{2})&\ldots&(\alpha_{2},\alpha_{k })\\ \ldots&\ldots&\ldots&\ldots\\ (\alpha_{k},\alpha_{1})&(\alpha_{k},\alpha_{2})&\ldots&(\alpha_{k},\alpha_{k })\end{pmatrix}  \tag{8}\]  
Equation (8) defines a matrix composed of the pairwise inner products of any k vectors in an n-dimensional Euclidean space, known as the Gram matrix of these k vectors. This paper employs the shallow and deep structures of the EfficientNet backbone network to extract global texture features of images. By calculating the Gram matrix from the feature vectors, the hidden relationships between image features can be revealed. The calculation method is detailed in Equation (9). The computational framework standardizes input tensor dimensions as (\(B\), \(C\), \(H\), \(W\)), where B denotes batch size, \(C\) represents channel count, and H/W correspond to spatial dimensions. The intermediate variable is reshaped into a two-dimensional form (1, H \(\times\) W) through Gram matrix operations, maintaining the tensor dimensions as (\(B\), \(C\), \(H\), \(W\)). \[Graml_{i,j}^{l}=\sum_{k}F_{ik}^{l}F_{jk}^{l} \tag{9}\]  
In Equation (9), \(F^{l}\) denotes the feature map at layer \(l\), with \(F_{ik}^{l}\) representing the \(k\)-th element of the \(i\)-th feature map at the same layer. Each element in the feature map indicates the intensity of a particular feature. \(Graml_{i,j}^{l}\) describes the entire feature map and is not constrained by the receptive field of the convolutional neural network, thus allowing the Gram matrix to capture long-range texture information within images.