# Fast Fourier Asymmetric Context Aggregation Network:
## 3 Proposed Method
### The Content Inference Stage  
In the content inference stage, the deepest encoding feature \(f_{N}\) is fed into the content inference module, which consists of \(R\) connected FF-CDRB blocks. This module synthesizes garment content by aligning texture and structure through frequency-domain characteristics. Next, we will provide a detailed description of the FF-CDRB. Figure 4: The positional information embedding process. Figure 3: Structure of the encoding block. Inspired by the residual design in ResNet [62], we introduce the Fast Fourier Channel Dual Residual Block (FF-CDRB) based on FFC, aiming to facilitate apparel content inference. The structure of FF-CDRB is shown in the lower part of Figure 2.  
The FF-CDRB consists of two serially connected FFCs. As shown in Figure 5, FFC divides the channels into a local branch and a global branch. The local branch captures local features using standard convolution, while the global branch interprets global context through FFT. In the global branch, FFC employs a spectral transformation module based on the Discrete Fourier Transform to convert signals from the spatial domain to the frequency domain, enabling convolution operations with a global receptive field. Finally, the conjugate symmetry of real-valued signals is used to perform an inverse transform to restore spatial structures. The specific operations in the global branch are as follows, including the real and complex spaces, respectively. Real and image denote the real and imaginary parts, respectively. Referring to [63], the specific operations of the global branch of FFC can be expressed as  
1. Apply real FFT to input features: _real_ FFT \(\left(\mathbb{R}^{H\times W\times C}\right)\rightarrow\mathbb{C}^{H\times \frac{W}{2}\times C}\), where \(H,W\), and \(C\) represent the height, width, and number of channels of the tensor, respectively, and \(\times\) represents multiplication, indicating that the dimensions of height, width, and channels are multiplied together to define the size of the feature map. \(\mathbb{R}^{H\times W\times C}\) and \(\mathbb{C}^{H\times\frac{W}{2}\times C}\) represent a real-valued tensor with spatial dimensions \(H\times W\times C\) and a complex tensor with spatial dimensions \(H\times\frac{W}{2}\times C\), respectively. _real_ FFT represents the real-valued Fourier transform, and a detailed explanation and derivation of FFT can be found in [64]. 2. Concatenates real and imaginary parts: \(\text{ComplexToReal}\Big{(}\mathbb{C}^{H\times\frac{W}{2}\times C}\Big{)} \rightarrow\mathbb{R}^{H\times\frac{W}{2}\times 2C}\), where ComplexToReal represents the concatenation of the real and imaginary parts of the input tensor. 3. Apply convolution operations in the frequency domain: \(\text{Conv}\Big{(}\mathbb{R}^{H\times\frac{W}{2}\times 2C}\Big{)} \rightarrow\mathbb{R}^{H\times\frac{W}{2}\times 2C}\), where Conv represents the convolution operation. 4. Apply inverse transform to recover a spatial structure: \(\text{RealToComplex}\left(\mathbb{R}^{H\times\frac{W}{2}\times 2C}\right) \rightarrow\mathbb{C}^{H\times\frac{W}{2}\times C}\), InverseRealFFT \(\left(\mathbb{C}^{H\times\frac{W}{2}\times C}\right)\rightarrow\mathbb{R}^{ H\times W\times C}\), where RealToComplex represents the conversion of a real-valued tensor into a complex-valued tensor for the application of the inverse transform. InverseRealFFT represents the application of the inverse real-valued FFT to restore the tensor to its real-valued form. Similarly, the detailed process of the inverse transform can be found in [64]. However, although the FFC can efficiently extract features via spectral transformation, it does not fully account for the relationship between the local and global feature branches. Specifically, since the two feature extraction branches in the FFC are independent, a simple concatenation of their outputs may lead to a loss of certain feature information.