# Semantic-Enhanced Foundation Model for Coastal Land Use Recognition from Optical Satellite Images
## 4 From Land Use Segmentation to Land Use Semantic Recognition  
### Land-Cover Form Frequency and Inverse Image Frequency  
In an optical satellite image that contains multiple coastal land covers, this image's content or land use might be hidden in the coastal land cover classification results. For example, the coastal land cover that includes buildings, piers, and sand may be neither an industrial harbor nor an entertainment beach. To answer the question about the coastal land use in optical satellite images, we focus on transforming the land use categories derived from the optical satellite image into a feature vector space to support a context-based semantic analysis model.  
The VSM identifies each text term or individual as a vector in a multi-dimensional space and then measures the similarity among each two terms and individuals [31; 32]. The multi-dimensional space comprises a set of linearly independent vectors, and each vector denotes one dimension in the vector space. The state-of-the-art VSMs were designed differently according to three representations of text information: term-document, word-context, and pair-pattern. The term-document model mainly indicates the meaning of each document, the term-context model focuses on the meaning of each term, and the pair-pattern model is concerned with the similarity among two complicated patterns. In this paper, we focus on the content (or land use) of an optical satellite image. The hypothesis is that the relation between land use categories and land uses is analogous to the term and document in a term-document VSM. Figure 4A illustrates this mapping between the term-document VSM and the land use category-image VSM.  
The land cover form and image are analogous to the term and document in the term-frequency and inverse document frequency model, which are depicted in Figure 4A. Based on the image gridding results, for optical satellite image Img(s,x/2k, y/2k), the xth (land use) category frequency \(cf_{i,x}\) is calculated by the following equation:  
\[cf_{i,x}=\begin{cases}\begin{array}{c}1,\ k=0\\ \sum_{k=1}^{k}\frac{freq_{i,x}(v_{i,x})}{2^{c+1}},\ k\geq 1\end{array}\end{cases} \tag{1}\]  
where \(k\) is the image gridding scale shown in Figure 3. \(freq_{i,x}(w_{i,x})\) denotes the number of land use forms, while \(w_{i,x}\) appears in the subregions of the scaled image \(c\). Specifically, the category frequency produced by Equation (1) is locally normalized. Then, we convert the category frequency by \(cf_{i,x}\times 2^{k_{max}\times 2}\) with \(k_{max}\) being the largest image gridding scale.  
The inverse image frequency is calculated by the following equation:  
\[inf_{i,x}=\log\left(\frac{N}{cf_{i,x}\times 2^{k_{max}\times 2}}\right),\ N= \begin{cases}\begin{array}{c}1,\ k_{max}=0\\ 2^{k_{max}\times 2}\,,k_{max}\geq 1\end{array}\end{cases} \tag{2}\]  
Figure 4: Matrix of VSM; (**A**) land use category frequency and inverse image frequency; (**B**) matrix structure; (**C**) an example of a VSM matrix.  
where \(N\) is the total number of subregions in the optical satellite image \(I_{i}\). Then, to quantitatively weight the importance of each category (\(w_{i,x}\)) in optical satellite image \(I_{i}\), we calculated the category frequency and inverse image frequency.  
\[w_{i,x}=cf_{i,x}\times imf_{i,x} \tag{3}\]