# MMDL-Net: Multi-Band Multi-Label Remote Sensing Image Classification Model
## 2 Materials and Methods
### Model Input Adaptation and Interpolation in MMDL-Net  
In order to accommodate the varying pixel sizes of remote sensing images in the BigEarthNet dataset, ranging from 20 \(\times\) 20, 60 \(\times\) 60, to 120 \(\times\) 120, we enhanced the input layer of the ResNet network by adjusting the commonly used standard 224 \(\times\) 224 size of RGB images to the maximum size within the dataset, which is 120 \(\times\) 120. This modification aims to reduce computational demands, enhance efficiency, and better capture the details and features present in the images. For images with dimensions smaller than 120 \(\times\) 120 pixels, specifically those measuring 20 \(\times\) 20 and 60 \(\times\) 60 pixels, bicubic interpolation is implemented. In the context of multispectral remote sensing imagery, bicubic interpolation provides smoother transitions at edges compared to nearest-neighbor and bilinear interpolation techniques, thereby maintaining greater detail and image sharpness upon enlargement. This is particularly critical for the analysis of remote sensing images as it aids in preserving the delineation and intricate features of land objects, contributing to enhanced classification and recognition of these features. Accurate color interpolation is essential when processing multispectral remote sensing images due to its relation to the identification of spectral characteristics of land objects. Bicubic interpolation facilitates a more precise estimation of intermediate color values, thereby better preserving the spectral attributes of the original image, which is crucial for subsequent spectral analysis and classification tasks. Additionally, bicubic interpolation more effectively maintains spatial consistency across multiple bands. In multispectral images, each band represents different spectral information, and it is imperative to maintain correct alignment among these bands during enlargement to prevent distortion of spectral information. Bicubic interpolation generates new pixel values by interpolating among known pixels. By taking into account the grayscale values and the distances of surrounding pixels, it yields a more accurate estimation of new pixel intensities, thereby preserving image details. This method also reduces the occurrence of aliasing, resulting in smoother edges in the enlarged images and consequently minimizing information loss as much as possible. The fundamental structure of the interpolation method is depicted in Figure 2.  
Figure 1: Structure of the multispectral stacking module. By mapping, the pixel values in the enlarged image are obtained through weighting in the neighborhood of the mapped points. Bicubic interpolation uses 16 neighboring points to calculate the weights, so a BiCubic function needs to be constructed. This function calculates the weights for the points based on the relative position between the neighboring points and the P point as follows:  
\[\text{W}(x)=\left\{ \begin{aligned} & x=\quad(\text{a}+2)|x|^{3}-( \text{a}+3)|x|^{2}+1\quad\quad\text{for }|x|\leq 1\\ & y=\quad\text{a}|x|^{3}-5\text{a}|x|^{2}+8\text{a}|x|-4\text{a} \quad\text{for }1<|x|<2\\ & z=\quad 0\quad\quad\text{otherwise}\end{aligned} \right. \tag{1}\]  
Here, a is set to \(-0.5\). To find the parameter \(x\) in the BiCubic function, we obtain the weights \(\text{W}(x)\) corresponding to the 16 pixels. Then, the pixel values of these 16 points are weighted and calculated using the interpolation formula as follows:  
\[f(x,y)=\sum_{i=0}^{3}\sum_{j=0}^{3}f(x_{i},y_{j})\text{W}(x-x_{i})\text{W}(y- y_{j}) \tag{2}\]  
Assuming the size of image A is m \(\times\) m, and after scaling it K times, the size of image B becomes M \(\times\) M. The pixel values of image A are known, while those of image B are unknown. The objective now is to find the value of each pixel D(\(X\),\(Y\)) in image B. To achieve this, we need to find the corresponding pixel point P(\(x\),\(y\)) in image A.