## 2 Materials and Methods
### Methods
#### 2.2.1. Feature Extraction from Remote Sensing Imagery  
Remote sensing imagery is an effective method for capturing surface information, allowing for the distinction between urban and rural areas based on their diverse land cover characteristics [9, 40, 41, 42]. This study employed high-resolution remote sensing imagery to represent daytime features and nighttime light (NTL) data to represent nighttime features.  
Our methodology rested on the basic idea that urban and rural areas show different aspects when visible in daytime and nighttime imagery. Urban areas are usually characterized by a high density of constructions, an expanse of regular geometric patterns with few overlaps between buildings and other artificial surfaces [43]. On the contrary, rural areas have vegetation, farmed land, and spread-out structures that are smaller in size [44]. Being a transitional zone, the urban-rural fringe is expected to show a combination of these aspects so that it slowly passes from having more urban traits to predominantly rural ones [45]. Similarly, in nighttime light (NTL) imagery, urban areas are represented by bright, polygonal regions, while rural areas appear as dark, patchy zones [46]. Consequently, the urban-rural fringe is likely to appear as a transition area with average bright values.  
For the high-resolution remote sensing imagery, we employed a deep learning approach using a modified VGG16 architecture, which was selected for its proven effectiveness in feature extraction from complex imagery and efficient transfer learning capabilities. The VGG16 model, pre-trained on ImageNet, was adapted to our specific task by modifying the second fully connected layer to output 64-dimensional features instead of the original 4096 dimensions [47]. We extracted these high-level semantic features before the final classification layer. This can be represented as:  
\[F_{rs}=FC2_{64}(FC14_{096}(VGG16_{conv}(x))) \tag{1}\]  
where \(x\) is the input image, \(VGG16_{conv}\) represents the convolutional layers of \(VGG16\), \(FC14_{096}\) is the first fully connected layer, and \(FC2_{64}\) is the modified second fully connected layer outputting 64-dimensional features. These features captured high-level representations of the urban-rural landscape, encompassing textures, patterns, and spatial arrangements characteristic of different land use types.  
For the NTL data, we first converted the digital number (DN) values to absolute radiance using the following equation specific to the Luojia-1 01 satellite:  
\[L=DN^{\frac{3}{2}}*10^{-10} \tag{2}\]  
where \(L\) is the calibrated radiance value in \(W/(m^{2}\cdot sr\cdot\mu m)\), and \(DN\) is the original image pixel value. Based on these calibrated NTL data, we calculated ten statistical features for  
Figure 2: The framework of this study: **(1)** feature engineering, **(2)** urban–rural fringe identification, **(3)** identification result analysis.  
each 250 m \(\times\) 250 m grid: minimum, maximum, range, mean, standard deviation, sum, mode, median, first quartile, and third quartile. These features provided a comprehensive characterization of the nighttime illumination patterns across the study area. The statistical values were organized into a ten-dimensional vector \(F_{ntl}\).