## 3 Methods
### Feature Extraction for Each Image Pixel
#### 3.2.2 Normalized Difference Spectral Indices  
In this study, NDWI, NDVI [52] and NDBI [53] were used as spectral features.  
Figure 3: Images and features of typical aquaculture areas: (**a**) Sentinel-2A multispectral image, (**b**) NDWI, (**c**) NDBI, (**d**) NDVI, (**e**) VV Polarization image, and (**f**) VH Polarization image.  
Normalized Difference Water Index (NDWI) (Equation (1)): NDWI was proposed by [PERSON] [54], based on the fact of strong spectral absorption of water body in the near-infrared (NIR) band, and it is a robust method for detecting aquaculture water surface and has proved effective in segmenting muddy aquaculture ponds [39]. Correspondingly, NDWI can be used to distinguish land and water bodies.  
\[\text{NDWI}=(\rho_{\text{green}}-\rho_{\text{mir}})/(\rho_{\text{green}}+\rho_ {\text{mir}}) \tag{1}\]  
where \(\rho_{\text{green}}\) is the reflectance of green band (B3 of MSI), and \(\rho_{\text{mir}}\) represents the reflectance of near-infrared band (B8 of MSI).  
In this study, the images with annual cloud cover less than 20% in 2020 were used to calculate a series of NDWI values. The NDWI series were sorted from small to large, and the 25% maximum NDWI values (located in the 75-100% of the sequence) were selected to calculate the average NDWI image. This preprocessing takes full use of all the image features for the whole year and eliminates the seasonal differences of aquaculture areas.  
Normalized difference vegetation index (NDVI) (Equation (2)): Generally, aquaculture ponds usually have higher nutrients than natural water bodies, and the algae concentration is also higher. The waterbodies with high algae concentration generally have high reflectance in NIR spectrum compared with natural waters (without aquaculture). Therefore, NDVI may separate aquaculture waters from natural waters at a certain degree.  
\[\text{NDVI}{=}(\rho_{\text{mir}}-\rho_{\text{red}})/(\rho_{\text{mir}}+\rho_ {\text{red}}) \tag{2}\]  
where \(\rho_{\text{red}}\) represents the reflectance of red band (B4 of MSI), and \(\rho_{\text{mir}}\) represents the reflectance of near-infrared band (B8 of MSI). Referring to the processing of NDWI, we also sorted and filtered the NDVI values (75-100%) to compose the final average NDVI image.  
Normalized difference built-up index (NDBI) (Equation (3)): NDBI is originally designed to detect built-up and barren areas. In practice, the extracted water mask often contains shadow noise with low reflectivity, which may be caused by tall buildings over built-up areas. The surrounding pixels of shadows usually have high NDBI values, and thus it is able to distinguish building shadows by analyzing their surrounding pixels.  
\[\text{NDBI}=(\rho_{\text{swirl}}-\rho_{\text{mir}})/(\rho_{\text{swirl}}+\rho_ {\text{mir}}) \tag{3}\]  
where \(\rho_{\text{swirl}}\) represents the reflectance of the shortwave infrared band (B10 of MSI), and \(\rho_{\text{mir}}\) represents the reflectance of the near-infrared band (B8 of MSI). To further reduce the potential effects of shadow noise, we also sorted and filtered the NDBI values (75-100%) to compose the final average NDBI image. The morphological operation is an effective way to examine the neighbors of a pixel. Since a higher NDBI indicates a higher possibility of a built-up pixel, an inflation operator was conducted on the NDBI image to eliminate lathy and small building shadows, and a corrosion operator was further adopted to restore the image.